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Experiments in electrostatic deflection of doped helium nanodroplets
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Experiments in electrostatic deflection of doped helium nanodroplets
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Experiments in Electrostatic Deflection of Doped Helium Nanodroplets by John Walter Niman A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) May 2023 Copyright 2023 John Walter Niman ii Acknowledgments I would first and foremost like to thank my advisor, Vitaly Kresin, whose guidance, patience, and integrity have helped me to grow into a scientist and the person I am today. I am extraordinarily lucky to have had Vitaly as my advisor and my time in the Nanocluster Physics Laboratory has been formative and productive under his instruction. I am also grateful to Ben Kamerin who has been my partner on the helium machine since nearly day one. His contributions are of vital importance to this work and the results presented here would not have been possible without his skilled hands and impactful discussions. I will treasure the memories of our many late nights in the lab beating the science out of our machine and ourselves. I would also like to thank Daniel Merthe and Lorenz Kranabetter for their mentorship and teaching me how to operate the helium machine. Their extensive knowledge of the field, guidance, and assistance collecting and analyzing data allowed me to hit the ground running on the helium project. It is a privilege to stand on the shoulders of these giants. I would also like to thank Will Liang and Teevie Villers for assistance with upgrades and maintenance on the machine and wish them both the best of luck with their endeavors in graduate school. I also thank our theorist collaborators, Tom Linker, Aiichiro Nakano, Jiří Suchan, and Petr Slavíček, whose assistance greatly improved our papers and understanding of the experiments. I am grateful that I have had the opportunity to work on the helium machine and to participate in the kind and thriving helium nanodroplets community. I would additionally like to thank my collaborators who participated in the CO2 project: Jan Krohn, Roope Halonen, Ruth Signorell, and Klavs Hansen. It was a pleasure to work with your data and learn about your experiments and techniques. This opportunity was greatly appreciated during covid isolation and the skills I learned during this period are invaluable. It is an honor to share authorship with all of you. iii I thank the members of my qualification exam and dissertation committee: Moh El-Naggar, Eli Levenson-Falk, Susumu Takahashi, and Alex Benderskii. A special thanks to Moh is in order for meeting with me at a coffee shop the day before the graduate school acceptance deadline. Your candor and willingness to go the extra mile convinced me that the USC Physics department is where I wanted to be, and I signed later that morning. I would also like to thank Andrey Vilesov who assisted me greatly in preparing my qualification exam and developing an understanding of helium nanodroplets. Extensive guidance from Randall Pedder on calibrating and troubleshooting our quadrupole mass spectrometer is also greatly appreciated. The mentorship that I received from Patrick Edwards has also been crucial for my development as a student and scientist. I was lucky that I did not have to look far to find a strong role model. Your expertise in the lab was also highly appreciated and it is a privilege to follow in your footsteps. Sean O’Connell provided similar mentorship, and has been an important teacher and colleague alongside Allie Feinberg and Swetha Erukala in the helium nanodroplet community. It has also been a privilege to share the lab with the overlapping students in the group, Abdelrahman Haridy, Atef Sheekhoon, Malak Khojasteh, Diego Hernandez, Elizabeth Zhou, Derrick Korponay, and Isaac Peña Dominguez. You have all made the lab a positive and friendly place to be. I also thank the many friends who have helped me maintain composure and sanity in graduate school, specifically: Brian Weaver, James Farmer, Ashton Lowenstein, Jason Williams, Aaron Wirthwein, Darian Hartsell, Anna Haynie, Marko Chavez, Jack Lashner, Gautam Rai, Robert Walker, Evangelos Vlachos, Remy Gerras, Lisa Pangilinan, Daniel Park, Jeff Yoshida, Patrick Templeton, Alex Lumnah, Marshall Trautman, Claire Cancilla, Lauren Rewers, and Tim iv O’Donnell. The time you all spent with me at varying points in this journey is very much appreciated. Thank you for being a friend. I am highly appreciative for support from my family, and everyone played a part in this achievement. I thank my mom and dad, Shari Clark and Dennis Niman for raising me to value education and always try my best. I especially want to thank the family members that could not be here to share the accomplishment with me: Lucille Niman, Walter Dodd, and Nancy Clark. I thank my brother, Scott Niman, who traversed graduate school with me in parallel and who I could always count on to commiserate and answer Chemistry questions. I look forward to your defense shortly after my own! I am eternally grateful to my wife, Christina Niman, who I had the good fortune to marry shortly before writing these acknowledgements. Without you, none of this would have been possible. I am truly blessed to have met you in our first year at USC where we began building our strong partnership and eventual loving relationship. Thank you for your support, and for pushing me to be the best I could be throughout this process. I am excited for our future together. v Table of Contents Acknowledgments........................................................................................................................... ii List of Tables ................................................................................................................................ vii List of Figures .............................................................................................................................. viii Abstract ........................................................................................................................................ xvi Chapter 1 – Introduction ............................................................................................................... 18 1.1 Motivation ........................................................................................................................... 18 1.2 Brief Overview of Cooling and Trapping Methods ............................................................ 20 1.3 Helium Nanodroplets Background ...................................................................................... 22 1.4 Characterization of Helium Nanodroplet Beam .................................................................. 27 1.5 Electrostatic Deflection ....................................................................................................... 34 1.6 Summary and Scientific Contributions ............................................................................... 42 Chapter 2 – Experimental Apparatus and Methods ...................................................................... 45 2.1 The Helium Nanodroplet Deflection Machine .................................................................... 45 2.2 Installation and Testing of New Quadrupole Mass Spectrometer ....................................... 52 2.3 Data Acquisition .................................................................................................................. 58 2.4 Beam Velocity Measurement .............................................................................................. 65 2.5 Deflection Simulation ......................................................................................................... 74 Chapter 3 – Orientation and Deflection of Helium Nanodroplets and a Study of Charge Transfer as a Function of Droplet Size ......................................................................................... 80 3.1 Introduction ......................................................................................................................... 80 3.2 Experimental ....................................................................................................................... 83 3.3 Deflections .......................................................................................................................... 86 3.4 Nanodroplet Sizes and Size Filtering .................................................................................. 89 3.5 Charge Transfer Probability ................................................................................................ 91 3.6 Conclusions ....................................................................................................................... 100 Chapter 4 – Electrostatic Deflection as a Probe of Polar Structure in Molecular Assemblies ..................................................................................................................................................... 103 vi 4.1 Introduction ....................................................................................................................... 103 4.2 Experimental ..................................................................................................................... 108 4.3 Dimethyl Sulfoxide Results and Discussion ..................................................................... 110 4.3.1 Deflections .................................................................................................................. 111 4.3.2 Dipole Moments ......................................................................................................... 115 4.3.3 Modeling of Molecular Complex Formation ............................................................. 116 4.3.4 Results of Modeling ................................................................................................... 118 4.4 Imidazole Results and Discussion ..................................................................................... 121 4.4.1 Deflections .................................................................................................................. 125 4.4.2 Dipoles and Parentage Assignment ............................................................................ 128 4.5 Conclusions ....................................................................................................................... 129 Chapter 5 – Probing the Presence and Absence of Charge Transfer in Metal-Fullerene Systems ....................................................................................................................................... 131 5.1 Introduction ....................................................................................................................... 131 5.2 Experimental ..................................................................................................................... 135 5.3 Results and Discussion ...................................................................................................... 137 5.3.1 Sodium ........................................................................................................................ 137 5.3.2 Ytterbium .................................................................................................................... 141 5.3.3 Magnesium ................................................................................................................. 146 5.4 Calculations of Structure and Dipole Moment .................................................................. 150 5.5 Conclusions ....................................................................................................................... 152 Chapter 6 – Summary and Future Work ..................................................................................... 155 6.1 Summary of Key Results ................................................................................................... 155 6.2 Potential Future Experiments ............................................................................................ 156 6.3 Magnetic Deflection and Preliminary Results .................................................................. 159 References ................................................................................................................................... 162 Appendices .................................................................................................................................. 179 Appendix A – LabVIEW Data Acquisition Code ................................................................... 179 Appendix B – Velocity Measurement Code............................................................................ 188 Appendix C – Deflection Simulation Code ............................................................................. 193 Appendix D – Useful Mathematica Functions ........................................................................ 210 Appendix E – Detector Slit Simulations ................................................................................. 219 vii List of Tables Table 2.1: Experimentally determined quadrupole optics to maximize mass spectrometer signal. The detected signal from the quadrupole strongly depends on the choice of optics voltages to improve the detection efficiency of various input mass ranges. In current experiments pusher mode is used in favor of low mass optics in the conversion mode since it gives generally superior signal intensity in the mass region up to a few hundred amu. In the conversion mode of operation, the most impactful optic for affecting low mass signal intensity is the quadrupole exit voltage. It was later determined that using the pusher mode with the standard high mass optics performed generally better. Resolution parameters are excluded in this table and are frequently reoptimized to get appropriate peak widths in the mass spectrum. Typical potentiometer values on the power supply are dM ≈ 9.0 and dRES ≈ 1.9. ..................................................................................................... 55 Table 5.1: DFT calculations for the dipole moment and binding energy of a Yb, Na, or Mg atom optimized on either the hexagonal or pentagonal face of the C60 fullerene. ............... 151 viii List of Figures Figure 1.1: A plot of techniques currently utilized to generate cold molecules along with an estimate of the temperature and density that can be achieved with each method. Gray diagonal lines show constant phase space density. The blue vertical dashed line gives the rough temperature of HNDs. This figure is adapted from Ref. [16] with permission from the publisher. .......................................................................................................................... 20 Figure 1.2: The apparatus used by Hartmann, Miller, Toennies, and Vilesov to measure the high-resolution infrared spectra of sulfur hexafluoride clusters and mixed sulfur hexafluoride-rare gas clusters. The beam is generated in the droplet source region, the clusters are embedded in the pick-up chamber, the doped droplets are excited with a diode laser, and ionized and detected by a mass spectrometer. Spectra are detected using beam depletion, where the laser excitation results in the boil-off of hundreds of helium atoms, reducing the probability of electron-impact ionization and therefore causing a dip in the mass spectrometer signal corresponding to spectral absorption. This figure is from Ref. [41]. Reprinted with permission from AAAS. ............................................................... 23 Figure 1.3: Average number of He atoms in a droplet as a function of the nozzle stagnation conditions. The diameter of the produced droplets is a function of the number of helium atoms and presented on the right vertical axis. Nozzle diameters for the measurements in the figure are between 2-5 microns. The expansion type is characterized by nozzle conditions, and breaks into four regimes relative to the liquid-vapor critical point and superfluid transition of helium [10,35,37,44]. This figure is reproduced from Ref. [55] with permission from the publisher. ...................................................................................... 27 Figure 1.4: Optical shadowgraphs of massive helium nanodroplets expanded in Regime IV with a stagnation pressure of 0.6 bar and nozzle temperature of 2.7 K. Control of uniform high-quality beams of this type are still not fully understood. Droplets of this size are many orders of magnitude too large to deflect with our technique, but the image demonstrates the principle of the individual flying cryostats. This figure is reprinted from Ref. [61], with the permission of AIP Publishing. ................................................................ 30 Figure 1.5: Scaled probability vs. droplet size data points and least-square fitted log-normal distributions at three different nozzle temperatures and identical stagnation pressure of 80 bar. The most probable droplet size is listed, and the average droplet size and FWHM can be estimated visually. The log-normal fit is in very good agreement with the data points and the trend is shown for a reasonably large range of droplet sizes. This figure is reprinted from Ref. [64], with permission from Elsevier. ..................................................... 32 Figure 1.6: Pick-up of SF6 Poisson curves showing beam depletion (which we may treat as relative pick-up probability) as a function of pick-up cell partial pressure. The pick-up of multiple SF6 molecules is well-described by the Poisson process described in Equation (1.4). Selective doping of droplets can be achieved using this method or the method described in the text. This figure is from Ref. [41]. Reprinted with permission from AAAS. ................................................................................................................................... 33 ix Figure 1.7: A cartoon showing the electric field direction (red), permanent dipole moment direction (blue) and the angle of orientation between them (𝜃 ). ........................................... 37 Figure 1.8: Orientation cosine provided by the Langevin function [Equation (1.10)] for three different polar molecules, cesium iodide (CsI; 11.7 D), dimethyl sulfoxide (DMSO; 3.96 D), and water (1.86 D). The former two being common highly polar dopants used in our experiments, and the latter likely being the most well-known polar molecule and also a common annoyance in vacuum systems. Water has a relatively small dipole when compared to the other two molecules, demonstrating additional scaling of the orientation cosine with the electric field strength. The gray line is approximately the strength of the electric field used in our experiments. ................................................................................... 38 Figure 1.9: (a) and (b) provide computed rotational Stark-shifted energies as a function of electric field strength for CsI and DMSO at the HND temperature of 0.37 K, while (c) and (d) show the associated thermally-averaged orientation cosines using the (classical) Langevin function and (quantum) energy eigenstates of the previously described Stark- corrected rigid body Hamiltonian. The black vertical line corresponds to the electric field strength typical in our experiments. This figure is adapted from Ref. [76] and is included and described in the supplemental information of Ref. [79]. ................................................ 41 Figure 2.1: Block diagram of the helium droplet deflection apparatus. Major components are labeled and described in detail in the text. Note that the position of the detection chamber is not fixed can translate laterally in the lab frame. The double-triangle symbols represent valves, and each chamber can be isolated from the others. ................................................... 46 Figure 2.2: Picture and schematic of the deflection electrodes. A rotation of 90 degrees counter-clockwise gives the orientation of the plates down the beam-axis, resulting in a deflection to the right in the lab frame. The origin in this diagram is the midpoint between the two circles, and the black bar specifies the position of the collimator. The parameters r and a define the geometry of the electrodes and are defined in the text. This image is taken from Ref. [76]. ............................................................................................................. 50 Figure 2.3: Magnitude of electric field in the region between the two Rabi “two-wire” electrodes with a potential difference of 20 kV which is standard in our experiments. From this point of view the measured deflection is in the -𝑥 ̂ direction, where the +𝑦 ̂ direction is down in the lab frame. The black rectangle specifies the helium beam after collimation. The photo displays the electrodes as they sit in the machine during experiments for further context. This image was taken during a recent alignment and is looking towards the source from the telescope at the end of the detection chamber. This figure is adapted from Ref. [76] where calculation details are provided. .............................. 51 Figure 2.4: Block diagram of the ionizer assembly and quadrupole. The beam passes through the ionizer assembly where the droplets are ionized. The ions are then deflected by the inner and outer poles and focused into the quadrupole region. The ions pass through a final focusing lens before reaching the conversion dynode and electron multiplier where the output signal from the quadrupole is detected. The filament is also is also displayed showing the wrapping of the filament wire. Proper filament resistance is achieved with five and a half turns per edge. ................................................................................................ 53 x Figure 2.5: A comparison of helium cluster peaks detected by the mass spectrometer for operation in conversion and pusher modes (dynode voltage of –5 kV and 0 kV respectively). HeN peaks are spaced by 4 amu and are easily visible past N = 35 here. The intensity is normalized such that He2 has an intensity value of unity. The second off-scale peak present in the spectrum at approximately 18 amu is related to background water in the machine which contaminates some of the droplets. The mass interval is 0.2 amu and each point is scanned for 0.75 seconds for each spectrum. The inset demonstrates that the pusher mode gives greater than ten times the signal of the conversion mode for optimized low mass optics. ..................................................................................................................... 56 Figure 2.6: Mass spectrum of FC-43 using high mass optics voltages. The prominent peaks are at m/z ≈ 69, 100, 119, 131, 219, 264, 414, 426, 466, 504, 576, and 614 [82]. The spectrum is scaled such that the m/z = 69 peak is set to have a normalized intensity of unity. This spectrum demonstrates that the new quadrupole is able to detect ions over a relatively wide mass range, and especially in the mass range of a few hundred amu. .......... 57 Figure 2.7: Schematic showing the various signals of the synchronous detector system. All gating is relative to the chopper reference signal, and the single synchronization pulse and AND gate ensure that both accumulators have an equal period of active time. The phase delay is the time that it takes for the beam to travel from the chopper to the detector modulo the chopper period. The phase delay is displayed in blue and is measured from the rising edge of the chopper to the rising edge of the signal at the detector and is measured using a multichannel scaler (see section 2.4). The gate widths are equivalent for each accumulator gate, and are drawn to be 0.50 of a chopper period in this diagram. Accumulator A accumulates counts in the green region while accumulator B accumulates counts in the red region. The discriminator pulses panel gives a cartoon of the signal in each accumulator region where additional signal comes from the beam. ............................. 61 Figure 2.8: A comparison between the lock-in rate (blue) and total rate of counts (yellow) for helium clusters. Background peaks are clearly visible in the total rate and include H2O (and derivatives) around 18 amu, N2 around 28 amu, O2 around 32 amu, and CO2 around 44 amu. The detector is synchronized to the helium dimer peak (8 amu) and background counts are highly suppressed by the synchronized detector. Both spectra are scaled from the total rate water peak which is set to unity. ....................................................................... 63 Figure 2.9: (a) MCS records for different nozzle temperatures at a stagnation pressure of 80 bar with a chopper frequency of 260 Hz. The MCS records have a dwell time (bin size) of 50 microseconds with a pass length of 200 (bins) summed over 20,000 passes. (b) Standardized record for the 15 K record with a cosine fit as described in the text. The depleted and undepleted portions of a single period of the record are denoted in red and green respectively. (c) Normalized MCS record (normalization procedure described in text) with the points to fit from each rising edge concentrated on the relevant rising edge of the record. .......................................................................................................................... 72 Figure 2.10: A fit of Equation 2.6 over the rising edge data in the MCS record for a nozzle temperature of 15 K and a stagnation pressure of 80 bar. The fitting procedure is described in the text. The width is computed as the fitted 𝑤 /𝑣 for the distribution shown in Equation 2.1. ......................................................................................................................................... 73 xi Figure 2.11: Computed velocities for nozzle temperatures between 14-20 K extracted from the MCS records displayed in Figure 2.9(a). As described in the text, these values are in excellent agreement with measured values available in the literature. Computed velocity distribution widths are also concentrated around ≈3% for these nozzle temperatures, with the width of the velocity distribution increasing for smaller droplets formed at higher nozzle temperature. ................................................................................................................ 74 Figure 2.12: A flowchart outlining how our simulation is used to determine unknown dipole moments from deflection profile measurements. Details are presented in the text. .............. 79 Figure 3.1: (a) Deflection of HeN nanodroplets with DMSO dopant. Squares: experimental data; blue line: pseudo-Voigt function [106] fit to the undeflected profile; red line: fit by simulation of the deflection process. (b) Same for CsI dopant. (c) Average deflection of the nanodroplets beam vs. electrode voltage. Its linear variation attests to the strong orientation of the cold dopant molecule along the field alongside calculated orientation cosine labels for 10 kV and 20 kV. (d) Average nanodroplet size as a function of nozzle temperature. Symbols: mean, 𝑁 ̅ , of the log-normal size distribution deduced from our deflection measurements; line: digitized data from Ref. [10]. .............................................. 87 Figure 3.2: Computed average droplet size as a function of position (open squares). The deflected beam profile is shown in light gray (corresponding to the right-axis) to indicate the average droplet size in corresponding positions of the deflected beam. The magnitude of deflection is greater for smaller (less-massive) droplets, providing smaller average droplet sizes at positions corresponding to larger deflections. .............................................. 90 Figure 3.3: Graphical representation of the charge transfer process described in the text where m represents the dopant molecule in the center of the droplet. It is also noted that fragmentation of the dopant may occur upon localization of the hole. In the final step, the droplet is fully evaporated by excess energy. This figure is based on a diagram presented in Ref. [131] initially describing the charge transfer process. ............................................... 93 Figure 3.4: Examples of beam profiles which serve as input to fitting Equation 3.4 for determining the ionization probability of a molecule embedded in a helium nanodroplet. The curves shown are skewed Pseudo-Voigt envelopes of the experimental beam profiles which were obtained using CsI dopant molecules with nanodroplet source temperature of 19 K and deflection electrode voltage of 20 kV. The curves are labeled according to the variable names used in Equation 3.4. .................................................................................... 97 Figure 3.5: Probability of ionizing charge transfer to embedded CsI molecules as a function of nanodroplet size. This probability was determined by a fit to the electric deflection profiles which spatially disperse nanodroplets according to their mass, as described in the text. The displayed size range was covered by measurements at three nozzle temperatures (13 K, 15 K, and 19 K) corresponding to mean droplet sizes 𝑁 ̅ of 3.7×10 4 , 2.2×10 4 and 9×10 3 atoms, respectively [see Fig. 1(d)]. At each of these temperatures the beam contained a log-normal distribution of droplet sizes which then spread out spatially upon deflection. This allowed the data to span a range of sizes, as marked by the three (overlapping) bands of color. For each of those bands the probability of dopant ion formation was fitted to the form 𝑃 𝑚 𝑚 [𝑁 ( 𝑥 ) ] = exp( −𝛾 𝑁 1/3 ) . The results are depicted as dashed lines in the figure, color-matched to the size band from which the corresponding xii value of 𝛾 was derived. The lines extend into neighboring bands in order to show the range of uncertainty in their slope; the fact that they are close demonstrates the consistency of the analysis..................................................................................................... 99 Figure 4.1: (a) Imidazole molecule, fully deuterated form (molecular mass 74 amu). The arrow marks the molecule’s electric dipole moment. (b,c) Linear dimer and trimer configurations, with calculated dipole moments (marked by arrows) of 9.1-9.6 D and 14.8 D, respectively [151–153]. The effect of deuteration on the ground-state dipole moments does not exceed a few percent [147]. Structures for DMSO are presented later in the chapter with extensive detail. .............................................................................................. 107 Figure 4.2: Representative mass spectra corresponding to deflection measurements on (DMSO)n-doped nanodroplets. The mass spectrometer was set to the masses of intact ions: (a) 78 amu for the monomer, (b) 156 amu for the dimer, (c) 234 amu for the trimer. ............................................................................................................................................. 111 Figure 4.3: Profiles of (DMSO)n-doped helium nanodroplet beams. Blue: zero-field profiles, orange: deflection by a field of 82 kV/cm strength and 338 kV/cm 2 gradient. Symbols: experimental data, lines: fits of the deflection process, as described in the text. ................ 113 Figure 4.4: Energy minima of the DMSO dimer, with their corresponding binding energies and dipole moments. ............................................................................................................ 118 Figure 4.5: Dipole moment of DMSO dimer complex along the intermolecular approach coordinate, as illustrated by the molecular dynamics simulation. ....................................... 119 Figure 4.6: Energy minima of DMSO trimers, with their corresponding binding energies and dipole moments. ................................................................................................................... 121 Figure 4.7: Mass spectra produced by electron impact ionization of helium nanodroplets doped with deuterated imidazole, IM. The top (a) and bottom (b) panels show the monomer and dimer regions, respectively. The lower (dashed) lines correspond to the same low-doping regime and the upper (solid) lines to the same higher-doping regime, see the text, and the vertical scale of the panels matches the relative magnitudes of all the peaks. The additional signal visible between the labeled ion peaks is believed to derive from partially undeuterated imidazole present in the original powder and from possible H/D exchange occurring within the vapor supply system. .................................................. 122 Figure 4.8: Extended electron impact ionization mass spectrum containing deuterated imidazole clusters. The higher and lower doping regimes are described in the text. The signal for (IM) + and (IM)D + clearly dominate in the spectrum in both doping conditions and these peaks are used to collect deflection profiles. Frequent peaks separated by four amu correspond to HeN + ions. The inset shows a zoom in of the high mass range unambiguously demonstrating the presence of the imidazole trimer and tetrameter in the high doping regime. The peaks between 180 and 200 amu are believed to come from Rhenium and Tungsten from filaments in the system. ........................................................ 125 Figure 4.9: Electrostatic deflection of (IM)n-doped helium nanodroplet beams. Blue: electric field off, orange: electric field on. The symbols are experimental data, the lines are fits of the deflection process, as described in the text. (a) IM + signal; (b,c) (IM)D + signal in the lower and higher doping regimes, respectively. The arrows denote the shift of the profile centroids. .............................................................................................................................. 126 xiii Figure 5.1: A cartoon showing the embedded alkali-fullerene system of interest, where here the alkali resides above the fullerene. Generally, alkali atoms will reside on the surface of the droplet, but by pre-doping the droplet with a polarizable fullerene molecule, the alkali atom may be drawn inside of the droplet. .................................................................. 133 Figure 5.2: Mass spectra of C60Nan + ions with the corresponding Na pick-up cell temperatures indicated. All spectra are scaled to the intensity of the C60 + peak. The C60Na + signal is weak for all temperatures. The gray peak is the C 60-water complex. Panels (a) and (b) show the conditions used for deflection measurements of the C60Na2 + and C60Na3 + peaks, respectively, while (c) gives the conditions for C60Na + and C60Na4 + deflections. .............. 139 Figure 5.3: Beam deflection measurements for nanodroplets containing C60Nan=1–4. Circles (crosses) denote data points with the electric field turned off (on). The counting rates of selected ions in the strongly collimated beam were on the order of a few per second. The solid-line profiles are smoothing fits to the “field-off” data points using a symmetric pseudo-Voigt function [106], while the dashed lines are asymmetric pseudo-Voigt fits to the “field-on” data. In all cases the beam deflection is negligible. ...................................... 140 Figure 5.4: Panel (a) shows the beam deflection measurements of nanodroplets containing C60Yb with the same notation as Figure 5.3 A slight offset of the second pick-up cell added minor skewness to the profiles, hence in this figure both the “field-off” and the “field-on” data were fit to an asymmetric pseudo-Voigt profile. The shift of the profile centroid is ≈1.4 mm. Panel (b) shows the same “field-on” profile (dashed line) and data points, together with the Monte Carlo simulation (solid line) for the optimized dipole moment value of 8 D. .......................................................................................................... 142 Figure 5.5: Root mean square deviation between the C60Yb profile data and the deflection simulation as a function of the assumed dipole moment of the complex. Crosses and circles correspond to dopant ionization probability parameters (described in the text) 𝛾 =0.06 and 𝛾 =0.12, respectively. ........................................................................................ 144 Figure 5.6: The crosses are beam deflection data points for nanodroplets containing C60Yb, and the dashed line is a smoothing fit to these points using an asymmetric pseudo-Voigt function. The colored lines are the results of Monte Carlo simulations assuming three different values of the dipole moment of the complex and a dopant ionization probability parameter 𝛾 =0.12. ................................................................................................................ 145 Figure 5.7: Mass spectra of the fullerene-magnesium system under different doping and droplet conditions used for deflection measurements. Note that the added water complexes may include or be missing additional hydrogen atoms from fragmentation of water complexes. The blue spectrum has the C60 held at 350˚ C and Mg held at 335˚ C and uses a nozzle temperature of 17 K. The yellow and green spectra use larger droplets with a nozzle temperature of 15 K and have the magnesium held at 365˚ C and C 60 held at 350˚ and 375˚ C, respectively. These spectra were taken in early experiments with C60, and thus the stability decayed in time. The C 60 signal intensity at the doping conditions used was ≈12000, 9000, and 9000 (a.u.) for the blue, yellow, and green curves, respectively. Labels for mass peaks of intertest are included. ............................................. 147 Figure 5.8: Deflection measurements for the ion peaks listed under droplet and doping conditions outlined in Figure 5.7 and the profile color matches each spectrum. (a) utilizes xiv smaller droplets but sees a lower deflection magnitude than (b) or (c). The relative broadness in (a) is explained by smaller droplets, while in (c) it comes from additional collision events and hotter dopants on average. Deflection magnitudes as measured by centroid shift for (b) and (c) are comparable. The fit lines are pseudo-Voigt functions. .... 149 Figure 6.1: Magnetic deflection of (red circles) FeCl2 and (blue crosses) (FeCl2)2 embedded in helium nanodroplets. The latter profile intensity is normalized to the former. The lines show asymmetric and symmetric pseudo-Voigt functions [106], respectively. The difference in centroids between the two fits is ≈0.80 mm. In contrast to the electric deflection where the beam is deflected towards more positive positions, the magnet is installed to deflect the beam towards more negative positions. The droplets in this experiment were some of the smallest produced in our apparatus and are estimated to have a mean size of ≈ 7000 helium atoms [10]. .................................................................. 160 Figure A.1: Front panel for the beam profile measurement VI. A .tsv file containing a list of position points is required as input to define the scanning domain. The phase delay for the chopper is also required to synchronize the detector. The number of scans and wait time are also user-defined. The user is automatically prompted to save all data after the scans have finished executing. ............................................................................................. 180 Figure A.2: The Run sub-VI constructs and fills the data arrays after each scan. It also communicates the current data to the front panel. This VI has been updated to save metadata and display the lock-in rate, dip, and total count rate. ......................................... 181 Figure A.3: The Collect Data Counters sub-VI programmatically moves the chamber to a specified position, initializes the counters, and collects data for a user-defined wait time. 181 Figure A.4: Front panel for digital counter mass spectrum VI. Lock-in rate, dip, and total rate are collected as a function of mass. Number of passes, mass range, and number of steps are user-defined. The maximum step resolution with the current equipment is five for each unit mass. The phase delay for the chopper is also required to synchronize the detector. ............................................................................................................................... 182 Figure A.5: The sub-VI shown here represents a single spectrum pass and is run repeatedly to collect and average mass spectra. The VI functions by making contact with the lock-in amplifier used to control the mass channel of the quadrupole using auxiliary output voltages. Then, for each mass (or fraction thereof) the counters are initialized, synchronized to the delayed chopper pulse, and collect data. The middle of the panel shows the counter synchronization and collection sub-VIs written by N. G. Guggemos and implemented here. ......................................................................................................... 183 Figure A.6: Front panel for the simple counter and quadrupole mass control diagnostic tool. The mass can also be controlled manually on its power supply, but this VI delivers a constant mass control voltage so that the mass used for beam profile measurements is maximally consistent. The simple counter gives an unsynchronized average count rate used for diagnostic purposes and comparison with the synchronized count rate from the other main VIs. The conversion between mass and voltage is approximately 1 amu to 5 mV. ...................................................................................................................................... 184 Figure A.7: Block diagram for lock-in amplifier auxiliary voltage control used for mass control of the Ardara quadrupole. The counter block in the middle of the diagram xv demonstrates the simplest counter control routine and can be used as a reference for the more complicated synchronizing routines. .......................................................................... 185 Figure A.8: Front panel for the analog signal mass spectrum VI used with the Ardara quadrupole. The VI requires both lock-in amplifier and scan parameters to function, and uses a similar architecture to the former analog signal mass spectrum VI. This VI also has mass command using the auxiliary outputs of the lock-in amplifier. .................................. 186 Figure A.9: Block diagram for the analog signal Ardara quadrupole mass spectrum VI. The construction of this VI is fairly simple and it has only been used for testing purposes in previous experiments. It is fully functional, but modifications may be useful for future experiments if it becomes a primary data acquisition tool. ................................................. 187 Figure E.1: Simulations of broadening due to the slit (1.27 mm) or ionizer aperture (5 mm) from an initial gaussian beam profile with width defined by (a) 𝜎 =1 and (b) 𝜎 =2. In each case the broadening is substantially larger for the ionizer aperture. A legend is provided under the figure for reference. ............................................................................................. 220 Figure E.2: Approximated deflection of broadened beam profiles by translation. The initial beam profile is assumed to be a normalized gaussian with 𝜎 =2. The blue profiles assume that the slit is in place while the red profiles assume that the beam directly enters the ionizer. The translated profiles are constructed with dashed lines, while the initial profiles use solid lines. ...................................................................................................................... 222 xvi Abstract This work describes a series of electrostatic deflection experiments performed in helium nanodroplets exploring a handful of molecular systems. The unique helium droplet medium cools the system to ≈0.37 K providing almost complete orientation of the embedded electric dipole moment in an external electric field. Owing to the high degree of orientation, the applied field gradient results in robust deflection of the doped droplets on the of the order of millimeters. These experiments represent the most massive neutral systems (~10,000 helium atoms) studied by so- called beam “deflectometry.” This technique is broadly applicable to trap, cool, and probe a multitude of nanoscopic systems. The electric dipole moment provides structural information and valuable insight on charge transfer and electrostatic deflection permits a direct measurement of the dipole moment of an embedded polar system. Beam deflection also provides spatial separation of droplets by virtue of the variable mass of the nanodroplet-system which creates the opportunity for size-dependent studies. An application to charge transfer probability from the helium droplet to an embedded molecule as a function of droplet size is presented for droplets doped with cesium iodide and dimethyl sulfoxide. Additional experiments studied the aggregation of both dimethyl sulfoxide (DMSO) and imidazole dimers and trimers where the formation of polar structures is directly confirmed by beam deflection measurements. In the cold helium nanodroplet environment long-range dipole-dipole forces play a crucial role in the final configuration of the dopant molecules, and DMSO dimers and trimers find themselves caught in highly polar metastable configurations. These results are compared with ab initio calculations to elucidate the assembly dynamics. Similar deflection xvii experiments were performed for imidazole and the measured dipole moments confirm the formation of highly polar linear chain structures. These measurements provide a direct complement to spectroscopic measurements and computational studies. The deflection technique was also utilized to examine charge-transfer reactions in metal- fullerene systems in the superfluid medium. Alkali metals are well-known to be heliophobic but interaction with the highly polarizable fullerene molecule may be able to successfully draw objects into the droplet with a long-range electron transfer reaction. The emergence of a dipole moment in these systems would indicate that charge transfer has taken place and is easily detected by beam deflection. No discernable dipole moment was found in sodium-fullerene systems for up to four sodium atoms. A comparative measurement using the rare-earth metal ytterbium alongside the fullerene is found to be highly polar in agreement with theory. Similar measurements with magnesium are also presented. An extension of the helium nanodroplet deflection technique using a magnetic field for deflection of magnetic systems is presented with promising preliminary results for embedded iron dichloride molecules. This upgrade to the deflection apparatus allows the already broadly applicable method to explore a variety of novel physical interactions. 18 Chapter 1 – Introduction 1.1 Motivation The electric dipole moment of a molecule or cluster describes the distribution of charge inside, providing fundamental structural information relevant to many physical and chemical processes [1]. A simple and effective method for determining dipole moments is to utilize electrostatic deflection. In fact, various beam deflection measurements have been done with free clusters yielding notable results [2–5]. However, rotational motion even at temperatures approaching a single Kelvin counteracts the effectiveness of direct deflection experiments. Ambient rotational motion prevents the dipole from orienting in the deflecting field, making the deflection method less instructive. Recently, pulsed laser-alignment techniques have been developed [6–9] to orient molecules, which could substantially improve deflection measurements. Unfortunately, laser-alignment has several drawbacks. It is confined to extremely short time- scales, has the potential to dissociate molecules, and is generally complicated to utilize. We employ an alternative method, where prior to deflection we embedded our system of interest in a helium nanodroplet (HND) and rely on the very low resulting temperature of the molecule to strongly orient it in an electrostatic field. With the benefit of nearly full orientation in the field, we observe robust deflections of the dopant-helium system despite its relatively high mass, negating the drawback of using a heavier system for deflection experiments. The use of HND embedding provides a novel extension to atomic and molecular beam deflection experiments. In the HND embedded system, the molecular species or cluster studied can be interrogated at a significantly lower temperature than generally attainable in molecular beam experiments alone, and is broadly applicable to nearly unlimited nanoscopic systems that 19 can be contained 1 in a helium nanodroplet [10]. Furthermore, the use of HNDs also creates the opportunity to study unique metastable molecular systems whose formation is mediated [11,12] by the helium environment and temperature of the droplet and thus inaccessible by other means. The high degree of orientation of polar objects in a HND using an electric field [13] allows for spatially controlled study of a molecular system through techniques such as spectroscopy [14], electron diffraction [15], and velocity-map imaging [8]. Beam deflection in these oriented HND systems provides a direct and straightforward method to determine the structure of the embedded dopant complex based on its electric dipole moment and serves as a strong complement to the aforementioned methods. The structure of larger and more complicated molecular systems can also be probed with a simple beam deflection measurement where spectroscopy and diffraction methods become increasing difficult to analyze. Additionally, the presence or absence of a dipole moment of an embedded complex unambiguously communicates spatial-charge information and demonstrates a method to explore charge-transfer reactions and bonding interaction between molecules within the nanodroplet. An embedded polar molecular also serves as a “handle” to move and manipulate the HND with the assistance of an external field, providing a probe to study the physics and chemistry of the interesting and idiosyncratic droplet itself. A brief review of cooling and trapping techniques below contextualizes the advantages of HNDs for beam deflection experiments. Helium droplets will then be discussed in detail alongside important results and useful characteristics for our deflection measurements in subsequent 1 Many atomic and molecular species have been shown to embed in helium nanodroplets, and the limiting factors for doping helium droplets are 1) the ability to produce a diffuse gas of the species of interest with vapor pressure in the 10 -5 -10 -6 Torr range to begin seeing pick-up events, and 2) generating droplets of a sufficient size to capture systems of the desired scale. One well-known exception to this rule is that solvation of alkali metals atoms and small alkali clusters is energetically unfavorable, and these objects instead remain on the surface of the droplet. Chapter 5 covers this exception in additional detail alongside our own relevant measurements of related systems. 20 chapters. The relevant physics for electrostatic deflection of a molecular beam will also be presented. A summary of completed experiments will follow, outlining the chapters of this dissertation. 1.2 Brief Overview of Cooling and Trapping Methods Figure 1.1: A plot of techniques currently utilized to generate cold molecules along with an estimate of the temperature and density that can be achieved with each method. Gray diagonal lines show constant phase space density. The blue vertical dashed line gives the rough temperature of HNDs. This figure is adapted from Ref. [16] with permission from the publisher. Outlined in a number of recent reviews [16–24], a variety of methods are currently available for trapping and cooling molecules for subsequent study. Figure 1.1 shows a sample of available techniques and the reported number densities and temperatures presently achievable by active research groups. There are two main approaches to obtaining cold molecules referred to as direct and indirect cooling. The former is to generate a beam of molecules and cool them using a 21 buffer-gas or decelerating fields, and the latter is to build cold molecules by forcing interactions between individual cold atoms [21]. Buffer-gas methods cool molecules through collisions with a cold gas, commonly helium or argon, and can achieve temperatures in the in the single-Kelvin range and are broadly applicable [24]. Seeded molecular beams formed by the co-expansion of a molecule of interest and a rare gas can produce even colder temperatures [3] but have more limited applicability [25]. Field-based methods, such as Stark and Zeeman deceleration, use a series of inhomogeneous electric and magnetic fields respectively to translationally slow molecules through carefully timed on/off switching of the fields. Optical deceleration works similarly through careful timing of lasers to generate an optical field [20]. In both direct cooling cases vibrational degrees of freedom are not easily cooled, and field-based methods also do not provide rotational cooling [19,20]. Indirect methods rely on cooling individual atoms, which are much easier to cool than molecules, and binding them together. These methods are powerful for getting molecules to their ground state, but generally apply only to diatomic molecules [19]. For both cooling methods, lasers and fields must be optimized to interact with a particular atom or molecule, making trapping wide ranges of molecules cumbersome. Noting the limitations of other cooling and trapping techniques, we focus on HNDs which are applicable to most molecular species. HNDs offer a “universal trap” and are very effective in cooling internal degrees of freedoms to the droplet temperature of 0.37 K [10,26,27]. Nearly all dopant molecules are drawn into the center of the droplet where they experience a confining potential similar to a particle-in-a-box [28,29]. Few species, such as the alkali metals, are bound to the surface of the droplet instead. Upon capture, the helium droplet rapidly boils-off helium atoms to maintain its low temperature [10]. These advantageous properties of HNDs have 22 generated substantial scientific interest, and the droplets have been referred to as “the ultimate spectroscopic matrix” [30]. 1.3 Helium Nanodroplets Background The earliest experimental evidence for the formation of HNDs was found in 1908 during early attempts to liquify Helium-4 by H. Kamerlingh Onnes [31]. E. W. Becker and co-workers later utilized molecular beam techniques to generate a beam of HNDs in 1961 using apparatus and experimental conditions closely resembling modern HND-machines [32]. In 1977, HNDs were also produced using 3 He (rather than 4 He which I will use as the default with reference to HNDs) by Gspann and co-workers who acknowledged Becker’s earlier results for encouraging interest in the field [33]. Study and characterization of HND beams flourished when J. P. Toennies and co- workers discovered in 1990 that HNDs could easily capture impurities through collisions with the beam [34,35]. It was also determined that the droplets cool the dopant object and maintain low temperature though evaporative cooling where the kinetic and internal energy of the dopant is transferred to the droplet resulting in the evaporation of helium atoms [26,36]. These discoveries demonstrated that the HNDs served as powerful cryostats to explore individual nanoscale systems in a controlled manner [10]. Numerous machines and experiments were subsequently developed to utilize this trapping and cooling technique. Generally, a HND-producing machine will consist of a few chambers arranged in a sequence: a source chamber to produce the beam of droplets, a pick-up chamber to embed dopants in the droplet, an interaction chamber (which may be a part of the following chamber) to probe the HND-dopant system, and a detection chamber where the droplets are ionized and detected by some form of mass spectrometry [37–39]. Typically, the entire system will be under very high vacuum, 23 such that a reasonable flux of HNDs is able to reach from one end of the machine to the other without scattering from collisions with background gasses [40]. Since the HNDs are produced in a free jet expansion of helium and form a beam of droplets at one end of the machine, they are examined in-flight with the standard lifetime of a droplet on the order of a few milliseconds before ionization and detection or crashing into the opposite wall of the machine [10]. Fortunately, this is ample time to observe a wide variety of atomic and chemical processes. A sample apparatus is shown in Figure 1.2, and showcases a machine with the four regions described above, where the interaction region involves the laser excitation of the doped HND [41]. Figure 1.2: The apparatus used by Hartmann, Miller, Toennies, and Vilesov to measure the high-resolution infrared spectra of sulfur hexafluoride clusters and mixed sulfur hexafluoride-rare gas clusters. The beam is generated in the droplet source region, the clusters are embedded in the pick-up chamber, the doped droplets are excited with a diode laser, and ionized and detected by a mass spectrometer. Spectra are detected using beam depletion, where the laser excitation results in the boil-off of hundreds of helium atoms, reducing the probability of electron-impact ionization and therefore causing a dip in the mass spectrometer signal corresponding to spectral absorption. This figure is from Ref. [41]. Reprinted with permission from AAAS. Early results in the field used infrared (IR) spectroscopy to characterize dopant molecules, initially using SF6 in HNDs [42–44]. Sharp rotational lines observed in early spectra of simple molecules were used to provide experimental evidence of the droplets’ very low rotational 24 temperature. Noting that the intensities of the rotational lines in the IR spectra obey a Boltzmann distribution, fitting the data determined that the rotational temperature of HNDs is ≈0.37 K [10,26,27]. The sharp rotational lines also suggested the free rotation of embedded molecules which was one of the early indications of superfluidity in the droplets. Superfluidity is a property that allows for fluid flow without viscosity, abnormally large heat conductivity, and quantum-mechanical phenomena such as the formation of quantized vortices [10,37,45]. While this property is not the focus of our experiments, it is useful in the electrostatic deflection of doped helium droplets, as it allows for a high degree of orientation with the field lines rather than being impeded by the helium medium. A more comprehensive description of this process is described later in this chapter. Superfluidity has been extensively studied in HNDs and is important in the history of the helium nanodroplet subfield. A clever experiment determined that superfluidity begins to manifest in helium droplets with only ≈60 4 He atoms, constituting a lower bound for the bizarre property [46]. Later experiments also confirmed the formation of quantized vortices by embedding silver atoms in HNDs. Subsequent deposition and imaging of the doped droplets showed continuous tracks of silver suggesting that filaments aggregated in the vortex cores [47]. Superfluity and the formation of vortices in helium nanodroplets is presently active, and recent ultrafast x-ray diffraction imaging has shown well-resolved images of Xenon-doped vortices in HNDs [48,49]. Despite the superfluity of the droplets and the sharply rotational lines observed, it was found that the rotational constants for embedded molecules are lower than the gas phase values [26]. It is understood that the dopant molecule weakly couples to the helium droplet resulting in the reduction of its rotational constants. This may be thought of classically as the 25 dopant molecule dragging neighboring helium atoms along while it rotates [10]. More recently, a quasiparticle approach describes this process quantum mechanically using “angulons”, or many body excitations interacting with the rotating dopant [50,51]. For a wide range of heavier molecules embedded in a HND it was experimentally determined that the effective moment of inertia is roughly two and a half times the gas-phase value [10]. Further work describing and manipulating rotational motion of dopants in helium nanodroplets was conducted by R. E. Miller and co-workers where they demonstrated the formation of pendular states for molecules embedded in HNDs in a strong uniform electric field [13]. It was shown that owing to the sub-Kelvin temperature of the droplets, strong orientation could be achieved in an electric field and the trapped molecule’s free rotational motion becomes bound to small, harmonic undulations about the field. The motion for the molecules in these states are described by a pendulum in three-dimensional space. A number of molecular systems have been explored using this so-called “pendular state spectroscopy” [14,52] and in one remarkable result it was shown that long (up to n=7) metastable linear chains of HCNn could be formed under the mutual dipole-dipole forces present in the system [12]. Additional experiments utilized Stark spectroscopy to measure dipole moments of embedded molecules by simulating spectra and fitting the dipole moment [53]. An extension of this technique utilizes the angle between the electric dipole moment and the vibrational transition moment associated with a given vibrational mode to extract structural information about the embedded molecule. The vibration transition moment angle (VMTA) [54] is determined by orienting a polar molecule in an electric field, then measuring absorption intensity for both parallel and perpendicular laser polarization for a given vibrational band. The VMTAs provide structural information about the molecular and can assist is assigning bands in measured spectra [14]. These early HND experiments using polar molecules in electric 26 fields provided critical groundwork for the electrostatic deflection measurements discussed in this dissertation which aim to operate in-tandem with spectroscopic results. The HND subfield has grown substantially since the foundational work 1990s with many reviews and textbook chapters written on HNDs and associated techniques for interrogation of trapped molecules, referenced above [10,14,29,37,38,40,44]. As of 2022 a full textbook [55] has been published on the helium nanodroplets subfield and is a phenomenal resource for those new to the field. Chapter 3 of this textbook briefly outlines active groups in the community and the appendix lists and outlines additional review papers on the multitude of modern nanoscale physics and chemistry research conducted in HNDs. 27 1.4 Characterization of Helium Nanodroplet Beam Figure 1.3: Average number of He atoms in a droplet as a function of the nozzle stagnation conditions. The diameter of the produced droplets is a function of the number of helium atoms and presented on the right vertical axis. Nozzle diameters for the measurements in the figure are between 2-5 microns. The expansion type is characterized by nozzle conditions, and breaks into four regimes relative to the liquid-vapor critical point and superfluid transition of helium [10,35,37,44]. This figure is reproduced from Ref. [55] with permission from the publisher. Helium is a unique element in that it remains a liquid as it approaches absolute zero Kelvin at atmospheric pressure. It remains gaseous at atmospheric pressure above roughly 4.2 K, and there is a second-order phase transition between a standard liquid ( 4 He I) and superfluid liquid ( 4 He II) phase at 2.17 K. The critical point for helium occurs at 2.27 bar and 5.2 K [55]. The different phases of helium allow for the formation of drastically different droplet characteristics depending 28 on the choice of expansion conditions. HNDs are created an expansion of helium through a cold micron-scale nozzle into vacuum where the helium is cooled adiabatically following isentropes on its phase diagram [10]. The average size and size distribution depend on the stagnation pressure and temperature of the nozzle, as well as its diameter. Typical nozzle conditions are 1-80 bar for the nozzle pressure and 3-40 K for nozzle temperature, with 5-micron nozzles being the best- characterized. There are four distinct expansion regimes as outlined in Figure 1.3 which also displays a condensed visual showing measured droplet sizes in the different regimes [10,55]. Subcritical expansion 2 (Regime I) produces the smallest droplets available. The average droplet size (𝑁 ̅ ) is roughly between 10 3 -10 4 helium atoms and has been measured using molecular beam scattering [56]. This is the expansion regime that our deflection experiments generally utilize, and subcritical expansions for the creation of helium nanodroplets have been studied in detail. In the subcritical expansion, the helium is gaseous upon leaving the nozzle, and the helium atoms collide and coalesce within a few millimeters of the source. This process results in a combination of small droplets which continue to evaporatively cool, as well as free helium atoms [10,35]. Our experiments generally use droplets formed in this expansion regime as a sufficient flux is generated while the droplets are light enough to be deflected considerably by an external field. Supercritical expansions (Regime III) produce larger droplets, so much larger that scattering measurements were insufficient to determine the average droplet size, but 𝑁 ̅ ≥ 10 5 atoms was concluded [57]. Later measurements obtained by attaching electrons to the larger clusters and 2 There appears to be an inconsistency on the nomenclature for these expansions in the field. The canonical Ref. [10] describes subcritical expansion conditions as expansion of gaseous helium and below the critical isentrope with respect to pressure, whereas the more recent textbook [55] describes subcritical expansion as the expansion of liquid helium in liquid phase below the critical isentrope with respect to temperature. Here I will use the former definition with which I have more familiarity. 29 deflecting them found average droplet sizes in the approximately 10 5 ≤ 𝑁 ̅ ≤ 10 7 atom range [58]. In a supercritical expansion the helium is liquid when leaving the nozzle, and the jet of liquid helium breaks up, creating larger droplets [57,59]. Under these expansion conditions the droplet sizes follow an exponential distribution [58]. In critical expansion (Regime II), the behavior is less understood than Regimes I and III, and the average size and velocity of the helium droplets are found to fluctuate significantly [37,57]. In each of the three types of expansion, the helium is expected to follow an isentrope on its phase diagram to its final state. In this particular case, the isentrope intersects the liquid vapor critical point [10,35,44]. Relatively few experiments have been conducted in this regime [55]. In another special case (Regime IV), very large droplets with 𝑁 ̅ ≥ 10 9 helium atoms are generated at very low nozzle temperatures (1.5-4.2 K), such that the expanding helium may already be superfluid. These droplets are large enough to have diameter on the order of microns, and thus the size of the droplets could be determined optically. Droplets of this size are produced by Rayleigh breakup and have highly uniform sizes which are determined to be in the 10 9 ≤ 𝑁 ̅ ≤ 10 12 range [37,60]. Recent work [61] with these massive droplets demonstrated the potential to generate helium beams with highly regular spacing and uniformity using optical shadowgraphy. An example of these beautiful results is shown in Figure 1.4 which encapsulates the idea of having a beam of individual cryostats to study molecular or cluster systems. 30 Figure 1.4: Optical shadowgraphs of massive helium nanodroplets expanded in Regime IV with a stagnation pressure of 0.6 bar and nozzle temperature of 2.7 K. Control of uniform high-quality beams of this type are still not fully understood. Droplets of this size are many orders of magnitude too large to deflect with our technique, but the image demonstrates the principle of the individual flying cryostats. This figure is reprinted from Ref. [61], with the permission of AIP Publishing. As described above, varying the expansion conditions allows for many orders of magnitude in the size of HND system allowing for a wide variety of possible experiments. It is noteworthy that the final temperature of the helium droplet is independent of the expansion conditions. It is determined through a statistical ejection of surface atoms where the evaporation rate is governed by the energy of excitations in the droplet relative to the binding energy of an emitted helium atom [36]. This binding energy approaches the bulk helium value of 7.2 K for clusters approaching a thousand atoms which is well below normal droplet sizes in our experiments [62]. With our standard nozzle conditions, we expect beam velocities in the range of ≈350-425 m/s with a roughly fixed velocity for a given experiment [63]. The forward velocity spread is also fairly small at only ≈1-3% of the beam velocity for our typical droplets [10,56,57]. Moreover, the size distribution of small droplets suitable for deflection measurements is well-characterized in the subcritical regime (Regime I) and generally follows a log-normal distribution which is common in nucleation processes [64,65]. Equation 1.1 gives the form of a log-normal distribution, 31 𝑃 ( 𝑁 ) = 1 √2𝜋 𝑁𝛿 𝑒 − ( 𝑙𝑛𝑁 −𝜇 ) 2 2𝛿 2 , (1.1) where 𝑁 represents the number of helium atoms in a droplet, while 𝜇 and 𝛿 represent the mean and standard deviation of the natural logarithm of 𝑁 [64]. The average droplet size, 𝑁 ̅ , and full width at half max (FWHM), 𝛥𝑁 , are determined using Equation (1.2) and Equation (1.3) below [44]: 𝑁 ̅ = 𝑒 𝜇 + 𝛿 2 2 , (1.2) ∆𝑁 = 𝑒 𝜇 −𝛿 2 +𝛿 √2𝑙𝑛 2 − 𝑒 𝜇 −𝛿 2 −𝛿 √2𝑙𝑛 2 . (1.3) Figure 1.5 shows Equation (1.1) fit to experimental scattering data. Two important parameters, the average droplet size, and FWHM can be determined from the log normal fit and are roughly equal. The data presented in Ref. [56] gives 𝛥𝑁 ≈ 0.9𝑁 ̅ . One caveat to the use of the log-normal distribution for small droplets is that later experiments which deflected ionized droplets uncovered a lower intensity exponential tail that extended more than an order of magnitude beyond the mean droplet size [55]. This exponential tail was initially overlooked in the aforementioned scattering experiments. The deviation from the log-normal distribution in the tail indicates that while a small average droplet may be detected, it is possible to find substantially larger droplets using the same nozzle conditions. 32 Figure 1.5: Scaled probability vs. droplet size data points and least-square fitted log-normal distributions at three different nozzle temperatures and identical stagnation pressure of 80 bar. The most probable droplet size is listed, and the average droplet size and FWHM can be estimated visually. The log-normal fit is in very good agreement with the data points and the trend is shown for a reasonably large range of droplet sizes. This figure is reprinted from Ref. [64], with permission from Elsevier. In addition to the size characteristics of the HND beam, doping is of critical importance to study embedded molecules. Dopant molecules are embedded through collisions between the desired molecule and HND. Typically, a partial pressure of ~10 -6 mbar is sufficient for single collisions with the droplet in a standard pick-up cell [10]. Due to the nature of the doping process, pick-up of dopants follows Poisson statistics according to Equation (1.4), 𝑃 𝑘 = ( 𝑛𝜎𝑙 ) 𝑘 𝑘 ! 𝑒 −𝑛𝜎𝑙 . (1.4) 33 Here, the probability of k pick-up events (𝑃 𝑘 ) is related to the number density of the dopant (𝑛 ), capture cross section (𝜎 ), and length of pick-up region (𝑙 ) [41]. The capture cross section is generally taken to be proportional to the droplet geometrical cross section 𝜎 ≈ 15.5𝑁 2/3 Å 2 [66]. The number density for given dopant molecules can be manipulated to increase the number of trapped molecules in a given droplet, typically by heating a sample of dopant molecules. Figure 1.6 provides example Poisson curves for multiply doped droplets. Figure 1.6: Pick-up of SF 6 Poisson curves showing beam depletion (which we may treat as relative pick- up probability) as a function of pick-up cell partial pressure. The pick-up of multiple SF 6 molecules is well- described by the Poisson process described in Equation (1.4). Selective doping of droplets can be achieved using this method or the method described in the text. This figure is from Ref. [41]. Reprinted with permission from AAAS. Using Poisson statistics, the expected number of dopants per droplet can be determined. In many of our experiments, it is important to dope only with a single polar molecule. Measuring the Poisson curves and staying in the low-pressure linear regime, we generally detect droplets where 34 monomer doping dominates. Single doping can also be reasonably approximated when higher order dopant mass peaks are absent in the mass spectra, which is often easier to measure. The same technique is extended when doping with a specific number is molecules is favorable. In the case that we utilize droplets with k observed doping events, and the doping conditions are optimized such that the k+1 doping events peak is minimized while the k doping events peak has sufficient intensity for a measurement. It is important to do this as carefully as can be managed, as higher order clusters can fragment and contaminate smaller mass peaks, complicating the measurement. The ability to manipulate the size distibution and doping conditions provides control over the system of interest when making beam deflection measurements. The physics of how the size and dipole moment of the HND system influence the deflection of the beam is covered in the following section. 1.5 Electrostatic Deflection It has been just over a century since beam deflection experiments were first proposed. H. Kallmann and F. Reiche [67] provided theoretical work suggesting that sending a beam of polar molecules through an inhomogeneous electric field and measuring a beam deflection would allow for calculation of the dipole moment of the molecular species. In the early 1920s it was unknown whether individual molecules had an electric dipole moment quantity or if this property arose from interactions with other nearby molecules. This work inspired O. Stern to write a theory paper [68] as a precursor to one of the landmark experiments of modern physics, famously known as the Stern-Gerlach Experiment, [69] in 1922 alongside experimental physicist W. Gerlach [70]. The Stern-Gerlach experiment attempted to disprove space quantization, which was a result of orbital quantization proposed by the Bohr model of the atom. The idea is that, oriented about some fixed 35 axis, the ground state orbital of an atom should have exactly two angular momentum values leading to two opposite magnetic dipole moments. Then, if passed through an inhomogeneous magnetic field the beam should experience two opposite forces and split in two. The experiment deflected a beam of silver atoms, and ultimately it was determined that the magnetic dipole moment came from electron spin rather than space quantization [71], but the beautiful idea and physics of external-field beam deflection remain valuable and applicable. 3 The first example of deflection using the electric dipole moment of a polar molecule in a molecular beam was measured by E. Wrede a few years later [73]. The physics of this process are outlined below for the case of electric deflection, though the case for magnetic fields and moments is analogous [1]. A permanent dipole (𝒑 ) 4 inside of an electric field (𝑬 ) experiences a torque (𝝉 ) to orient the itself with the field, 𝝉 = 𝒑 × 𝑬 , (1.5) but does not experience a force unless the field gradient is nonzero. This is shown by writing the potential energy (𝑈 ) of the same dipole in an external field, 𝑈 = −𝒑 ∙ 𝑬 , (1.6) then taking the gradient to determine the force on the dipole shown in Equation (1.5) [1], 𝑭 = ( 𝒑 ∙ 𝛁 ) 𝑬 . (1.7) 3 In addition to following in the footsteps of Stern and Gerlach’s field of research, I have also experienced their experimental privilege of late nights with a molecular beam machine. In a recent publication honoring the 100-year anniversary of the famous experiment [72], an account of Stern states: “I recruited Gerlach as a collaborator. He was a skillful experimentalist, and I was not. In fact, each part of the apparatus that I constructed had to be remade by Gerlach.” Cheerfully, Stern also said: “We were never able to get the apparatus to work before midnight.” Much of the data presented in the following chapters of this dissertation was collected in the early hours of the morning following a day of experimental set-up and signal optimization for the system at hand. 4 Bold is used to indicate vector quantities. 36 We see that it is required to have an inhomogeneous electric field in order to deflect a dipole passing through it. Taking the direction of the field and gradient as the z-direction and using kinematics, we can estimate the deflection of a polar object using Equation (1.8), 𝑑 𝑧 = ( 𝐿 1 2 2 + 𝐿 1 𝐿 2 ) 𝑚 𝑣 2 〈𝑝 𝑧 〉 𝜕𝐸 𝜕𝑧 . (1.8) Here 𝑚 is the mass of the polar object, 𝑣 is the velocity along the beam axis, 𝐿 1 is the length of the field region, 𝐿 2 is the length of free flight after passing through the electrodes, and 〈𝑝 𝑧 〉 is the expectation value of the permanent dipole in the 𝑧 -direction [1,74]. As demonstrated by Equation (1.8), our deflection estimate scales inversely proportional to its mass which creates a problem with using HNDs where the mass of the droplet can easily exceed the mass of the dopant by multiple orders of magnitude. Typical dopants in our experiments have masses of ~10 2 amu while the droplets frequently used for deflection have thousands to tens of thousands of helium atoms resulting in masses of 10 4 -10 5 amu. The resolution to this problem lies in the 〈𝑝 𝑧 〉 term, where the low temperature of HNDs provides an advantage. It is noteworthy that the deflection is maximized when both the field and field gradient point in the same direction since optimally the dipole will fully align with the field. The construction of electrodes that produce a field with colinear field and gradient is important in experiments of this type and will be discussed in Chapter 2. 37 Figure 1.7: A cartoon showing the electric field direction (red), permanent dipole moment direction (blue) and the angle of orientation between them (𝜃 ). The 〈𝑝 𝑧 〉 term is proportional to the orientation that can be achieved between the direction of the dipole moment and the direction of the electric field. Orientation is defined by the angle (𝜃 ) between the dipole moment and the electric field, while aligned means that the dipole and field are collinear, but may be oriented opposite each other. Figure 1.7 provides a visual of this concept for a dipole embedded in the droplet. We can define the expectation value of the orientation cosine as: 〈cos 𝜃 〉 = 〈𝑝 𝑧 〉/𝑝 . (1.9) Here 𝑝 is the magnitude of the total dipole moment, typically expressed in units of Debye (D) or 3.336×10 -30 C∙m. For a collection of molecules with a known dipole moment at fixed temperature in an external field, the Langevin function provides the orientation cosine in the classical limit, 〈cos 𝜃 〉 = coth( 𝑝𝐸 /𝑘 𝐵 𝑇 )− 𝑘 𝐵 𝑇 /𝑝𝐸 , (1.10) where 𝑘 𝐵 is Boltzmann’s constant and 𝑇 is the system temperature [1,75]. Figure 1.8 shows the average orientation cosine as a function of field strength at temperatures corresponding to a HND and 5 K to represent typical buffer gas cooled molecular beam experiments where a temperature 38 between 1-10 K is standard [24,76]. Buffer gas cooled molecular beams are used for comparison as they have similarly broadly applicable compared to HNDs. Figure 1.8: Orientation cosine provided by the Langevin function [Equation (1.10)] for three different polar molecules, cesium iodide (CsI; 11.7 D), dimethyl sulfoxide (DMSO; 3.96 D), and water (1.86 D). The former two being common highly polar dopants used in our experiments, and the latter likely being the most well-known polar molecule and also a common annoyance in vacuum systems. Water has a relatively small dipole when compared to the other two molecules, demonstrating additional scaling of the orientation cosine with the electric field strength. The gray line is approximately the strength of the electric field used in our experiments. Figure 1.8 demonstrates the advantage in embedding the dopant molecule in a helium droplet: substantially higher orientation with the field even for more modest dipole moments. The low temperature of the helium environment allows for a very high degree of orientation with the electric field, ameliorating the drawback of substantially higher mass. Even for relatively weakly 39 polar species a strong degree of alignment is expected. Deflections of the doped system for typical droplet conditions and dopants results in deflections of ~1 millimeter. While this deflection may appear small, it is easily measured in the laboratory environment. It should be emphasized that the scale of the objects deflected are massive from a molecular beam standpoint and the deflection comes from a polar, yet electrically neutral dopant. The degree of orientation in helium droplets has an additional benefit in that the measured beam deflects rather than broadens in the case of weakly oriented systems. In the case that strong reorientation of the polar object does not occur, the beam will smear-out and broaden due to variation in the average dipole moment along the field direction when computing the deflection [1,77]. While beam broadening is also a useful metric for obtaining quantitative results, deflection in the highly oriented case is straightforward to interpret and the dipole moment of a system can be quickly estimated from Equation (1.8) while collecting data. 5 The orientation of a polar molecule becomes more complicated in the quantum mechanical picture. In this case the molecule exists in some quantum state, where different rotational and vibrational states typically do not have the same effective dipole moment [1]. At the very low temperature of the droplet only a handful of rotational states are occupied and the dopants are confined to their lowest vibrational states. As polar molecules enter the electric field region their internal energies are shifted by interactions with the field. The energy shift experienced by the molecule in the field depends its rotational state and thus the total orientation cosine depends on 5 In reality there is also asymmetric broadening that occurs when using helium droplets due to the distribution of sizes produced during the beam generation. However, an estimate of the average droplet size, orientation cosine, and other beam characteristics allows the experimentalist to make informed decisions during an experiment that would be more challenging if a more strenuous data analysis is required. 40 the populated states [3,78]. These aforementioned “pendular states” [52] describe the mixture of the rotational states and the field interaction. Solving the problem of rotational motion in an external electric field with quantum mechanical treatment is achieved by constructing the Hamiltonian (𝐻 ̂ ) for rigid body rotation and including the Stark term, 𝐻 ̂ = 𝐴 𝐽 ̂ 𝑎 2 + 𝐵 𝐽 ̂ 𝑏 2 + 𝐶 𝐽 ̂ 𝑐 2 − 𝑝𝐸𝑐𝑜𝑠𝜃 . (1.11) Here 𝑎 , 𝑏 , and 𝑐 are the principal axes and 𝐴 , 𝐵 , 𝐶 and 𝐽 ̂ are the rotational constants and angular momentum operators respectively about the principal axes [76,78]. The last term in Equation (1.11) is the Stark term. For the general case of an asymmetric rotor where 𝐴 , 𝐵 , and 𝐶 are each different, which applies to many of the molecules we study, this problem is not analytically solvable. However, there exist numerical solutions to this problem where the Hamiltonian is diagonalized on the set of Wigner D-Matrices and the eigenvalues are the Stark-shifted energies. This process is described in detail in Refs. [74,78] and includes expressions for the nonzero matrix elements and the latter provides a software package for calculating the shifted energies. The expectation value of the orientation cosine is defined for a given energy eigenstate (𝘀 ) with Equation (1.12): 〈cos 𝜃 〉 = 〈𝑝 𝑧 〉 𝑝 = − 1 𝑝 𝜕𝘀 𝜕𝐸 . (1.12) Taking an average over all available rotational states at the temperature of the droplet gives: 〈cos 𝜃 〉 = − 𝑘 𝐵 𝑇 𝑝 𝜕 𝜕𝐸 (𝑙𝑛 ∑ 𝑒 − 𝘀 𝑘 𝐵 𝑇 𝘀 ) . (1.13) Solving for the orientation cosine in this way provides a more complete description of the behavior of the trapped individual molecules in an external electric field. A former graduate student on the 41 helium droplet project, D. J. Merthe, wrote simulation code following the method of Ref. [78] to construct and diagonalize the Hamiltonian given in Equation (1.11) and compute the Stark-shifted energies. Using these shifted energies, the orientation cosines can then be determined for molecules used in our deflection experiments [76]. Figure 1.9 (a) and (b) shows the Stark curves computed with this process alongside orientation cosines for both the quantum and classical treatments for CsI and DMSO which are explored in Ref. [79]. This code and a number of updates are described in additional detail in Chapter 2. Figure 1.9: (a) and (b) provide computed rotational Stark-shifted energies as a function of electric field strength for CsI and DMSO at the HND temperature of 0.37 K, while (c) and (d) show the associated thermally-averaged orientation cosines using the (classical) Langevin function and (quantum) energy eigenstates of the previously described Stark-corrected rigid body Hamiltonian. The black vertical line corresponds to the electric field strength typical in our experiments. This figure is adapted from Ref. [76] and is included and described in the supplemental information of Ref. [79]. 42 Figure 1.9 (c) and (d) demonstrate that CsI is nearly fully oriented in both the classical and quantum mechanical treatments. We may expect this result for the heavy diatomic, which behaves more like a classical rotor under these conditions. The more complicated polyatomic DMSO achieves respectable orientation using the quantum mechanical treatment, with an orientation cosine approaching 0.80, certainly sufficient to show visible deflection. It should also be noted that the quantum mechanical treatment shown in Figure 1.9 assumes gas-phase rotational constants from Refs. [80–82]. In reality the reduced rotational constants from weak coupling with the helium environment cause the orientation cosine under the quantum mechanical treatment to move toward the classical value, but the gas-phase rotational constants are provided to establish a lower bound in absence of exact values for the modified constants. 1.6 Summary and Scientific Contributions The first electrostatic deflections of neutral doped helium nanodroplets were completed and published by D. J. Merthe in Ref. [83] and described in his dissertation [76]. These earlier experiments demonstrated that measurements of this type for this system were possible, but it was later discovered that the deflections measured in Ref. [83] extended beyond the detector and were artificially clipped. In reality the deflection of doped helium droplets was larger than originally anticipated. Improvements were made to the experimental apparatus to extend the detection region by allowing the entire detection chamber to spatially translate and collect the entirety of the beam deflection. In the beginning of my tenure as a graduate student I assisted D. J. Merthe on preliminary measurements with the modified apparatus which are included in Ref. [76]. I completed and extended these initial measurements and co-authored two publications in 2019 [79,84]. Later deflection experiment projects resulted in two additional publications in 43 2020 [85] and 2022 [86]. The COVID-19 pandemic interrupted research in the Spring and Summer terms of 2020 and deflection projects were temporarily stalled while lab access was restricted. During this time, I began a computational project under the guidance of K. Hansen of Tianjin University analyzing mass spectra collected in the Signorell Group at ETH Zurich. The results of this project which explored evaporation and shell structure in CO2 clusters were published in 2022 [87]. Current experiments on the helium project led by B. S. Kamerin are attempting to extend the deflection technique to magnetic deflection of magnetic dipoles of molecules and atoms embedded in helium droplets. Chapter 2 of this document will outline our experimental apparatus and its improvement, including data acquisition hardware, software and analysis tools which I have developed or modified. The addition and tuning of a new, higher mass-range quadrupole mass spectrometer and implementation of background-subtracting digital pulse-counting software will be discussed here. Chapter 3 will cover my first publication which demonstrates the ability of our technique to strongly orient and deflect polar dopants embedded in HNDs on the order of millimeters. The process is shown for both the simple linear diatomic molecule CsI as well as the more complicated polyatomic DMSO to reveal the applicability of the technique. This project also demonstrates spatial separation of the doped helium beam and the ability to size-select helium droplets based on the magnitude of deflection. An application of this size-filtering is applied to model charge transfer probability in helium droplets as a function of droplet size. Chapter 4 describes measurements of DMSO and imidazole dimer and trimer complexes in helium droplets. The DMSO measurements demonstrate the formation of metastable structures guided by dipole-dipole interactions in the helium medium. The imidazole measurements provide experimental evidence to validate dipole moments for the highly polar complexes in helium 44 droplets. These measurements also offer a tool to explore the parentage of different fragments in a mass spectrum using the magnitude of deflection observed. Both projects demonstrate the use of electrostatic deflection as a tool to directly and definitively explore the structure of molecular complexes in helium droplets as a complement to spectroscopic and computational methods. Chapter 5 will discuss the results of our most recent publication probing the presence and absence of charge transfer in fullerene-metal systems. These measurements utilize electrostatic deflection to directly and unambiguously determine if charge is transferred in these systems based on the formation of an electric dipole moment. This chapter presents the first results utilizing the upgraded mass spectrometer and pulse-counting software. Finally, Chapter 6 will summarize completed projects, outline future work, and present preliminary work on magnetic deflection of doped helium droplets. While the completed project involving shell structure in CO2 clusters generally falls into the category of cluster physics, it is far enough removed from the main body of work in this dissertation that it will not be covered here. 45 Chapter 2 – Experimental Apparatus and Methods 2.1 The Helium Nanodroplet Deflection Machine The helium machine was built roughly two decades ago and the only major component from the original construction on the current iteration is the source. Many of the modern updates to the machine including the upgrades to the pick-up chamber, addition of the deflection plates, and mobility of the detection chamber were completed by my predecessor and coworker D. J. Merthe who completed his Ph.D. in 2017. Figure 2.1 presents a block diagram with the design of the helium machine used for the projects completed during my tenure as a graduate student. As of the summer of 2022, a further major upgrade has taken place with the inclusion of a second deflection chamber, this time containing a strong permanent magnet [88] to explore magnetic deflection of doped helium droplets. However, the block diagram is accurate for the displayed experiments discussed in the subsequent chapters. Ref. [76] describes much of the design of the helium machine in extensive detail and an overview is presented here. A beam of HNDs is generated in the source chamber from expansion of helium gas (Ultra High Purity or Research Grade, 99.999% and 99.9999% helium respectively, Gilmore Liquid Air) through a 5-micron nozzle aperture. The nozzle in use in our helium machine is modeled from the famous University of Gottingen design [35,61,89]. Excellent schematics of this design can be found in Ref. [76] (our nozzle) and in the supplemental information for Refs. [61,89]. The nozzle is mounted onto the second stage of a cold head refrigeration unit (DE- 204-FF, Advanced Research Systems) and the nozzle temperature is monitored using two silicon 46 diode temperature sensors (DT-670-DI, Lakeshore). The beam of droplets then passes through a 200-micron hole in a conical skimmer 6 before entering the pick-up chamber. Figure 2.1: Block diagram of the helium droplet deflection apparatus. Major components are labeled and described in detail in the text. Note that the position of the detection chamber is not fixed can translate laterally in the lab frame. The double-triangle symbols represent valves, and each chamber can be isolated from the others. The droplets then pass through a mechanical chopper wheel which breaks the beam into discrete packets. The chopper has 10 blades even spaced between openings of the same size leading to a 50% duty cycle in operation. The beam passes through the chopper at roughly 12 o’clock towards the edge of the wheel and spins clockwise if looking from the pick-up chamber towards the source. An optical switch mounted between 2 and 3 o’clock outputs an approximately square- wave signal describing when the chopper is open or closed. Typically chopping frequencies are between 250 and 500 Hz. Using a telescope placed at the end of the detection chamber and a light 6 The skimmer is placed roughly 1 cm following the nozzle opening. Precise alignment of the skimmer relative to the nozzle is critical to open strong beam signal intensity. The nozzle assembly is locked vertically and rotationally by screws and clamps on the top of the source chamber, but can be translated both laterally and along the beam axis. When beam signal cannot be found, misalignment of the nozzle and skimmer is an excellent candidate to examine. 47 in the source chamber passing through the skimmer, we determined that despite triggering on different blades of the chopper, the rising edge captured by the optical switch coincides with the opening of the beam. The droplets are subsequentially doped with one or more chemical species of interest. Generally, we dope using a heated stainless-steel pick-up cell, but more volatile dopants can also be fed into the pick-up chamber through an external cuvette with controlled flow through a short Swagelok line and micrometer needle valve. The stainless-steel cells are heated with four 1/4" diameter, 2" long cartridge heaters (Firerod E2A55, Watlow) and maintained at a nearly constant temperature using a PID controller (CN9000A, Omega) to narrowly oscillate about a set temperature. Later experiments simply used a constant voltage applied to the heaters from the power supply and achieved stable temperatures. The pick-up chamber also contains an ultraviolet (UV) lamp (UVB-100, RBD Instruments) to desorb water on the walls of the pick-up cells and chamber. The addition of the UV lamp significantly decreased the water measured in the helium beam, though water is still present in the beam. After the doping region, the beam travels into the deflection chamber, where it is collimated by a 0.25 mm by 1.25 mm slit and moves through a deflection region composed of electrodes in a Rabi “two-wire” configuration described in detail below. The plates have a length of 15 cm along the beam axis. With an applied voltage of 20 kV, a field strength of approximately 82 kV/cm and a field gradient of 338 kV/cm 2 are achieved [79], resulting in the orientation and deflection of polar objects. Next, the beam moves through a 125-cm free-flight region where it then encounters a 1.27 mm slit before individual droplets are ionized and detected using a quadrupole mass spectrometer in the detection chamber. Directly beneath the position of the slit, the chamber is mounted on a precision linear translation stage (SIMO Series 20", PBC Linear). The full free-flight region and 48 detection chamber are free to move through a small angle using a using this translation stage and a flexible bellows between the deflection chamber and flight tube. The rotation about the pivot point is driven by a stepper motor (NEMA 17) with a stepper motor driver (ST5 Stepper Motor Driver, Applied Motion) which causes the detection chamber to translate perpendicular to the beam axis in order to detect the full intensity of the deflected (or undeflected) beam as a function of position [76]. In a typical experiment, the detection chamber will translate roughly 20 millimeters in order to fully capture the deflection profiles. Deflection profiles are collected by setting the mass spectrometer a fixed peak in the mass spectrum and translating the detection chamber on the precision linear slide, controlled by a stepper motor, to a number of positions with a predetermined interval. Measurements are made under two conditions: “field-off” and “field- on.” The former establishes the original cross section of the beam, and the latter determines the magnitude of beam deviation under the influence of the electric field [86]. In order to measure detectable signal stemming from the beam of helium droplets, a robust vacuum must be maintained. The helium machine generally operates under high-vacuum conditions [90] with chamber pressures in the range 10 -7 -10 -8 Torr excluding the source chamber, which is a couple of orders of magnitude higher in pressure. Ion gauges are attached to each chamber to monitor pressure. The source chamber is pumped by a large diffusion pump (PMCS 10C, Consolidated Vacuum Corporation) mounted at the bottom of the chamber and backed by a roots blower (Kinney KMBD-400) which is backed by a rotary vane vacuum pump (Varian SD700). We installed a water baffle in the source chamber to mitigate oil flow from the diffusion pump towards the nozzle assembly. At the cost of pumping speed, the baffle has improved the cleanliness of the nozzle and drastically slowed the rate of oil coating the super insulating sheets 49 protecting the cold head 7 . The pick-up chamber is also pumped by a diffusion pump (Varian VHS- 6 0184) mounted at the bottom of the chamber. Since the pick-up chamber introduces a large variety of dopants, including corrosives, and has the propensity for these dopants to fall from the pick-up cells into the chamber, a diffusion pump is a robust choice to tolerate these issues 8 . Between the chamber and diffusion pump there is a gate valve and a liquid nitrogen baffle which is filled automatically with a solenoid valve and operated during experiments to prevent the flow of oil into the chamber. There is also a side-mounted turbomolecular pump (Varian TV301 Navigator) to assist with pumping the chamber. The diffusion pump and turbomolecular pumps are each backed with a mechanical pump (Welch 1397 and Welch 1402, respectively). The deflection and detection chambers are each pumped by a turbomolecular pump (Alcatel 5150 and Leybold Turbovac 361, respectively) mounted below the chamber and jointly backed by a mechanical pump (Welch 1397). Two small liquid nitrogen traps are placed in the pick-up chamber and flight tube region of the machine to reduce water contamination in the beam. These traps are manually filled roughly every 90 minutes during experiments. 7 Over time, we noticed that the ultimate temperature achieved by our nozzle was rising. The concern is that oil made its way from the diffusion pump to the super insulating sheets protecting the cold head. Replacing the super insulating sheets with ≈5 wraps of new sheets solved the problem. The sheets are held in place and spaced out using small amounts of copper wire. In current experiments the nozzle is heated to 335 K the day before the experiment while the chamber is pumped by the large diffusion pump. This has led to more consistent performance from the nozzle and generally the nozzle reaches an ultimate temperature of ≈10 K before heating and stabilizing at chosen experimental conditions. The working theory is that heating and pumping overnight bakes off and removes water that was previously freezing on the main stage of the cryocooler assembly. 8 Heating dopants like cesium iodide and C 60 powders can cause some of the material to diffuse and collect in the bottom of the chamber. An earlier pick-up cell design also had trouble locking in the chamber and the lid of the cell was inadvertently fed to the diffusion pump during an experiment. 50 Figure 2.2: Picture and schematic of the deflection electrodes. A rotation of 90 degrees counter-clockwise gives the orientation of the plates down the beam-axis, resulting in a deflection to the right in the lab frame. The origin in this diagram is the midpoint between the two circles, and the black bar specifies the position of the collimator. The parameters r and a define the geometry of the electrodes and are defined in the text. This image is taken from Ref. [76]. Our electrostatic deflection plates were originally built by K. L. Clemenger at the University of California Berkeley [91] and this electrode configuration has been successfully employed by other groups [92–94] and previous members of the Kresin Lab [95–98] for deflections of other molecular beams. Figure 2.2 presents a photo and diagram of the electrodes used in the helium machine. The distance 2a represents the distance between the “two-wires” that define the field [95], though in reality there are no wires and the field is generated by two equipotential surfaces. The surfaces are defined by the dimensions r and a with values of 2.39 mm and 2.07 mm respectively. The beam passes through the electrodes with dimensions defined by the collimator and is placed 1.14 mm above the grounded electrode, which corresponds to a center 1.13a from the origin, or the midpoint between the circles as defined in the literature [96]. The total distance between the two electrodes along the vertical axis in Figure 2.2 is approximately 2.5 mm [91]. The electrodes are made from aluminum with a mirror finish polish, and are side- mounted in the electric field chamber with a high voltage feedthrough to measure the potential 51 applied to the plates [76]. If exposed to atmosphere, the plates are cleaned via glow discharge under argon gas [91]. The field contours between the “two-wire” electrodes are shown in Figure 2.3 and were computed in Mathematica by D. J. Merthe [76] alongside a reference image from a recent alignment. In this electrode configuration, both the electric field and the electric field gradient are collinear [96] which is optimal for both orienting and deflecting a polar object. Additionally, in the region where the beam travels the electric field gradient is approximately constant, changing only by a few percent [74,95]. This means that the force experienced by each droplet is roughly uniform regardless of its position in the helium beam [1,3,74]. Note that Ref. [95] describes a larger change in deflecting force over the beam region, but in these experiments measuring cluster polarizability the deflecting force varies with the gradient squared rather than the gradient and will be discussed in the following chapter. Figure 2.3: Magnitude of electric field in the region between the two Rabi “two-wire” electrodes with a potential difference of 20 kV which is standard in our experiments. From this point of view the measured deflection is in the -𝑥 ̂ direction, where the +𝑦 ̂ direction is down in the lab frame. The black rectangle specifies the helium beam after collimation. The photo displays the electrodes as they sit in the machine during experiments for further context. This image was taken during a recent alignment and is looking towards the source from the telescope at the end of the detection chamber. This figure is adapted from Ref. [76] where calculation details are provided. 52 2.2 Installation and Testing of New Quadrupole Mass Spectrometer In 2020 the mass spectrometer on the helium machine was upgraded from the Balzers QMG 511 model to a new custom-built mass spectrometer from Ardara Technologies. This upgrade extended our mass-filtering range from 512 amu to approximately 2000 amu and increased the sensitivity of our measurements by allowing for digital pulse-counting detection. Quadrupole mass spectrometer theory is extensive [99] and the basic principles of operation are outlined below. Mass filtering is provided by four cylindrical rods in a square pattern and spaced such that the center between the rods approximates a hyperbolic field. This is achieved by spacing opposite rods 1/1.148 times the rod diameter between faces [100]. A combination of RF and DC voltages applied to the rods produces stable trajectories for ions of a given mass to traverse the quadrupole, where higher and lower mass objects will have unstable trajectories within the rods and will crash before reaching the end of the quadrupole region [29]. Quantitatively, the ion trajectories are solutions to the second-order Mathieu differential equation which take the form of an infinite sum of sines and cosines characterized by the mass of the ion, the applied RF and DC voltages, and the geometry of the rods [100,101]. 53 Figure 2.4: Block diagram of the ionizer assembly and quadrupole. The beam passes through the ionizer assembly where the droplets are ionized. The ions are then deflected by the inner and outer poles and focused into the quadrupole region. The ions pass through a final focusing lens before reaching the conversion dynode and electron multiplier where the output signal from the quadrupole is detected. The filament is also is also displayed showing the wrapping of the filament wire. Proper filament resistance is achieved with five and a half turns per edge. Figure 2.4 provides a block diagram of the ionizer assembly and quadrupole with the order and position of the ion optics. The helium beam enters the 5 mm diameter circular ionizer aperture where droplets are struck by electrons with energies in the range of 30-110 eV (typically 70 eV) producing ions to be detected. Electrons for this electron impact ionization are produced by a hot tungsten filament constructed in a 4-series-parallel arrangement with a typical filament current of 1 mA. The ions have an energy defined by the potential difference between the ion region and the 54 pole bias region and a number of electrostatic lenses then focus the ions through the ionizer assembly to the quadrupole region. The filtering poles are oriented 90 degrees from the beam axis, and a deflecting region is used bend the ions upward in the lab frame into the quadrupole. After being filtered by the quadrupole in standard operation the ions strike the conversion dynode where electrons are emitted into the horn-shaped electron multiplier, which causes secondary electron emission leading to a cascade of collected electrons producing a detectable signal. This process is more efficient for heavier ions, and we recently found that operating the detector without the conversion dynode dramatically increases the signal for low mass ions, which is especially useful to detect signal from helium clusters and low-mass dopants. Normally, the dynode is held at -5 kV and the multiplier is held around -2 kV, but when the dynode voltage is set to zero instead of the incoming ions being attracted to the dynode they are instead “pushed” toward the multiplier rather than being converted to electrons by the dynode. We refer to this mode of operation as “pusher mode” compared to “conversion mode”. When initially tuning the quadrupole, we found two sets of optics voltages that provided strong relative signal for the low mass and high masses ranges in conversion mode and they are presented alongside the values for pusher mode in Table 2.1. Since the mass-range of the new quadrupole is relatively large, adjustments to the optics can give increased signal over the mass region of interest. The “Low Mass” optics voltages in this table where experimentally determined to optimize the signal of the helium beam and dopants with masses of 50-200 amu prior to the use of pusher mode which now supersedes the low mass conversion optics. A mass spectrum comparing the low mass conversion settings to the pusher mode of operation is shown in Figure 2.5 with all other scans parameters identical. Here it is clear that the signal intensity is substantially stronger in this low mass range when the conversion dynode is not used. Initial discussion with 55 the quadrupole manufacturer suggested that the signal should fall-off quickly after about 50 amu, but we have found that the signal intensity for HeN peaks remains strong past 250 amu. Current experiments using monomer, dimers, and trimers of FeCl2 confirm that signal intensity for dopants in the mass range ≈50-250 amu is also relatively strong in this mode of operation. Conversion Mode Pusher Mode Ion Optic High Mass Low Mass Ion Region 5 V 5 V 5 V Extractor -6 V -6 V -6 V Def. Entrance -50 V -50 V -50 V Def. Exit -60 V -60 V -60 V Inner Poles -300 V -300 V -300 V Outer Poles -40 V -40 V -40 V Quad. Entrance -12 V -19 V -12 V Quad. Exit -15 V -100 V -15 V Pole Bias -1.5 V -1.5 V -1.5 V Dynode -5 kV -5 kV 0 kV Multiplier -2 kV -2 kV -2 kV Table 2.1: Experimentally determined quadrupole optics to maximize mass spectrometer signal. The detected signal from the quadrupole strongly depends on the choice of optics voltages to improve the detection efficiency of various input mass ranges. In current experiments pusher mode is used in favor of low mass optics in the conversion mode since it gives generally superior signal intensity in the mass region up to a few hundred amu. In the conversion mode of operation, the most impactful optic for affecting low mass signal intensity is the quadrupole exit voltage. It was later determined that using the pusher mode with the standard high mass optics performed generally better. Resolution parameters are excluded in this table and are frequently reoptimized to get appropriate peak widths in the mass spectrum. Typical potentiometer values on the power supply are dM ≈ 9.0 and dRES ≈ 1.9. 56 Figure 2.5: A comparison of helium cluster peaks detected by the mass spectrometer for operation in conversion and pusher modes (dynode voltage of –5 kV and 0 kV respectively). He N peaks are spaced by 4 amu and are easily visible past N = 35 here. The intensity is normalized such that He 2 has an intensity value of unity. The second off-scale peak present in the spectrum at approximately 18 amu is related to background water in the machine which contaminates some of the droplets. The mass interval is 0.2 amu and each point is scanned for 0.75 seconds for each spectrum. The inset demonstrates that the pusher mode gives greater than ten times the signal of the conversion mode for optimized low mass optics. The “High Mass” optics voltages were originally used to boost the signal of C 60 (≈720 amu) detected in the helium beam, and it was found that these values were generally useful for masses above a few hundred amu. The critical point where the high mass optics voltages begin to give a relative boost in signal over the low mass optics voltages is around ≈300-400 amu. We collected mass spectra using perfluorotributylamine (FC-43, Scientific Instrument Services), a well-known calibration chemical, to ensure that the quadrupole was performing properly over the relatively long mass range visible from the fragments of FC-43. To collect these spectra, we bled liquid FC-43 contained in a small cylinder through a needle valve directly into the detection chamber and monitored pressure using the ion gauge attached to this chamber. Spectra were taken under different choices of quadrupole optics with a chamber pressure of ≈10 -6 Torr. An example 57 mass spectrum showing the FC-43 fragmentation pattern for our high mass optics voltages is shown in Figure 2.6. Comparing our spectrum to Ref. [82] we see that all of the major fragments are visible in the spectrum and that the latter half of the mass range has enhanced signal intensity. In addition to the installation and tuning of the new quadrupole mass spectrometer, data acquisition software had to be written to interface with the new equipment. Fortunately, synchronous digital pulse-counting data acquisition software has been developed and used in our group [98] previously and could be integrated on the helium machine. Figure 2.6: Mass spectrum of FC-43 using high mass optics voltages. The prominent peaks are at m/z ≈ 69, 100, 119, 131, 219, 264, 414, 426, 466, 504, 576, and 614 [82]. The spectrum is scaled such that the m/z = 69 peak is set to have a normalized intensity of unity. This spectrum demonstrates that the new quadrupole is able to detect ions over a relatively wide mass range, and especially in the mass range of a few hundred amu. 58 2.3 Data Acquisition Data acquisition software was written using LabVIEW 2016. Two virtual instruments (VIs) are required for measurements on the helium machine: one to collect mass spectra and the other to collect beam deflection profiles. For analog detection in earlier work a lock-in amplifier (SR830 DSP Dual Phase Lock-In Amplifier, Stanford Research Systems) is used to collect data and these two VIs were written by D. J. Merthe, described in Ref. [76]. Briefly, the mass spectrum VI uses the Balzers QMG 511 controller to trigger the start of a temporal scan on a digital oscilloscope (TDS 1012B, Tektronix) and signal is simultaneously collected by reading the output of the lock- in amplifier. The lab PC hosting the LabVIEW VIs collects the time-axis data from the oscilloscope and converts it to mass with user-defined scan parameters, and matches it with the signal intensity data from the lock-in amplifier, representing a mass spectrum. Multiple scans can be initiated and averaged automatically. As discussed earlier, the beam profiles are collected by locking the mass spectrometer on a mass peak of interest, then commanding the stepper motor to a set of positions and collecting signal from the lock-in amplifier with a user-defined dwell time at each position. This VI used a uniform interval in position-space and the chamber is translated to the predetermined positions in a random order to minimize systematic errors. Communication with the oscilloscope and lock-in amplifier in LabVIEW is straightforward, and both drivers and pre-written sub-VIs in LabVIEW are available for both instruments. The computer communicates with the stepper motor via serial commands facilitated by LabVIEW. The stepper motor position has been found to be highly accurate over the course of many experiments. However, micrometers are mounted adjacent to the detection chamber to periodically physically check the position of the chamber. Stalling and skipping of the stepper motor are rare, but errors related to the stepper motor can be easily caught by monitoring the physical position of the zero of the stepper motor which is 59 recorded in LabVIEW. It is important to check the zero of the chamber position at the start and end of an experiment (at a minimum) to ensure that there is no systematic drift while collected beam profiles. With the new quadrupole, digital pulse-counting software was adapted in place of the lock- in amplifier. The output of the new quadrupole is passed through a discriminator (F-100TD, Advanced Research Instruments Corporation) which outputs narrow TTL pulses corresponding to signal from the multiplier exceeding the discriminator threshold. The discriminator is tuned such that nearly zero counts are detected when the ionizer is off, which is a measure of the electronic noise floor of the system and a typical display value for this setting is 50 mV. The discriminator pulses are then routed to a counter board (PCI-6602, National Instruments) where the output signal is recorded. In the simplest case, these counts as a function of time, mass, or position without further processing represent our measurement, and the direct output of this signal is often useful. Noting that the beam arrives at the detector as pulses from the integration with the chopper, synchronization of the detector with the chopped beam pulses allows for the rejection of signal unsynchronized to the beam. The basis for the synchronous detector hardware and software is documented extensively in Ref. [98], and the code to synchronize and start the counters is used in the new mass spectrum and beam profile VIs on the helium machine. The synchronous detector uses five counters on the counter board: two are used to accumulate counts, while the other three are used to generate pulses to gate the accumulation counters. The principle with the gating of the accumulation counters is that the beam will be allowed through the chopper in pulses with a well- defined frequency and will have a measurable delay between being chopped and being detected. Using the chopper frequency as a reference, one accumulator (A) will count when the beam passes through the chopper wheel and is being detected, and the other accumulator (B) will count when 60 the beam is not detected because it has been blocked by the chopper. The final counter acting as a gate outputs a single synchronization pulse (“C pulse” in Ref. [98]) to ensure that accumulators A and B are active for an equal time interval of full reference chopper cycles. The synchronization pulse is triggered by the rising edge of the chopper reference and is delayed by 0.6 of a chopper cycle such that the measurement begins with the chopper signal in the low state. The width of the synchronization pulse is determined by the dwell time of a given measurement. The synchronization pulse and chopper reference are gated with an AND logic chip (74HC08) to set the measurement interval. The gates for accumulators A and B act as a synthetic chopper with a phase delay included in order to mimic the chopper signal as if it were at the detector. The gate width of the synthesis chopper determines the fraction of chopper cycle that the accumulators are armed to collect counts. There is some drift in the chopper frequency over time, and the chopper can drift ≈10 Hz as the pick-up cells heat the chopper motor assembly. The chopper frequency tends to stabilize as the temperature of the pick-up cell stabilizes. A gate width of 0.45 of a chopper period has been found to robustly synchronize the detector to the beam and suppress issues caused by changing frequency and the finite chopping speed of the beam, at the cost of less than a 10% reduction in raw signal. The gate width and phase delay are the same for the gates for the A and B accumulators. The gate for accumulator A triggers on the rising edge of the AND-gated chopper reference while the gate for accumulator B triggers on the falling edge so one chopper cycle triggers each accumulator exactly once. A schematic of the various signals discussed is presented in Figure 2.7 for a visualization of the synchronous detector system. 61 Figure 2.7: Schematic showing the various signals of the synchronous detector system. All gating is relative to the chopper reference signal, and the single synchronization pulse and AND gate ensure that both accumulators have an equal period of active time. The phase delay is the time that it takes for the beam to travel from the chopper to the detector modulo the chopper period. The phase delay is displayed in blue and is measured from the rising edge of the chopper to the rising edge of the signal at the detector and is measured using a multichannel scaler (see section 2.4). The gate widths are equivalent for each accumulator gate, and are drawn to be 0.50 of a chopper period in this diagram. Accumulator A accumulates counts in the green region while accumulator B accumulates counts in the red region. The discriminator pulses panel gives a cartoon of the signal in each accumulator region where additional signal comes from the beam. The phase delay is measured from the rising edge of the chopper reference signal to the rising edge of the detected signal from the beam. Since the beam comes in periodic pulses, synchronizing the detector to any rising edge is equivalent, and synchronizing to the nearest rising edge minimizing detection delays. Additionally, the phase delay measurement contains information about the time required to traverse the quadrupole, and thus the phase delay will be 62 different for different masses in a mass spectrum. For deflection measurements, a phase delay should be measured for each mass of interest for optimal synchronization. The synchronized detector uses three quantities to describe the measured signal, called the lock-in rate, dip, and total rate [98]. They are defined by the following equations: 𝑑𝑖𝑝 = 𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑜𝑟 𝐴 −𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑜𝑟 𝐵 1 2 ( 𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑜𝑟 𝐴 +𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑜𝑟 𝐵 ) , (2.1) 𝑡𝑜𝑡𝑎𝑙 𝑟𝑎𝑡𝑒 = 𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑜𝑟 𝐴 +𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑜𝑟 𝐵 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 𝑇𝑖𝑚𝑒 , (2.2) lock-in 𝑟𝑎𝑡𝑒 = 𝑑𝑖𝑝 ∗ 𝑡𝑜𝑡𝑎𝑙 𝑟𝑎𝑡𝑒 . (2.3) The dip is a measure of synchronization between the beam and the detectors and is confined to the range [-2,2]. We assume that the background counts are random and uncorrelated with the beam. A dip of zero indicates that the detector and beam are not synchronized, i.e., the beam is not distinguished from the background. A positive value of dip indicates that the signal is synchronized with the chopper and measurable, and a dip of two indicates that there is no measurable background and the beam is fully contained in the counts for Accumulator A 9 . The total rate represents the count rate for both accumulators normalized over the measurement time, and contains useful information when the background is low and can also reveal persistent background peaks. The total rate can often be used to find a signal of interest initially, then a proper phase delay can be measured to optimize the dip. The lock-in rate defines the synchronized signal, and can also be thought of as extrapolating the synchronized signal over the full-time interval for both accumulators. 9 This is somewhat experimentally unrealistic, though a dip very close to two has been measured at high mass where there is nearly zero background and when the count rate from the beam is low. For helium peaks with low background it is also typical to have a dip greater than ≈1.5. 63 A comparison of the total rate and lock-in rate is presented for helium clusters in Fig 2.8 using the same data as Figure 2.5. The beam is synchronized using the phase delay measured for the helium dimer. One can see that the degree of synchronization and the counts pertaining to background gases including H2O (and derivatives), N2, O2, and CO2 are heavily suppressed. The water and nitrogen counts are suppressed by nearly a factor of 20, and the lock-in rate demonstrates that some of these background gases end up in the droplets. It is also seen that the degree of synchronization declines as a function of mass, as the phase delay begins to change. However, the degree of synchronization remains high. Figure 2.8: A comparison between the lock-in rate (blue) and total rate of counts (yellow) for helium clusters. Background peaks are clearly visible in the total rate and include H 2O (and derivatives) around 18 amu, N 2 around 28 amu, O 2 around 32 amu, and CO 2 around 44 amu. The detector is synchronized to the helium dimer peak (8 amu) and background counts are highly suppressed by the synchronized detector. Both spectra are scaled from the total rate water peak which is set to unity. For the digital pulse-counting VIs, the function of the lock-in amplifier is replaced with the synchronous detection system. The mass spectrum VI is streamlined from the analog version and 64 uses the auxiliary output voltages from the lock-in amplifier for mass control which have a resolution of 1 mV. The quadrupole controller selects masses in external mode using an input voltage where 5 mV = 1 amu from an interval of zero to ten volts. Other auxiliary output voltages are available to toggle commands on the quadrupole controller including setting an offset to the mass resolution and pole bias, and placing the quadrupole in resolving mode. The output of the chopper optical switch is also run through the lock-in amplifier to convert it to a proper TTL pulse. An additional version of this VI was written to use the lock-in amplifier to measure analog signal while keeping the same mass command capability. The beam profile measurement VI uses an identical infrastructure to the previous version, but instead of referencing the lock-in amplifier to collect signal the synchronous detector is instead used. An additional upgrade changed the sampled positions from uniform values placed over a pre-defined interval to instead accept positions as input from a tab separated variable file. This allows a precise placement of points to measure the beam more closely over the deflection region, or any region of interest, while still measuring a handful of data points further from the center. A user-input phase delay field is included in each VI to synchronize the detector, and lock-in rate, dip, and total rate are all displayed on the front panels. These three parameters are automatically saved at the end of execution for each VI. Since the frequency of the chopper shifts over time [76], a frequency measurement is made [98] for each scan of the mass spectrum, and each scan of the position-set in the profile measurement. An auxiliary VI is also used for simplified counting and mass control during experiments. The VI simply averages all counts over a user-defined interval of time, and is useful when tuning quadrupole optics parameters or sanity checking results between mass or profile scans. The mass 65 control function is also used to lock-on to a mass peak consistently when using the profile VI, rather than doing so manually. Annotated LabVIEW code is provided in Appendix A. All experiment data collected on the helium machine alongside the relevant notes is saved in a google drive account (hdroplets@gmail.com) and passed between members of the helium project. This way the lab easily retains access to data and analysis between students and experimental results are backed-up. 2.4 Beam Velocity Measurement In order to properly characterize the helium beam and determine the expected electrostatic deflection of the helium droplets, the speed of the beam must be known. For the experiments discussed here, two methods have been utilized and both rely on the beam chopper located in the pick-up chamber. The first was suggested and used by D. J. Merthe [76] and is measured using the lock-in amplifier when measuring synchronized analog signal with the lock-in method. The measurement is straightforward and only requires varying the frequency of the chopper and reading the phase difference (α) between the reference (chopper) signal and the ion signal at the detector. The phase difference is given by α = 2𝜋𝑓𝐿 𝑣 where 𝑓 is the chopper frequency, 𝑣 is the average velocity of the signal, and 𝐿 is the distance between the chopper and the detector and is ≈213.36 centimeters. Once the initial phase difference between the reference and ion signal is recorded, the chopper frequency is modulated by changed the voltage of its power supply (6234A Dual Output Power Supply, Hewlett Packard) until the phase difference traces out 2π, i.e., the measured phase difference is the same but the chopper now has a different frequency. The velocity of the beam is then computed using 𝑣 = 𝐿 ∆𝑓 . To obtain the speed of the beam, it is typical to make 66 this measurement while recording the signal of the mass spectrometer locked at the position of the helium dimer. Ref. [76] claims that this method reproduces the results of Ref. [63] within 2%. We have found that our velocity measurements with this technique generally agree with the literature [55], albeit a marginally higher deviation of ≈3% while measuring droplets with higher stagnation pressure and faster average speeds than Ref. [63]. Using this technique with our lock- in amplifier it was found that the phase difference fluctuates by a few percent of π between sequential measurements, so an exact measurement of ∆𝑓 is somewhat prone to error. Additionally, small changes in the chopper power supply voltage result in large changes in the frequency, though this shortcoming can be ameliorated using a more precise power supply. Using the new digital pulse-counting detection scheme, a second measurement of the beam velocity is possible, this time using a more extensive method outlined in Ref. [98] with some modifications. This measurement relies on a multichannel scaler (Ortec/Ametek EASY-MCS; “MCS”) to collect unsynchronized counts from the chopped beam, where the rising edge of the MCS record communicates information on both the speed and width of the velocity distribution. The method described in Ref. [98] is a simplification of more accurate, and more hardware- intensive, methods using photodepletion of the beam [102] or a double-chopper configuration [96] to eliminate systematic measurement errors. Despite the shortcoming of the simplified method which ignores systematics such as detector delay [103] and assumes that the beam and optical switch are located at the same position relative to a chopper blade, without corrections the method gives accurate velocities within 3% of Ref. [55]. Additionally, only the average velocity of the beam is needed and the width of the velocity distribution is of lesser importance as the helium beam forward velocity distribution is well-known to be sharp [10]. 67 The MCS functions by collecting counts as a function of time and is triggered on the rising edge of external signal source following the detection of the prior falling edge. In our case the external trigger is the chopper signal originating from the optical switch mounted on the chopper assembly. The MCS collects counts for a user-defined pass length (time-interval) following the external trigger and completes a user-defined number of passes. The pass length determines the time-interval of the MCS record as the number of passes times the dwell time. Typically, the dwell time is set to be 10-50 microseconds, and the pass length is set experimentally to cover 2-4 chopper cycles, though only one rising edge of the beam is strictly required for a velocity measurement. Counts are summed between passes in standard operation and the chopper external trigger ensures that the MCS record properly records the chopped beam pulses synchronized between passes. When locking the mass spectrometer on signal originating from the beam, be it helium or dopant signal, oscillations in counts as a function of time become apparent as a function of the chopper wheel blocking the beam or allowing the beam to pass through. Given the 50% duty cycle of the chopper, the high and low components of the signal oscillation are roughly equal in time- interval. Even in noisy environments where much of the signal corresponds to background gases 10 the MCS record reliably captures beam pulses and the record normalization procedure described below and outlined in Figures 2.9 and 2.10 to measure velocity. The form of the velocity distribution is taken to be that of a supersonic cluster beam [102,104]: 10 After switching from analog lock-in to digital pulse-counting detection, we noticed that for hot dopants in the vertical cell (e.g. cesium iodide held at approximately 400 C) that a considerable amount of gas-phase signal is present at the detector and unsynchronized with the beam. This may come from spray at the outlet of the vertical cell which is close to the edge of the pick-up chamber and is more likely to diffuse down the beam path. However, since synchronized signal is used for both analog and digital detection, this gas phase signal is rejected. 68 𝑓 ( 𝑢 ) = 𝑢 3 exp(− ( 𝑢 − 𝑣 𝑤 ) 2 ) √𝜋 𝑤 𝑣 3 (1 + 3 2 ( 𝑤 𝑣 ) 2 ) , (2.4) where 𝑢 is the beam velocity, 𝑤 is the width of the distribution, and 𝑣 is the velocity in the limit of 𝑤 → 0. From Equation 2.1, the mean beam velocity is given by Equation 2.5: 〈𝑢 〉 = ∫ 𝑢𝑓 ( 𝑢 ) 𝑑𝑢 = 𝑣 1 + 3 ( 𝑤 𝑣 ) 2 + 3 4 ( 𝑤 𝑣 ) 4 1 + 3 2 ( 𝑤 𝑣 ) 2 . (2.5) To compute the mean beam velocity, 𝑤 and 𝑣 are fit to the rising edge of an MCS record using Equation 2.6 which describes the rise of the beam signal following a depletion event which in our case is the chopper blade blocking the beam: 𝑆 ( 𝐿 , 𝑡 ) = 𝑆 0 − 𝑆 0 [ 1 2 (erf( 𝑣 𝑤 ) ± erf( 𝑧 ) ) − 𝑤 𝑣 exp( −𝑧 2 ) 𝑔 ( 𝑤 𝑣 , 𝑧 )], (2.6) with 𝑧 ≡ − ( 𝑣 𝑤 ) + ( 𝐿 𝑤𝑡 ) and erf is the error function defined as erf( 𝑧 ) = 2 √𝜋 ∫ exp( −𝑡 2 )𝑑𝑡 𝑧 0 . The ± is assigned according to the sign of z, where for our experimental parameters z is positive and the sign of the second error function is also positive. The function 𝑔 ( 𝑤 𝑣 , 𝑧 ) has nonlinear dependence on 𝑤 , 𝑣 , and 𝑧 but is of order unity [98,102] and is not included in the fitting procedure to improve fit stability. 𝐿 is once again the distance between the chopper and the detector. Equation 2.3 assumes that the beam is fully depleted by the depletion event 11 and is constructed such that 𝑆 ( 𝐿 , 0) = 0 and 𝑆 ( 𝐿 , 𝑡 ) = 𝑆 0 for large t, i.e., when the chopper crosses the beam, the detected signal is zero and some time later the beam has fully recovered. The MCS records are processed 11 Ref. [102] also describes the derivation of Equation 2.6 for incomplete depletion, though in our experiments full depletion is very well-approximated by the chopper wheel blocking the beam. Nonzero signal in the MCS record generally comes from sources unrelated to the beam. 69 such that the normalized signal is set to span the range of approximately [0,1] which represents a fully depleted beam and 𝑆 0 is set to unity. Figure 2.9(a) shows MCS records for nozzle temperatures between 14-20 K at 80 bar. It is evident that the speed of the beam if affected by the change in nozzle temperature as the MCS record is shifted along the time axis corresponding to a longer or shorter time to reach the detector. It is also clear that the signal strength scales with nozzle temperature where the signal for larger droplets is enhanced as seen by the total counts. I wrote Mathematica code to extract the velocity of the beam building on the strategy of N. G. Guggemos [98] for a general MCS record and it is included in Appendix B. The procedure is the following: An MCS record is standardized by subtracting the mean value of the record from each channel, then dividing each channel by the maximum minus the minimum value divided by two. This results in a standardized signal roughly in the range [-1,1], depending on how many chopper cycles are covered in the record. Next, the standardized record is fit to a cosine function of the form 𝐴 cos( 𝜔 ( 𝑡 − 𝜙 ) )+ 𝑑 where 𝐴 , 𝜔 , and 𝜙 are constrained to be positive to fit a consistent phase position in each record. The cosine fit is used to automatically find segments of the record that correspond to the depleted (beam blocked by chopper) and undepleted (beam passes through chopper) regions of the record. These regions are required to normalize the chopper record to fit Equation 2.4. The undepleted signal value (𝑆 𝑢 ) is determined by averaging points ± 𝜋 4𝜔 around the fitted phase, 𝜙 , while the depleted signal value (𝑆 𝑑 ) averages the points ± 𝜋 4𝜔 around 𝜙 + 𝜋 𝜔 . The results of these steps are demonstrated in Figure 2.9(b) where the standardized data is plotted alongside the fitted cosine 70 function and the red and green points correspond to the depleted and undepleted regions respectively. The MCS record is then normalized according to the undepleted and depleted signal values to constrain the record to the range approximately [0,1]. The formula for the normalized MCS record is: 𝑀𝐶 𝑆 𝑛𝑜𝑟𝑚 = 𝑀𝐶 𝑆 𝑠𝑡𝑎𝑛𝑑 − 𝑆 𝑑 𝑆 𝑢 − 𝑆 𝑑 , (2.7) where 𝑀𝐶 𝑆 𝑛𝑜𝑟𝑚 is the normalized MCS record displayed in Figure 2.9(c) and 𝑀𝐶 𝑆 𝑠𝑡𝑎𝑛𝑑 is the standardized MCS record displayed in Figure 2.9(b). The fit region is then extracted from the normalized MCS record. In order to maximally use the collected data, points from all rising edges of the MCS record are included in the fit and the domain of the fit is shifted in order to match the physically expected range of beam velocity. Essentially only one rising edge corresponds to the delay between the chopping of the beam, and all of the data is shifted to the rising edge that measures a physically meaningful velocity in the range ≈300-450 m/s [63] which is typical for our nozzle conditions. This process is demonstrated in Figure 2.9(c) where the points from the first and third rising edge of the record are shifted to coincide with the second rising edge. The fit region includes a half-period of the data and is computed by taking the normalized MCS record time-domain minus the fitted phase modulo the period of the record. Sorting this result and taking the latter half of the record gives all points corresponding to the half-period of the data corresponding to the rising edges in the record. An initial guess of the velocity is used to place the fit region on the correct rising edge of the time domain, and if the correct rising edge does not appear on the record, shifts of the data by a full period are applied to place the rising edge data correctly. 71 After extracting the fit region of the data, Equation 2.6 with 𝑆 0 and 𝑔 ( 𝑤 𝑣 , 𝑧 ) set to unity is fitted with least squares minimization over the subset of the MCS record and the average beam velocity and width are displayed. The fit is insensitive to the fraction of the period used as long as the rising edge of the record is included. Figure 2.10 shows this fit to the MCS record for a nozzle temperature of 15 K and stagnation pressure of 80 bar. This procedure has been found to be robust over a large set of nozzle conditions, and the results of this velocity measurement for each of the MCS records presented in Figure 2.9(a) is shown in Figure 2.11 where velocity is presented as a function of nozzle temperature. The computed velocities are in strong agreement with Ref. [10] and are within 3% of the overlapping values. Our measured beam velocity is systematically slower partially due to detector delay from the measured ion signal traversing the quadrupole 12 . Accounting for detector delay improves the agreement to within 2%. 12 The detector delay for the helium dimer is estimated to be small at ≈30 microseconds for typical ion voltages and assuming that the ion traverses 35 centimeters in the quadrupole. Experimentation with the fit suggests that a shift of 10 microseconds in the time-domain of the MCS record results in a velocity shift of less than 1 m/s. 72 Figure 2.9: (a) MCS records for different nozzle temperatures at a stagnation pressure of 80 bar with a chopper frequency of 260 Hz. The MCS records have a dwell time (bin size) of 50 microseconds with a pass length of 200 (bins) summed over 20,000 passes. (b) Standardized record for the 15 K record with a cosine fit as described in the text. The depleted and undepleted portions of a single period of the record are denoted in red and green respectively. (c) Normalized MCS record (normalization procedure described in text) with the points to fit from each rising edge concentrated on the relevant rising edge of the record. 73 Figure 2.10: A fit of Equation 2.6 over the rising edge data in the MCS record for a nozzle temperature of 15 K and a stagnation pressure of 80 bar. The fitting procedure is described in the text. The width is computed as the fitted 𝑤 /𝑣 for the distribution shown in Equation 2.1. 74 Figure 2.11: Computed velocities for nozzle temperatures between 14-20 K extracted from the MCS records displayed in Figure 2.9(a). As described in the text, these values are in excellent agreement with measured values available in the literature. Computed velocity distribution widths are also concentrated around ≈3% for these nozzle temperatures, with the width of the velocity distribution increasing for smaller droplets formed at higher nozzle temperature. 2.5 Deflection Simulation As noted previously, the original version of the simulation was written and used by D. J. Merthe [76,83] and the orientation of the dopant within the helium droplet in the electric field is modeled after code developed in Ref. [78]. The solved equation of motion for the droplet is derived for the droplet in Ref. [76] and it includes the motion of the droplet in both the field region and beyond the field region during free-flight. A correction for the polarization of the weakly polarizable [105] helium droplet is also included, where the droplet is approximated as a spherical dielectric shell with a point dipole at its center in an external electric field [83]. Modifications to 75 this initial simulation code to account for additional physics involved with the beam deflection including: accounting for reduced rotational constants of dopants [10], boil-off of helium atoms, a modification to doping and ionization probability using the droplet cross section, and the probability of charge transfer from the helium matrix to the dopant [79]. The simulation begins by taking a zero-field profile as input, which implicitly accounts for the transverse velocity of the helium droplets as well as geometrical effects that affect the beam between the source and detector 13 . The experimental profile is frequently fit to a function to smooth and extrapolate the data. A pseudo-Voigt function [106] has been found to be an excellent candidate for fitting both the zero-field and deflected beam profiles. The fitted zero-field profile is broken into uniform interval of discrete points over a user-defined range. The intensity of the points in the profile determines how many droplets to deflect from each position in the initial profile, where the maximum-intensity point corresponds to a user-defined number of droplets to deflect. The simulated deflection uses a Monte Carlo method and computes the orientation cosine in the quantum mechanical picture if the rotational constants and dipole projections about the principal axes are known, and uses the classical (Langevin-Debye) method for novel structures. Data files for each dopant are loaded into the simulation that include relevant parameters including the mass (amu), rotational constants (MHz) and dipole projections (Debye), and an approximation of the radius (nm) of the cavity around the dopant. Rotational constants are corrected to account for the helium interaction in this input file, which can be approximated by a division of ≈2.5-3 [10]. 13 An important note is that the deflection simulation assumes a free-flight path between the deflection plates and the position of the slit, rather than the ionizer (detector) entrance. This is because the beam position is measured from the linear slide position which is a few centimeters in front of the detector and coincides with the slit. The additional deflection occurring between the slit and detector can be treated as negligible. 76 Each generated droplet is sampled from a lognormal distribution [56] with the mean droplet size (𝑁 ̅ ) and ratio (𝑟 ) of standard deviation to 𝑁 ̅ specified by the user to determine the shape of the distribution. This distribution represents the droplet distribution formed at the nozzle for a given experiment set-up. The parameters 𝜇 and 𝛿 which describe a lognormal distribution presented in Chapter 1 can be derived from 𝑁 ̅ and r as: 𝜇 = 𝑙𝑛 ( 𝑁 ̅ √1+𝑟 2 ), (2.8) 𝛿 = √𝑙𝑛 ( 1 + 𝑟 2 ) , (2.9) where the average droplet size and ratio parameters for given nozzle temperatures and stagnation pressures can be generally found in the literature [55,56]. However, using the simulation we can determine our droplet size distribution parameters independently and self-consistently by deflecting droplets with a known-dipole moment and comparing the simulated and experimental results for given input parameters. It was found that our results using this process are in good agreement with published average droplet sizes [79]. A linear fit of the data presented in Ref. [56] suggests that a standard value of the ratio of the standard deviation of the droplet size distribution to the mean size is 𝑟 ≈ 0.70 for droplets in a similar, but generally smaller size regime. We have found that a broader size distribution with 𝑟 ≈ 0.90 generally provides a better fit to our experimental data, where our expansion conditions are closer to the critical regime of helium nanodroplet expansion [10,55]. With this choice the computed FWHM, Δ𝑁 is still in excellent agreement with Ref. [56]. The doping process introduces a complication, where the size of droplets carrying dopant molecules is affected by the cross section of the droplet, evaporation due to energy imparted by the dopant, and the probability of charge transferring to the dopant following ionization. Correcting 77 factors are applied to the initial size distribution of helium droplets such that the simulation reflects droplets that are successfully doped, ionized, and detected. The capture cross section of the droplet scales with 𝑁 2/3 and capture events are more probable for larger droplets by virtue of the larger cross section [107]. The same process holds true for ionization, where a larger droplet is more likely to be struck by an electron and create an ion for detection. To account for this, droplets sampled from the initial lognormal distribution are accepted with a probability scaling with 𝑁 2/3 . This biasing process is normalized by assuming that there is a theoretical maximum droplet size (𝑁 𝑀 ) which will successfully capture a dopant (or ionize the droplet). This value is typically taken to be the droplet in the 98 th percentile in the underlying lognormal distribution, in general agreement with largest observed droplets in the tail of the distribution in Ref. [55]. The acceptance probability is then taken as the relative probability 𝑁 2/3 / 𝑁 𝑀 2/3 . A competing process is the probability of charge transfer from the helium matrix to the dopant. The process has been explored in depth [108–111] and will be discussed extensively as a result in the following chapter. Smaller droplets are much more likely to successfully transfer charge to the dopant molecule following ionization of the droplet, while the probability of charge transfer decreases rapidly for larger droplets. Our chosen model of charge transfer probability [79] takes the form exp ( −𝛾 𝑁 1/3 ) , where 𝛾 is a parameter relating to the mean free path of the ionizing electron. The probability of charge transfer model is taken directly as an acceptance probability. Correction factors are included with a nested Monte Carlo method where every time a droplet is generated, a random number in the interval [0,1) is generated and compared with the probability of each of the correction factors above. Only droplets that survive this process are counted and deflected in the simulation. 78 Each doping step in the simulation also includes a reduction in droplet size to account for evaporation of helium atoms following a collision event. The translational kinetic energy deposited into the moving helium droplet by a dopant molecule was recently determined [112] and has the form: 〈𝐸 𝑡 〉 = 𝑘 𝐵 𝑇 ( 𝜇 𝑚 ) Θ( 𝑥 ) Ψ( 𝑥 ) , (2.10) where 𝜇 is the reduced mass of the dopant-droplet system, 𝑚 is the mass of the dopant, 𝑇 is the initial temperature of the dopant, and 𝑘 𝐵 is Boltzmann’s constant. Θ( 𝑥 ) and Ψ( 𝑥 ) are functions defined below and 𝑥 is the speed of the droplet divided by the most probable speed of the dopant, Θ( 𝑥 ) = 𝑥 ( 5 2 + 𝑥 2 )𝑒 −𝑥 2 + √𝜋 ( 3 4 + 3𝑥 2 + 𝑥 4 )erf( 𝑥 ) , (2.11) Ψ( 𝑥 ) = 𝑥 𝑒 −𝑥 2 + √𝜋 ( 1 2 + 𝑥 2 )erf( 𝑥 ) . (2.12) Energy from rotational motion is determined by 〈𝐸 𝑟 〉 = 1 2 𝑘 𝐵 𝑇 for each non-symmetric rotational axis, and the evaporation energy from vibrational cooling is given by: 〈𝐸 𝑣 〉 = ∑ 𝑛 ℎ𝜈 𝑒𝑥𝑝 ( 𝑛 ℎ𝜈 𝑘 𝐵 𝑇 ) − 1 𝑛 ,𝜈 , (2.13) where the vibrational frequencies, 𝜈 , are typically determined from spectroscopic data, ℎ is Planck’s constant, and 𝑛 is increased until the incremental change in energy becomes small. The energy cost of vibrationally cooling the dopant molecule is computed externally and included directly as a number of atoms evaporated. The number of evaporated helium atoms is determined by dividing the expectation value of the energy by the binding energy of a helium atom in the droplet [10]. In the case of multiple dopants in a droplet, the binding energy is also included in the 79 evaporation step and generally these values must either be found in the literature or computed by colleagues. The simulation is often utilized to determine the droplet size-distribution for given experimental conditions by fitting the output of the simulation to an experimental deflected profile for a molecule with a known dipole moment. Once we determine the droplet size distribution matching our experimental conditions, we can reverse the process. With a known size-distribution, we can iteratively fit dipole moments to our experimental deflection profile to determine the dipole moment of an unknown molecule or complex. This process was used previously to determine the dipole moments of the amino acids tryptophan and histidine [83] and is described by the flowchart in Figure 2.12. The procedure is also used in Refs. [84–86] and discussed in the following chapters. Figure 2.12: A flowchart outlining how our simulation is used to determine unknown dipole moments from deflection profile measurements. Details are presented in the text. The simulation code discussed here is written in Python, and is annotated alongside a series of support functions written in Mathematica for data analysis in Appendices C and D. The support functions in Mathematica are useful for fitting the experimental profiles, computing fit error, computing centroids, and other useful tools for analyzing data during and after experiments. Plotting code written in Mathematica [113] is also available in the experimental logs section of the helium project google drive alongside completed analysis documents for previous experiments. 80 Chapter 3 – Orientation and Deflection of Helium Nanodroplets and a Study of Charge Transfer as a Function of Droplet Size This chapter is based on our published work. Text and figures are reproduced with permission from the American Physical Society (APS): J. W. Niman, B. S. Kamerin, D. J. Merthe, L. Kranabetter, and V. V. Kresin, “Oriented polar molecules trapped in cold helium nanodroplets: Electrostatic deflection, size separation, and charge migration”, Physical Review Letters 123, (2019) 043203. [79] This chapter describes early work demonstrating the electrostatic deflection technique for neutral doped helium nanodroplets. This broadly applicable method allows even polyatomic molecules to attain sub-Kelvin temperatures and nearly full orientation in the field. The resulting intense force from the field gradient strongly deflects even droplets with tens of thousands of atoms, the most massive neutral systems studied by beam “deflectometry.” We use the deflections to extract droplet size distributions. Moreover, since each host droplet deflects according to its mass, spatial filtering of the deflected beam translates into size filtering of neutral fragile nanodroplets. As an example, we measure the dopant ionization probability as a function of droplet radius and determine the mean free path for charge hopping through the helium matrix. The technique will enable separation of doped and neat nanodroplets and size-dependent spectroscopic studies. 3.1 Introduction If the internal and relative motion of molecules is cooled into the sub-Kelvin range, it becomes possible to observe and steer their reactions with precision, to determine their physical parameters and structures with high accuracy, and to use external fields to finely control their motion and orientation [22,114–116]. For example, buffer-gas cooling [117] can be employed as an entryway to electrostatic guiding and ultracold trapping [118,119], merged beams enable exploration of chemical reactions in the quantum regime [120], and Stark deflection of small molecules in a supersonic beam can be used to spatially separate their low rotational states and conformers [3]. 81 While high level of control has been demonstrated for individual small molecules, pursuing it for larger polyatomic systems becomes increasingly demanding [121]. Their rotational spectra are more congested, their degrees of freedom are less efficiently and uniformly cooled by nozzle expansion [121,122], and their higher masses reduce the deflection. A powerful tool to cool and study molecules of a wide range of sizes is “helium nanodroplet isolation” [10,37,39,55,123]. Molecules are entrapped and transported by a beam of 4 HeN nanodroplets generated by expansion of helium gas through a cryogenic nozzle. Nanodroplets cool by evaporation upon exiting the nozzle, reaching an internal temperature of only 𝑇 0 = 370 mK and turning superfluid. This temperature is set by the surface binding energy of helium atoms [36,124] and has been verified, as has the onset of superfluidity, by rotational spectroscopy of entrapped molecules [10]. When the droplet beam passes through one or more vapor-filled cells, atoms and molecules are readily picked up, cooled by heat transfer to the helium matrix (evaporation of surface helium atoms promptly returns the complex to 𝑇 0 ), and carried along by the droplet beam. This method is unique in being applicable to a variety of molecules and atoms: essentially all that is required for embedding is the availability of ~10 -4 -10 -6 mbar of vapor. Its other key feature is that it cools all the degrees of freedom of the dopants and ensures that only their lowest vibrational, and in some cases even rotational, levels are occupied. Quantum effects in bimolecular reactions can already become pronounced at 𝑇 0 (e.g., Ref. [125]) and may remain undisrupted by the viscosity-free superfluid matrix. Furthermore, by using sequential pickup it is possible to co- embed multiple (identical or distinct) atoms or molecules in order to explore their interactions and to generate novel or metastable complexes that would be unobtainable by other means. In the context of control and manipulation by external fields, consider nanodroplet embedding of polar molecules. The salient fact is that by cooling to T0 in this superfluid 82 environment, they become cold enough to strongly (often almost fully) orient themselves along an applied static electric field as noted previously. Their rotations transform into “pendular” states, employed in landmark spectroscopic studies [14] and discussed previously. Molecular alignment effects within helium nanodroplets were also recently demonstrated using short laser pulses [9]. Here we subject these systems to the method of electrostatic deflection [1,3,74,126]. A doped nanodroplet beam passes through an inhomogeneous electric field and its resulting deflection is measured with high accuracy. The attractiveness of such a measurement is that it can be performed using a broad array of molecules (diatomic, polyatomic, complex, agglomerates) and directly yields quantitative observables, without needing to refer to a potentially complex spectroscopic analysis. However, two potential problems must be considered. First, deflecting neutral droplets by a measurable amount may appear simply unworkable. Indeed, in typical experiments on beams of individual polar molecules or clusters the deflection is at most by a few milliradians, more commonly a fraction of that (translating into millimeters, or fractions thereof, displacement at the detector). Consequently, loading a molecule with a massive coat of barely polarizable helium ought to result in undetectable deflections. Second, the nanodroplets are not identical. Their size distribution is generally log-normal, as is typical of particle growth processes, with a mean that can be shifted by varying the expansion conditions. Can this hinder a deflection experiment? We report on two principal results. First, we demonstrate that electrostatic deflection of nanodroplets doped with polar molecules is not merely measurable, as demonstrated in Ref. [83], but turns out to be remarkably strong. This is due to the aforementioned orientation effect: when the dipoles’ rotational motion is frozen out and they point along the field axis, the resulting great increase in the deflecting force can easily compensate for the additional helium mass. Such a robust 83 effect, in combination with the fact that these may be the most massive (tens of thousands of Daltons) neutral beams subjected to “molecular deflectometry” to date, is noteworthy. The magnitude of the deflections implies that they can be employed for accurate measurements of the dipole moments of complex molecules and to segregation of doped and undoped nanodroplets. Second, we demonstrate that instead of hindering deflection analysis, droplet size spread can be turned into an informative resource. We show that deflection measurements can be employed to calibrate the nanodroplet size distribution. Even more valuably, deflection can be used to achieve droplet mass filtering, by spatially dispersing the nanodroplets according to their size. This establishes a novel way to perform spectroscopic experiments on neutral nanodroplets as a function of size. As an application and illustration of this method, we study the droplet size dependence of dopant ionization probabilities and determine the mean free path for the migration of positive charge (He + hole) through the liquid helium matrix. 3.2 Experimental A supersonic nanodroplet jet is generated by expanding He gas at 80 bar pressure through a cryogenic nozzle, and passes through a pick-up cell positioned downstream. This methodology is described in detail in Chapter 2, see also Refs. [76,83]. Dopants chosen for the present work are dimethyl sulfoxide (CH3)2SO (“DMSO,” p=4.0 Debye) and CsI (p=11.7 D). These dopants are both strongly polar and have favorable vapor pressures for controlled doping in helium droplets. DMSO vapor is introduced into the beam from a stainless-steel Swagelok cylinder exterior to the pick-up chamber with an assembly described in Ref. [76]. The cylinder contains liquid DMSO at room temperature, and vapor is evaporated from this reservoir. The vapor flow is 84 controlled with a micrometer needle valve and the vapor pressure is directly measured with a Bayard-Alpert pressure gauge (IGM400 Hornet Ionization Gauge, InstruTech) located just beyond the valve. CsI vapor is supplied to the droplets using the heated stainless steel pick-up cell. Roughly 10 grams of CsI powder was initially packed into the bottom of the horizontal pick-up cell. It was found that saturating the powder with methanol and pressing it into the cell before loading the chamber improved the signal stability during measurements. After loading, the powder was quickly heated to ≈200 C while the pick-up chamber was pumped out. The procedure improves the thermal contact of the CsI powder with the pick-up cell making the measured ion signal more responsive to changes in temperature and slowing the rate of signal decay [76]. The beam is subsequently collimated by a 0.25 mm by 1.25 mm slit and travels through the ≈2.5 mm gap between two 15 cm-long electrodes which create an inhomogeneous electric field of the “two-wire” geometry [74,96]. As described previously, the field orients the polar molecule while its gradient exerts a strong deflecting force on this oriented dipole. The field and gradient strengths range up to ≈85 kV/cm and ≈350 kV/cm 2 , respectively. After a free-flight region of 1.25 meters at the exit of the electrodes the beam enters an electron-impact ionizer using an electron energy of 90 eV, then enters a 0.25 mm-wide slit. The resultant ions are detected by a quadrupole mass analyzer. This work utilized the QMG 511 quadrupole before the installation of the Ardara quadrupole discussed previously. The arrival of a doped nanodroplet is registered by setting the analyzer to one of the characteristic fragment peaks of the dopant [82]. With the collimator and slit in place the measured ion intensity decreases by approximately a factor of 20, and the mass resolution is decreased such that Δm ≈ 2 amu in order to recover sufficient signal intensity for a measurement. In order to isolate the beam-carried signal, the analyzer’s output is read via a lock-in amplifier synchronized with a rotating wheel chopper. 85 Additionally, the phase delay between the chopper and analyzer outputs yields the beam velocity, 𝑣 , which ranges from ≈365 m/s at 13 K nozzle temperature to ≈415 m/s at 19 K in this work. Importantly for deflection measurements, the velocity distribution is very narrow, 1- 3% [10,35,57]. The deflection angle of a nanodroplet is the ratio of the sideways impulse it receives while traversing the field, 𝐹 𝑧 ∆𝑡 ∝ 〈𝑝 𝑧 〉 ( 𝜕 𝐸 𝑧 𝜕𝑧 )𝑣 −1 to its original forward momentum, 𝑚𝑣 . Since the field gradient is proportional to the deflection plate voltage 𝑉 , the droplet’s deflection is 𝑑 = 𝐶 〈𝑝 𝑧 〉𝑉 /( 𝑚 𝑣 2 ) where 𝐶 is a constant calculated from the apparatus geometry. In monitoring the dopant peak in the mass spectrum, one needs to be certain that it is not a fragment of a larger agglomerate deriving from the pick-up of multiple molecules. The probability of embedding dopants is approximately Poissonian [10] and the mean number of pick-up collisions is proportional to the vapor density as discussed previously. Thus, the cell vapor pressure must be low enough for a single collision event to be favorable, while multiple collisions are rare. For DMSO we adjusted the vapor pressure to produce a usable monomer signal and used the parent 78 amu ion peak in the mass spectrum for deflection measurements while minimizing the corresponding dimer signal at 156 amu. This doping condition corresponded to a display pressure on the inlet gauge of ≈200 μTorr. The temperature of CsI was increased to produce sufficient vapor pressure to generate a detectable signal for the Cs + mass peak at 133 amu which predominantly derives from dissociative ionization of the CsI monomer and not of larger clusters [127]. The temperature of the pick-up cell was fixed between ≈395-405 C, where the higher temperatures correspond to the conditions with smaller average droplet sizes where the nozzle temperature is higher. 86 3.3 Deflections Beam profiles in the detector plane are recorded by measuring the intensity of the chosen ion peak as a function of the ionizer entrance slit position. Initiatory deflection measurements scanned this entrance slit in front of the quadrupole’s ionizer and suggested beam deflections on the order of a few tenths of a mrad (translating into shifts of a few tenths of a mm in our apparatus) [83]. This was already substantial, but further examination revealed that the actual deflections were considerably larger: we discovered that they extended all the way to the edge of the ionizer’s entrance aperture and were artificially clipped there. In order to accommodate such large displacements, we now fix the slit in the middle of the aperture and upgraded the detection chamber such that the entire detector chamber rests on a precision linear slide. This enables us to obtain accurate beam profiles extending as far as 20 mm (16 mrad) from the central axis. Figures 3.1(a) and (b) show the deflections for a polyatomic dopant (a) and diatomic dopant (b), both cooled to ≈0.37 K by immersion in the superfluid droplet. The strong deflection of a polyatomic dopant in particular confirms the broad applicability of the technique. 87 Figure 3.1: (a) Deflection of He N nanodroplets with DMSO dopant. Squares: experimental data; blue line: pseudo-Voigt function [106] fit to the undeflected profile; red line: fit by simulation of the deflection process. (b) Same for CsI dopant. (c) Average deflection of the nanodroplets beam vs. electrode voltage. Its linear variation attests to the strong orientation of the cold dopant molecule along the field alongside calculated orientation cosine labels for 10 kV and 20 kV. (d) Average nanodroplet size as a function of nozzle temperature. Symbols: mean, 𝑁 ̅ , of the log-normal size distribution deduced from our deflection measurements; line: digitized data from Ref. [10]. 88 The plotted beam profiles contain a wealth of information. For example, Figure 3.1(c) shows that the average deflection is proportional to the deflector voltage. This is fundamentally different from the linear susceptibility regime where 〈𝑝 𝑧 〉 ∝ 𝐸 𝑧 and therefore 𝑑 ∝ 𝐸 𝑧 ∙ ( 𝜕 𝐸 𝑧 𝜕𝑧 ) ∝ 𝑉 2 , as commonly observed in cluster beam experiments [1,74,126]. He we can directly see the benefit of deflections in the helium medium where few rotational states are populated. For rotational temperatures above several K and practical electric field strengths, rotational motion severely suppresses the polarizing action of the external field. This may be seen using the aforementioned Langevin function where in the limit 𝑝𝐸 /𝑘 𝐵 𝑇 ≪ 1 the oriented dipole moment scales as 〈𝑝 𝑧 〉 → 𝑝 2 𝐸 /3𝑘 𝐵 𝑇 [1]. It is only when 𝑇 becomes very low, as enabled here by helium nanodroplet isolation, that the orientation can approach saturation: 〈𝑝 𝑧 〉 → 𝑝 . In this case the deflection varies only with the strength of the field gradient, i.e., linearly with the applied voltage 𝑉 . This is precisely what is confirmed by Figure 3.1(c) above roughly 2.5 kV (corresponding to an electric field of ≈10 kV/cm). The minor non-linearity for low applied voltage represents the region where the orientation cosine is not yet saturated due to the low field strength. The dependence plotted in Figure 3.1(c) implies saturated susceptibility and provides unambiguous proof that the dopant dipoles are strongly oriented by the applied field. The orientation cosines (and thus deflected profiles) are computed using the rigid rotor Hamiltonian with a Stark term method described in Chapter 1 and diagonalized with the set of Wigner D- matrices as a basis [78]. The rotational constants used in this work are 0.235 cm -1 , 0.231 cm -1 , and 0.141 cm -1 for DMSO [80,81], and 0.0236 cm -1 for CsI [82]. The orientation cosine represents a thermal average over rotational states at the temperature of the droplet representing our measurements which detect the average deflection of a superposition of rotational states, as 89 opposed to other molecule beam work [3,128] which focus on resolving the deflections of individual quantum rotational states. Of course, if molecules can be made even colder then even weaker dipoles can be oriented with even weaker fields. For example, full orientation of KRb (𝑝 =0.16 D) in an optical trap at temperatures below 1 µK was achieved with a field of 4 kV/cm [129]. A crucial point regarding superfluid nanodroplets is that by offering a “universal” trap at T0=0.37 K they make it possible to strongly orient molecules which are too large and complex for optical trapping methods. 3.4 Nanodroplet Sizes and Size Filtering Each measured profile represents the convolution of single nanodroplet deflections with the distribution of droplet masses, the distribution of their pick-up and ionization cross sections, boil-off events, and the shape of the original undeflected beam. By fitting these profiles to a simulation of the pick-up, boil-off, deflection, and detection steps, we deduce the mean and the width of the droplet size distribution produced by the nozzle. As shown in Figure 3.1(d), the fitted mean droplet size is in excellent agreement with the standard literature values [10,56] and the FWHM used in the fitting procedure is ∆𝑁 = 0.85𝑁 ̅ in excellent agreement with Ref. [56]. The strong agreement validates our analysis and Figure 3.1(d) represents an extension of the droplet size calibration curve. An inspection of Figure 3.1(a) and (b) reveals that the electric field not only shifts the doped droplet beam profile, but also makes it asymmetric. The reason is that smaller, lighter droplets deflect stronger than larger, heavier ones. This immediately suggests that spatial filtering of the deflected beam will translate into size filtering of the neutral nanodroplets. Using our 90 simulation, we record the droplets sampled to simulate the deflected profile binned by position to determine the mean droplet size at each deflected position. This filtering effect is demonstrated in Figure 3.2, where on average droplets are smaller at more deflected positions. The mean droplet size is superimposed over the deflected droplet profile for CsI shown in Figure 3.1(b) for comparison. Figure 3.2: Computed average droplet size as a function of position (open squares). The deflected beam profile is shown in light gray (corresponding to the right-axis) to indicate the average droplet size in corresponding positions of the deflected beam. The magnitude of deflection is greater for smaller (less- massive) droplets, providing smaller average droplet sizes at positions corresponding to larger deflections. The ability to scan through nanodroplet sizes within the same beam and within a single experiment is highly appealing, making it possible to explore the influence of droplet size on the spectroscopy and dynamics of embedded molecules. By deflecting a beam of helium droplets, subsequent probing of the droplets could be performed as a function of position as direct proxy for system-size. Compared to milestone experiments on droplet sizing by crossed-beam 91 scattering [56,64], here the deflection angles, the size range, and the intensity of the deflected beam are all markedly higher. A proof-of-principal experiment of this type is presented below, where the spatial dispersion of doped helium droplets is utilized to study charge transfer probability (CTP) from the helium matrix to the dopant molecule as a function of droplet size. 3.5 Charge Transfer Probability Charge transfer within HNDs is an important process in nearly all studies of the embedded dopant. Many experiments utilize mass spectrometry to “see” the droplets and their constituents after some earlier probing, and many experiments additionally utilize electron impact ionization as a first step toward getting a signal on the mass spectrometer. Understanding the probability of charge transfer between the helium droplet and dopant molecule and the associated ionization process is crucial in detecting dopant molecules and generally determining what species are available within the droplet. Charge transfer probability also suggests an effective maximum droplet size for which dopant ion signal can be recorded on a mass spectrometer in droplets [111,130]. The process of charge transfer between the helium matrix and the dopant molecule or cluster is non-trivial. It has been explored by a number of groups, first using direct mass spectrometry and comparing peak intensities [108,109], and later with a more advanced technique called optically selected mass spectrometry (OSMS) [110]. These results were subsequently examined in a theory paper [111]. OSMS ensures that detected ions come exclusively from droplets with the exact molecular specifies of interest inside, and not from other n-mers or background contaminated droplets. This brilliant technique synchronizes the detector with an infrared laser pulse to vibrationally excite a specific dopant molecule, leading to an evaporation of helium atoms from the droplet and thus 92 reducing the ionization cross-section and detected signal. Combining this process with mass spectrometry, mass spectra with only peaks corresponding to ionization of the doped droplets of interest are collected. A comparison of these helium-derived and dopant-derived peaks provides a measure of the likelihood of charge transfer from the helium to the dopant. This work provided interesting results on CTP with well-controlled method and different droplet sizes were generated by changing nozzle conditions. The deflection technique to spatially separate droplets as a function of size presents the opportunity to study CTP with an additional degree of control over the size of the system at fixed nozzle conditions. Our exploration of charge transfer aims to validate our beam deflections as a technique to size select doped droplets as a function of position. Consider the steps involved in electron-impact ionization of doped droplets [37,131]. Since helium atoms surround and greatly outnumber the dopant, an electron strike predominantly results in the creation of a He + ion. The positive hole then resonantly hops on a femtosecond timescale [132] from one adjacent helium atom to another, generally toward the impurity in the middle, until one of two outcomes occurs: it “self-traps” by forming He2 + followed by the potential nucleation of larger Hen + cluster ions 14 , or it reaches and ionizes the dopant. Both outcomes are accompanied by significant energy release which boils off the helium and ejects the ion from the nanodroplet [37]. This process is shown graphically in Figure 3.3 where “m” represents the variable dopant molecule. It follows that the probability of dopant ion formation can be viewed according to Beer’s law: 𝑃 𝑚 = exp(− ), where is the distance which the positive charge needs to travel before reaching the impurity and is its mean free path before self-trapping. Since scales with the 14 Mass spectra demonstrate that He 2 + is drastically favored as the outcome of this process, though larger clusters are also observed as a result of this process with decreasing probability. 93 droplet radius R (see below), a measurement of 𝑃 𝑚 as a function of droplet size will yield the important physical parameter . As noted previously, the droplet radius scales with 𝑁 1/3 leading to a model of CTP of the form 𝑃 𝑚 ∝ exp ( −𝛾 𝑁 1/3 ) in agreement with extensive simulation work following the initial studies of charge-transfer [111]. Additional simulation work in the early stages of this project detailed in Ref. [76] also suggests that the above model qualitatively agrees with the models of charge migration proposed in Refs. [109–111] with the exception of assuming a random walk for the charge randomly ionized in the droplet. However, it is noted that this model is inconsistent with prior experimental results [111]. Figure 3.3: Graphical representation of the charge transfer process described in the text where m represents the dopant molecule in the center of the droplet. It is also noted that fragmentation of the dopant may occur upon localization of the hole. In the final step, the droplet is fully evaporated by excess energy. This figure is based on a diagram presented in Ref. [131] initially describing the charge transfer process. 94 The concept of the measurement is as follows. If a droplet undergoes electric deflection, this automatically implies that it carries an impurity molecule. However, in the mass spectrum it can register either at the impurity mass or at the helium fragment mass. The ratio between these two outcomes, which is precisely 𝑃 𝑚 , can be traced as a function of the droplet’s deflection, i.e., of its size. We developed a procedure to subtract the undoped beam’s contribution to the signal and to fit the dopant ion yield to a model of charge transfer probability, which is taken as the exponential model described previously. Our procedure is derived below. We begin by turning on the deflecting field and denote the position of the detector entrance collimator (the profile position coordinate) by 𝑥 , the dopant molecule ion signal profile by 𝑆 𝑚 ( 𝑥 ) , and the helium ion signal profile by 𝑆 𝐻𝑒 ( 𝑥 ) . The latter can be measured under two conditions: when the pick-up cell is empty and when it is filled with dopant vapor. We label the corresponding profiles as 𝑆 𝑒 𝐻𝑒 ( 𝑥 ) and 𝑆 𝑣 𝐻𝑒 ( 𝑥 ) . These ion signals are precisely what are measured in our deflection profiles. The helium peaks in the mass spectrum can derive from three sources: (i) pure undoped helium droplets; (ii) droplets doped with the polar molecule of interest; and also (iii) droplets containing a background gas molecule (H2O, O2, N2, CO2, etc.) unpreventably picked up along the path from the skimmer to the deflection plates. This flight path region is kept at background vacuum levels below ≈10 -7 torr and the interior of the pick-up chamber is additionally desorbed of water vapor by UV irradiation and additional water is mitigated by liquid nitrogen cold-traps during operation. Therefore, all the pick-up probabilities are small and we make the assumption that a nanodroplet can contain at most a single impurity, either the polar dopant or a background molecule. We denote the incoming neutral nanodroplet fluxes corresponding to cases (i), (ii), and 95 (iii) by 𝐼 𝑢 ( 𝑥 ) , 𝐼 𝑚 ( 𝑥 ) , and 𝐼 𝑏 ( 𝑥 ) , respectively. Then the ion signal profiles defined above can be expressed as follows: 𝑆 𝑒 𝐻𝑒 ( 𝑥 ) = ϵ He {𝐼 𝑢 ( 𝑥 )+ 𝐼 𝑏 ( 𝑥 ) 𝑃 𝐻𝑒 𝑏 }, (3.1) 𝑆 𝑣 𝐻𝑒 ( 𝑥 ) = ϵ He {𝜂 [𝐼 𝑢 ( 𝑥 )+ 𝐼 𝑏 ( 𝑥 ) 𝑃 𝐻𝑒 𝑏 ] + 𝐼 𝑚 ( 𝑥 ) 𝑃 𝐻𝑒 𝑚 }, (3.2) 𝑆 𝑚 ( 𝑥 ) = ϵ 𝑚 𝐼 𝑚 ( 𝑥 ) 𝑃 𝑚 𝑚 . (3.3) Here 𝑃 𝑚 𝑚 and 𝑃 𝐻𝑒 𝑚 respectively represent the probabilities that electron-impact ionization of a nanodroplet containing a polar molecule will produce either a molecular ion or a helium ion. Similarly, 𝑃 𝐻𝑒 𝑏 is the probability that a nanodroplet containing a background impurity will yield a helium ion. In principle, all three are functions of nanodroplet radius, however we can make the simplifying assumption that 𝑃 𝐻𝑒 𝑚 ≈ 𝑃 𝐻𝑒 𝑏 ≈ 1, because for the droplet sizes studied here the self- trapping of the positive charge is a significantly more likely outcome than its reaching and ionizing the dopant, i.e., 𝐻𝑒 𝑛 + is the heavily favored outcome of ionization, even for nonempty droplets. Thus, we retain only the droplet size dependence of the latter outcome, which is therefore dependent on the deflection coordinate 𝑃 𝑚 𝑚 = 𝑃 𝑚 𝑚 ( 𝑥 ) = 𝑃 𝑚 𝑚 [𝑁 ( 𝑥 ) ]. The coefficients 𝜖 𝐻𝑒 and 𝜖 𝑚 are the mass spectrometer’s detection efficiencies of the helium ions and molecular ions. Since these masses are not radically different (∆𝑚 ≈100 amu), it is adequate to approximate the efficiencies as equal to each other. Finally, the factor 𝜂 represents the decreased flux of nanodroplets which do not contain the dopant molecule of interest. This decrease derives from various scattering processes of the primary beam in the vapor cell, all of which are proportional to the droplet cross section. Therefore, we write 𝜂 ≈ 1 − 𝑐 𝑁 2/3 . Physically, the second term should be on the order of 𝑛𝐿𝜎 , where 𝑛 is the number density of molecular vapor in the pick-up cell described by 𝑛 = 𝑃 𝑣𝑎𝑝𝑜𝑟 /( 𝑘 𝐵 𝑇 𝑐𝑒𝑙𝑙 ) , 𝐿 is the 96 path length through the cell, and 𝜎 = 𝜋 𝑅 2 ≈ 𝜋 ( 2.2Å) 2 𝑁 ̅ 2/3 . With the experimental parameters for CsI: 𝑇 ≈680 K, 𝑃 𝑣𝑎𝑝𝑜𝑟 ≈5×10 -3 Pa [133], and 𝐿 ≈2.75 cm, we expect the fit parameter 𝑐 ≈10 -3 , and this indeed is the average value of 𝑐 which comes out of the data fits described in the next paragraph. This confirms the applicability of the expression for 𝜂 . Using the series of above approximations and substituting Equations 3.1 and 3.3 into Equation 3.2 results in our fitting equation for charge transfer probability using our measured deflected profiles: 𝑆 𝑣 𝐻𝑒 ( 𝑥 ) ≅ (1 − 𝑐 𝑁 ̅ 2 3 )𝑆 𝑒 𝐻𝑒 ( 𝑥 )+ 𝑆 𝑚 ( 𝑥 ) 𝑃 𝑚 𝑚 [𝑁 ( 𝑥 ) ] . (3.4) The experimental procedure consists of measuring three beam profiles in the presence of the deflecting electric field as described above. These profiles are displayed in Figure 3.4. The nanodroplet sizes in the beam and for a given position in the deflection profiles is computed using our simulation outlined previously and demonstrated in Figure 3.2. The CTP term is taken to be 𝑃 𝑚 𝑚 [𝑁 ( 𝑥 ) ] = exp( −𝛾 𝑁 1/3 ) for comparison with Beer’s law and setting the pre-factor to unity reduces the fitted parameters to two (𝑐 and 𝛾 ) and is in good agreement with the model of Ref. [111]. 97 Figure 3.4: Examples of beam profiles which serve as input to fitting Equation 3.4 for determining the ionization probability of a molecule embedded in a helium nanodroplet. The curves shown are skewed Pseudo-Voigt envelopes of the experimental beam profiles which were obtained using CsI dopant molecules with nanodroplet source temperature of 19 K and deflection electrode voltage of 20 kV. The curves are labeled according to the variable names used in Equation 3.4. Two additional notes are in order. First of all, we have been referring to the “helium ion signal” and to the “dopant molecule ion signal.” In actuality the helium droplets produce a mass spectrum consisting of a sequence of Hen + peaks whose intensity decreases with 𝑛 . Likewise, a polyatomic molecule will produce a pattern of fragment ions. For the fit using Equation 3.4 we measured the profiles of the most intense peaks (He2 + and (DMSO) + ) and scaled them by the ratio of these peaks’ area to the area under all the fragment ion peaks in the full beam’s mass spectrum [134] (≈70% and ≈30%, respectively). We integrated over helium peaks up to He25 + after which the peak intensity becomes negligible [110]. Secondly, the fitting of the deflection profiles and Equation 3.4 must be performed self- consistently. Initially the charge transfer probability factor 𝛾 is unknown, and thus it cannot be 98 incorporated in the deflection simulation to determine the position-dependent droplet sizes in the beam. The simulation and fitting of Equation 3.4 are preformed iteratively where initially the deflection simulation generates droplets simply according to the user-defined lognormal distribution without sampling corrections for pick-up, ionization, or charge-transfer. Only the previously discussed mean droplet size parameter is adjusted here to fit the deflected profile. Once the mean droplet size, and thus the average droplet size by deflection position, are known, these values alongside the measured deflection profiles are fit to Equation 3.4 to determine a first-order approximation of 𝛾 . The deflection simulation is then rerun now accounting for pick-up, ionization, and charge-transfer and a new mean droplet size is fitted. This process of fitting for mean droplet size and 𝛾 is repeated iteratively until the value of 𝛾 converges. 𝛾 typically converges to the second decimal points within four iterations. Figure 3.5 assembles the results of measurements using CsI doping performed at three nozzle temperatures, i.e., for strongly distinct mean droplet sizes and spanning a wide range of droplet sizes, 𝑁 . It is therefore satisfying that over this full range practically the same value of 𝛾 (±17%) is found, as anticipated for the ionization pathway described above. From the form of our CTP model compared to Beer’s law, 𝛾 encapsulates the mean free path and average distance traveled by the charge within the droplet, . In order to compute the mean free path, must be estimated. The He + hole is originally created at a random location within the droplet [37]. For its subsequent motion, two models are considered. One [111] assumes that the positive charge hops radially inwards, the other (similar to Ref. [110]) that it hops along the dipole’s electric field lines all the way from its initial location to the molecule’s negative end. Simulating both scenarios using the code described in Ref. [76] and assuming that the dopant occupies a cavity of ≈4 Å radius [135] 99 at the center, we find ≈0.7R for the former case 15 and ≈1.0R for the latter. This neglects method the density gradient near the droplet surface which should not appreciably affect the estimation of the mean free path 𝜆 [111]. With 𝑅 = 2.22𝑁 1/3 Å [10], this translates into ≈ ( 1.6 − 2.2) 𝑁 1/3 Å for the two models, respectively, or 𝜆 ≈ ( 1.6 − 2.2) /𝛾 Å. Figure 3.5: Probability of ionizing charge transfer to embedded CsI molecules as a function of nanodroplet size. This probability was determined by a fit to the electric deflection profiles which spatially disperse nanodroplets according to their mass, as described in the text. The displayed size range was covered by measurements at three nozzle temperatures (13 K, 15 K, and 19 K) corresponding to mean droplet sizes 𝑁 ̅ of 3.7×10 4 , 2.2×10 4 and 9×10 3 atoms, respectively [see Fig. 1(d)]. At each of these temperatures the beam contained a log-normal distribution of droplet sizes which then spread out spatially upon deflection. This allowed the data to span a range of sizes, as marked by the three (overlapping) bands of color. For each of those bands the probability of dopant ion formation was fitted to the form 𝑃 𝑚 𝑚 [𝑁 ( 𝑥 ) ] = 𝑒𝑥𝑝 ( −𝛾 𝑁 1/3 ) . The results are depicted as dashed lines in the figure, color-matched to the size band from which the corresponding value of 𝛾 was derived. The lines extend into neighboring bands in order to show the range of uncertainty in their slope; the fact that they are close demonstrates the consistency of the analysis. 15 This coefficient has a straightforward origin: for charges created at a random location within a sphere and neglecting the small dopant cavity, the average distance from the center is 1 𝑉 ∫ 𝑟𝑑𝑉 = 3 4 𝑅 𝑅 0 . 100 Averaging our results over the estimated range and 𝛾 parameter for different mean droplet sizes for different nozzle conditions we estimate a mean free path of ≈16 Å (𝛾 ≈0.12). Similar measurements with DMSO yielded a larger mean free path of ≈34 Å (𝛾 ≈0.06), but due to the smaller dipole moment the deflection magnitude is weaker providing a more limited spread of droplet sizes and thus a potentially less accurate result. Our measured mean free paths are in reasonable agreement with the estimates of 28-35 Å for droplets doped with HCN and HCCCN found in Refs. [110,111] and measured using OSMS. The referenced estimates are larger than determined here for CsI, but they were deduced for beams centered at considerably smaller average droplet sizes and containing broad size distributions with limited ability to mitigate the large spread in droplet size. This is avoided in the present approach which scans through narrower nanodroplet size groupings by spreading out the full distribution along the deflection axis. 3.6 Conclusions Cold polar molecules entrapped within superfluid helium nanodroplets can be nearly fully oriented by an external electric field. We showed that this can be exploited in beam deflection experiments. Since the electrostatic deflecting force experienced by an oriented molecular dipole becomes extremely large, we observed that an entire beam of massive nanodroplets, containing up to tens of thousands of He atoms, deflects by impressively large angles. As demonstrated here, if nanodroplets carry a molecule with a known dipole moment the deflection measurement can be used to calibrate the droplet size distribution in the beam. Conversely, by comparing the deflections of a beam doped with a reference molecule and the same beam doped with another species, one can “read out” the dipole moment of the latter in a model- free approach. Since, as emphasized, nanodroplet embedding is applicable to a broad range of 101 molecules (in particular polyatomic and biological) this introduces a correspondingly broad method of measuring molecular dipole moments. (Note that direct measurements on isolated complex molecules began relatively recently [126] and many tabulated values still come from liquid phase data with potentially significant uncertainties [105].) The same approach can be employed with interesting and unusual agglomerates produced via sequential pick-up, a unique capability of helium nanodroplet embedding. For example, it can detect the formation of novel metastable assemblies of cold polar molecules, as we have demonstrated for DMSO dimers and trimers [84] and will be discussed in the next chapter. It should also be usable for the identification of polar vs. nonpolar conformers similar to Ref. [126]. For molecular characterization, it should also be possible to use strong electrostatic deflections to separate doped and undoped nanodroplets, which is important for emerging applications aiming at structural analysis of embedded molecules by x-ray, EUV, and electron pulses [38,136–138]. Finally, we pointed out that since the deflection angle of a doped nanodroplet depends on its mass, the broad size distribution contained within the original beam becomes spatially spread out by the time it reaches the detector plane. In other words, the deflection process disperses the HeN population and establishes a means to probe the behavior of neutral nanodroplets as a function of their size 𝑁 . To illustrate this, we measured how the dopant charge transfer probably varies with droplet radius and thus determined the mean free path for the migration of positive charge through the helium matrix. In this process we developed a framework to compare deflected beam profiles and fit a charge transfer probability parameter as a function of position (size). The results of this proof-of-principle experiment are validated by general agreement with experiments and theory utilizing different methods. Size dispersion and selection as a function position represents a novel 102 feature of the electrostatic deflection technique. This droplet size-filtering technique can also be applied to size-resolved spectroscopy of cold dopants and dopant reactions. 103 Chapter 4 – Electrostatic Deflection as a Probe of Polar Structure in Molecular Assemblies This chapter is based on our published work. Text and figures are reproduced with permission from the Royal Society of Chemistry (RSC) and the American Institute of Physics (AIP): J. W. Niman, B. S. Kamerin, L. Kranabetter, D. J. Merthe, J. Suchan, P. Slavíček, and V. V. Kresin, “Direct detection of polar structure formation in helium nanodroplets by beam deflection measurements”, Physical Chemistry Chemical Physics 21, (2019) 20764. [84] B. S. Kamerin, J. W. Niman, and V. V. Kresin, “Electric deflection of imidazole dimers and trimers in helium nanodroplets: Dipole moments, structure, and fragmentation”, The Journal of Chemical Physics 153, (2020) 081101. [85] This chapter describes work we performed that investigated the structure formed by dimers and trimer of dimethyl sulfoxide (DMSO) and deuterated Imidazole (IM) molecules in two separate but similar projects. The deflection measurement establishes the complexes’ electric dipole moments, and thus structure. In consequence, the introduced approach is complementary to spectroscopic studies of low-temperature molecular assembly reactions. For DMSO we see that long-range intermolecular forces are able to steer polar molecules submerged in superfluid helium nanodroplets into highly polar metastable configurations. We demonstrate that the presence of such special structures can be identified, in a direct and determinative way, by electrostatic deflection of the doped nanodroplet beam. We interpret the experimental results with ab initio theory, mapping the potential energy surface of DMSO complexes and simulating their low temperature aggregation dynamics. For IM, previous spectroscopic studies and calculations have identified potential geometries and dipole moments for small complexes and here we provide complementary results and experimentally determined dipole moments for comparison. Monitoring the deflection profile of (IM)D + mass peak provides a direct way to establish that it is the primary product of the ionization-induced fragmentation both of (IM)2 and (IM)3, providing a demonstration of the ability of the deflection technique to establish fragmentation parentage. Very large measured dipole values confirm theoretical predictions and derive from a polar chain bonding arrangement of the heterocyclic imidazole molecules. 4.1 Introduction Long-range intermolecular forces play a crucial role in reactions at sub-Kelvin temperature (see, e.g., the reviews in Refs. [16,20,21,23]). For example, long-range interactions between polar molecules embedded in helium nanodroplets often dominate the outcome of their assembly reactions. This is facilitated by the low internal temperature (370 mK) of the nanodroplet medium 104 as well as by its superfluidity [10]. As a result, molecular reorientation and intermolecular reactions within nanodroplets are not perturbed by inhomogeneities present in other low- temperature surface and matrix isolation environments, making these “nano-cryo-traps” excellent hosts for exploring the physics and chemistry of cold molecular systems [30]. A landmark demonstration of the action of long-range forces was furnished by experiments on HCN molecules sequentially picked up by a helium nanodroplet beam [12]. These linear molecules were guided by dipole-dipole forces to self-assemble into long chains aligned head-to- tail inside the nanodroplet. HCCCN was found to behave similarly [52]. These chains rank among the most polar molecular systems ever observed in a molecular beam. In an “ordinary” environment thermal motion would drive them out of this type of metastable configuration, but within a very cold and inert liquid helium droplet they become long-lived. Data on formic acid [139], imidazole [54], and acetic acid [140,141] dimers suggested an analogous alignment mechanism. However, such an outcome is not universal in nanodroplet embedding. For example, two HCl molecules arrange themselves nearly at a right angle to each other [142,143] while water clusters form cyclic structures [144]. The “decision” by polar molecules how to orient themselves upon approach depends on the strength of their dipoles, on their responsiveness to the mutually reorienting torques (i.e., their rotational constants and their accessible rotational quantum states), and on the directionality and flexibility of their bond formation. That is to say, the outcome depends on the shape of the intermolecular potential energy surface and on the barrier heights encountered on the path to the final configuration. It is therefore interesting and informative to establish whether a molecular formation within a nanodroplet can reach its global energy minimum or finds itself trapped in a polar metastable 105 state. However, often this is not a straightforward determination. The studies cited above based their conclusions on the interpretation of dopant infrared spectra or on inference from electron attachment mass spectrometry. Such assignments grow more difficult and less definitive with increasing size and/or complexity of the embedded molecules and their assemblies. In this work we describe a measurement which directly establishes the polarity of a molecular assembly, as well as determines its dipole moment. It makes use of electrostatic deflection of the doped nanodroplet beam [79,83]. The technique is based on the fact that polar structures embedded within the superfluid matrix can be made nearly fully oriented by an external static electric field [14,79] and consequently experience an extremely large deflecting force from the field’s gradient. This high degree of orientation has been taken advantage of in the aforementioned experiments using pendular-state spectroscopy [12,14]. Such a high degree of orientation is unattainable for bare polyatomic complexes in a molecular beam. Whereas some relatively small and light molecules reach rotational temperatures below 1 K with the use of seeded supersonic expansions and exhibit large deflections (see for example Refs. [3,145]), this becomes impractical for heavier systems. This is a conveniently unambiguous measurement applicable to a wide range of molecules, from diatomic to polyatomic (including biological). Practically any molecular species that can be brought into the vapor phase with a pressure of only ≈10 -4 -10 -6 mbar can be picked up by the nanodroplet beam and thermalized within the inert viscosity-free medium. The thermalization proceeds by evaporative cooling: the molecules’ translational and internal energies are transferred to the superfluid matrix which has a very high thermal conductivity, and released via evaporation of surface helium atoms, promptly bringing the nanodroplet back to the original temperature [10]. Here the deflection technique is applied to two distinct systems of polyatomic molecules. 106 We first applied the deflection method to monomers, dimers and trimers of the dimethyl sulfoxide molecule [“DMSO,” (CH3)2SO, molecular mass 78 amu]. The molecule is nearly an oblate symmetric top, with rotational constants of [80,81] 0.235 cm -1 , 0.231 cm -1 , and 0.141 cm -1 and its total dipole moment is [105] 𝑝 =4.0 D.. The measurement clearly reveals the presence of highly polar dimers and trimers, i.e., the formation of metastable polar configurations abetted by the cryogenic nanodroplet environment. To our knowledge, this is the first direct non- spectroscopic identification of such a cold polar molecular assembly and a demonstration of the deflection technique for measuring the dipole moments of embedded molecular complexes. We subsequently applied the deflection technique to Imidazole [“IM,” C3H4N2, molecular mass 68 amu; see Figure 1(a)] which is an important, extensively studied constituent of proteins and biologically active compounds. The structural and electronic properties of imidazole complexes have also attracted a lot of interest because the molecule acts both as a proton donor (via its N–H constituent) and a proton acceptor (via the other nitrogen atom). It was recognized a long time ago [146] that this can enable IM to form linear structures in non-polar solvents. Furthermore, IM is a strongly polar [147] (p=3.7 D) and polarizable [148,149] ( =7.4 Å 3 ) molecule and also approximates an oblate symmetric top with rotational constants of [147] 0.325 cm -1 , 0.313 cm -1 , and 0.159 cm -1 . The formation of a strong N–H···N bond, has been predicted to endow IM oligomers with very large dipole moments [54,150–153] [see Figure 4.1 (b) and (c)]. To the best of our knowledge, however, these dipole moments have not been directly measured up to now 16 . 16 The angle between the vibrational transition moment and the permanent dipole moment of IM dimers and trimers has been measured in Refs. [54,151,152], but it is not sensitive to the permanent dipole moment’s precise magnitude [154]. 107 Experiments on the stability, spectroscopy, and photochemistry of gas-phase IM clusters, from dimers [54,151,153] to larger structures [152,155], have been carried out to gain insight into the formation and structure of hydrogen-bonded IM complexes. An integral tool for studying size- dependent cluster properties is mass spectrometry, for which the particles need to be ionized. However, cluster ionization is typically accompanied by fragmentation and proton transfer, resulting in ions of uncertain parentage. The dominant products of electron-impact ionization of bare IM clusters are a series of (IM)nH + peaks [156], while clusters embedded in helium nanodroplets yield both (IM)nH + and a weaker (IM)n + series [157]. We show that the series of strongly polar structures measured permit identification of the provenance of some of the small detected cluster ions. Figure 4.1: (a) Imidazole molecule, fully deuterated form (molecular mass 74 amu). The arrow marks the molecule’s electric dipole moment. (b,c) Linear dimer and trimer configurations, with calculated dipole moments (marked by arrows) of 9.1-9.6 D and 14.8 D, respectively [151–153]. The effect of deuteration on the ground-state dipole moments does not exceed a few percent [147]. Structures for DMSO are presented later in the chapter with extensive detail. 108 4.2 Experimental The experimental set-up for each dopant is as described previously. Helium was expanded through a 5-micron nozzle with a stagnation pressure of 80 bar. Unfortunately, during the DMSO experiments the nozzle was experiencing difficulties reaching standard operating temperatures as the insulation on the nozzle was becoming saturated with diffusion pump oil. This led to some drift in nozzle temperature over time during these experiments (≈0.2 K for the dimer experiments lasting ≈30 hours and ≈0.3 K for the trimer experiments lasting ≈20 hours). The nozzle temperature ranged from 15.5-15.6 K for the dimer profile measurements, and 16.2-16.4 K for the trimer profile measurements. This issue was corrected for the later IM experiments which occurred over a half a year later and the nozzle was fixed at 15 K in this case. The pick-up cell for DMSO was the same as discussed in the previous chapter and used in Refs. [76,79]. IM was substantially more challenging to introduced into the droplets in a controlled manner. In early experiments we placed the IM in the standard interior stainless steel pick-up cell, but even at room temperature the high vapor pressure of the powder produced an intense mass spectrum with imidazole clusters larger than the monomer present in with large magnitudes. The evaporating flux of IM also led to an ambient pressure in the pick-up chamber more than an order of magnitude higher than normal operating conditions. Without the ability to control the doping in the configuration, the exterior cell (used for DMSO) had to be adopted with modifications. Rather than using the external stainless-steel cylinder for DMSO, IM resided in a heated glass vessel outside the chamber and its vapor was fed into the cell through a heated narrow tube and heated needle valves. It was found that without heating the exterior tubing, the IM would condense on inner surfaces and clog the assembly. Additionally, it was found that the IM 109 condensation was damaging to the gauge filament in the injection-line and rendered the attached pressure gauge inoperable. The injection-line was heated with heating tape carefully wrapped around the full extent of the line and valves, avoiding gaps where the IM would condense. I also lathed an aluminum cylinder to fit inside of the larger glass cylinder housing the imidazole to substantially reduce the volume and provide more consistent heating to the IM sitting on top of the cylinder. Temperature was monitored with a thermocouple pressed at the top of the glass vessel where the IM was housed. With careful heating we were able to achieve stable signals for the 4–6 hour duration of a full deflection measurement cycle In order to better separate the peaks of IM and its fragments in the mass spectra, we used fully deuterated imidazole (98% purity, CDN Isotopes). This doubled the separation between neighboring peaks in the mass spectrum used for deflections, and it was found that initially the peaks could not be reliably separated at the measurement resolution Following the doping process, collimated by a 0.25 mm by 1.25 mm slit and passes between two 15 cm-long high voltage plates which create an electric field and a strong collinear field gradient directed perpendicular to the beam axis. Then, after a 1.25 m field-free flight path, the beam enters an electron-impact ionizer (90 eV electron energy) through another narrow slit, and the resulting molecular ions are recorded by a quadrupole mass spectrometer (Balzers QMG- 511) synchronized with a beam chopper. Deflections induced by the electric field on neutral doped nanodroplets are determined by setting the mass spectrometer to a particular ion mass and comparing its “field-on” and “field-off” spatial profiles. Both profiles are mapped out by translating the detector chamber, including its entrance slit, on a precision linear stage. 110 4.3 Dimethyl Sulfoxide Results and Discussion Molecules are picked up by helium nanodroplets via successive collisions in a Poisson process [10]. Therefore, it is important to correlate measured beam deflections with the specific number of molecules embedded in the droplet. Dopants within nanodroplets are ionized indirectly via charge transfer to He + produced by electron bombardment; this transfer is a highly exothermic process which can cause fragmentation [37]. Consequently, when mapping out the deflection profile of a dopant ion peak in the mass spectrum, we need to ensure that it is not a fragment of a larger agglomerate. This is done by gradually increasing the vapor pressure in the pick-up cell and monitoring the mass spectrum for the appearance of molecular ions characteristic of progressively larger entities. For example, monomer ionization produces a strong (DMSO) + signal [82] at 𝑚 =78 amu, hence if we measure beam profiles with the mass spectrometer set to this mass peak but with the vapor pressure low enough to suppress the corresponding characteristic (DMSO)2 + peak at 𝑚 =156 amu, then we can be confident that the deflection principally corresponds to droplets carrying the monomer. Similarly, profiles measured at 𝑚 =156 amu but before the appearance of the trimer’s signal must derive from the dimer, etc. The mass spectra corresponding to the subsequent deflection profiles is presented in Figure 4.2. 111 Figure 4.2: Representative mass spectra corresponding to deflection measurements on (DMSO) n-doped nanodroplets. The mass spectrometer was set to the masses of intact ions: (a) 78 amu for the monomer, (b) 156 amu for the dimer, (c) 234 amu for the trimer. 4.3.1 Deflections Figure 4.3 shows the deflection profiles of helium nanodroplets containing one, two, and three DMSO molecules. The deflections are substantial despite the fact that the droplets are truly massive (~1×10 4 –3×10 4 He atoms, as described below). Therefore, we are immediately and directly informed by Fig. 1(b) that (DMSO)2 settles into a strongly polar configuration and not into its global minimum structure, because the latter would be symmetric with a zero dipole moment [158]. 112 In order to assign an absolute value of the dipole moment to the dopant, we must keep in mind that the host nanodroplets are not all of the same size. The size distribution produced by the nozzle expansion is log-normal, and this translates into a convolution of pick-up cross sections, deflection angles, and ionization efficiencies. Our procedure is to start with the profile corresponding to a single DMSO dopant molecule whose dipole moment is known. A fit to the deflected profile (by a Monte Carlo simulation of the pick-up, evaporation, deflection, and detection steps) is used to calibrate the droplet size distribution. Both charge transfer probability parameters discussed in the previous chapter are used in the analysis in parallel, providing bounds for the fitted dipole moments and sizes. By repeating the deflection measurement and its simulation with doubly- and triply-doped nanodroplets produced and detected under the same conditions, we can deduce the electric dipole moments corresponding to the dimer and the trimer. 113 Figure 4.3: Profiles of (DMSO) n-doped helium nanodroplet beams. Blue: zero-field profiles, orange: deflection by a field of 82 kV/cm strength and 338 kV/cm 2 gradient. Symbols: experimental data, lines: fits of the deflection process, as described in the text. These dipole moments enter the fitting procedure at the step where the deflecting electrostatic force is calculated. As described previously, this requires knowing 〈𝑝 𝑧 〉, i.e., the degree of orientation induced by the applied field. For the DMSO monomer this is carried out by diagonalizing the rotational Stark effect matrix [78] using the components of the molecule’s dipole 114 moment about the principal axes [81]. For the heavier dimer and trimer the classical Langevin- Debye formula is sufficiently accurate [159]. In calculating the monomer’s Stark spectra one should keep in mind that rotational coupling to the superfluid [51] enhances the moments of inertia of the heavier molecular rotors by an average factor of ~2.5-3 compared with their gas phase value [10,14]. Since DMSO’s specific renormalization factor is not known, it was set to 2.6 in our data fitting procedure. We found that the inclusion of this factor had practically no effect on the deduced dipole of the dimer but shifted that of the trimer upward by 10%-15%. For the final fitted dipole values listed below, the (DMSO)n orientations within an applied 82 kV/cm field were found to be 86%, 97%, and 98% for 𝑛 =1-3, respectively. As noted earlier, the dimer and trimer deflection profiles were taken during different experiments, and thus each require a monomer profile (measured in the same experiment) in order to calibrate the droplet size parameters. Figure 4.1(a) shows the monomer deflection profiles taken alongside the dimer profiles in Figure 4.1(b). The monomer profiles used to calibrate the trimer profiles in Figure 4.1(c) are not pictured for brevity, but are qualitatively the same with larger deflection due to the smaller average droplet size expected for a warmer nozzle. The fitted mean droplet size for the former case is 𝑁 ̅ 2.3×10 4 and the latter gives 𝑁 ̅ 1.4×10 4 . The FWHM in each case is Δ𝑁 0.85𝑁 ̅ . The gradual increase of the profile width with the number of dopant molecules is believed to be caused by transverse momentum transfer associated with each pick-up collision. A concern is that broadening could indicate that multiple structural configurations with different dipole moments could be present in the profile, i.e., the dimer profile could contain both the strongly polar configuration as well as the ground state. In this case the deflected profile would be broadened both by the distribution of droplet sizes as well as the deflection of multiple dipole 115 magnitudes. The net profile measured would then be a weighted average of the deflections of dipoles of different magnitudes, which would intrinsically be broader than the profile for a single embedded dipole similar to the asymmetric broadening from the droplet size distribution [79]. However, this picture is unlikely as in this case as substantial contribution from a non-polar dopant should be seen as a strong left-shoulder in a profile measurement, or even a binodal structure in the measured deflected profile. Moreover, the undeflected profile is also commensurately broader for each subsequent profile. This profile is agnostic to the magnitude of the dipole(s) contained in the droplet and is thus evidence that the broadening simply comes from the momentum imparted during the doping process. 4.3.2 Dipole Moments From analysis of the measurements, we assign effective electric dipole moments of 7.2 D to (DMSO)2 and 8.6 D to (DMSO)3, with an estimated accuracy of ±0.2 D and ±0.6 D, respectively. These values, which can be compared with the ground state moments of 0 D for the aforementioned symmetric dimer and 4.2 D for the trimer [158] (essentially a nonpolar dimer plus an unpaired monomer), establish the presence of highly polar metastable structures. In the cold superfluid environment these structures are steered into formation by the long-range intermolecular forces and are then unable to overcome the potential barrier leading to the global minimum configuration. The stated uncertainty derives partially from the uncertainty in the aforementioned renormalization factor of the rotational constants. The upper and lower bounds represent the average for previously studied heavy molecules [10] and the value used in Ref. [54] for the similar IM molecule of similar weight. The uncertainty primarily derives from the fitted dipole moment assuming the two distinct charge transfer parameters measured in Ref. [79]. The stated dipole 116 moments represent an average with bounds given from the small variations in analysis. 4.3.3 Modeling of Molecular Complex Formation To facilitate the interpretation of the above results, we 17 supplemented the experiments with ab initio modeling of DMSO condensation. The geometry of DMSO dimers and trimers was optimized with the B3LYP functional with the aug-cc-pVDZ basis set. The DMSO complexes are dominantly bound by electrostatic forces but the dispersion interactions still play a non-negligible role. We have therefore applied the D2 correction of Grimme [160]. The approach was tested against the CCSD(T)/aug-cc-pVTZ method for the DMSO dimer, yielding similar energetics. All calculations were performed in the gas phase: by considering complexes with helium atoms or within a dielectric continuum we found that the helium environment had a negligible effect on the structure and energetics. The potential energy surfaces (PES) were pre-screened with molecular mechanics (MM)-based metadynamics simulations [161] and the structures were then recalculated at the DFT level. The process of DMSO dimer formation was modeled with molecular dynamics (MD) simulations within the canonical ensemble. We used the Nosé-Hoover thermostat with a rather small value of = 0.01 ps. This corresponds to fast draining of extra energy from the system, so that at each time it essentially remains in equilibrium. A temperature of 5 K was chosen in order to accelerate the simulations. It is higher than in the experiment but the difference is small compared with the accuracy of the PES. 17 It should be noted that calculations discussed in this section were performed by our theorist collaborators in Prague, Jiří Suchan and Petr Slavíček, and are included here as they are relevant to the story. However, our involvement in these calculations was the discussion of the set-up based on the experiment conducted. 117 We started with two DMSO molecules positioned at a distance of 20 Å between the two sulphur atoms with a random orientation. We then performed molecular mechanics simulations with the MM force field [162]. The molecules gradually approached each other while aligning their dipole moment. Since the MM force field does not reproduce the energetics of the minima sufficiently well, at the intermolecular distance of 10 Å we reset the simulations, switching from the force field to the more accurate semiempirical density functional tight binding (DFTB) method [163] with D3 dispersion correction [164,165]. The system then continued to evolve in time for another 500 ps with a time step of 1 fs, using the velocity Verlet integrator. Dipoles along the path were recalculated at the B3LYP/aug-cc-pVDZ level. The DFT and CCSD(T) calculations were performed in Gaussian09 [166]. Molecular dynamics simulations were performed in GROMACS 2018.4 [167] and the DFTB simulations in the DFTB+ 18.2 code [163]. In-house (UCT Prague) MD code, ABIN [168], was also utilized. Additional details for the calculations performed and free energy surfaces can be found in the electronic supplemental information for Ref. [84]. 118 4.3.4 Results of Modeling Figure 4.4: Energy minima of the DMSO dimer, with their corresponding binding energies and dipole moments. Figure 1.4 shows several low-lying minima of the DMSO dimer obtained from extensive mapping of its potential energy surface. The structures are divided into two classes of minima: non-polar and polar. The global minimum (complex D1) of (DMSO)2 has a symmetrical configuration with a zero dipole moment, consistent with the aforementioned work [158]. Structures D2 and D3 also belong to the low dipole manifold. Complexes D4 and D5 represent polar type structures. The experimental data suggest that the highly polar structure D5, with an almost orthogonal arrangement of dipoles, predominantly forms within nanodroplets. It is separated from the global minimum by a barrier of 0.08 eV, which is more than sufficient to prevent a D5 → D1 transition and thus continue to be trapped in a metastable state. Structure formation under cryogenic conditions is therefore likely to proceed as follows. At large separation the dominant force is the dipole-dipole interaction which aligns the two DMSO 119 molecules. The detailed calculations [84] demonstrate a barrierless pathway between this structure and the D5 minimum. Therefore, the molecules approach each other gradually within the helium environment to which all excess energy is almost immediately drained. The (DMSO)2 ends up trapped within the basin of complex D5. Molecular dynamics (MD) simulations of the binary encounter under conditions of very efficient energy transfer to the environment, as specified above, support this scenario. Initially the two dipoles are assigned a random relative orientation, but the trajectory shown in Figure 4.5 demonstrates that it becomes correlated already at large distances. At closer approach the total dipole moment transiently increases. The molecular dipoles at that point are still parallel, hence the bump in the dipole moment is caused by mutual induction. Finally, the dimer quenches into one of the potential minima. In accord with the experiment, no formation of a zero-dipole structure is found. The majority of the trajectories end up in the D5 minimum with a dipole of 6.4 D, some of them end up in the D4 minimum with a somewhat lower dipole moment than detected in the experiment. Figure 4.5: Dipole moment of DMSO dimer complex along the intermolecular approach coordinate, as illustrated by the molecular dynamics simulation. 120 Figure 4.6 displays the computed structures for the trimer similar to Figure 4.4 for the dimer. The trimer displays a series of diverse structures. The lowest energy structure is cyclic with a dipole moment of 4.25 D (complex T1). Its formation is kinetically hindered. As mentioned above, it represents the global dimer minimum to which the third molecule is added; since in the nanodroplets the former structure is not formed, neither will the cyclic trimer. We have located linear structures (T6, T7) with a much higher dipole near 10 D. There are multiple other minima with intermediate dipoles. It follows from our simulations that a rather complex mixture of these metastable structures may be formed under the experimental conditions, and its precise assignment is beyond the reach of theory. The effective dipole moment of 8.6 D deduced from the deflection experiment likely represents the population average of the kinetically accessible structures. 121 Figure 4.6: Energy minima of DMSO trimers, with their corresponding binding energies and dipole moments. 4.4 Imidazole Results and Discussion Imidazole deflection profiles were taken at two temperatures as measured at the top of the vessel, providing partial pressures for doping referred to as “higher” and “lower” doping regimes. 122 These regimes correspond to a temperature of 50º C and 30º C respectively. As described below, in the former case we identify the majority of resulting dopant formations to be IM dimers, and in the latter case trimers. Figure 4.7 shows the peaks in the monomer and dimer regions of the mass spectrum in the two different doping regimes for the deuterated IM molecule. The peak at 72 amu corresponds to the molecular ion (C3D4N2) + and the one at 74 amu to (C3D4N2)D + . We see that the latter grows far more rapidly with increased molecular vapor pressure, indicating that it derives from progressively larger complexes forming inside the droplet. Figure 4.7: Mass spectra produced by electron impact ionization of helium nanodroplets doped with deuterated imidazole, IM. The top (a) and bottom (b) panels show the monomer and dimer regions, respectively. The lower (dashed) lines correspond to the same low-doping regime and the upper (solid) lines to the same higher-doping regime, see the text, and the vertical scale of the panels matches the relative magnitudes of all the peaks. The additional signal visible between the labeled ion peaks is believed to derive from partially undeuterated imidazole present in the original powder and from possible H/D exchange occurring within the vapor supply system. 123 In the lower-doped regime the (IM)3 + peak was virtually absent in the mass spectrum (see Figure 4.8). Previously published mass spectra [157] suggest that ~5%-10% of imidazole cluster ionization products in helium nanodroplets are detected as (IM)n + , therefore the absence of any trimer signal implies that in this case the (IM)D + signal originates primarily from dimers. Furthermore, the (IM)2 + peak is much weaker than (IM)D + , therefore the latter is the dominant dimer ionization channel. In the higher-doped regime both (IM)2D + and (IM)D + grow substantially, implying that the droplets now contain many trimers (and possibly a minor fraction of tetramers or higher order oligomers) which therefore contribute the main portion of the (IM)D + signal. Figure 4.8 shows an extended spectrum demonstrating the presence of larger imidazole clusters present in the beam. The scale here is the same as Figure 4.7, though in this picture it is clearly seen that the IM + and (IM)D + peaks are dominant over the given range. Deflection measurements require tight beam collimation; hence we need to select sufficiently intense peaks in the mass spectrum and these peaks were chosen. While deflections of the parent peaks, (IM)2 + and (IM)3 + may be more convincing for measurements of the dimer and trimer respectively, these intensities were insufficient for reliable measurements after placing the collimator and slit. Increasing the pick-up pressure to measure these peaks directly would certainly increase the density of higher order oligomers in the beam and contaminate the interpretation of the data. However, as we describe below, the measurement of a fragment in the mass spectra provides information about its parentage. There is also a peak at 70 amu corresponding to deuterium loss, (C3D3N2) + . Both the pressure dependence of this peak’s intensity and its deflection profile suggested that it is primarily a product of the ionization of IM monomers. Interestingly, this peak does not appear nearly as 124 prominently in the electron-impact mass spectrum of pure gas-phase imidazole [82]. However, it is known that ionization branching ratios within nanodroplets are not always identical to those of free molecules [169,170]. Additionally, the detected ions are produced by charge exchange between the dopants and He + acceptors created within the nanodroplets by electron bombardment [37]. The resulting energy release can be accompanied by substantial fragmentation of the dopant molecules. This process is governed solely by the dopant-acceptor interaction and therefore no difference in the relative ion intensity pattern was observed even at one-third of the above electron impact energy. As remarked above, the deflection method makes it possible to support such considerations in a more quantitative manner. The data discussed in the following section confirm that the IM + signal derives primarily from monomers, while dimers and trimers indeed undergo extensive fragmentation and are detected in the (IM)D + channel. 125 Figure 4.8: Extended electron impact ionization mass spectrum containing deuterated imidazole clusters. The higher and lower doping regimes are described in the text. The signal for (IM) + and (IM)D + clearly dominate in the spectrum in both doping conditions and these peaks are used to collect deflection profiles. Frequent peaks separated by four amu correspond to He N + ions. The inset shows a zoom in of the high mass range unambiguously demonstrating the presence of the imidazole trimer and tetrameter in the high doping regime. The peaks between 180 and 200 amu are believed to come from Rhenium and Tungsten from filaments in the system. 4.4.1 Deflections Figure 4.9 shows the deflection profiles for the IM + peak under the lower doping regime (a) and (IM)D + under the lower and higher doping regimes [(b) and (c), respectively]. One can immediately see from the figure that the deflection of the deuterated (IM)D + ion [corresponding to the 74 amu peak in Figure 1.7(a)] significantly exceeds that of the monomer parent molecular ion (72 amu) and, furthermore, that this deflection is stronger under the higher doping condition. From this we see that larger IM clusters are more polar, and that we gather a larger number of them on the (IM)D + mass peak when the doping pressure increases. 126 Figure 4.9: Electrostatic deflection of (IM) n-doped helium nanodroplet beams. Blue: electric field off, orange: electric field on. The symbols are experimental data, the lines are fits of the deflection process, as described in the text. (a) IM + signal; (b,c) (IM)D + signal in the lower and higher doping regimes, respectively. The arrows denote the shift of the profile centroids. The magnitudes of these complexes’ dipole moments can be determined from the amount of deflection shown by the profiles in Figure 4.9. The magnitudes of the dipole moments for the dimer and trimer of imidazole are extracted with an identical method as used for DMSO. The rotational constants are once again corrected by a factor of 2.5-3. The end result for the orientation cosine, 〈𝑐𝑜𝑠𝜃 〉 ≈0.90, was insensitive to the precise value. The molecular polarizability term, 𝐸 , can be neglected in the analysis as it comprises less than 0.1% of the permanent dipole moment. 127 The droplet sizes for the beam are calibrated with the IM monomer in Figure 1.9(a) with a mass peak of 72 amu. This mass peak overlaps with the mass of the He18 + nanodroplet fragment. Its intensity was corrected by subtracting the average of the neighboring He17 + and He19 + peaks, and its undeflected and deflected profiles were corrected by subtracting the profiles of the He2 + peak scaled to the He18 + intensity. The profiles are fitted with pseudo-Voigt [106] functions before the subtraction, and the resulting profile is also fit to a pseudo-Voight function. The helium background was found to represent approximately 20% of the total intensity at 72 amu. The idea is that helium contamination of this mass peak marginally suppresses the measured deflection intensity, and by subtracting the helium deflection contribution the deflection of the IM monomer is better represented. Fits of the Monte Carlo deflection simulation result in average size of 𝑁 ̅ 1.2×10 4 and width ΔN 1.010 4 similar to the values observed in other experiments [56]. 18 Using the HeN diameter D 4.4N 1/3 Å [10] and the bond lengths of the IM molecule and dimer [171], the average nanodroplet can be visualized as being roughly 25 monomers or 10 dimers across. This information now can be used with the same simulation to deduce the electric dipole moments corresponding to the deflection profiles in Figure 1.9(b) and 1.9(c), i.e., the profiles measured with the mass spectrometer set to detect the (IM)D + ion. Since the corresponding electric dipole values are large, the orientation cosines used in these fits can be accurately represented by the Langevin-Debye function. The rigid chain model is applicable in view of the extremely low temperature: even the lowest-energy vibrational frequencies of the IM dimer (monomer rocking 18 The determined droplet size here is somewhat lower than expected from previous experiment (i.e., DMSO). This is the first experiment we performed that attempted to subtract non-polar contamination from the deflection channel, which is intended to make the resulting calibration measurement more accurate and results in a smaller average droplet size. Moreover, the experiments are performed at different points in time where small shifts in the position of the beam and skimmer can result in different parts of the beam being sampled. Additionally, our nozzle conditions near the critical remine of expansion represent a less- studied size regime where large changes in size may be expected from small perturbations [55]. 128 and twisting [171]) lie above 10 cm -1 , i.e., forty times above the thermal energy. This represents an interesting contrast with hydrogen-bonded complexes at higher temperatures, where flexible vibrational motion can lead to a sizeable electric dipole moment [172]. 4.4.2 Dipoles and Parentage Assignment The fitted dipole moments are 8.8 D and 14.5 D for the “lower” and “higher” doping regimes, respectively, with an estimated error of 0.6 D. Within the accuracy of the measurement, these values are persuasively in agreement with the computed dipole moments [54,151,152] of the strongly polar imidazole dimer and trimer structures, listed in the caption of Figure 4.1 in the introduction. The uncertainty range in the measurement has the same source as the DMSO measurements, where it represents the range of outcomes the analysis branches. Higher-order oligomers are also present in the beam under the higher-doping conditions, as evidenced by the (IM)3D + peak in the corresponding mass spectrum as shown in Figure 4.8. However, the fact that this peak is very much weaker than (IM)2D + and (IM)D + suggests that the admixture of larger clusters is small and does not strongly “contaminate” the deflection measured on the (IM)D + channel. The consistency between experimental and theoretical values supports this conclusion. Therefore, two important deductions can be made: First, the doped nanodroplet deflection method, in a direct and quantitative way, confirms the prediction of a remarkably strong dipole moments of these complexes, deriving from their aligned structure and facilitated by the formation of a strong hydrogen bond and mutual polarization. There is no evidence for the formation of cyclical IM3 structures [173] within the 129 nanodroplets: they would have manifested themselves as a secondary peak near the zero position in the deflection profile. Second, the method unambiguously corroborates the fact that the (IM)D + ion is the dominant product of the ionization of both IM2 and IM3. With weak doping, this mass peak corresponds primarily to doping from the molecular dimer, while for stronger doping this shifts to the molecular trimer. This ability to ascertain fragment parentage is a useful and novel supplement to mass spectrometry. The ability of the deflection technique to probe the origin of mass peaks based on the magnitude of deflection represents another broadly applicable benefit of the tool. 4.5 Conclusions In this chapter we have demonstrated that the deflection technique can probe the structure of embedded molecular agglomerates using its’ dipole moment for two distinct systems. For DMSO we have demonstrated that the presence of metastable polar structures, formed by sequential embedding of polar molecules into superfluid helium nanodroplets, can be clearly and directly detected by electrostatic deflection of the doped nanodroplet beam. We find that they form dipole-aligned dimer and trimer structures, steered by long-range electrostatic interactions. The formation mechanism and the magnitudes of the dipole moments are in good agreement with calculations describing molecular interactions and structure formation in the viscosity-free cryogenic environment. For Imidazole, we find that strongly polar structures are formed in the droplet environment in agreement with theoretical predictions. The strong dipoles derive from the IM molecules arranging themselves into highly polar linear chains facilitated by a strong proton bond between the nitrogen atoms in adjacent rings. The same bond is responsible for the dominance of proton transfer upon excitation, as observed in our mass spectra. 130 The deflection technique can also be used to determine the origin-complex of peaks in the mass spectrum. The imidazole measurements show that dimers and trimers extensively fragment upon ionization, with the dominant channel being the formation of the protonated imidazole ion. This fragmentation tracing technique can be extended to larger systems, by using precise vapor pressure control in the pick-up cell in order to generate a sequence of incrementally larger oligomers within the nanodroplets. Since the electric dipole moment is sensitive to the geometric structure of a molecule and its charge density distribution, deflection measurements can serve as a valuable complement to spectroscopy and mass spectrometry of molecular complexes, including oligopeptides and clusters of heterocyclic compounds. This has been illustrated, for example, in experiments on gas-phase peptides [174]. The use of helium nanodroplet isolation extends this approach by enabling the formation of a variety of complexes using successive pickup steps, and by simplifying the deflection analysis thanks to freezing out the vibrational degrees of freedom of nonrigid systems. An interesting future extension to this process would be to use fields or lasers in the pick-up chamber in order to steer the formation of particular molecular agglomerates, where the final structure of the system could be verified using deflection. 131 Chapter 5 – Probing the Presence and Absence of Charge Transfer in Metal-Fullerene Systems This chapter is based on our published work. Text and figures are reproduced with permission from the Royal Society of Chemistry (RSC): J. W. Niman, B. S. Kamerin, T. H. Villers, T. M. Linker, A. Nakano, and V. V. Kresin, “Probing the presence and absence of metal-fullerene electron transfer reactions in helium nanodroplets by deflection measurements”, Physical Chemistry Chemical Physics 24, (2022) 10378. [86] Metal-fullerene compounds are characterized by significant electron transfer to the fullerene cage, giving rise to an electric dipole moment. We use the method of electrostatic beam deflection to verify whether such reactions take place within superfluid helium nanodroplets between an embedded C60 molecule and either alkali (heliophobic) or rare-earth (heliophilic) atoms. The two cases lead to distinctly different outcomes: C60Nan (n=1-4) display no discernable dipole moment, while C60Yb is strongly polar. This suggests that the fullerene and small alkali clusters fail to form a charge-transfer bond in the helium matrix despite their strong van der Waals attraction. The C60Yb dipole moment, on the other hand, is in agreement with the value expected for an ionic complex. Some related unpublished work with C60 and the alkaline earth metal, magnesium is also shown here, though the results are somewhat speculative and further work is required on this system for a complete picture. 5.1 Introduction Since their discovery in 1985 [175], fullerenes have generated scientific attention in molecular physics and chemistry, materials, and nanoscience. Later study of alkali-doped fullerides and their superconductivity [176,177], demonstrated that metal atom-fullerene structures with significant charge transfer are readily formed in the bulk, surface [178], and gas phases [179–181]. Gas-phase studies are informative because they permit a molecular-level analysis of the charge transfer process. The formation of an ion pair implies the appearance of a large dipole moment, and indeed studies of fullerene-alkali systems by molecular beam electric deflection [126] have demonstrated high electric susceptibilities related to extremely large (~10–20 D) dipole moments in these 132 systems. Interestingly, these experiments showed that at higher temperatures the alkali metal atoms and clusters appear to skate about the surface of the fullerene. Analogously, complexes of C 60 with transition metals were found to have dipole moments of 6-10 D [182]. Helium nanodroplet embedding offers a method to assemble and study such systems at very low temperatures and within a superfluid environment [10]. Rotational and vibrational motion are greatly suppressed at the nanodroplet temperature of 0.37 K and the configuration of the fullerene-metal system is frozen in place. If a polar complex is formed in can be strongly oriented by an external electric field and interrogated by electrostatic deflection [79]. However, there is a hurdle: alkali atoms are strongly heliophobic and are not wetted by the helium medium [183]. Alkali atoms and small clusters are unable to overcome Pauli repulsion between s valence electrons and do not submerge into helium nanodroplets and instead reside in surface dimples [37,39,184,185]. For sufficiently large alkali clusters however, van der Waals attraction becomes strong enough for the cluster to be encapsulated by a bubble and solvate in the droplet [184]. For Na clusters in particular, the predicted threshold size for submersion is 21 Na atoms [186] and this value was later experimentally confirmed [187]. Recent work by Renzler et al. [188] provided evidence, based on electron ionization mass spectrometry, that co-doping helium nanodroplets with the highly polarizable C60 molecule induces Na atoms, as well as small clusters of Na and Cs, to submerge into the nanodroplet. Figure 5.1 shows a cartoon of the joint fullerene-alkali system of interest embedded in a helium droplet. Specifically, the authors demonstrated that the (C60)2Nan=1–2 + and (C60)2Cs2 + ion yield scaled with rising electron energy, indicating that the measured signal comes from charge transfer from He + inside of the droplet rather than direct surface ionization. The authors note that their result was unaffected by the number of fullerene molecules in the detected signal. It was suggested that 133 submersion of the alkalis could derive from the strong long-range van der Waals attraction between the partners [189] or from electron transfer via a harpoon reaction. A follow-up computational study [190] suggested that harpoon-type charge transfer does take place between Cs2 and fullerene dopants. Figure 5.1: A cartoon showing the embedded alkali-fullerene system of interest, where here the alkali resides above the fullerene. Generally, alkali atoms will reside on the surface of the droplet, but by pre- doping the droplet with a polarizable fullerene molecule, the alkali atom may be drawn inside of the droplet. The presence or absence of an ion pair within a nanodroplet can be directly established by the electrostatic deflection method. In this chapter we first apply it to the sodium-C60 system and demonstrate that for C60Nan=1–4 there is in fact no evidence of a strong electric dipole appearing in the system, and hence of the partners approaching closely enough to form an ionic bond. For a comparative measurement, we performed a deflection measurement for nanodroplets doped with C60 and ytterbium atoms. Yb was chosen due to the combination of a favorable 134 ionization energy and vapor pressure. It is also pertinent that ytterbium-intercalated fulleride conductors have been synthesized [191] and were found to exhibit superconductivity. While to the best of our knowledge Yb previously has not been used as a nanodroplet dopant, it is unambiguously expected to solvate, analogously to Eu, another rare-earth atom [192]. Here we observe a sizable deflection indicative of the formation of a large electric dipole. The magnitude of the dipole is in very good agreement with the computed dipole moment for a Yb atom positioned on a pentagonal face of the fullerene, implying that an electron is readily transferred and a bound C60Yb system is formed. An additional set of measurements were collected droplets doped with C60 and magnesium. These measurements are unpublished and incomplete, but preliminary work shows potentially interesting behavior, though our deflection results are currently inconclusive. This added section represents a potential for future work related to this project and may be of use to the reader. In contrast to Na atoms which sit on the surface of the droplet, the energetically favorable position for Mg atoms in helium droplets is more ambiguous. A model for solvation [193], uses a dimensionless parameter 𝜆 = 2 −1/6 𝜌𝘀 𝑟 𝑚𝑖𝑛 𝜎 −1 to determine the favorability of a surface or solvated state in superfluid helium. In this model, 𝘀 and 𝑟 𝑚𝑖𝑛 give the well depth and equilibrium separation of the interaction potential between the helium and dopant, while 𝜎 and 𝜌 give the surface tension and density of the helium medium. Mg has a value of 𝜆 near the critical valve for solvation and thus it is difficult to model the likelihood of solvation accurately [194]. Mg has been experimentally shown to enter helium nanodroplets [194,195] and previous Penning ionization experiments suggest that single Mg atoms will find an equilibrium position close to the surface [196]. Doping a helium droplet with multiple Mg atoms is also shown to form a metastable foam with each atom separated by a helium layer [11]. The solvation behavior of Mg is unusual, 135 and may act as a bridge between the alkali metals and other metals as far as interactions with C 60 in the helium is concerned. 5.2 Experimental A supersonic beam of helium nanodroplets is generated by expansion of ultrahigh purity grade helium gas at 80 bar stagnation pressure through a 5-micron nozzle held at a temperature of 15 K. The beam is skimmed, and chopped by a rotating wheel; the beam velocity is measured to be ≈375 m/s. It then passes through two heated stainless steel pick-up cells, with the first containing C60 powder (99.9%, Solaris ChemTech) and the second a small lump of Na (99.99%, loaded under hexane to combat oxidation), Yb chips (99.95%, Luciteria Science), or Mg lumps and powder filed from a large rod (99.9%). The dopants are picked up by sequential collisions with the droplet beam and their thermal energy is promptly dissipated by partial evaporation of the droplet [10]. The pick-up process follows Poisson statistics. The cell temperatures were stabilized to optimize the signal to a desired average number of dopants. The temperature of C60 was generally fixed to a value between 370˚ C and 380˚ C. This yielded sufficient intensity in the mass spectrum at the single C60 + mass while keeping the intensity of the C60 dimer to a negligible level. At this temperature many of the fullerene’s vibrational modes [197] are activated, hence pick-up of one molecule results in the nanodroplet shrinking by ≈9000 He atoms, limiting the nanodroplets from the likelihood of multiple fullerene pick-up events. Deflection measurements of C60Nan were taken with the metal-containing cell temperature ranging from 190˚ C to 210˚ C, and of C60Yb with this cell at 360˚ C. A subset of the Mg measurements utilized smaller droplets from a nozzle temperature of 17 K, and a lower C60 temperature of 350˚ C was used with Mg held at 335˚ C in the smaller droplet condition and 365˚ C for larger droplets. For each metal, it was found that the 136 signal stability was improved by initially heating the metal to a point higher than the final stabilization temperature. The Na was initially heated to 260˚ C, Yb was initially heated to 420˚ C, and Mg was heated to 400˚ C. The fullerene powder signal stabilized after roughly an hour at the measurement temperature after decaying from an initial intensity. It was also found that the fullerene powder was sensitive to small fluctuations in temperature when using a PID controller to heat the pick-up cell, so a constant current applied to the cartridge heaters was adopted to heat the cell. The beam then travels to the deflection chamber where it is collimated by a 0.25 mm by 1.25 mm slit, and passes between two 15 cm-long high voltage electrodes which create an electric field and a collinear field gradient directed perpendicular to the beam axis. With an applied voltage of 20 kV, a field strength of 82 kV/cm with a gradient of 338 kV/cm 2 is achieved [96]. The nanodroplets then traverse a 1.25 m free-flight region and enter the aperture of a quadrupole mass spectrometer (Ardara Technologies). The droplets are then ionized by electron impact with an electron energy of 70 eV and detected using a pulse-counting channeltron multiplier with a digital counter system synchronized to the chopper [98,198]. These experiments were the first successful measurements with this detection arrangement on the helium apparatus. It was found that deflection profiles can be acquired even with counting rates as low as a few per second. In the C60Yb and C60Mg measurements an additional slit (1.25 mm width) was placed in front of the 5 mm quadrupole mass spectrometer aperture to improve the spatial resolution of the beam. In the C60Nan measurements this slit was omitted to improve the signal intensity, and it was found that the deflection was negligible, eliminating the need for the additional slit as beam broadening does not affect the result or its interpretability in this case. Additional details and simulations can be found in Appendix E. 137 Deflections profiles are collected by translating the detection chamber on a precision linear slide controlled by a stepper motor under two conditions: “field-off” and “field-on”. As discussed previously, the former condition measures the spatial shape of the beam without the influence of the dipole moment of the object inside of the droplet. The latter profile is compared with the former to extract the magnitude of deflection from the deviation of the beam when exposed to the electric field. 5.3 Results and Discussion Mass spectra and deflection measurements, as well as the dipole moment measurements for C60Yb are presented and discussed separately below. Among the peaks in the mass spectrum there are those which correspond to bare C60M + ions, where M is a metal atom or cluster. These ions are ejected from the droplet following charge exchange with a He + hole generated by electron- impact ionization [37]. Note that they may derive either from post-ionization encounters between C60 + and M (or between C60 and M + ), or from the ionization of bound C60M complexes preformed in the nanodroplets. The aim of the measurement is to ascertain whether nanodroplets contain any polar complexes of the latter type, formed by a charge transfer reaction. It is worth reiterating that the deflection step occurs before ionization of the beam, and therefore the reactants and the complexes are electrically neutral. 5.3.1 Sodium Figure 5.2 displays the C60Nan mass spectra over the temperature range used for deflection measurements. The peak widths are partially due to the presence of 13 C isotopes in the fullerene, which causes the fullerene to be detected at a mass one amu higher roughly 30% of the time, and 138 two amu higher roughly 10% of the time. Note that the ion signals are quite weak compared to the intensity of the bare fullerene peak. The C60Na + signal is the weakest of all, including at cell temperatures outside of the range shown. Thus, sodium has a low propensity for forming bound complexes with C60. To determine whether they ever establish direct contact as neutral dopants, we look for evidence of the formation of a dipole moment. Electrostatic beam deflections were performed at the temperatures shown in Figure 5.2. At these settings a given mass peak acquires sufficient intensity for a profile measurement, while the larger ones remain weak, minimizing the likelihood of their fragmentation contaminating the peak of interest. This strategy could not be adopted for C60Na due to its low peak intensity but was followed for C60Na2-4. Figure 5.3 shows the undeflected and deflected beam profiles acquired with the mass spectrometer set to the C60Nan + peaks. For all measured n the deflection is essentially negligible within the accuracy of the measurement. This is in striking contrast with the 14–16 D dipole moment of the ionic C60Na molecule [182,199], which would have resulted in deflections on the order of several millimeters 19 , and confirms that no charge-transfer bound complexes between the fullerene cluster and the sodium atom form within the nanodroplet. Note that the average nanodroplet size in this work is approximately 25 times smaller than in Ref. [188], and the average radius is therefore almost three times smaller ( 60 Å vs. 175 Å) [10]. It is evident that this decrease in separation does not facilitate a charge-transfer reaction. 19 While Figure 5.2 shows that water, which is a ubiquitous contaminant in vacuum systems, is also present in the beam, the fact that there are no noticeable C 60Na nH 2O + peaks indicates that the detected beam profiles are uncontaminated. Furthermore, even the adsorption of a water molecule would not be enough to extinguish the enormous predicted dipole moment of the fullerene-sodium system. 139 Figure 5.2: Mass spectra of C 60Na n + ions with the corresponding Na pick-up cell temperatures indicated. All spectra are scaled to the intensity of the C 60 + peak. The C 60Na + signal is weak for all temperatures. The gray peak is the C 60-water complex. Panels (a) and (b) show the conditions used for deflection measurements of the C 60Na 2 + and C 60Na 3 + peaks, respectively, while (c) gives the conditions for C 60Na + and C 60Na 4 + deflections. 140 Figure 5.3: Beam deflection measurements for nanodroplets containing C 60Na n=1–4. Circles (crosses) denote data points with the electric field turned off (on). The counting rates of selected ions in the strongly collimated beam were on the order of a few per second. The solid-line profiles are smoothing fits to the “field-off” data points using a symmetric pseudo-Voigt function [106], while the dashed lines are asymmetric pseudo-Voigt fits to the “field-on” data. In all cases the beam deflection is negligible. 141 5.3.2 Ytterbium The case for fullerenes and Yb atoms is qualitatively different. This was already hinted at by the mass spectra shown in Figure 5.2, where the ratio of the C60Yb + :C60 + peak intensities was an order of magnitude higher than for C60Nan + :C60 + , indicating that the Yb may find the fullerene more easily. Deflection measurements demonstrate that the situation with Yb is clearly different. Figure 5.4(a) shows the “field-off” and “field-on” profiles of the C60Yb + ion peak. A very sizable deviation is immediately evident, in contrast with the results for sodium, and establishes that the embedded complex has a large permanent electric dipole moment. Following the fitting procedure described previously, we deduce the magnitude of this dipole moment. The deflecting force is proportional to the degree of orientation induced by the applied electric field onto the molecular dipole. Since the rotational constant of the C 60Yb complex is small, it is accurate to use the classical Langevin-Debye expression for the orientation cosine [200,201]. Indeed, the fullerene rotational constant is 0.003 cm -1 [202] and that of the surface-bound Yb atom can be estimated by approximating its radial coordinate by the radius of C60. The result is 0.024 cm -1 = 3.5 mK, which is two orders of magnitude lower than the nanodroplet temperature, and therefore many rotational states are occupied. For the given electric field strength, nanodroplet temperature, and the dipole moment quoted below the orientation cosine is 0.98 indicating that the complex becomes essentially completely oriented along the field. Since both pick-up cells are occupied in these experiments, the sizes must be calibrated in a separate experiment performed shortly after the original. The initial nanodroplet size distribution in the beam is calibrated by deflections using a dopant with a known dipole moment, in this case CsI. For the conditions employed in the present measurements, the mean size was found to be ≈2×10 4 helium atoms per droplet. 142 Figure 5.4: Panel (a) shows the beam deflection measurements of nanodroplets containing C 60Yb with the same notation as Figure 5.3 A slight offset of the second pick-up cell added minor skewness to the profiles, hence in this figure both the “field-off” and the “field-on” data were fit to an asymmetric pseudo-Voigt profile. The shift of the profile centroid is ≈1.4 mm. Panel (b) shows the same “field-on” profile (dashed line) and data points, together with the Monte Carlo simulation (solid line) for the optimized dipole moment value of 8 D. 143 Figure 5.4(b) displays the result of the optimized fit and demonstrates good agreement with the experimental data. Based on this procedure we assign a dipole moment of 8 ± 1.5 D to the C60Yb complex. The estimated error bar derives largely from the data fit and partially from the uncertainty in the branching ratio involved in the charge exchange between He + and the dopant. Figure 5.5 displays the computed error in dipole moment fit as a function of dipole moment for each of the two charge transfer parameters described in Chapter 3. The probability of charge transfer takes the form exp ( −𝛾 𝑁 1/3 ) where 𝑁 is the number of helium atoms in a given droplet and 𝛾 is the charge transfer parameter determined to be in the range ≈0.06-0.12 [79]. This range translates into an uncertainty in the average nanodroplet size and, correspondingly, in the magnitude of the dipole moment. In both cases, the optimal fit is found for a dipole magnitude of ≈8 D, and the uncertainty derives from the range of error-minimizing values. The quality of fit from the simulated deflection values is shown for bounds of 6-10 D in Figure 5.6, alongside the asymmetric pseudo-Voigt fit of the experimental deflection profile. The simulated profiles are presented assuming 𝛾 =0.12, though qualitatively these fits are identical for values of 𝛾 within the stated range above. The deflection result unambiguously demonstrates that the rare earth metal atom contacts and donates charge to the fullerene. Independent of the exact magnitude of the dipole moment, the relatively robust deflection confirms that a polar object is formed in the droplet in the C60Yb + mass channel. 144 Figure 5.5: Root mean square deviation between the C 60Yb profile data and the deflection simulation as a function of the assumed dipole moment of the complex. Crosses and circles correspond to dopant ionization probability parameters (described in the text) 𝛾 =0.06 and 𝛾 =0.12, respectively. 145 Figure 5.6: The crosses are beam deflection data points for nanodroplets containing C 60Yb, and the dashed line is a smoothing fit to these points using an asymmetric pseudo-Voigt function. The colored lines are the results of Monte Carlo simulations assuming three different values of the dipole moment of the complex and a dopant ionization probability parameter 𝛾 =0.12. As shown with the theoretical calculations below, the experimentally deduced value of the dipole moment is in good agreement with a calculation of the C60Yb complex, in particular for Yb atoms positioned at the pentagonal face of the fullerene. According to the computation, this situation has a marginally advantageous binding energy (although it is known that systems embedded in helium nanodroplets are not always able to reach their lowest energy geometries). Measurements of crystalline fullerene-ytterbium compounds suggest that the pentagonal face indeed is preferred for charge transfer [191,203], supporting our results. 146 5.3.3 Magnesium In contrast to what was seen with sodium and fullerenes in helium droplets, the C 60Mg + ion peak is clearly visible in the mass spectrum. With reasonable doping conditions the ratio of the fullerene mass peak to the fullerene-magnesium peak is ~10, indicating that the two are apparently able to make contact in the droplet. Figure 5.7 shows three overlapping mass spectra utilizing three sets of deflection conditions used to explore the system. The blue mass spectrum uses a nozzle temperature of 17 K, and therefore smaller droplets on average than the other two spectra taken at 15 K. For the yellow spectrum, secondary mass peaks corresponding to higher order Mg peaks and the same with the attachment of water (or water-related complexes 20 ) are easily visible. Whereas the green mass spectrum was taken some time later after the Mg signal had decayed, and in this case the C60MgH2O + peak is relatively prominent. Additional doping conditions are provided in the figure caption. One deflection measurement for each spectrum in Figure 5.7 was taken, and the colors of the deflection profiles match the relevant spectrum. Figure 5.8 shows these deflections, where (a) and (b) represent the C60Mg + mass peak with two distinct droplet sizes (smaller and larger, respectively), and (c) shows a deflection of C60MgH2O + under the latter conditions. The behavior is peculiar: the fullerene-magnesium mass peak clearly deflects more with the larger-droplet condition, which is counterintuitive if the same polar complex is formed in each case as more massive droplets should display weaker deflection. Based on the difference in centroid between the zero-field and deflected profiles, the deviation in Figure 5.8(b) is roughly three times that of Figure 5.8(a). Moreover, the deflection of the C60Mg + mass peak for smaller droplets is only ≈0.2- 20 Oxygen also overlaps in this region of the mass spectrum, though there is evidence in helium droplets that magnesium complexes are formed without oxidation [184]. 147 0.3 mm, which is not indicative of the formation of a particularly polar object. From this deflection measurement, it would appear that there is not a strong charge transfer taking place, though it is unknown as whether this is due to a small dipole moment or an inability for the Mg and fullerene to make contact prior to ionization due to a possible helium layer [11]. Figure 5.7: Mass spectra of the fullerene-magnesium system under different doping and droplet conditions used for deflection measurements. Note that the added water complexes may include or be missing additional hydrogen atoms from fragmentation of water complexes. The blue spectrum has the C 60 held at 350˚ C and Mg held at 335˚ C and uses a nozzle temperature of 17 K. The yellow and green spectra use larger droplets with a nozzle temperature of 15 K and have the magnesium held at 365˚ C and C 60 held at 350˚ and 375˚ C, respectively. These spectra were taken in early experiments with C60, and thus the stability decayed in time. The C 60 signal intensity at the doping conditions used was ≈12000, 9000, and 9000 (a.u.) for the blue, yellow, and green curves, respectively. Labels for mass peaks of intertest are included. The case is clearly different in Figure 5.8(b) where larger droplets are utilized. Here there is a visible deflection, though weaker than observed for the C60Yb system. The larger deflection measured for larger droplets on the same mass peak is inconsistent with the formation of C60Mg 148 in the droplet if the deflection in Figure 5.8(a) represents this outcome. The mass spectrum in Figure 5.7 demonstrates that larger order Mg clusters and water complexes are present in the beam when larger droplets were utilized. This is consistent with the larger cross-section of the droplets and the increase in Mg doping temperature. A resolution to the apparent increase in deflection measured for larger droplets is that the larger dipole moment arises due to contamination from larger order Mg clusters and/or the addition of water-complexes. This claim is partially evidenced by the deflection of the C60MgH2O + mass peak in Figure 5.8(c), where the magnitude of deflection is approximately equal to the C60Mg + mass peak with the same droplet sizes. The deviation of the centroid in each case is ≈0.7-0.8 mm. The exact source of the deflection and dipole moment for the latter two deflections cannot be determined without additional experiments. It is unfortunate that the doping conditions changed between these deflections due to decay in dopant signal and the C60 cell was heated in the latter case, so the comparison is not precisely one-to-one. The increased broadness of the profiles in Figure 5.8(c) may be attributed to the higher C60 temperature, or additional collision events. 149 Figure 5.8: Deflection measurements for the ion peaks listed under droplet and doping conditions outlined in Figure 5.7 and the profile color matches each spectrum. (a) utilizes smaller droplets but sees a lower deflection magnitude than (b) or (c). The relative broadness in (a) is explained by smaller droplets, while in (c) it comes from additional collision events and hotter dopants on average. Deflection magnitudes as measured by centroid shift for (b) and (c) are comparable. The fit lines are pseudo-Voigt functions. 150 From the present data, the influence of the water-complexes and higher order Mg cluster dopant cannot be disentangled. Some water is clearly present in the deflections with smaller droplets and could contribute to the small deflection measured. However, water molecules are not confined to entering the droplets in the pick-up chamber, or even before the deflection plates, and thus their influence on the deflection of the droplet is also difficult to attribute. A future experiment utilizing deuterated water molecules could help lift this limitation. It would appear that the addition of water or additional Mg molecules does lead to the formation of a polar object in the droplets, in contrast to the case where only C60Mg is likely and a nonpolar or only weakly polar object is formed. Theoretical calculations below indicate that the formation of a weakly polar system is possible, though further experiment is needed to fully confirm the computation. 5.4 Calculations of Structure and Dipole Moment To further validate the result for C60Yb, the dipole moments and binding energies of free- space molecules were computed 21 by plane-wave based Density Functional Theory (DFT). Calculations were performed in the Vienna Ab-Initio Software Package (VASP) [204,205]. Electronic states were computed within the frozen core approximation using the projected augmented wave-vector (PAW) method [206,207] with projectors generated for the Carbon 2s and 2p states and the Yb 6s and 5p states. The strongly correlated Yb f electrons were assumed not to be involved in bonding and were kept within the core of the pseudopotential. A plane wave cut- off energy of 500 eV and the Perdew–Burke–Ernzerhof (PBE) [208] styled generalized gradient approximation (GGA) for the exchange-correlation functional were used. The C60 and C60Yb 21 Here we once again thank our computational physicist colleagues, Thomas M. Linker and Aiichiro Nakano, for their assistance here. Even as an experimentalist it is certainly advantageous to take a computational physics course and make friends! 151 molecules were placed in the center of a non-cubic 15 Å 18 Å 20 Å box to remove spurious image interactions. Optimization was first performed on the C 60 molecule to obtain its ground state structure. For computation of the binding energies and dipole moment the ground state C60 structure was kept frozen during the optimization of C60Yb. Linear dipole corrections were used to correct the errors introduced by the periodic boundary conditions [209]. The results of these calculations are presented in Table 5.1 alongside similar ones for the dipole moment of isolated C60Na and C60Mg. The calculations for sodium are in reasonable agreement with previous computations [199] and partially validate the present results for C60Yb. As mentioned in the preceding section, it is found that settling the Yb atom on the pentagonal face yields a marginally higher binding energy and a noticeably lower dipole moment. The computed dipole moment is small for Mg, in partial agreement with the experimental data. Dipole moment (D) Binding energy (eV) Pentagon Hexagon Pentagon Hexagon C60Yb 8.5 13 0.58 0.54 C60Na 13.4 12.8 1.16 1.21 C60Mg 0.96 0.11 0.16 0.14 Table 5.1: DFT calculations for the dipole moment and binding energy of a Yb, Na, or Mg atom optimized on either the hexagonal or pentagonal face of the C 60 fullerene. 152 5.5 Conclusions The experiments detect no sizable electric dipole moment appearing when a fullerene molecule, followed by between one and several sodium atoms, are embedded in helium nanodroplets. Therefore even if a heliophobic alkali atom is pulled inside the nanodroplet by the presence of C60 [188], it appears that they continue to be separated by a helium barrier and neither short-range electron transfer nor a longer-range harpoon reaction take place. The measurement does not provide information about the size of this separation barrier, and therefore an interesting question for further theoretical and experimental analysis is whether the Na atom and C 60 form a weakly bound van der Waals-type complex, and how far apart they remain. As for the absence of an electric dipole moment for C60Na2-4, one can envision two scenarios. One is that the sequentially picked up atoms assemble into a small sodium cluster on or near the droplet surface but still fail to approach the fullerene within the droplet sufficiently to transfer charge and form a bond. This contrasts with C 60Nan agglomerates forming in neat molecular beams [94]. An alternative possibility is that multiple sodium atoms do attach to the fullerene but arrange themselves in symmetric configurations, as calculated for lowest-energy structures due to Coulomb repulsion between positive sodium ions [199]. This cannot be excluded, but would require either a sequence of individual atom-C60 agglomeration events (which appear unlikely within the nanodroplets in view of the data), or attachment of a Na cluster followed by its separation into individual atoms and their subsequent rearrangement around the cage (which, however, would need to proceed in the very low-temperature nanodroplet environment). Consequently, the data do not support the theoretical picture [190] of an alkali dimer undergoing a harpoon reaction with C60 and settling into an ionic arrangement with the latter. 153 In contrast to sodium, we observe that a very strong permanent dipole moment is formed between ytterbium atoms (which are wetted by helium) and C60, revealing successful electron transfer and bond formation in this system. Comparison with modeling of the C60Yb molecule suggests that the ytterbium atom prefers to locate above the pentagonal face of the fullerene. Interestingly, while the harpoon reaction is suppressed in binary collisions in the gas phase [189] due to unfavorable Franck-Condon factors [210], in the present case the strong reactive channel is kept open thanks to removal of the accompanying vibrational excitation by the helium matrix. It would be interesting to extend such measurements to larger alkali clusters, because above a certain critical size they begin to submerge into the nanodroplet by themselves [186,187]. This should promote charge transfer and dipole formation, analogous to observations on C 60-alkali cluster complexes in free space [126]. Interesting complementary information also could be derived from spectroscopic experiments, since near-IR absorption peaks of the fullerenes have been shown [211] to be sensitive to the oxidation state of C60 n– . Additional study of the sodium- fullerene system would also be useful with the inclusion of a laser, where excitation of the sodium atoms could induce charge-transfer. Further study of this system as a function of droplet size may also be stimulating, where some critical droplet size may also permit charge-transfer to the fullerene for a single Na atom. The preliminary results for magnesium and fullerenes suggest that future work on this system may be productive. In the more controlled single-Mg doping condition we find what is likely a weakly polar system in agreement with the theoretical calculations performed. This is a possible indication that the fullerene successfully pulls the Mg atom inside of the droplet and the two make contact. However, with less-controlled doping where larger-order Mg clusters or water complexes may contribute to the structure of the embedded system, a moderate deflection 154 magnitude is observed for both the C60Mg + and C60MgH2O + ion channels. Some degree of charge- transfer must occur in these systems to induce the deflection, though the influence of water versus larger magnesium clusters is presently unknown. Magnesium agglomerates as small as the dimer have been shown to be metastable in helium droplets [11] and recent work on embedded magnesium foams [107,212] explore stability and suggest that highly excited states may form when the foam collapses. The interplay of this strange behavior with an embedded fullerene is unclear and poses an opportunity for future work in this system. It would also be interesting to explore the scaling of the dipole moment of the system as the number of magnesium atoms is increased. 155 Chapter 6 – Summary and Future Work 6.1 Summary of Key Results Thus far we have demonstrated the merit of the electrostatic deflection of helium nanodroplets technique with a number of projects and experiments [76,79,83–85,87]. We have shown: (i) robust electrostatic deflection of neural, doped helium droplets, (ii) measurements of dipole moments of embedded molecular complexes, (iii) the formation of metastable dimethyl sulfoxide structures formed by dipole-dipole interactions in the droplet, (iv) a confirmation of the formation of highly polar linear chains in embedded imidazole complexes as well as an assignment of fragment parentage, (v) an examination metal-fullerene charge transfer (or lack thereof) in the helium droplet medium, and, (vi) size filtering by position and an application to modeling charge transfer probability from the helium matrix to the dopant as a function of droplet size. The electrostatic deflection technique serves as a strong complement to other methods used in helium nanodroplet isolation. It is also a novel extension of molecular beam deflection, utilizing the many advantages of helium nanodroplets: primarily the ability to cool dopant systems to their lowest rotational and vibrational states [10] and therefore achieve a high degree of orientation [14,79] in an electric field leading to a strong deflection force, even for polyatomic systems. Size filtering provided by deflection presents an opportunity to study embedded objects as a function of system size and could be used in-tandem with other techniques such as spectroscopy [39,44,194], diffraction-imaging [48,137,213], or deposition [214–216]. Our machine is the first of its kind for electrostatic deflection of helium nanodroplets. The technique is also easily scalable to more complicated embedded systems, and limited mainly by the size of the helium droplets and degree of polarity of the embedded system. 156 Fortunately, many molecules can be easily doped in small droplets suitable for deflection [12,107]. The deflection technique also becomes more powerful with the extension of the free-flight path (an upgrade which was completed following the measurements described here) or an increase in the electric field gradient [76,91], increasing the resolution of what can be discerned from the deflection or allowing the assembly of larger embedded systems in larger droplets. Of course, the experiments discussed represent a small subset of possible systems to explore and helium nanodroplets are broadly capable of embedding almost any molecular system [10,55] for subsequent study. In the previous chapters some proposed experiments were discussed for future experiments in similar systems (e.g., further work on fullerene-magnesium systems). Some ongoing and future experiments in systems-of-interest are outlined below. 6.2 Potential Future Experiments Helium droplets provide an ideal tool to study processes that involve step-by-step addition of dopants to molecular systems. A particularly interesting application is understanding the elementary steps involved in acid solvation. We can embed an acid molecule within a droplet, followed by doping with a variable numbers of water molecules [144]. By measuring the dipole moment of the combined system, we may detect the number of water molecules required to break up the acid. Previous work from our group attempted to find the number of water molecules required to dissociate deuterium chloride (DCl) by deflection of doped water clusters [198]. Where DCl (instead of hydrochloric acid) was utilized to disentangle the acid-water mass peak from neat water peaks in the mass spectrum since the Cl atom is lost during electron-impact ionization. Here, a change in electric dipole moment, indicating a separation of charge, was used as a hallmark of acid dissociation for the acid-water clusters. Dipole moments were calculated by measuring the 157 cluster polarizability, and a jump in the dipole moment was found for acid-water clusters containing 5-6 water molecules [98,198]. However, a follow-up paper relying on ab initio path integral simulations computed geometries and dipole moments for the mixed clusters under the previous experimental conditions [217]. It found that at 200 K, the temperature of the water clusters, both dissociated and undissociated acids would be found in the water clusters with four or more water molecules. Further, the water molecules could even rearrange themselves to screen the large dipole moment to be expected from the charge separation of the dissociated acid. They concluded that the size of the electric dipole could not be used as an indicator of acid dissociation in the water clusters [217]. However, we may experience a different scenario in the cold helium droplet medium. At the very low droplet temperature the accessibility of dissociated and un-dissociated water-acid structures will be limited, and our ability to orient and deflect the resulting “locked-in” dipole moment [84] may provide conclusive evidence for dissociation. Recent IR spectroscopy studies have shown evidence of HCl-dissociation in HNDs through the formation of hydronium (H3O + ) with the addition of four water molecules, indicating that the acid is broken up [218–220]. In fact, the most recent study showed that the acid dissociation is dependent on the water-acid doping order, suggesting that the dopants are quickly frozen into specific formation [220]. With our deflection technique we can directly measure the dipole moment of the formed acid-water structure, providing complementary measurements and providing a definitive answer to whether or not the dipole moment can distinguish the dissociation of the acid. On the topic of changing structure in helium droplets, it would be both useful and interesting to steer the assembly of nanostructures formed in the droplet through the use of external fields. Experiments in Chapter 4 described the formation of metastable states formed in DMSO 158 dimers and trimers [84] influenced by mutual dipole-dipole interactions. In this case, the reaction outcome was uncontrolled, and the ultimate configuration was determined by the reactants and the metastable state assembled was forced by the cold environment and mutual dipole-dipole forces. A similar outcome was found in helium droplets doped with formic acid dimers [139] where a polar state is formed by long range dipole-dipole interactions and is caught in a local minima of the potential energy surface. Accompanying calculations demonstrated that the optimized dimer structure is dependent on the initial relative orientation of the individual molecules. A novel extension of these experiments could utilize external fields to guide the formation of nanostructures by pre-orienting the reactant molecules [221,222]. The combination of the droplet environment permitting the formation of metastable states and the use of external fields to provide a handle on the dopant molecules could be used to grow specific nanostructures. While the addition of an electrostatic field in the pick-up region of the machine would be a non-trivial upgrade, we have already shown that polar molecules can be strongly oriented at the droplet temperature [79,83] which would provide consistent interaction conditions. The deflection technique also provides the ability to directly check [84] the structure formed using the magnitude of its’ dipole moment. Hetero-doping using different pick-up cells and selective use of an external field can be used to synthesize structures that may be impossible to construct outside of the helium nanodroplet medium. Structures in helium droplets also have the potential to be soft-landed in deposition experiments for subsequent study with techniques such as transmission electron microscopy or electron tomography [215,223–225]. Deflection can be used to probe the formed structure in small droplets initially, then the same structure could be grown in larger droplets suitable for soft-landing. 159 6.3 Magnetic Deflection and Preliminary Results With the successes of the electrostatic deflection of doped helium nanodroplets, extending this strategy to magnetic systems could generate valuable physical insights. Extensive deflection experiments on magnetic atoms [69,226], molecules [227,228], and clusters [229–233] have been conducted in the gas-phase, yielding a plethora of interesting results. As in the electric variation, helium droplets present an opportunity to strongly orient embedded magnetic objects in an external magnetic field, and probe the behavior of the system at ≈0.37 K [10]. Until recently, no data existed on the orientation and deflection behavior of molecules embedded in helium droplets. In the summer of 2022 an additional deflection chamber containing a strong permanent magnet with a gradient of ≈334 T/m [88] was installed by B. S. Kamerin and T. H. Villers. Initial experiments were performed with bismuth and europium atoms, but these early deflection attempts were inconclusive as the resulting profiles were difficult to resolve. These systems are likely to be revisited as the earlier attempts used larger droplets than current experiments and the beam alignment and collimator positioning have been improved. Ongoing experiments have focused on another magnetic system, ferrous chloride (FeCl2) [234]. FeCl2 is nearly linear [235] and the chlorine atoms are expected to pull electrons from the iron, leading to a strong magnetic dipole moment similar to Fe 2+ with a magnitude of ≈5.4𝜇 𝐵 [236], where 𝜇 𝐵 is the Bohr magneton. Figure 6.1 shows deflections of FeCl2 + and (FeCl2)2 + using the FeCl + and Fe2Cl3 + fragment ion peaks, respectively. This figure demonstrates the first unambiguous magnetic deflection of doped helium nanodroplets. The magnetic deflection set-up uses a permanent magnet fixed in the vacuum chamber, and thus an undeflected profile for a given ion peak is not available for immediate comparison. The undeflected profile can be approximated by a normalized undoped 160 helium profile, representing the position of the beam. However, the (FeCl2)2 is evidently non- magnetic where the ground state geometry has the Fe magnetic moments aligned antiferromagnetically [237], and therefore acts as a zero-field profile in this system. In our measurements we find that the magnetic “deflection” of the FeCl2 dimer is approximately equal to that of the only weakly diamagnetic helium dimer mass peak as confirmation of this claim. Both of these systems exhibit essentially no deflection. A planned upgrade to the magnetic deflection set-up will introduce an additional collimator in a zero-field region of the magnetic deflection chamber for one-to-one comparison of deflected and undeflected profiles for a chosen mass peak. Figure 6.1: Magnetic deflection of (red circles) FeCl 2 and (blue crosses) (FeCl 2) 2 embedded in helium nanodroplets. The latter profile intensity is normalized to the former. The lines show asymmetric and symmetric pseudo-Voigt functions [106], respectively. The difference in centroids between the two fits is ≈0.80 mm. In contrast to the electric deflection where the beam is deflected towards more positive positions, the magnet is installed to deflect the beam towards more negative positions. The droplets in this experiment were some of the smallest produced in our apparatus and are estimated to have a mean size of ≈ 7000 helium atoms [10]. 161 The magnetic deflection of FeCl2 is robust, and interestingly is one-sided representing strong orientation of the dipole in the magnetic field. This further indicates that the dopant undergoes relaxation and thermalizes with the helium droplet, rather than a beam-broadening stemming from different magnetic spin projections which would deflect the droplets in different directions. The spin relaxation mechanism in the superfluid helium medium is not currently understood, but will be explored in-depth in the dissertation work of my colleague B. S. Kamerin. While not yet fully elucidated, preliminary results on this novel system are an exciting extension of the electrostatic deflection experiments addressed previously. Further experiments are planned to explore other magnetic systems of interest including dimers and trimers of sodium where weakly-bound high-spin states can be stabilized on the droplet surface as opposed to low-spin states where the large binding energy may fragment the droplet [238,239]. Magnetic deflection of these systems can confirm the stabilization of high-spin states, and deflection can be used to confirm the presence or absence of low or no-spin systems on the droplet. It may also be possible to explore this behavior as a function of droplet size. Since the helium machine is now equipped for both electric and magnetic deflections, it is possible to explore dopants with both a magnetic and electric dipole moment. TEMPO is a stable radical possessing an electric dipole moment of 2.8 D [240] and an unpaired electron spin making it a strong candidate for future study. 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These VIs as well as VIs not pictured with annotations can be found in the google drive under prog/VIs, where the “digital counters” variations are generally used with the Ardara Quadrupole. For improved readability and context, it is highly recommended that this code is viewed in the LabVIEW program. Previous versions of VIs utilizing the Balzers quadrupole written by D. J. Merthe are also found in this directory. Many of the current VIs were built on-top of or modified from existing VIs written by D. J. Merthe or N. G. Guggemos and detailed in Refs. [76,98]. The google drive also contains a number of utility sub-VIs utilized in the presented programs. Original versions of these initial VIs can be found in the google drive or in the respective dissertations for further reference. In order, the VIs and sub-VIs here refer to the beam profile and mass spectrum measurements using the digital counters, a utility VI for controlling the quadrupole mass alongside a simple unsynchronized counter for reference, and a second mass spectrum VI for measuring analog signal. For analog beam profile measurements, the original Merthe Beam Profile Measurement VI is recommended. All of these VIs utilize a LabVIEW library designed to interface with the Stanford Research Systems SR830 Lock-in Amplifier. 180 Figure A.1: Front panel for the beam profile measurement VI. A .tsv file containing a list of position points is required as input to define the scanning domain. The phase delay for the chopper is also required to synchronize the detector. The number of scans and wait time are also user-defined. The user is automatically prompted to save all data after the scans have finished executing. 181 Figure A.2: The Run sub-VI constructs and fills the data arrays after each scan. It also communicates the current data to the front panel. This VI has been updated to save metadata and display the lock-in rate, dip, and total count rate. Figure A.3: The Collect Data Counters sub-VI programmatically moves the chamber to a specified position, initializes the counters, and collects data for a user-defined wait time. 182 Figure A.4: Front panel for digital counter mass spectrum VI. Lock-in rate, dip, and total rate are collected as a function of mass. Number of passes, mass range, and number of steps are user-defined. The maximum step resolution with the current equipment is five for each unit mass. The phase delay for the chopper is also required to synchronize the detector. 183 Figure A.5: The sub-VI shown here represents a single spectrum pass and is run repeatedly to collect and average mass spectra. The VI functions by making contact with the lock-in amplifier used to control the mass channel of the quadrupole using auxiliary output voltages. Then, for each mass (or fraction thereof) the counters are initialized, synchronized to the delayed chopper pulse, and collect data. The middle of the panel shows the counter synchronization and collection sub-VIs written by N. G. Guggemos and implemented here. 184 Figure A.6: Front panel for the simple counter and quadrupole mass control diagnostic tool. The mass can also be controlled manually on its power supply, but this VI delivers a constant mass control voltage so that the mass used for beam profile measurements is maximally consistent. The simple counter gives an unsynchronized average count rate used for diagnostic purposes and comparison with the synchronized count rate from the other main VIs. The conversion between mass and voltage is approximately 1 amu to 5 mV. 185 Figure A.7: Block diagram for lock-in amplifier auxiliary voltage control used for mass control of the Ardara quadrupole. The counter block in the middle of the diagram demonstrates the simplest counter control routine and can be used as a reference for the more complicated synchronizing routines. 186 Figure A.8: Front panel for the analog signal mass spectrum VI used with the Ardara quadrupole. The VI requires both lock-in amplifier and scan parameters to function, and uses a similar architecture to the former analog signal mass spectrum VI. This VI also has mass command using the auxiliary outputs of the lock-in amplifier. 187 Figure A.9: Block diagram for the analog signal Ardara quadrupole mass spectrum VI. The construction of this VI is fairly simple and it has only been used for testing purposes in previous experiments. It is fully functional, but modifications may be useful for future experiments if it becomes a primary data acquisition tool. 188 Appendix B – Velocity Measurement Code This appendix includes the Mathematica code used to extract the beam velocity from our multichannel scaler records as described in extensively Chapter 2. The code alongside relevant annotations here can be found in the google drive for the helium project under Logs/Instrumentation/MCS. The main function requires an initial guess for the beam velocity and the MCS record and returns a plot with the fit to the record listing the speed and spread of the beam. Support functions are referenced in the main code and are included below. Note that the addition of the magnetic chamber extended the total length between the chopper and detector to 2.13 m to approximately 2.53 m. This dimension is required for an accurate velocity measurement. -- Main[data_, guessV_] := Module[{undepl, depl, frequency, phase, period, fitRegion, prenorm, normMCS, A, \[Omega], \[Phi], d, soln, L, v, w, t, fitPts, plot, spread, meanVel, cosFit}, L = 2.1336; (*Electric*) (* Distance from Chopper to Detector in meters *) (*L = 2.5336; (* Magnetic *);*) prenorm = PreNormMCS[data]; cosFit = 189 FindFit[prenorm, {A*Cos[\[Omega]*(t - \[Phi])] + d, A > 0, \[Phi] > 0, \[Omega] > 0}, {A, \[Omega], \[Phi], d}, t, MaxIterations -> 1000, Method -> "NMinimize"]; frequency = \[Omega] /. cosFit; phase = \[Phi] /. cosFit; depl = getAverageRegionsMCS[prenorm, frequency, phase][[2]]; undepl = getAverageRegionsMCS[prenorm, frequency, phase][[1]]; normMCS = MCSNorm[prenorm, depl, undepl]; fitRegion = ModifyRecord[normMCS, guessV, frequency, phase, L]; soln = FindFit[fitRegion, {1 - (1/2 (Erf[v/w] + Erf[-(v/w) + (L/(w*t))]) - w/v Exp[-(-(v/w) + (L/(w*t)))^2]), 1 > v > 0, w > 0.001}, {v, w}, t, MaxIterations -> 1000, Method -> "NMinimize"]; meanVel = v*(1 + 3*(w/v)^2 + 3/4 (w/v)^4)/(1 + 3/2 (w/v)^2) /. soln; spread = 100*w/v /. soln; 190 fitPts = Transpose[{fitRegion[[All, 1]], 1 - (1/2 (Erf[v/w] + Erf[-(v/w) + (L/(w*t))]) - w/v Exp[-(-(v/w) + (L/(w*t)))^2]) /. soln /. t -> (fitRegion[[All, 1]])}]; plot = ListLinePlot[{Transpose[{fitRegion[[All, 1]], fitRegion[[All, 2]]}], fitPts}, PlotRange -> Full, GridLines -> Automatic, ImageSize -> 1000, Joined -> {False, True}, PlotStyle -> {Blue, Red}, AxesLabel -> {"Time [ms]", "Normalized Intensity [a.u.]"}, PlotLabel -> "Velocity Fits", PlotLegends -> Placed[{"Velocity"*"m/s"*1000*meanVel, "Spread"*"%" spread}, Below]]; Return[plot]] PreNormMCS[data_] := Module[{preNormData, min, max, mean}, mean = Mean[data[[All, 2]]]; max = Max[data[[All, 2]]]; min = Min[data[[All, 2]]]; 191 preNormData = Transpose[{data[[All, 1]], (data[[All, 2]] - mean)/Abs[(max - min)/2]}]; Return[preNormData]] MCSNorm[data_, depl_, undepl_] := Module[{normMCS}, normMCS = Transpose[{data[[All, 1]], (data[[All, 2]] - depl)/(undepl - depl)}]; Return[normMCS]] getAverageRegionsMCS[data_, frequency_, phase_] := Module[{avgHigh, avgLow, period, i, sumHigh, counterHigh, sumLow, counterLow, pointsHigh, pointsLow}, sumLow = 0; counterLow = 0; sumHigh = 0; counterHigh = 0; period = 2*Pi/frequency; pointsHigh = {}; pointsLow = {}; For[i = 1, i <= Length[data], i++, If[data[[All, 1]][[i]] <= (phase + period/8) && data[[All, 1]][[i]] >= (phase - period/8), sumHigh = sumHigh + data[[All, 2]][[i]]; counterHigh++; pointsHigh = AppendTo[pointsHigh, data[[i]]]]; If[data[[All, 1]][[i]] <= (phase + period/2 + period/8) && 192 data[[All, 1]][[i]] >= (phase + period/2 - period/8), sumLow = sumLow + data[[All, 2]][[i]]; counterLow++; pointsLow = AppendTo[pointsLow, data[[i]]]]; ]; avgHigh = sumHigh/counterHigh; avgLow = sumLow/counterLow; Return[{N[avgHigh], N[avgLow], pointsHigh, pointsLow}]] ModifyRecord[data_, guessV_, frequency_, phase_, L_] := Module[{modData, risingEdge, dataToFit, M, holdM}, modData = Transpose[{Mod[data[[All, 1]] - phase, 2*Pi/frequency], data[[All, 2]]}]; risingEdge = Take[SortBy[modData, First], -Ceiling[Length[modData]/2]]; (* need to sort first in order to take the latter half of the data *) holdM = Solve[L/(0.001*guessV) == M*2*Pi/frequency + phase + Mean[risingEdge[[All, 1]]], M][[1]]; (* Determine Horz. Shift *) dataToFit = Transpose[{risingEdge[[All, 1]] + 2*Pi*Round[(M /. holdM)]/frequency + phase, risingEdge[[All, 2]]}]; Return[dataToFit]] 193 Appendix C – Deflection Simulation Code This appendix contains the deflection simulation code described in Chapter 2. The original deflection simulation code was written by D. J. Merthe and a prior version of the code can be found in the appendices of Ref. [76] alongside the support functions referenced below. No modifications were made to the support functions. Additional prior versions of the deflection code can be found with the representative code below in the helium project google drive in the Simulated Deflection Profile III folder. The code was originally written in Python 2 and recently updated to Python 3 and tested by B. S. Kamerin. -- import csv import os import sys from PySide import QtGui import time from math import exp, sqrt, log, sinh, cosh, floor import numpy as np from scipy import interpolate from scipy.special import erfinv # Modified code to include ionization factor (N^2/3) from scipy.special import erf # Needed for Kinetic Boil-off with JL's Formula import matplotlib.pyplot as plt import sd_functions_b_Hend as funcs #File containing some helper functions; See Merthe Thesis 2017 194 reload(funcs) plt.close() #close any open plot figures ### Global Parameters ### kB = 1.38064852e-23 #Boltzmann constant chiHe = 5.7e-2 #Susceptibility of liquid helium mHe = 6.6464764e-27 #Mass of helium atom in kg eHe = 9.94066934e-23 #Per atom binding energy of helium droplet #eBind = 1.474e-19 #Binding energy of DMSO trimer in J #eBind = 5.6076e-20 #Binding energy for DMSO dimer in J T0 = 0.37 #Temperature of droplet in Kelvin rat = float( raw_input("What Ratio are you using from SimDef?: ") ) #0.649336 originally used ratio of standard deviation to average droplet size v0 = float( raw_input("Average droplet Velocity (Calculated from phase delay): ") ) #average forward (z-direction) velocity -- Variable vx = 0.0 #velocity in the x-direction for a particular droplet; used by Droplet() & Deflection() vz = 0.0 #velocity in the z-direction for a particular droplet; used by Deflection() l1 = 0.15 #length of deflection plates l2 = 1.65 #length of free flight region; 1.25 before magnetic chamber added sw = 1.25 #scanning slit width; currently unused NI = int(1e5) #Max number of trials per position in zero field data NP = int(75) #Number of points in output profile 195 xmin = -10.0 xmax = 17.0 xstp = (xmax-xmin)/(NP-1) pos = np.zeros(NP) #Output Profile prof = np.zeros(NP,dtype=np.float) #Output Profile profHe = np.zeros(NP,dtype=np.float) #Output Droplet Profile sizes = np.zeros(NP,dtype=np.float) #Average size of droplets as a function of position def Droplet(): 'Make droplet of size N, pick up dopant and boil off excess energy' global vx, vz y = np.random.random() thres = 1.0 #1 for log-normal and 0 for exponential if y>thres: #Sample from droplet size distribution N = int(np.random.exponential( aveN )) else: N = int(np.random.lognormal( mu , sig )) vz = np.random.normal(v0, 0.03*v0) #Forward velocity #If there are not enough atoms to boil off, set to zero return N 196 # Deposited kinetic energy equation from J Liang and V Kresin JCP 2020 def JLEquation(N,vz): enTemp = 0.0 vProb = sqrt(2.0*kB*TDop/mDop) xJL = vz/vProb mReduced = (mDop*N*mHe)/(mDop+N*mHe) enTemp = kB*TDop*(mReduced/mDop)*(xJL*(5.0/2.0 + xJL*xJL)*exp(-xJL*xJL) + sqrt(np.pi)*(3.0/4.0 + 3.0*xJL*xJL + xJL**4.0)*erf(xJL))/(xJL*exp(-xJL*xJL)+sqrt(np.pi)*(0.5 + xJL*xJL)*erf(xJL)) return enTemp def Boiloff(N,Molname,vz): # additional molecules added as needed; test is the file with modified rotational constants # JL formula above implemented after the IM experiments, number for other molecules below are here for historical value dN = 0.0 if(molName=='CsI'): ### eDop = 2.0/2.0*kB*TDop # Average rotational degrees of freedom from equipartition (Only two because we have a linear rotor) eDop += JLEquation(N,vz) dN = int(floor(eDop/eHe)) # of evaporated helium atoms due to absorbing dopant translational/rotational energy 197 dN += 557 #Calculated helium atoms lost due to vibrational energy at 400 C if(molName=='CsItest'): ### eDop = 2.0/2.0*kB*TDop # Average rotational degrees of freedom from equipartition (Only two because we have a linear rotor) eDop += JLEquation(N,vz) dN = int(floor(eDop/eHe)) # of evaporated helium atoms due to absorbing dopant translational/rotational energy dN += 574 #Calculated helium atoms lost due to vibrational energy at 410 C ### if(molName=='DMSO'): eDop = 3.0/2*kB*TDop # Average translational and rotational degrees of freedom from equipartition (1) eDop += 0.5*mDop*(3*kB*TDop/mDop)*(1-mDop/(mDop + mHe*N)) + 0.5*mHe*N*(vz**2)*(1-(mHe*N)/(mDop + mHe*N)) # Energy dissipated in inelastic collision (2) dN = int(floor(eDop/eHe)) # of evaporated helium atoms due to absorbing dopant translational/rotational energy dN += 334 #Calculated helium atoms lost due to vibrational energy at Room Temp ### if(molName=='DMSOtest'): eDop = 3.0/2*kB*TDop # Average translational and rotational degrees of freedom from equipartition (1) eDop += 0.5*mDop*(3*kB*TDop/mDop)*(1-mDop/(mDop + mHe*N)) + 0.5*mHe*N*(vz**2)*(1-(mHe*N)/(mDop + mHe*N)) # Energy dissipated in inelastic collision (2) 198 dN = int(floor(eDop/eHe)) # of evaporated helium atoms due to absorbing dopant translational/rotational energy dN += 334 #Calculated helium atoms lost due to vibrational energy at Room Temp ### if(molName=='IMtest'): eDop = 3.0/2*kB*TDop # Average rotational degrees of freedom from equipartition (1) eDop += 0.5*mDop*(3*kB*TDop/mDop)*(1-mDop/(mDop + mHe*N)) + 0.5*mHe*N*(vz**2)*(1-(mHe*N)/(mDop + mHe*N)) # Energy dissipated in inelastic collision (2) dN = int(floor(eDop/eHe)) # of evaporated helium atoms due to absorbing dopant translational/rotational energy dN += 68 #Calculated helium atoms lost due to vibrational energy at 50 C if(molName=='IM'): eDop = 3.0/2*kB*TDop # Average translational and rotational degrees of freedom from equipartition (1) eDop += 0.5*mDop*(3*kB*TDop/mDop)*(1-mDop/(mDop + mHe*N)) + 0.5*mHe*N*(vz**2)*(1-(mHe*N)/(mDop + mHe*N)) # Energy dissipated in inelastic collision (2) dN = int(floor(eDop/eHe)) # of evaporated helium atoms due to absorbing dopant translational/rotational energy dN += 92 #Calculated helium atoms lost due to vibrational energy at Room Temp if (dN<N): N -= dN #Remove evaporated helium atoms # double/triple for dimer/trimer else: N = 0 #If there are not enough atoms to boil off, set to zero 199 return N def Deflection(N): 'Implement deflection of the droplet between deflection plates through free flight region' p = pEff #Effective dipole moment p += funcs.pInd(N, p, E0, molR) #Add polarization of the helium droplet mDrop = N*mHe + mDop #Total mass of the doped helium droplets om = sqrt(abs(p*E2/mDrop)) #Time constant in dynamics a0 = p*E1/mDrop #Initial acceleration #Position at exit of deflection plates x1 = ( a0/(om*om) )*(cosh(l1*om/vz) - 1.0) #Transverse velocity at exit of deflection plates v1 = ( a0/om )*sinh(l1*om/vz) #Position at end of free flight path x2 = -1000*(x1 + v1*l2/vz) return x2 def IonYieldHe(N): # Original attempt; can be adjusted; not currently implemented 200 'Determines whether the droplet is ionized or not' #probHe = 1-exp(-0.1*(N**(1.0/3.0))) return 1.0 def IonYield(N): #not currently implemented 'Determines whether the dopant is ionized or not' #probDop = exp(-0.1*(N**(1.0/3.0))) return 1.0 ### Input Parameters ### #Get beam profile at zero field prof0 = np.array([[np.nan,np.nan,np.nan]]) #zero-field profile will go here #Import zero field data prof0Dir = "C://Users//Hend//Google Drive//" #prof0Dir = '/Users/dmerthe/Google Drive/Logs/Experiments' prof0File, _ = QtGui.QFileDialog.getOpenFileName(None, 'Choose file',prof0Dir) #File containing zero field (seed) profile prof0TSV = csv.reader(open(prof0File,'r'), delimiter = "\t") 201 for row in prof0TSV: if len(row) == 3: prof0 = np.append(prof0,[row],axis=0).astype(float) #put into the array if len(row) == 2: prof0 = np.append(prof0,[[row[0],row[1],'0']],axis=0).astype(float) #if only 2 columns in data, then zero the third element prof0 = prof0[1:] #Take out the NaN at the beginning pos0, prof0 = np.transpose(funcs.R(prof0)) #Get the amplitude from X and Y values #Droplet info #nozzT = float( raw_input("Nozzle Temperature: ") ) aveN = float( raw_input("Average Droplet Size (N): ") ) - 500 ### #Molecule info molName = raw_input("Molecule: ") directory = "G:/.shortcut-targets-by- id/0B9Ekf3SxBCyDamhIV3l1a1VXbnM/Notes/Computational Results/Simulated Deflection Profile III/Molecules/" #directory = '/Users/dmerthe/Google Drive/Notes/Computational Results/Simulated Deflection Profile III/Molecules/' molFile = open(directory+molName+'.csv','r') 202 molDat = csv.reader(molFile) print 'Loading data for '+molDat.next()[0]+'...' mDop = float(molDat.next()[0])*1.66E-27 #Mass converted from amu to kg Bs = map(float, molDat.next()) #Rotational constants of dopant p = np.array(map(float, molDat.next())) #Dipole moment of dopant pDop = 3.336e-30*sqrt( p[0]*p[0] + p[1]*p[1] + p[2]*p[2] ) #Total dipole moment molR = float(molDat.next()[0])*1.0e-9 #I = funcs.Renormalize(I) #Renormalize the moments of inertia molFile.close() TDop = float( raw_input("Dopant Temperature (K): ") ) #Field info volts = float( raw_input("Voltage (kV): ") ) if volts == 0.0: volts = 0.001 #The equation of motion breaks down for zero voltage, so just make it very small # Calculated for Collimator Position of 0.385 mm ### E0 = volts*(411413.0) #Electric field at center position E1 = volts*(-1.68888e8) #First derivative of electric field E2 = volts*(6.18785e10) #Second derivative of electric field 203 ### ### Calculate or Import Stark Energies and Alignments ### #Get Stark curves for this molecule funcs.StarkRotor(molName,Bs,E0,p) #Calculate Stark energies for the rigid rotor and save to file; see Merthe Thesis 2017 #Check to see if the Stark curves have been calculated eigsExst = os.path.isfile(directory+molName+'_eigen.csv') if eigsExst==False: print "Stark curves not found!" sys.exit() #Set average direction cosine based on Stark pEff = funcs.PEffQ(molName,E0,T0) #Average direction cosine of the molecule, based on quantum rigid rotor model #pEff = funcs.PEffC(pDop,E0,T0) #based on classical rigid rotor model print "Degree of Alignment = ", pEff / pDop ### Calculate Deflections ### ttotstart = time.time() np.random.seed() 204 rat = rat - 0.05 #aveN += (4)*500 for w in range(1): #use if calculating profiles with different ratios rat += 0.05 print rat #aveN -= (4)*500 #from line above for z in range(6): xAve = 0.0 aveN += 500 print "This Run (N, rat):", aveN, ",", rat mu = 0.5*log( (aveN*aveN) / (1.0 + rat*rat) ) sig = sqrt( log(1.0 + rat*rat ) ) #sigma in log-normal distribution ### maxN = np.exp(sqrt(2.0)* sig * erfinv(2.0 * 0.98 - 1.0) + mu) #Actually 98th percentile droplet, which we'll call maximum ionNorm = maxN**(2.0/3.0) for i in range(NP): 'Setup the x-axis and zero the profile' prof[i]=0 pos[i] = xmin + (float(i) / (NP-1))*(xmax-xmin) prof0max = max(prof0) #maximum of the zero field profile 205 pos0min = pos0[0] #domain of zero-field profile pos0max = pos0[-1] ### totalDrops = 0 NIsur = 0 NIHesur = 0 NItot = 0 totalSizes = 0.0 prof0interp = funcs.interpextrap(pos0, prof0) #Use an interpolation to deflect zero-field profile for i in np.argwhere( np.logical_and(pos <= pos0max, pos >= pos0min) )[:,0]: x0 = pos[i] #Position at detector without deflection NIcrit = 0 #for j in range( int(np.around(NI*prof0interp(x0) / prof0max)) ): #number of trials = zero field profile at x0 while NIcrit < int(np.around(NI*prof0interp(x0) / prof0max)): N = Droplet() totalDrops += 1 if np.random.random() < N**(2.0/3.0)/ionNorm: #Dopant pick up as a function of cross section 206 N = Boiloff(N,molName,vz) if np.random.random() < N**(2.0/3.0)/ionNorm: #Line to account for change in droplet profile due to ionization as a function of cross section # add additional lines when there are multiple doping events if np.random.random() < exp(-0.12*(N**(1.0/3.0))): #Line to account for change in droplet profile due to CTP NIcrit += 1 #Keeps track of the total number of iterations NItot += 1 if N>0: x = x0 + Deflection(N) #net deflection of a doped helium droplet k = int(round( (x - xmin)/xstp )) #Find abcissa nearest position, x yld = IonYield(N) #yield of dopants yldHe = IonYieldHe(N) #yield of droplets NIsur += yld #Keeps track of the total number of droplets that survive the capture process NIHesur += yldHe #Keeps track of the total number of droplets that survive the capture process if k<len(prof): #If position in range 207 prof[k] += yld # if molecule is ionized, then add to profile profHe[k] += yldHe #relative yield of dopants sizes[k] += N totalSizes += N sizes = sizes / profHe.astype(float) prof = (float(NItot)/float(NIsur)) * prof0max * prof.astype(float) / float(NI) #renormalize profile to match zero-field profile profHe = (float(NItot)/float(NIHesur)) * prof0max * profHe.astype(float) / float(NI) #renormalize profile to match zero-field profile print "Average Deflection = ", sum(pos*prof)/sum(prof) - sum(pos0*prof0)/sum(prof0), " mm" print "Average N = ", totalSizes/NItot print "Total Droplets Generated = ", totalDrops print "Total Droplets Successfully Ionized = ", NItot ### plt.plot(pos0, prof0) plt.plot(pos, prof) plt.show() 208 directory = "/".join(prof0File.split('/')[0:-1]) #Put the output profile into the same directory as the zero-field profile deflFile = open(directory+"/"+molName+'_'+str(aveN)+'_'+str(volts)+'_'+'r'+str(rat)+'_deflections.csv','wb') #profHeFile = open(directory+"/"+molName+'_'+str(aveN)+'_'+str(volts)+'_deflectionsHe.csv','wb') profSizesFile = open(directory+"/"+molName+'_'+str(aveN)+'_'+str(volts)+'_'+'r'+str(rat)+'_deflectionsSizes.csv' ,'wb') deflWriter = csv.writer(deflFile) for i in range(NP): deflWriter.writerow([pos[i],prof[i]]) deflFile.close() #profHeWriter = csv.writer(profHeFile) # #for i in range(NP): # profHeWriter.writerow([pos[i],profHe[i]]) # #profHeFile.close() profSizesWriter = csv.writer(profSizesFile) 209 for i in range(NP): profSizesWriter.writerow([pos[i],sizes[i]]) ## profSizesFile.close() ttotfinal = time.time() print('Time Elapsed',ttotfinal-ttotstart) 210 Appendix D – Useful Mathematica Functions This appendix includes some useful Mathematica functions for data analysis and interacting with the output data files for collected profiles and spectra. This set of functions is not exhaustive, and other Mathematica notebooks used for analysis, code, and summaries can be found in the google drive for the helium project in the Logs/Experiments directory. The code here can be found under Logs/Instrumentation/Useful Functions. Descriptions are provided below. -- NormToOne takes in deflection profile data directly from the imported .tsv data file and scales the profile such that the maximum intensity point is set to unity. This is useful for a quick comparison of profiles with varying intensities. NormToOne[data_] := Module[{newData}, newData = Transpose[{data[[All, 1]], 1/Max[data[[All, 2]]] data[[All, 2]]}]; Return[newData]] RelNorm takes in two deflection profiles and the former is normalized to the latter such that the sum of the intensity points in each profile are equal. This approximates the area under the curve for each profile being the same. RelNorm[data_, normtodata_] := Module[{newData}, newData = Transpose[{data[[All, 1]], Total[normtodata[[All, 2]]]/Total[data[[All, 2]]]* Length[data[[All, 2]]]/Length[normtodata[[All, 2]]]*data[[All, 2]]}]; Return[newData]] 211 Centroid takes in profile data and computes the centroid of the position of the data. The function is essentially an intensity-weighted average of the positions. The centroid of the undeflected and deflected profiles is often a useful way to compare the magnitude of the deflection between them. Centroid[data_] := Module[{centroid}, centroid = Total[data[[All, 1]]*data[[All, 2]]]/Total[data[[All, 2]]]; Return[centroid]] FitPVSymmetric fits a symmetric pseudo-Voigt function to the profile data. This fit is useful for non-deflecting or zero-field profiles. Fitting profile data using the function is often used before feeding the fitted profile into the deflection simulation. This function and the asymmetric variant both rely on the built-in FindFit function in Mathematica for nonlinear fitting. The upper and lower inputs represent the minimum and maximum values of the domain for the fitted profile output. The default output resolution is a tenth of a millimeter. FitPVSymmetric[data_, lower_, upper_] := Module[{fitparas, fitdata, f, A, \[Gamma], x, \[Mu]}, (* lower and upper are the bounds on the output function; extrapolated over the range according to the fit parameters *) fitparas = FindFit[data, {(f)*(2*A/(Pi*\[Gamma]))/( 1 + 4*((x - \[Mu])/\[Gamma])^2) + (1 - f)*(A/\[Gamma]*((4*Log[2])/Pi)^(1/2)* 212 Exp[-4*Log[2]*((x - \[Mu])/\[Gamma])^2]), 0 < f < 1}, {{f, 0.5}, {A, Max[data[[All, 2]]]}, {\[Gamma]}, {\[Mu], Mean[data[[All, 1]]]}}, x]; fitdata = Transpose[{Range[lower, upper, 0.1], (f)*(2*A/(Pi*\[Gamma]))/( 1 + 4*((x - \[Mu])/\[Gamma])^2) + (1 - f)*(A/\[Gamma]*((4*Log[2])/Pi)^(1/2)* Exp[-4*Log[2]*((x - \[Mu])/\[Gamma])^2]) /. fitparas /. x -> Range[lower, upper, 0.1]}]; Return[fitdata]] FitPVAsymmetric fits an asymmetric pseudo-Voigt function with a sigmoidally varying width parameter to the profile data (this function is described and referenced extensively in the main text). This fit is useful for strongly deflecting and generally skewed profiles. The upper and lower inputs represent the minimum and maximum values of the domain for the fitted profile output. The default output resolution is a tenth of a millimeter. FitPVAsymmetric[data_, lower_, upper_] := Module[{fitparas, fitdata, f, A, \[Gamma], x, \[Mu], a}, 213 (* lower and upper are the bounds on the output functon; extrapolated over the range according to the fitparameters *) (* Updated 12 12 2022; see Stancik and Brauns (2008) *) fitparas = FindFit[data, {(f)*( 2*A/(Pi*((2 \[Gamma])/(1 + Exp[a*(x - \[Mu])]))))/( 1 + 4*((x - \[Mu])/((2 \[Gamma])/( 1 + Exp[a*(x - \[Mu])])))^2) + (1 - f)*(A/((2 \[Gamma])/(1 + Exp[a*(x - \[Mu])]))*((4*Log[2])/ Pi)^(1/2)* Exp[-4*Log[2]*(( x - \[Mu])/((2 \[Gamma])/(1 + Exp[a*(x - \[Mu])])))^2]), 0 < f < 1}, {{f, 0.5}, {A, Max[data[[All, 2]]]}, {a}, {\[Gamma]}, {\[Mu], Mean[data[[All, 1]]]}}, x]; fitdata = Transpose[{Range[lower, upper, 0.1], (f)*(2*A/(Pi*((2 \[Gamma])/(1 + Exp[a*(x - \[Mu])]))))/( 214 1 + 4*((x - \[Mu])/((2 \[Gamma])/( 1 + Exp[a*(x - \[Mu])])))^2) + (1 - f)*(A/((2 \[Gamma])/(1 + Exp[a*(x - \[Mu])]))*((4*Log[2])/ Pi)^(1/2)* Exp[-4*Log[2]*(( x - \[Mu])/((2 \[Gamma])/( 1 + Exp[a*(x - \[Mu])])))^2]) /. fitparas /. x -> Range[lower, upper, 0.1]}]; Return[fitdata]] SquareError is a basic function used to compute the square error between two input profiles. The magnitude of the error is arbitrary but is relative to the intensity of the input profiles. The function is useful when comparing simulation output to experimental deflection data and specifically for assigning a best-fit dipole moment or mean droplet size. SquareError[data1_, data2_] := Module[{error}, (* For two functions with the same domain *) error = Total[(data1[[All, 2]] - data2[[All, 2]])^2]; Return[error] ] SquareErrorUnequalDomain is conceptually the same to the simple SquareError function, but specifically computes the square error using interpolated points for a user-defined range and 215 interval. The interpolation method used is a simple first order (linear) interpolation (connecting the dots). This function is more general than the previous, but is often unnecessary. SquareErrorUnequalDomain[data1_, data2_, lower_, upper_, increment_] := Module[{error, data1Interp, data2Interp, x}, (* For two functions with unequal domains; Points are chosen at fixed points and taken from the data with \ linear interpolation *) (* lower and upper specify the range over which error is measured, increment gives the points to measure error between them; *) (* A reasonable guess for this value would be (upper - lower)/100; or something like 0.1 for bounds on the order of 10 *) (* lower and upper should be chosen to be the overlapping region \ between data profiles *) data1Interp = Interpolation[data1, InterpolationOrder -> 1]; data2Interp = Interpolation[data2, InterpolationOrder -> 1]; error = Total[((data1Interp[x] /. x -> Range[lower, upper, increment]) - (data2Interp[x] /. 216 x -> Range[lower, upper, increment]))^2]; Return[error]] -- In 2022 the main LabVIEW data acquisition code was upgraded to save the metadata of the profile and mass spectra scans rather than just the average values of the total rate, lock-in rate, and dip. Now in addition to these quantities that virtual instrument saves a .tsv file with these quantities appended for each scan such that signal evolution can be tracked in time and outliers can be examined. The functions listed below are used to unwrap and provide statistics for the appended metadata file for analysis in Mathematica. -- GetMetaRun takes in the metadata file and extracts a single scan of the lock-in rate, dip, or total rate depending on the dataCol option (1,2, and 3 respectively). The desired scan number is also taken in as input. getMetaRun[meta_, points_, scanNum_, dataCol_] := Module[{builtList}, builtList = Transpose[{points, Take[meta[[All, dataCol]], {1 + Length[points]*(scanNum - 1), Length[points]*(scanNum)}]}]; Return[builtList]] GetAllMetaPoints uses the previous function and takes in the metadata file alongside a list of the relevant position points. The total number of scans is also required as well the aforementioned 217 dataCol option. This function provides an appended list of tuples of the position and the lock-in rate, dip, or total rate across the requested number of scans. GetAllMetaPoints[meta_, points_, dataCol_, totalScans_] := Module[{allPoints, i}, allPoints = {}; For[i = 1, i <= totalScans, i++, allPoints = Join[allPoints, GetMetaRun[meta, points, i, dataCol]]]; Return[allPoints]] GetAverageAndSD gives the average and standard deviation of the lock-in rate, dip, or total rate alongside the position of the extracted metadata points from the previous function. GetAverageAndSD[metaPoints_] := Module[{metaASD, i}, metaASD = {}; For[i = 1, i <= Length[GatherBy[metaPoints, First]], i++, metaASD = AppendTo[metaASD, {GatherBy[metaPoints, First][[i]][[1]][[1]], Mean[GatherBy[metaPoints, First][[i]][[All, 2]]], StandardDeviation[GatherBy[metaPoints, First][[i]][[All, 2]]]}]]; Return[metaASD]] 218 GetUncertaintyPoints takes the output of the previous function as input and provides a tuple of the position and average of the aforementioned quantities with error bars defined by the standard deviation of the data. This the output of this function can be put directly into a Mathematica ListPlot for easy review of the data and gives a good visual indication of how noisy the data is. GetUncertaintyPoints[data_] := Module[{dataU, i}, dataU = {}; For[i = 1, i <= Length[data], i++, dataU = AppendTo[dataU, Around[data[[All, 2]][[i]], data[[All, 3]][[i]]]]]; Return[dataU]] 219 Appendix E – Detector Slit Simulations As noted in Chapter 5, the fullerene-sodium measurements did not utilize the slit in front of the ionizer opening in order to measure sufficient signal intensity. Initially there were some concerns that measurements without the slit would be insufficient to discern a deflection, but further examination and simulations demonstrate that this is not the case. It is worth reiterating that when measuring beam profiles, the entire chamber is translated spatially in the lab frame. When the slit is in-place, it does not move relative to the ionizer. The ionizer aperture is 5 mm and the slit is roughly one quarter of this opening size at 1.27 mm. The signal intensity will fall with increasing position from the beam center as long as the ionizer width does not encompass the entire beam at any given translated position, which is certainly not the case. The beam itself can be approximated by a normalized gaussian profile with some arbitrary intensity and width parameter. The normalized gaussian form is given in Equation (E.1), 𝐺 𝑁 ( 𝑥 ) = 1 𝜎 √2𝜋 exp(− ( 𝑥 − 𝜇 ) 2 2𝜎 2 ) , (E.1) where 𝜎 represents broadness and 𝜇 gives the horizontal translation from the origin. The interaction with the slit or larger ionizer aperture can then be thought of as integrating all of the arriving beam intensity over the interval defined by the position of the chamber and width of the slit or ionizer aperture. Collecting this integrated intensity as a function of chamber position then renormalizing approximates the blurring from the finite width of the slit or ionizer aperture. With proper centering of the slit, the process results in symmetric broadening of variable degree, depending on the broadness of the initial profile and the width of the detector aperture. This process 220 is shown graphically in Figure E.1 where simulated broadening for both the slit and ionizer aperture are shown from an initial gaussian beam with specified width. Figure E.1: Simulations of broadening due to the slit (1.27 mm) or ionizer aperture (5 mm) from an initial gaussian beam profile with width defined by (a) 𝜎 =1 and (b) 𝜎 =2. In each case the broadening is substantially larger for the ionizer aperture. A legend is provided under the figure for reference. 221 The shape and broadness of the beam profile without the slit in place is representative of typical measurements under standard droplet conditions, indicating that the width of the gaussian indicating that the real beam is roughly approximated within the bounds for 𝜎 presented in Figure E.1(a) and (b). For reference, a normalized gaussian fit to a beam profile using the slit in the main fullerene-sodium experiment gives 𝜎 ≈1.6, though variation is expected from different droplet sizes and variable beam conditions in general. It is clear that the use of the slit noticeably sharpens the beam profile, relative to the much larger ionizer opening, meaning that in general use of the slit is preferable if sufficient signal intensity is available. It is important to note that the broadening is symmetrical: to discern actual deflection of the beam, for a sufficiently polar dopant, the slit should not be critically important. Figure E.2 shows the two broadened profiles in Figure E.1(b) alongside the same profile translated by 2 mm. These profiles represent the broader initial beam, and the simulations without the slit represent the case where discerning the deflection may be more challenging. In reality, the beam will broaden asymmetrically in the case of deflection, making the picture more complicated, but it is clear from the idealized case of translation that a deflection of 2 mm is easily discernable with or without the slit. In the case of asymmetric broadening, the right shoulder of the profile should also clearly deviate if deflection occurs. For the predicted fullerene-sodium complex the dipole moment is very large as described in Chapter 5, and ≈2 mm of deflection is expected based on the field gradient, mean droplet size, and dipole moment. It is thus reasonable to conclude that this highly polar structure is not formed, even with measurements without the slit in front of the ionizer. In general, the clarity and contrast between undeflected and deflected beam profiles is improved with the use of the slit. 222 Figure E.2: Approximated deflection of broadened beam profiles by translation. The initial beam profile is assumed to be a normalized gaussian with 𝜎 =2. The blue profiles assume that the slit is in place while the red profiles assume that the beam directly enters the ionizer. The translated profiles are constructed with dashed lines, while the initial profiles use solid lines.
Abstract (if available)
Abstract
This work describes a series of electrostatic deflection experiments performed in helium nanodroplets exploring a handful of molecular systems. The unique helium droplet medium cools the system to ≈0.37 K providing almost complete orientation of the embedded electric dipole moment in an external electric field. Owing to the high degree of orientation, the applied field gradient results in robust deflection of the doped droplets on the of the order of millimeters. These experiments represent the most massive neutral systems (~10,000 helium atoms) studied by so-called beam “deflectometry.” This technique is broadly applicable to trap, cool, and probe a multitude of nanoscopic systems.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Niman, John Walter
(author)
Core Title
Experiments in electrostatic deflection of doped helium nanodroplets
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Physics
Degree Conferral Date
2023-05
Publication Date
04/04/2023
Defense Date
03/22/2023
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
electric dipole moment,electrostatic deflection,helium nanodroplets,low temperature physics,molecular beams,molecule trapping,OAI-PMH Harvest
Format
theses
(aat)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Kresin, Vitaly (
committee chair
), Benderskii, Alexander (
committee member
), El-Naggar, Moh (
committee member
), Levenson-Falk, Eli (
committee member
), Takahashi, Susumu (
committee member
)
Creator Email
jniman@usc.edu,johnwniman@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC112932379
Unique identifier
UC112932379
Identifier
etd-NimanJohnW-11562.pdf (filename)
Legacy Identifier
etd-NimanJohnW-11562
Document Type
Dissertation
Format
theses (aat)
Rights
Niman, John Walter
Internet Media Type
application/pdf
Type
texts
Source
20230405-usctheses-batch-1016
(batch),
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
electric dipole moment
electrostatic deflection
helium nanodroplets
low temperature physics
molecular beams
molecule trapping