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Infrared and Raman spectrosopy of molecules and molecular aggregates in helium droplets

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Infrared and Raman spectrosopy of molecules and molecular aggregates in helium droplets

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Content INFRARED AND RAMAN SPECTROSCOPY OF MOLECULES AND MOLECULAR AGGREGATES IN HELIUM DROPLETS by Russell Thomas Sliter 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 (CHEMISTRY) May 2011 Copyright 2011 Russell Thomas Sliter ii Dedication To my parents for their constant support To my wife, Dania, for her love and patience iii Acknowledgments I would first like to thank my scientific advisor, Professor Andrey Vilesov, for his constant support during my graduate career at USC. He has a comprehensive experimental repertoire of knowledge that he has always been willing to share with me. As a result, I attribute most of my success as a scientist to him. In addition, his office has always been open to discuss not only science but life in general and I have been very fortunate to have worked in his group. I am also very grateful to Professor Hanna Reisler for her constant support and attention she has provided me over the years while at USC. Her interest in the success of students outside her own research group is sincere and inspirational. I would also like to thank the remaining members of my qualifying exam committee, Professor Vitaly Kresin, Professor Chi Mak, and Professor Thomas Flood, for their support. In addition, I would like to thank Professor Curt Wittig for his wisdom and always strong personality. I would like to thank Professor Stephen Bradforth and Professor Susumu Takahashi for their support while a T.A. for CHEM 332L. Many problems in the lab would not have been fixed if not for their advice and guidance. In addition, I would like to thank Jaime Avila, the department computer consultant, for his assistance in the lab. When I first joined the Vilesov group, I was slightly overwhelmed. Fortunately, veteran graduate students Kirill Kuyanov and Dmitry Skvortsov were there to show me the ropes in the laboratory. As a result, I would like to thank them for all of their help. Although he was not at USC for very long, I would like to thank our previous post-doc iv Dr. Myong Yong Choi, as he was always willing to help. I would also like to thank several undergraduates who have passed through our lab and assisted me in experiments: Michael Gordon, Michael Makris, Melody Sun, and Melissa Gish. Due to his constant assistance and broad knowledge in the lab, I would like to thank our recent post-doc, Dr. Evgeny Loginov. There was never a time he wouldn’t offer to help me in the lab or discuss a scientific problem I was having. For that, I am grateful. As long as I have been at USC, our group has never really been much larger than 4 people. For the most part, it has consisted of 2: Luis Gomez and I, in which we entered graduate school the same year. As a result, we have had to rely predominantly on each other in the lab. Without his collaboration and assistance, research would have been less productive and dull. I am grateful to have worked with him. As always, graduate life would not be complete were it not for all the graduate students from the Chemistry department with whom I have interacted with, borrowed equipment from, and had fruitful conversations with over the years. I would like to thank Oscar Rebolledo-Mayoral, Bill Schroeder, Jordan Fine, and Chris Nemirow from the group of Curt Wittig as well as previous members George Kumi and Sergey Malyk; Mikhail Rayzanov and Blithe Rocher from the group of Hanna Reisler as well as previous members Andrew Mollner and Igor Fedorov; Christi Schroeder and Tom Zhang from the group of Stephen Bradforth as well as previous members Chris Rivera and Diana Warren; and Nikolay Markovskiy, a previous member from the group of Chi Mak. v I would like to thank all the personal of the USC Machine shop. In addition, I would like to thank Ross Lewis from the department’s electronic shop. Without their valuable work, most experiments would not have been completed. I would like to offer a special thanks to Valerie Childress, Michele Dea, and Katie McKissick for their professionalism and willingness to help with all my questions, paperwork, and day-to-day events that make working at USC so much easier. vi Table of Contents Dedication .............................................................................. ii Acknowledgments ................................................................ iii List of Tables ........................................................................ xi List of Figures...................................................................... xii Abstract............................................................................. xxiii Chapter I. General Introduction......................................... 1 1.1. Scope of Work ......................................................................... 1 1.2. Experimental Techniques ........................................................ 3 1.3. Content of Chapters ................................................................. 4 Chapter 1 Bibliography..................................................................... 6 Chapter II. Helium Nanodroplets....................................... 7 2.1. Introduction ............................................................................ 7 2.2. Fundamentals of He Droplet Formation................................. 8 2.2.1. Supersonic ExpansionsScope of Work............................. 8 2.2.2. Helium Expansion Regimes ........................................... 11 2.3. Size Distribution of Very Large He Droplets....................... 14 2.3.1. Introduction..................................................................... 14 2.3.2. Continuous Nozzle He Droplet Apparatus..................... 15 vii 2.3.3. Signal Acquisition and Computer Interfacing................ 16 2.3.4. Average He Droplet Size................................................ 17 2.3.5. Counting Pulses from Very Large He Droplets ............. 18 2.3.6. Size Distributions of Very Large He Droplets ............... 24 2.3.7. Conclusions..................................................................... 33 Chapter 2 Bibliography................................................................... 35 Chapter III. Pulsed He Droplets ....................................... 36 3.1. Introduction .......................................................................... 36 3.2. Continuous vs. Pulsed He Droplet Formation...................... 37 3.3. Experimental Setup of Pulsed He Droplet Apparatus.......... 38 3.4. Characterization of He Droplets using Pulsed Nozzle......... 43 3.4.1. Pulsed Nozzle Operation ................................................ 43 3.4.2. Optimization of He Droplet Formation .......................... 47 3.4.3. Large Ionized Droplets ................................................... 58 3.5. Mass Spectroscopic Characterization of He Droplet Sizes ...................................................................................... 60 3.6. Electron-Impact Ionization of He Droplets.......................... 64 3.7. Model of He Ionization and Excitation in He Droplets ....... 65 Chapter 3 Bibliography................................................................... 71 Chapter IV. Coherent Anti-Stokes Raman Scattering of Condensed Phase H 2 ....................................................... 73 4.1. Introduction .......................................................................... 73 4.2. Principles of CARS Technique ............................................ 73 4.3. CARS Optical Setup............................................................. 76 4.4. H 2 Cluster Formation via Supersonic Co-expansion of H 2 and He.............................................................................. 83 viii 4.5. Sample Preparation............................................................... 83 4.6. Electronics and Computer Interfacing.................................. 84 4.7. Vibrational CARS of H 2 Molecules and Clusters in He Droplets ................................................................................ 85 4.8. Rotational CARS of H 2 Molecules and Clusters in He Droplets ................................................................................ 94 4.8.1. Experimental Setup of Rotational CARS....................... 95 4.8.2. Gas Phase Rotational CARS of H 2 ................................. 95 4.8.3. Rotational CARS of H 2 in Clusters ................................ 97 4.8.4. Spectral Anomalies in Rotational CARS of H 2 Clusters ...................................................................... 99 Chapter 4 Bibliography................................................................. 113 Chapter V. Structure of Cold, Mixed Para-H 2 – D 2 Clusters .............................................................................. 114 5.1. Introduction ........................................................................ 114 5.2. Experimental Technique.....................................................116 5.3. Results ................................................................................ 118 5.4. Discussion........................................................................... 123 5.5. Conclusions ........................................................................ 134 Chapter 5 Bibliography................................................................. 135 Chapter VI. Temperature Dependence of the Raman Spectra of Liquid Para-hydrogen .................................... 138 6.1. Introduction ........................................................................ 138 6.2. Experimental Technique.....................................................139 6.3. Results ................................................................................ 141 6.4. Discussion........................................................................... 146 ix 6.5. Conclusions ........................................................................ 151 Chapter 6 Bibliography................................................................. 153 Chapter VII. Fast Nuclear-Spin Conversion in Water Clusters and Ices ............................................................... 156 7.1. Introduction ........................................................................ 156 7.2. Experimental Technique.....................................................158 7.3. Results ................................................................................ 159 7.4. Discussion........................................................................... 172 7.5. Conclusions ........................................................................ 179 Chapter 7 Bibliography................................................................. 180 Chapter VIII. Conclusions and Future Works.............. 184 8.1. Conclusions ........................................................................ 184 8.2. Future Works ...................................................................... 185 8.2.1. Superfluidity of Para-H 2 Clusters................................. 185 8.2.2. Nuclear Spin Conversion in H 2 O.................................. 188 8.2.3. Vibrationl Spectroscopy of Ions in Helium Droplets........................................................... 188 8.2.3.1. Introduction ....................................................... 188 8.2.3.2. Proposed Experimental Setup............................ 190 Chapter 8 Bibliography................................................................. 194 Comprehensive Bibliography........................................... 196 Appendix. Pulsed Valve Modifications and Assembly ......................................................... 209 Design and Principles of Operation.............................................. 209 x Poppet Changing Procedure ......................................................... 210 Poppet Performance Check........................................................... 211 Modifications ................................................................................ 213 xi List of Tables Table 2.1. 33 Ratios of relative average droplet sizes obtained by pulse counting for several operating conditions. Ratios of absolute droplet sizes measured in Fig. 2.3 are shown for comparison. Table 3.1. 39 Typical pressures achieved at a stagnation pressure of 20 bar and stagnation temperatures ranging from room temperature to about 15 K for pulsed valve operation at 200 μs duration. Table 7.1. 165 Frequencies (cm -1 ) and assignments of absorption lines of single H 2 O molecules in the ν 1 , ν 2 and ν 3 regions in solid argon at 4 K. Table 7.2. 173 Band origins and rotational constants (in cm -1 ) of single water molecules in the ν 1 , ν 2 and ν 3 regions in solid argon at 4 K and in the gas phase. xii List of Figures FIG. 2.1. 13 Average He droplet size and mean diameter measured at different stagnation pressures as a function of nozzle temperature. Red dots correspond to typical expansion conditions of P 0 = 20 bar.Schematic diagram of the He droplet apparatus. See text for details. FIG. 2.2. 16 Schematic of He droplet apparatus. NZ – cold nozzle, SK –skimmer, PC1 and PC2 – pickup cells, BG – Baratron vacuum gauge, IG1 and IG2 – ion gauges, SH1 and SH2 – beam shutters, A1 and A2 – 6 mm diameter apertures, GV1 and GV2 – gate valves, EI – electron impact ionizer, IB – ion bender, QMS – quadruple mass spectrometer. FIG. 2.3. 18 Average He droplet size obtained at varying nozzle temperatures from a continuous expansion of He gas at a stagnation pressure of 20 bars and through a 5 μm nozzle. The results of the titration measurements with Ar and He gas are shown by solid squares and triangles, respectively, as obtained previously. Results of previous deflection measurements are shown by stars. Corresponding droplet diameters (nm) are given on the right-hand side. FIG. 2.4. 20 10 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2400 V. The results were obtained using a 100 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. FIG. 2.5. 21 100 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2400 V. The results were obtained using a 35 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. FIG. 2.6. 22 20 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2300 V. All panels were obtained using a 100 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. xiii FIG 2.7. 23 100 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2300 V. All panels were obtained using a 35 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. FIG. 2.8. 24 1000 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 1800 V. All panels were obtained using a 35 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. FIG. 2.9. 25 Ratio of integrated peak area to peak amplitude (A/I) vs. peak amplitude for a variety of peaks as obtained at T 0 = 6.0 K and P 0 = 20 bar. The solid line is an approximate fit and is given numerically in the lower right-hand side of the figure. FIG. 2.10. 27 Log-Log plot of He droplet size distributions at various temperatures as obtained with a 100 μm pinhole at P 0 = 20 bar and 2400 electron multiplier voltage. FIG. 2.11. 28 He droplet size distributions at various temperatures as obtained with a 35 μm pinhole at P 0 = 20 bar and 2400 V electron multiplier voltage. FIG. 2.12. 29 He droplet size distributions at various temperatures as obtained with a 100 μm pinhole at P 0 = 20 bar and 2300 V electron multiplier voltage. FIG. 2.13 30 He droplet size distributions at various temperatures as obtained with a 35 μm pinhole at P 0 = 20 bar and 2300 V electron multiplier voltage. FIG. 2.14. 31 He droplet size distributions at various temperatures as obtained with a 35 μm pinhole at P 0 = 20 bar and 1800 V electron multiplier voltage. FIG. 3.1. 39 He apparatus. FIG. 3.2. 41 Attachment of pulsed valve to second stage of closed cycle refrigerator. The current setup contains a copper sheet fitted around the pulsed valve housing (not shown) which is then attached by copper wires to the copper stage. xiv FIG. 3.3. 45 Mass spectrum obtained via pulsed gas expansion of pure helium and detected by quadrupole mass spectrometer. The signal was recorded using a boxcar integrator set at delay of 3.2 ms and Δt = 3 μs. The large intensity peak in the range of M = 17 – 19 stems from water molecules and dimers trapped in He droplets. FIG. 3.4. 46 Temporal profile of the droplet signal as measured at m/z = 4 and 8. T V = 16 K, P 0 = 15 bar at 200 μs nominal pulse duration and 20 Hz repetition rate. FIG. 3.5. 48 Temperature dependence (T V ) of m/z = 8 signal using pulsed nozzle at a repetition rate of 20 Hz and nominal pulse width of 200 μs. FIG. 3.6. 49 Temperature dependence (T V ) of time-delayed signal at t = 4.0 ms for M = 8 at P 0 = 15 bar, 200 μs pulse duration and various pulse repetition rates. FIG. 3.7. 50 Temperature dependence on the velocity of the droplets for pulsed and continuous nozzles at several operating conditions for M = 8 amu. Solid line indicates estimated velocity of ideal gas as calculated using gas kinetic theory. FIG. 3.8. 51 m/z = 8 signal dependence vs. nominal pulse duration at T V = 16 K, P 0 = 20 bar, and 20 Hz repetition rate. FIG. 3.9. 52 m/z = 8 temporal profiles at various pulse durations (a – c) at T V = 16 K, P 0 = 20 bar, and 20 Hz repetition rate. FIG. 3.10. 53 Pressure in nozzle and QMS chambers vs. pulse duration at T V = 17 K, P 0 = 20 bar, and 20 Hz repetition rate. QMS pressure is factored by 10 3 for scaling purposes. FIG. 3.11. 54 m/z = 8 signal vs. He backing pressure at T V = 20 K, 200 μs pulse duration, and 20 Hz repetition rate. FIG. 3.12. 55 Dependence of the pressure rise in the nozzle and QMS chambers vs. nozzle He backing pressure at T V = 20 K, 200 μs pulse duration, and 20 Hz repetition rate. The QMS pressure is scaled by 2·10 2 for comparison. xv FIG. 3.13. 56 M = 8 signal vs. repetition rate as heated at T V = 16 K. FIG. 3.14. 56 Velocity of M = 8 signal vs. repetition rate as heated at T V = 16 K. FIG. 3.15. 57 Temperature of the pulsed valve (T V ) and cold head (T C ) as a function of repetition rate of pulsed nozzle at 15 bar and 200 μs pulse duration. FIG. 3.16. 58 Pressure rise in nozzle and QMS chambers vs. repetition rate at T V = 16 K, P 0 = 20 bar, and 200 μs pulse duration. QMS pressure scaled by 2·10 2 for comparison. FIG. 3.17. 59 Temporal profiles of m/z = 8 at T V = 15 K, P 0 = 5 bar, 200 μs pulse duration, and 20 Hz repetition rate for various ion energies. FIG. 3.18. 62 Ratio of (He) 4 + /(He) 2 + signals at various temperatures for continuous (T 0 ) and pulsed nozzles (T V ). The pulsed nozzle was operated at P 0 = 15 bar and 200 μs pulse duration for various repetition rates. FIG. 3.19. 62 Ratio of (He) 4 + /(He) 3 + signals at various temperatures for continuous (T 0 ) and pulsed nozzles (T V ). The pulsed nozzle was operated at P 0 = 15 bar and 200 μs pulse duration for various repetition rates. FIG. 3.20. 63 Mass spectra for cw nozzle (T 0 = 9.5 K, P 0 = 20 bar) and pulsed nozzle (T V = 16 K, P 0 = 20 bar, 200 μs pulse duration, 20 Hz repetition rate) with comparable I 16 /I 8 ratio. Mass spectra are normalized with respect to their corresponding M = 8 value. FIG. 3.21. 67 Illustration of possible outcomes (A – C) for two electron impacts on different He atoms by a single electron with initial energy of 100 eV. FIG. 3.22. 68 Cross-sections for electron impact ionization (solid squares) and excitation (open squares) for atomic He as a function of electron energy. xvi FIG. 3.23. 69 Ratio of (He) 4 + /(He) 2 + signals as obtained by experiment using cw nozzle (solid squares) and theory (solid line) as obtained by our modeling of ionization and excitation probabilities in helium droplets. FIG. 4.1. 75 Energy diagram of vibrational CARS process. Two incident waves ( ω 1 ) and two outgoing waves ( ω 2 ) and ( ω 3 ) are shown by solid arrows. Ground and vibrationally excited states are denoted by ν = 0 and ν = 1, respectively as solid lines. Virtual levels are shown by dashed horizontal lines. FIG. 4.2. 78 CARS optical setup. The outer frame of the illustration denotes the borders of the optical table. The pump and Stokes laser beams are depicted by solid and dotted lines, respectively. Arrows correspond to the beams traveling to and from the pulsed cryogenic jet (not pictured here). The returning anti-Stokes signal is shown by a dashed line and is detected by a PMT. FIG. 4.3. 79 Diagram illustrating folded BOX CARS geometry. k 1 vectors are in the horizontal plane whereas k 2 and k 3 vectors are in the vertical plane. The vector sum of Δk = 0 satisfies momentum conservation. FIG. 4.4. 81 Schematic of helium droplet machine. Pump (solid lines) and Stokes (dotted line) beams are focused onto the expanding jet. An anti-Stokes signal (dashed line) is generated which is isolated by means of an aperture (A), a diffraction grating (B), and interference filters (C). In the case of high intensity, additional neutral filters (D) have been added to avoid saturation of the PMT (E). A lens (F) is placed after the first turning mirror to compensate for the divergent anti-Stokes signal generated while an additional lens (G) is used to focus the signal into a pinhole (H) located in the housing of the PMT (C). FIG. 4.5. 84 Schematic of pulse nozzle timing diagram. A TTL trigger pulse signals for pulse valve to open. Nozzle valve opens approximately 350 μs after initial trigger. The laser is triggered to temporally overlap with the gas expansion at the focal point, as illustrated by the delay between laser pulse and nozzle, which is exaggerated for clarity. FIG. 4.6. 86 Vibrational CARS spectra of H 2 molecules obtained upon expansion of 0.5% n-H 2 in He at T V = 300 K and P 0 = 20 bar. The spectrum is calibrated against known position of the lines in the gas phase. xvii FIG. 4.7. 88 CARS signal dependence as a function of nozzle position parallel to pump and Stokes beam, Y, at T V = 300 K for Z = 6 mm (a) and Z = 45 mm (b). Expansion of n-H 2 at P = 20 bar. FIG. 4.8. 89 Schematic of nozzle chamber housing cold head from top-view. The cold head is installed on a platform which is then inserted into the nozzle chamber. The cold head can be positioned by using small steel blocks with mounted, threaded bolts. The Y- and Z- positions are defined from the edge of the nozzle chamber platform to the edge of the corresponding small blocks used for adjustments, as shown by arrows. FIG. 4.9. 90 CARS signal dependence vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver. n-H 2 expansion at T V = 300 K, P = 20 bar, nominal pulse duration: 200 μs, and Z = 45 mm. Measurements were obtained at the maximum of the o-H 2 gas line. FIG. 4.10. 91 CARS signal dependence vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver. Expansion of 1% n-H 2 in He at T V = 60 K, P = 20 bar, nominal pulse duration: 200 μs, and at Z = 6 mm (a) and Z = 27 mm (b). Measurements were obtained at the maximum of the o-H 2 gas line. FIG. 4.11. 92 Vibrational CARS spectra of 1% p-H 2 in He at T V = 21 K and P 0 = 20 bar. FIG. 4.12. 93 CARS signal dependence vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver. Expansion of 1% p-H 2 mixture in He at T V = 21 K, P 0 = 20 bar, nominal pulse duration: 200 μs, and Z = 6 mm (a) and Z = 24 mm (b). Measurements were obtained at the maximum of the p-H 2 cluster line. FIG. 4.13. 94 Log-Log plot of cluster CARS signal vs. distance from nozzle, Z, for a 1% n-H 2 mixture in He at T V = 25 K and P 0 = 20 bar. FIG. 4.14. 96 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of pure p-H 2 at T V = 300 K and P 0 = 5 bar without (a) and with (b) an etalon. The spectra are calibrated against the known position of the line in the gas phase. xviii FIG. 4.15. 97 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at T V = 60 K and P 0 = 20 bar without (a) and with (b) an etalon. FIG. 4.16. 98 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of liquid p-H 2 at T V = 26 K and P 0 = 20 bar at various pump and Stokes laser energies. Dotted and dashed lines refers to p-H 2 spectra obtained in hcp and fcc crystal lattice structures. FIG. 4.17. 100 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of liquid p-H 2 at T V = 25 K and P 0 = 20 bar at various Stokes pulse energies and constant pump energy. FIG. 4.18. 101 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at various nozzle temperatures: P 0 = 20 bar, Z = 5 mm. FIG. 4.19. 102 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at T V = 40 K, P 0 = 20 bar, Z = 5 mm. Panels (a) and (b) shows spectra with and without a 70% optical transmission filter, respectively. FIG. 4.20. 103 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at T V = 20 K, P 0 = 20 bar, Z = 5 mm, and without an etalon. Panels (a) and (b) refer to spectra obtained at Y = 38 and 39 mm, respectively. FIG. 4.21. 104 Rotational CARS spectra obtained at different pulse delays upon expansion of a 1% p-H 2 mixture in He at T V = 20 K, P 0 = 20 bar, Z = 5 mm, Y = 38 mm, and without an etalon. FIG. 4.22. 105 Rotational CARS spectra obtained at different Z-positions upon expansion of a 2% p-H 2 mixture in He at T V = 23 K, P 0 = 20 bar, Y = 36 mm, and without an etalon. FIG. 4.23. 106 Rotational CARS spectra obtained at different Y-positions upon expansion of a 2% p-H 2 mixture in He at T V = 23 K, P 0 = 20 bar, Z = 5 mm. Panels (a) - (b) were obtained without an etalon while panel (c) was obtained with an etalon. FIG. 4.24. 107 Rotational CARS signal dependence of 2% p-H 2 mixture in He at the gas line vs. Y- position at T V = 40 K (a) and T V = 23 K, respectively. xix FIG. 4.25. 108 Vibrational CARS frequency of the Q 1 (0) line in clusters as a function of p-H 2 molecules in expanding He gas. Horizontal dashed lines show the Q 1 (0) frequencies in solid p-H 2 at 4 K and in liquid p-H 2 at 18 K. Solid squares are points from previous work while open squares are from current work. FIG. 4.26. 109 Rotational CARS signal dependence of p-H 2 gas line vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver for various pulse durations at T V = 60 K. FIG. 4.27. 110 Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 0.5% p-H 2 mixture in He at T V = 20 K, P 0 = 20 bar, Z = 5 mm, Y = 37 mm, and without an etalon. FIG. 4.28. 111 Rotational CARS signal dependence of 0.5% p-H 2 mixture in He at the max of the cluster peak in Fig. 4.27 vs. Z-position at T V = 20 K. FIG. 5.1. 119 CARS spectra of the Q 1 (0) transition of p-H 2 molecules in clusters obtained upon expansion of gas having X = 1% p-H 2 /D 2 (a - c) and X = 8% (d - f). The fraction of D 2 in the expanding gas (Y) as well as nozzle temperature is shown in each panel. The spectra were measured at L = 10 mm without an intra-cavity etalon. FIG. 5.2. 120 CARS spectra of the Q 1 (0) line of p-H 2 clusters at X = 100% with varying D 2 content, Y, obtained upon expansion at T = 22 K and P = 3 bar and measured without an intra-cavity etalon. Traces (e) – (f) were measured with intra-cavity etalon. All spectra represented were obtained at L = 10 mm. FIG. 5.3. 122 Frequencies of the Q 1 (0) line in p-H 2 /D 2 clusters versus the deuterium content, Y, at X = 100%, 8%, and 1% in panels a), b), and c), respectively. Solid squares represent frequencies measured at distances of L = 10 mm while open squares indicate measurements obtained at longer distances as specified in each panel. Solid and open triangles indicate the higher energy peaks for L = 10 and 35 mm, respectively, in panel a) as observed from Fig. 2. The error bars represent mean square deviation of several measurements. Lines are linear fits according to eqs. (5.1 – 5.3). The dashed line represents the dependence expected in bulk. FIG. 5.4. 128 Fraction of D 2 in the pH 2 rich phase as a function of the fraction of D 2 in the prepared gas sample. Solid shapes indicate points obtained at L = 10 mm while open circles represents points obtained at L = 20 mm for X = 1%. xx FIG. 5.5. 132 Phase diagram of p-H 2 /D 2 mixture at low temperature based on eqs. 5.5 and 5.6. FIG. 6.1. 142 CARS spectra of the S 0 (0) transition in both solid (a) – (c) and liquid (d) – (f) pH 2 at different temperatures as measured without an intra-cavity etalon. Measurements in liquid were obtained at P = 2 bar. The frequency of the S 0 (0) line in the gas phase at 354.37 cm -1 is shown by a dashed vertical line. FIG. 6.2. 143 CARS spectra of the Q 1 (0) line of pH 2 at different temperatures as obtained with an intra- cavity etalon. Traces (a) and (b) are in solid, whereas traces (c) – (h) are in liquid. All spectra in the liquid were obtained at a constant pressure of 3 bar except trace (h) which was measured at 9 bar and without an intra-cavity etalon. FIG. 6.3. 144 Frequencies of the Q 1 (0) line in liquid pH 2 at different temperatures and pressures as indicated in the legend. Lines are linear fits to the results. Open circles show the results at constant pressure in the cell of about 3 bar and at indicated temperatures. FIG. 6.4. 145 Frequencies of the Q 1 (0) line in both solid and liquid pH 2 . Results in liquid were obtained at a constant pressure of 3 and 9 bar, as shown by open squares and circles, respectively, and were linearly extrapolated to SVP based on the results shown in Figure 3. Frequencies in liquid measured directly at SVP (solid squares) are also included for comparison. The only previous measurement of liquid pH 2 at 18 K and SVP is shown by a star. Frequencies obtained in solid in this work and at SVP are shown by regular and upside down triangles, respectively. FIG. 6.5. 147 Density vs. temperature in solid (squares) and liquid (triangles) pH 2 . The dotted line indicates the fitted density of liquid hydrogen, which includes an extrapolation into the metastable range below the freezing temperature. FIG. 6.6. 148 Q 1 (0) frequencies measured in this work for solid and liquid pH 2 are shown by filled squares. The experimental points in liquid were obtained at 3 and 9 bar and extrapolated to SVP. Solid curves show the fits of both solid and liquid pH 2 results to Eq. (6.1) with identical parameters. The Q 1 (0) frequency in solid at SVP obtained by Kerr et. al is shown by triangles. The dotted curve shows the estimated frequency in the liquid below the freezing point, which was obtained from Eq. (6.1) using the estimated density of liquid pH 2 at low temperature as shown in Fig. 6.5. xxi FIG. 7.1. 158 Schematic of cryogenic copper cell. The 3-cm long copper cell has an 18 mm diameter optical clearance enclosed by two 3-mm thick CaF 2 windows. The adjacent side of the cell provides a 9 mm clearance in which a stainless steel adapter with 1/16” thick copper tubing is attached for gas mixture introduction. FIG. 7.2. 160 Energy level diagram of water molecules. Rotational level labels to the left of the lines represent J KaKc and correspond with the ortho- and para- labels on the right; o and p, respectively. Solid arrows indicate observed ro-vibrational transitions in ν 1 , ν 2, and ν 3 bands at low temperature. FIG. 7.3. 161 IR absorption spectra of the ν 1 , ν 2, and ν 3 regions of H 2 O of a 1:2000 H 2 O:Ar sample. Panels (a) and (b) refer to spectra obtained after completing ~ 70 min deposition at a nominal temperature of 4 K and after an additional 1400 min, respectively. FIG. 7.4. 164 IR absorption spectra of the ν 1, ν 2 and ν 3 regions of H 2 O in a 1:2000 H 2 O:Ar sample at 4 K (a) and 50 K (b). Timeline refers to spectra obtained after completing ~ 70 min deposition of mixture. FIG. 7.5. 167 IR spectra in the ν 3 / ν 1 region upon completion of ~ 40 min. 1:1000 H 2 O:Ar sample deposition at 4 K (a), ~1730 min. conversion at 4 K (b), annealing to T = 30 K within 1 min (c), after constant heating for 5 min at 30 K (d), and after re-cooling the sample back to 4 K (e). FIG. 7.6. 168 IR spectra of a 1:1000 H 2 O:Ar sample in the ν 3 / ν 1 region upon completion of ~ 40 min. deposition at 4 K (a), annealing to T = 30 K within 1 min (b), after constant heating for 5 min at 30 K (c), and after re-cooling the sample back to 4 K (d). FIG. 7.7. 169 Normalized IR absorption spectra of ν 1 / ν 3 region of H 2 O at various temperatures after conversion to p-H 2 O and subsequent fast annealing, (a) – (c). Panel (d) shows comparable spectra of normal H 2 O at 1 mbar and T = 295 K. FIG. 7.8. 170 Magnified spectra of traces (b) - (d) from Fig. 7.7 in the range of 3750 – 3850 cm -1 . Solid lines represent o-H 2 O transitions while dashed lines represent p-H 2 O transitions. Unlabeled lines represent overlaps of ortho and para transitions. xxii FIG. 7.9. 171 IR absorption spectra of ν 1 / ν 3 region of 1:100 H 2 O:Ar samples at T = 4 K after ~ 40 min completed deposition (a) and after 1500 min conversion (b). The panels are scaled to illustrate dimer features. FIG. 8.1. 187 Density of 4 He as a function of temperature. FIG. 8.2. 192 Argon predissociation spectra of (H 2 O) N ·H + for N = 2 – 11 with N decreasing down the figure. FIG. 8.3. 193 Preliminary timing schematic for ionization and IR probing of molecules in pulsed helium droplets. FIG. A1.1. 209 The draft of the pulsed valve (099-0215-900 Solenoid Valve, Axial,28 V DC, SST body, conflat,0.039" orifice (1 mm),Kel-F poppet, copper gasket). (A) – wires to the driver, (B) – A-lock type tube fitting, (C) – body, and (D) – faceplate. FIG. A1.2. 213 Three different faceplate orifice cross sections. FIG. A1.3. 214 Final modification of pulsed valve faceplate. xxiii Abstract This dissertation covers several different aspects of spectroscopy of molecules and molecular clusters embedded in low-temperature matrices, such as helium droplets. First, details on the formation and optimization of He droplets will be discussed. A new method of measuring droplet sizes for cw nozzle expansions using mass spectrometry was developed. The results of the measurements of the sizes of the droplets in pulsed expansion as a function of temperature will be described. Details on the electron-impact ionization of He droplets will also be discussed as well as a simple method of modeling the ionization and excitation of He atoms in the droplet. In addition, preliminary measurements on the size distribution of He droplets produced at very low temperature of 5 – 7 K in continuous expansion will be addressed. Using matrix isolation in He droplets, vibrational spectra of clusters consisting of para-H 2 or para-H 2 /D 2 have been obtained using coherent anti-Stokes Raman spectroscopy (CARS). The vibrational frequency of para-H 2 molecules obtained upon expansion of neat para-H 2 /D 2 gas or liquid was found to be very similar to that in bulk solid samples having equal composition. On the other hand, spectra in clusters obtained upon expansion of 1% para-H 2 /D 2 clusters seeded in He are liquid and have a considerable frequency shift, which indicate phase separation of the two isotopes in clusters at low temperature. The onset of phase separation in para-H 2 /D 2 mixtures is predicted at approximately 3 K providing further evidence of super-cooled liquid hydrogen clusters. xxiv To address the Raman spectra observed in liquid H 2 clusters, vibrational and rotational spectra of bulk liquid para-H 2 at temperature of T = 14 – 26 K and of solid at T = 6 – 13 K have been obtained using coherent anti-Stokes Raman scattering technique. The vibrational frequency in the liquid increases with temperature by about 2 cm -1 , and the shift scales with the square of the sample’s density. An extrapolation of the vibrational frequency in the metastable para-H 2 liquid below the freezing point is discussed. The results indicate that the vibron hopping between the molecules is active in the liquid, similar to that previously found in the solid. Matrix isolation has also been performed in argon solid matrices based on a custom-made cryogenic optical cell. Single water molecules have been isolated in solid Ar matrices at 4 K and studied by ro-vibrational spectroscopy using FTIR in the regions of the ν 1 , ν 2 , and ν 3 modes. Upon nuclear spin conversion at 4 K, essentially pure para- H 2 O was prepared followed by subsequent fast annealing generating ice particles. FTIR studies of the vapor above the condensed water upon annealing to T ≥ 250 K indicate fast re-conversion of nuclear spin to equilibrium conditions. Our results indicate that nuclear spin conversion is fast in water dimers and larger clusters, which preclude preparation of concentrated samples of para-H 2 O, such as in ice or vapor. Chapter I. General Introduction 1.1. Scope of Work This thesis can be separated into projects focused into four major areas. Although distinct, each project highlights the use of matrix isolation as an advantageous tool for studying molecules and molecular aggregates. In addition, by coupling matrix isolation with rotational and vibrational spectroscopy, both fundamental and practical information about these systems can be obtained. The first project is devoted to measuring He droplet size distributions for droplets formed at cw source temperatures in the range of 5 – 7 K. Due to experimental difficulties, this temperature range was not covered by previous measurements, so that the droplet size distribution was unknown before this study. Since the He droplet size is a necessary parameter for the spectroscopy of molecules and molecular aggregates embedded inside the droplets, detailed knowledge of droplets in the 5 – 7 K range is of critical importance for the interpretation of the experimental results. Here we have developed a novel technique for measuring droplet size distributions and report first results. The second project is a continuation of our previous study 1,2 of liquid hydrogen clusters at very low temperature, such as supercooled para-H 2 clusters. In this work, we have discovered a phase separation in cold liquid p-H 2 /D 2 clusters isolated in He droplets via vibrational CARS spectroscopy of the p-H 2 molecules in the cluster. Based on our 1 observation and modeling of phase separation in p-H 2 /D 2 clusters, an approximate temperature of 3 K is necessary for phase separation to occur, providing further indication of supercooled liquid clusters 1 . Our CARS study of H 2 clusters in He droplets has employed a pulsed cryogenic nozzle expansion. Pulsed He droplet formation is much less characterized as compared to its continuous source counterpart. As a result, sufficient discussion is provided in characterizing the formation of He droplets in pulsed He gas expansion. In addition, due to the sensitive nature of the CARS experiments, very detailed Raman spectra of H 2 clusters have been obtained in the course of this work. The third section is devoted to the systematic study of the temperature dependence of the Raman spectra in bulk para-H 2 . This study focuses on the temperature dependence in bulk liquid para-H 2 for two reasons: 1) No systematic temperature dependence study of the Raman spectra in bulk para-H 2 currently existed prior to our work and 2) the observed temperature dependence in bulk liquid spectra aided previous complications in the Raman spectra of cold liquid para-H 2 clusters 1 , validating the observation of supercooled, metastable liquid clusters. The fourth project focuses on the nuclear spin conversion of water molecules. Similar to hydrogen molecules, H 2 O consists of either ortho and para nuclear spin isomers. There is a considerable interest in the ability of isolating nuclear spin components of water as they may have some important applications. Previous work has shown that matrix isolation in low temperature rare gases can be used for conversion from ortho-H 2 O to para-H 2 O. However, the conversion back to ortho-H 2 O has never 2 fully been addressed. In this work, we converted normal H 2 O to almost pure para-H 2 O by matrix isolation in solid Ar and studied the conversion by FTIR spectroscopy. Upon annealing the sample, we observed the progression of para-H 2 O back to the typical 3:1 equilibrium of ortho:para. 1.2. Experimental Techniques Two of the four projects focus on encapsulation of molecules and molecular aggregates in pulsed superfluid He droplets as described in Chapters 2 - 5. Helium droplets provide a gentle matrix for the spectroscopic studies of molecules and clusters whereby the interaction of embedded species with the He droplet is minimal as compared with other matrices. In addition, the local temperature of the He droplet is T = 0.37 K thereby reducing species to their lowest rotational and vibrational states. Due to the short flight time of molecules in a typical helium droplet apparatus and the slow nuclear spin conversion of water molecules, a different matrix isolation approach is needed for our current study of water. Fortunately, matrix isolation in solid rare gas matrices (RGM’s) has been known for some time. More specifically, matrix isolation of water molecules in solid Ar has been studied quite sufficiently. 3 The other advantage of using RGM’s is that FTIR spectroscopy is a straightforward experimental technique, whereas experiments in He droplets must employ infrared laser sources. 3 1.3. Content of the Chapters The current dissertation is outlined as follows: Chapter 2 is dedicated to the fundamentals of He droplet formation as well as preliminary experiments for the experimental determination of He droplet size distributions in the range of expansion temperatures of 5 – 7 K. Chapter 3 is devoted to the operation and characterization of our current pulsed He droplet apparatus. This is rather recent experimental technique and detailed knowledge of droplet sizes and corresponding distributions is lacking. In this chapter characterization of He droplets produced by pulsed nozzle beam expansion is addressed via mass spectrometry. Chapter 4 focuses on the Coherent Anti-Stokes Raman spectroscopy (CARS) of H 2 molecules and clusters in pulsed beams. It will start with a brief introduction of the theory of the CARS technique. A detailed description of the experimental setup and characterization and optimization of vibrational and rotational CARS spectra will be given. Chapter 5 extends our CARS experiments to include measurements on H 2 isotopic mixtures (para-H 2 /D 2 ). 4 Based on known vibron hopping in bulk hydrogen, we were able to deduce the relative abundances of hydrogen isotopes present in clusters as compared to the mixtures prior to expansion. For H 2 /D 2 mixtures, phase separation was observed for the first time and is addressed in simple thermodynamic terms. Chapter 6 concentrates on a systematic study of the vibrational spectra of solid and liquid hydrogen in the bulk. 2 This work provides an important calibration for our previously observed spectra of liquid hydrogen clusters and the subsequent shift in 4 vibrational frequency upon size of H 2 cluster. The frequency shift in clusters can be either due to a temperature dependence or cluster size effect. Current measurements of the rotational and vibrational CARS spectra in both bulk solid and liquid H 2 indicate the presence of vibron hopping which is dictated by the density of the material and subsequently the temperature. The temperature dependence on the vibrational frequency is quantitatively explored and extrapolated to supercooled liquid temperatures providing an estimate of the temperature of clusters currently studied. Chapter 7 describes results of our nuclear spin conversion study of water molecules by FTIR spectroscopy. 5 At low temperature, we observe the almost complete nuclear spin conversion from ortho-H 2 O to para-H 2 O. By rapid annealing, we were able to cluster the para-H 2 O in ice which was subsequently heated to T = 250 – 300 K. Our results indicate complete re-conversion to the 3:1 equilibrium abundance, and show the isolation of ortho and para isomers of water at room temperature are impractical. 5 Chapter 1 Bibliography 1 K. Kuyanov-Prozument and A. F. Vilesov, Physical Review Letters 101 (20), 205301 (2008). 2 R. Sliter and A. F. Vilesov, Journal of Chemical Physics 131 (7) (2009). 3 L. Abouaf-Marguin, A. M. Vasserot, C. Pardanaud, and X. Michaut, Chemical Physics Letters 447 (4-6), 232 (2007); L. Abouaf-Marguin, A. M. Vasserot, C. Pardanaud, and X. Michaut, Chemical Physics Letters 480 (1-3), 82 (2009); G. P. Ayers and A. D. E. Pullin, Spectrochimica Acta Part a-Molecular and Biomolecular Spectroscopy 32 (11), 1689 (1976); H. P. Hopkins, R. F. Curl, and K. S. Pitzer, Journal of Chemical Physics 48 (7), 2959 (1968); K. E. Kuyanov, M. N. Slipchenko, and A. F. Vilesov, Chemical Physics Letters 427 (1-3), 5 (2006); X. Michaut, A. M. Vasserot, and L. Abouaf-Marguin, Low Temperature Physics 29 (9-10), 852 (2003); X. Michaut, A. M. Vasserot, and L. Abouaf-Marguin, Vibrational Spectroscopy 34 (1), 83 (2004); J. P. Perchard, Chemical Physics 273 (2-3), 217 (2001); R. L. Redington and D. E. Milligan, Journal of Chemical Physics 37 (10), 2162 (1962). 4 R. Sliter and A. F. Vilesov, In Preparation (2011). 5 R. Sliter, M. Gish, and A. F. Vilesov, Journal of Physical Chemistry A, Submitted (2011). 6 Chapter II. Helium Nanodroplets 2.1. Introduction The study of He droplets is an active area of research. Small He droplets have demonstrated unique behavior which relates to the superfluid nature of bulk helium below 2.17 K. Microscopic manifestations of superfluidity in helium clusters have been observed by a variety of methods, both theoretically 1 and experimentally 2,3 . Of these approaches, the most interesting and applicable method is the capture of various foreign atoms and molecules and their subsequent laser spectroscopic study. Due to the superfluidity of the droplets, viscous drag on the motion of the foreign species in the droplets is vanishingly small. As a result, high-resolution spectra of molecules in He droplets can be obtained. Several detailed reviews are available regarding the spectroscopy of atoms and molecules in helium droplets. 3 This chapter is dedicated to reviewing our current knowledge of the helium droplet technique which is used in this work. This chapter is organized as follows: 1) brief overview of helium droplet technology, and 2) size distributions of large droplets (> 10 8 He atoms) produced by a continuous nozzle source. 7 2.2. Fundamentals of Helium Droplet Formation 2.2.1. Supersonic Expansions Detailed descriptions of free jet expansions can be found in several excellent reviews. 4 As a result, only a general description is provided for clarity. A free-jet atomic or molecular beam is a neutral beam that is extracted from a supersonic jet expansion from a high-pressure gas source into a low-pressure ambient background (P b ). The gas starts from a negligibly small velocity at a stagnation pressure (P ) and temperature (T 0 0 ). Due to the imposed pressure difference (P – P 0 b ), the gas accelerates toward the source exit. The gas will exit the source at different speeds depending on whether or not the pressure ratio P ( ( ) ) ( ) 1 / − γ γ /P exceeds a critical value, , where γ ≡ C /C 2 / 1 + ≡ γ G 0 b p v . If the pressure ratio is much less than this critical value, the gas will exit at subsonic speeds, velocities lower than local speed of sound, with exit pressure nearly equal to P b and without any further expansion. As the pressure ratio is increased beyond the critical value, the flow is considered under-expanded and subsequently expands. Due to the low background pressures, the expansion is isentropic and the gas cools due to pressure flow work generated from the pressure gradient. The cold molecules from the expansion eventually collide with warm background molecules present in the vacuum chamber and a shock wave is formed. Assuming the expansion of an ideal gas and neglecting the effects of heat conduction and viscosity, the temperature, pressure, and number density can be 8 calculated as a function of distance from the expansion source. For an isentropic expansion at constant γ: 2.1 2.2 In this approach, the final parameters only depend on the initial conditions and the Mach 2.3 where for a monotonic gas γ = 5/3 and A = 3.3. For large P 0 /P b , the dimensions of the rom conversion of the enthalpy of the expanding gas to translational velocity and is given by equation 2.4: ( ) () () 1 / 2 1 / 0 0 2 1 1 / − − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = γ γ γ γ γ R M T T P P ( ) number M(R), which reflects the velocity of the expansion and is dependent on P 0 /P b . At sufficiently large distances from the source (R/d > 10), the jet can be approximated as a spherical expansion from a point source and the Mach number can be evaluated analytically according to equation 2.3. shock wave become sufficiently large in comparison with the size of the apparatus that the shock wave structure disappears and a free molecular flow occurs. Considering energy conservation, the cooling process results f () () 1 / 1 2 1 / 1 0 2 1 1 / / − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = γ γ ρ ρ R M T T n n () − γ 0 0 1 − ⎟ ⎞ ⎜ ⎛ ≈ γ R A R M ⎠ ⎝ d 9 2.4 where V is the velocity of the expanding gas, h is the enthalpy, and h 0 is referred to as the stagnation enthalpy per unit ma nt throu hout th exp sion n any mline. Assuming an ideal gas, the change in enthalpy as a function of temperature at constant pressure is the heat capacity, C . Assuming C is a constant over the temperature range, the maximum velocity of the expanding gas is given by equation 2.5: 0 2 2 h V h = + ss and is consta g e an o strea p p ( ) T T C V p − ⋅ = 0 2 2.5 As a result, if the final velocity is known, the temperature can be calculated. The supersonic expansion discussed above does not take into account the effects ch complicates understanding due to the rapidly changing param such as temperature, pressure, and density involved in nucleation which overlaps the properties of the clusters with the expanding gas which cannot be separated. General properties of free jet expansions can be utilized to provide qualitative insight into clustering in the case of He droplets. For example, three-body collisions are responsible for the formation of clusters and scale with p 2 d/T 2 , where p is the initial density, d is the diameter of the orifice, and T is the stagnation temperature. 5 As a result, cluster formation is enhanced by using small nozzle orifices, large backing pressures, and low temperatures. of clustering whi eters 0 0 0 0 10 2.2.2. Helium Expansion Regimes In the case of continuous nozzles, helium droplets can be produced by supersonic expans id helium at high pressures through a small nozzle orifice, typically 5 μm, into vacuum. Characteristic parameters of He droplets depend ozzle temperatures are T 0 = 10 - 35 K for stagnation pressures P 0 = 20 - 80 bar. 10 K for stagnation pressures P 0 = 20 - 80 bar. ion of pre-cooled helium gas or liqu on the expansion conditions as shown in Fig. 2.1 for different regimes of continuous modes of jet operation. One can see that there are four distinct regimes for He droplet production: 1) Sub-critical – He droplets are produced from condensation of cooled He gas. Corresponding n 2) Critical – He droplets formed near the critical point. For example, production occurs for nozzle temperature approximately T = 10 K at a stagnation pressure P 0 0 = 20 bar. 3) Super-critical – Large He droplets are produced by the break-up of a liquid helium at the later stages of the expansion. Corresponding nozzle temperatures are T = 8 - 0 4) Finally, at T < 4 K a well collimated liquid jet is formed with subsequently break up into very large He droplets, having diameter comparable to the nozzle diameter. 11 Pro on the larger clusters can be formed in the range of 10 5 – 10 7 atoms (T 0 = 10 – 8 K). The size of the He droplet under sub-critical expansion conditions follows a log- where σ and μ are the standard deviation and mean of the distribution for the natural log of the size and can be transformed into the average droplet size as: 2.7 mal distribution is comparable with the value of 〈N 〉. duction of He droplets in the sub-critical regime yields smaller average droplet sizes order of 10 3 4 – 10 atoms (T = 17 - 11 K). In the super-critical regime, much 0 normal distribution 6,7 : 2.6 () ( ) ⎟ ⎟ ⎜ ⎜ − = N exp N P ⎠ ⎞ ⎝ ⎛ − 2 2 2 σ μ lnN N σ 2 π 1 ⎟ ⎟ ⎞ ⎜ ⎜ ⎛ + = σ μ exp N 2 ⎠ ⎝ 2 where the full width at half maximum (FWHM) of the log-nor 12 FIG. 2.1. Average He droplet size and mean diameter measured at different stagnation pressures as a function of nozzle temperature. 8 Red dots correspond to typical expansion conditions of P = 20 bar. 0 13 2.3. Size Distribution of Very Large He Droplets 2.3.1. Introduction The average values obtained in Fig. 2.1 were measured by the deflection of a continuous beam of He droplets upon capture of Xe atoms from a secondary beam 6,7 or by the deflection of negatively charged droplets 9 in an electric field for N He < 10 4 and 10 5 < N <10 7 He , respectively. Unfortunately, these experiments are not universal in which these results cannot be applied to different systems in other laboratories. For example, the recent introduction of a pulsed nozzle He expansion cannot rely on continuous nozzle results. Due to the delicate nature of these experiments, reproduction is difficult and specialized. In addition, these experiments cannot be applied to systems larger than 10 7 atoms. Fig. 2.1 shows there is a considerable range of temperatures of 5 – 7 K which has not been characterized, i.e., of unknown average size and size distribution. Here we will present the first determination of the size distribution of the droplets in this regime. Recently, a method of measurements of average droplet sizes has been developed in our laboratory 10 which is based on the extinction of the droplets in collision with room temperature He gas. The results are in quantitative agreement with previous works in regime 3 in Fig. 2.1. 6,7,9 In addition, this technique has also provided average sizes of the droplets obtained at T 0 = 5 – 7 K. Here, we have developed a method for measuring the droplet size distribution. Details on the experiments for measuring clusters sizes can be found elsewhere. 10 The remainder of this chapter is devoted to measurements on the size 14 distribution of He droplets produced by cw nozzle expansion at temperatures lower than T 0 = 7 K. The technique is based on intensity measurements of the ion signal produced upon electron beam ionization of single droplets. 2.3.2. Continuous Nozzle He Droplet Apparatus The schematic of the molecular beam apparatus is shown in Fig. 2.2. Helium droplets are formed by expanding high purity (99.9999%) He gas at a pressure of P 0 = 20 bars into vacuum through a 5 μm diameter nozzle at temperatures in the range of T 0 = 4 – 25 K. The beam is collimated by a 0.5 mm diameter skimmer and passes through two 6- cm long pickup cells in the main vacuum chamber. Further downstream, the droplet beam passes through a differential pumping stage and enters a UHV detection chamber, which hosts a quadrupole mass spectrometer, Extrel MAX300, equipped with an electron impact ionizer. In order to detect single droplet events, the droplet beam was attenuated by approximately a factor of 3·10 3 and 3·10 4 by placing 100 and 35 μm diameter orifices, respectively, on the beam axis. The orifices have been mounted on a manipulator arm and hosted in the differential pumping stage. 15 FIG. 2.2. Schematic of He droplet apparatus. NZ – cold nozzle, SK –skimmer, PC1 and PC2 –pickup cells, BG – Baratron vacuum gauge, IG1 and IG2 – ion gauges, SH1 and SH2 – beam shutters, A1 and A2 – 6 mm diameter apertures, GV1 and GV2 – gate valves, EI – electron impact ionizer, IB – ion bender, QMS – quadruple mass spectrometer. 2.3.3. Signal Acquisition and Computer Interfacing For droplet size distributions measurements, we utilize the fast response time of the electron multiplier of the mass spectrometer housed in the detection chamber. Consider for example the ionization and detection of a single droplet. The time of flight of a droplet through the ionization region amounts to about 50 – 100 μs. During this time, a droplet experiences a large number (10 3 – 10 4 ) of collisions with 100 eV electrons. Ion fragments obtained upon electron-impact ionization are mass-selected using the quadrupole mass spectrometer. The (He + 2 ) fragment (M = 8) is the largest contributor from droplets and is best suited for droplet detection. Here, once the (He + 2 ) ions collides with the detector’s cathode, an avalanche of electrons are produced which 16 lasts for a few nanoseconds. Thus, a series of pulses are generated during the flight of the droplet through the ionizer. Due to the slow response time of the pre-amplifier of about 10 μs, these individual pulses cannot been resolved As a result, the signal from one droplet produces a pulse having width of about 100 μs. The attenuation of the droplet beam eliminates the effects of simultaneous detection of multiple droplets. The droplet pulses have been recorded by a fast digitizer (National Instruments PCI-MIO-16E-4) having resolution of 10 μs per channel. A LabView data acquisition program is employed to record the total events that occur. Large time segments of about 10 seconds each have been recorded to ensure sufficient number of detected pulses. As a result, several thousands of events were recorded each time. 2.3.4. Average He Droplet Sizes Fig. 2.3 illustrates results 10 of the average helium droplet size for various temperatures based on the attenuation of the He droplet beam upon multiple collisions with Ar and He atoms at room temperature, as shown by solid squares and triangles, respectively. These results were measured in our laboratory by Luis Gomez and are presented here for convenience. Detailed discussion on the average droplet size can be obtained elsewhere. 10 Previous deflection results are shown by stars. 6,9,11 17 4 6 8 1012 1416 18 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 100 1000 N(He) via He gas N(He) via Ar gas <N(He)> (table) Droplet diameter, nm N He Nozzle temperature, K FIG. 2.3. Average He droplet size obtained at varying nozzle temperatures from a continuous expansion of He gas at a stagnation pressure of 20 bars and through a 5 μm nozzle. The results of the titration measurements with Ar and He gas are shown by solid squares and triangles, respectively, as obtained previously. 10 Results of previous deflection measurements 6,9,11 are shown by stars. Corresponding droplet diameters (nm) are given on the right-hand side. 2.3.5. Counting Pulses from Very Large He Droplets Fig. 2.4 illustrates a series of time resolved measurements for a variety of nozzle temperatures below T 0 = 6.5 K for a 100 μm pinhole at an electron multiplier voltage of 2400 V. Each panel represents a time period of about 10 ms. Counts from droplets at temperatures higher than T = 6.5 K cannot be obtained reliably due to the small 0 18 magnitude of the pulses. Due to dark noise at high applied multiplier voltage, a small number of counts are still observed even in the absence of He droplets. This noise is due to the increased level of spontaneous electron emission at high voltages as well as due to some ionization of the background gas in the detection chamber as well as cosmic rays. In addition, the higher the electron multiplier voltage, the larger the rate of the background counts. As a result, the right-hand side panels of Fig. 2.4, (e) – (h), represent pulse counts with the direct He beam blocked from reaching the ionizer by half-closing valve GV2. Using GV2 allows us to account for the background pressure due to He gas. Panels (a) – (d) represent total signal from both He droplets and background. As shown in Fig. 2.4 for the case of attenuation by 100 μm pinhole, some of the pulses are overlapped with other pulses, which may influence the statistics of the signal. Therefore the flux was further reduced by employing a 35 μm orifice, as shown in Fig. 2.5, which shows no pulse overlaps. Here the total number of counts is reduced due to a factor of about 8 smaller cross section of the 35 μm pinhole. Comparison between panels (d) and (h) in Fig. 2.5 at T 0 = 6.5 K for droplets and background, respectively, show similar count amplitudes. The pulses observed in panel (h) are due to single electrons, in which the intensity distribution reflects the different level of amplification of the electrons. 19 0 1 2 3 4 5 a) T 0 = 5.4 K T 0 = 5.4 K T 0 = 5.7 K T 0 = 6.0 K T 0 = 6.5 K 0.0 0.1 0.2 e) 0 1 2 3 b) T 0 = 5.7 K Intensity, V 0.00 0.05 0.10 0.15 0.20 f) 0.0 0.5 1.0 1.5 2.0 c) T 0 = 6.0 K 0.00 0.05 0.10 0.15 0.20 g) 0.0 0.2 0.4 0.6 d) Time, ms Background T 0 = 6.5 K Time, ms Droplets 0.00 0.05 0.10 10 0 10 h) 0 FIG. 2.4. 10 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2400 V. The results were obtained using a 100 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. 20 0 2 4 6 8 T 0 = 5.4 K a) 0.0 0.1 0.2 T 0 = 5.4 K 0 1 2 T 0 = 5.7 K b) 0.0 0.1 0.2 0.3 0.4 T 0 = 5.7 K T 0 = 6.0 K T 0 = 6.5 K 0 1 2 T 0 = 6.0 K Intensity, V c) 0.0 0.1 0.2 0.3 0.0 0.2 0.4 100 100 T 0 = 6.5 K Time, ms Time, ms Background d) d) c) b) a) Droplets 0 0.0 0.1 0.2 0.3 0.4 0 FIG. 2.5. 100 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2400 V. The results were obtained using a 35 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. Although not shown by the sample pulse measurements in Figs. 2.4 – 2.5, the intensity of some of the pulses is higher than the maximum input voltage of the data acquisition card of 10 V. As a result, Figs. 2.6 and 2.7 show sample pulse count results for an electron multiplier voltage of 2300 V for a 100 and 35 μm orifice, respectively. Here, similar results are observed as shown in Figs. 2.4 – 2.5. 21 0 1 2 3 4 T 0 = 5.4 K a) 0.00 0.05 0.10 0.15 0.20 e) f) g) h) T 0 = 6.5 K T 0 = 6.0 K T 0 = 5.7 K T 0 = 5.4 K 0 2 4 T 0 = 5.7 K b) 0.00 0.05 0.10 0.15 0.20 0.25 0.0 0.2 0.4 0.6 0.8 1.0 T 0 = 6.0 K c) 0.00 0.05 0.10 0.15 0.20 0.0 0.1 0.2 0.3 0.4 0.5 T 0 = 6.5 K d) Intensity, V Time, ms 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Background 20 0 20 Time, ms 0 0 20 Droplets FIG. 2.6. 20 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2300 V. All panels were obtained using a 100 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. 22 FIG. 2.7. 100 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 2300 V. All panels were obtained using a 35 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. In order to address the large number of background counts as well as the possible effect of saturation on the electron multiplier, Fig. 2.8 demonstrates pulse counting results for a 35 μm at 1800 V electron multiplier voltage at T 0 = 5.4, 5.7, and 6.0 K. Due to the lower level of amplification, reliable results could not be obtained for T 0 = 6.5 K. In addition, data was collected for several minutes to provide sufficient counts for 23 statistical purposes. As a result, 1000 ms time periods are shown. In addition, significant reduction in background counts is observed at low voltage of the multiplier. FIG. 2.8. 1000 ms segment of signal for a variety of source temperatures at P 0 = 20 bar and electron multiplier voltage of 1800 V. All panels were obtained using a 35 μm pinhole. Panels (a – d) represent pulse counts for He droplets while panels (e – h) represent background counts where direct droplet beam was blocked. 2.3.6. Size Distribution of Very Large He Droplets The counts are analyzed using the peak finder utility in ORIGIN computer application which defines peak positions and peak amplitudes based on defined parameters. It is important to note that the widths of small and large amplitude peaks are 24 somewhat different. However, it is the integral of the peaks which is representative of the droplet size. As a result, Fig. 2.9 illustrates the normalized dependence of the integrated area per unit amplitude (A/I) as a function of the amplitude (I) for a series of small, medium, and large amplitude peaks. From these results, larger peaks can be corrected for their increased width in which the area of the peaks can be obtained. Due to the large size of the droplets, we have assumed that the detected ionization signal scales with the geometrical cross-section of the droplet as (N 2/3 ) He . As a result, we can assign each count to a droplet size based on the area of the peak. -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 A/I Peak Amplitude, V A/I = 0.99 -0.26*exp(-1.48*I) FIG. 2.9. Ratio of integrated peak area to peak amplitude (A/I) vs. peak amplitude for a variety of peaks as obtained at T 0 = 6.0 K and P 0 = 20 bar. The solid line is an approximate fit and is given numerically in the lower right-hand side of the figure. 25 Fig. 2.10 shows a frequency count as a function of droplet size for a variety of temperatures below T 0 ≤ 6.5 K using a 100 μm pinhole at an electron multiplier voltage of 2400 V. The average size is shown for each temperature. For T 0 = 5.4 K, a bi-modal distribution is observed. For higher temperatures, only a single exponential decay is observed. The described measurements provide relative measurements of droplet sizes. In order to obtain the absolute size distribution, the sizes should be scaled with the known average size values, such as in Fig. 2.3. The ratio of the averages sizes at different temperatures should be similar to that obtained in Fig. 2.3, in which a factor of 10 decrease in droplet size is expected from T = 5.4 K to T 0 0 = 5.7 K and a factor of 250 from T = 5.4 K to T = 6.5 K. However, the ratio of averages between T = 5.4 K and T 0 0 0 0 = 6.5 K is only about a factor of 25. In addition, ratios between T = 5.7 K and T 0 0 = 6.0 K are comparable in which a factor of 5 is expected. Table 7.1 summarizes the ratios obtained by current size distribution measurements for all conditions studied as well as those obtained from Fig. 2.3. 26 0.1 1 10 1 10 100 Frequency Counts Droplet Size, a.u. a) T 0 = 5.4 K <N> = 2.91 1 10 100 <N> = 0.55 T 0 = 5.7 K b) 1 10 100 1000 <N> = 0.41 T 0 = 6.0 K c) 1 10 100 1000 <N> = 0.19 T 0 = 6.5 K d) FIG. 2.10. Log-Log plot of He droplet size distributions at various temperatures as obtained with a 100 μm pinhole at P = 20 bar and 2400 electron multiplier voltage. 0 Fig. 2.11 shows similar size dependence for a 35 μm pinhole at similar conditions. However, at T 0 = 5.4 K in panel (a), the bi-modal distribution is less apparent due to the reduced number of counts available. However, the ratio of average sizes is comparable to that in Fig. 2.10. 27 0.1 1 10 1 10 b) T 0 = 5.4 K) Frequency Counts Droplet Size, a.u. a) 1 10 <N> = 0.91 T 0 = 5.7 K) 1 10 <N> = 0.66 c) T 0 = 6.0 K) 1 10 100 <N> = 0.20 d) T 0 = 6.5 K) <N> = 4.75 FIG. 2.11. He droplet size distributions at various temperatures as obtained with a 35 μm pinhole at P = 20 bar and 2400 V electron multiplier voltage. 0 As discussed previously, saturation of the data acquisition card at 10 V was observed for an electron multiplier potential of 2400 V. Figs. 2.12 – 2.13 show results obtained at a reduced voltage of 2300 V for a 100 and 35 μm diameter orifice. For T 0 = 5.4 K in Fig. 2.12 (a), a bi-modal distribution is observed. However, the ratio of average sizes deviates slightly from results obtained at 2400 V. This discrepancy is not well understood and could be due to the saturation of signal at 2400 V. However, only a limited number of pulses exceeded the 10 V threshold. 28 0.1 1 10 0.1 1 10 100 1000 Frequency Count Droplet Size, a.u. 0.1 1 10 100 1000 0.1 1 10 100 1000 0.1 1 10 100 1000 d) T 0 = 6.5 K) <N> = 0.06 c) T 0 = 6.0 K) <N> = 0.21 b) T 0 = 5.7 K) <N> = 0.59 a) T 0 = 5.4 K) <N> = 0.96 FIG. 2.12. He droplet size distributions at various temperatures as obtained with a 100 μm pinhole at P 0 = 20 bar and 2300 V electron multiplier voltage. 29 0.01 0.1 1 10 0.1 1 10 100 Frequency Count Droplet Size, a.u. 0.1 1 10 100 0.1 1 10 100 1 10 100 d) T 0 = 6.5 K) <N> = 0.10 c) T 0 = 6.0 K) <N> = 0.38 b) T 0 = 5.7 K) <N> = 0.41 a) T 0 = 5.4 K) <N> = 1.63 FIG. 2.13. He droplet size distributions at various temperatures as obtained with a 35 μm pinhole at P = 20 bar and 2300 V electron multiplier voltage. 0 Fig. 2.14 shows a droplet size distribution as obtained using a 35 μm orifice at similar conditions but with a reduced electron multiplier voltage of 1800 V. Here, significant reductions in total counts are observed in which counts at T 0 = 6.5 K could not be obtained. In addition, the reduced potential significantly reduced background noise. The obtained average size ratios from Fig. 2.8 for T = 5.4 K and T 0 0 = 5.7 K indicate the appropriate factor at around 10 as expected from Fig. 2.3. However, T = 5.7 and T 0 0 = 6.0 K show comparable ratios. 30 0.01 0.1 1 1 10 100 1000 <N> = 0.15 T 0 = 5.4 K c) Frequency Count Droplet Size, a.u. 1 10 100 1000 <N> = 0.017 T 0 = 5.7 K b) 0.1 1 10 100 1000 T 0 = 6.0 K a) <N> = 0.015 FIG. 2.14. He droplet size distributions at various temperatures as obtained with a 35 μm pinhole at P = 20 bar and 1800 V electron multiplier voltage. 0 Table 7.1 summarizes the results of ratios of average size droplets (relative) as obtained from the pulse counting technique in Figs. 2.10 – 2.15 at various conditions. The ratio of absolute average droplet sizes 10 as obtained from Fig. 2.3 are also shown for comparison. Note that all ratios provided in Table 7.1 are with respect to the sizes obtained at T 0 = 5.4 K for each experimental parameter. Ratios for average sizes obtained at 2400 V multiplier voltage for both 100 and 35 μm orifices are reproducible between each other, specifically at T = 5.7 and 6.0 K. There is less agreement with T 0 0 = 31 6.5 K. Nevertheless, a qualitative trend is observed. However, comparison to absolute average sizes shows that the relative average sizes are about a factor of 2 less for T 0 = 5.7 K and by more than a factor of 10 less for T 0 = 6.5 K. Similar results are observed for 2300 V multiplier voltage data. Here, however, a discrepancy exists for the T 0 = 5.7 ratios between 100 and 35 μm orifices. In addition, only the T 0 = 6.5 K ratio is approximately constant for both multiplier voltage and orifice parameters. Ratios for a multiplier voltage of 1800 V show improvement in which the T 0 = 5.7 K ratio is approximately a factor of 10 as expected. Furthermore, the T 0 = 6.0 K ratio also improves but is still a factor of 5 lower than expected. Pulse counts at T 0 = 6.5 K at 1800 V could not be currently obtained due to signal constraints. 32 Table 2.1. Ratios of relative average droplet sizes obtained by pulse counting for several operating conditions. Ratios of absolute droplet sizes 10 measured in Fig. 2.3 are shown for comparison. Orifice Absolute Multiplier <N > He Diameter T (K) <N > 0 He Voltage (kV) Ratio Ratio 10 ( μm) 5.4/5.7 5.29 10.6 5.4/6.0 100 7.10 2.4 56.0 5.4/6.5 15.3 267 5.4/5.7 5.22 10.6 5.4/6.0 35 7.20 2.4 56.0 5.4/6.5 23.8 267 5.4/5.7 1.62 10.6 5.4/6.0 100 4.57 2.3 56.0 5.4/6.5 16.0 267 5.4/5.7 3.97 10.6 5.4/6.0 35 4.29 2.3 56.0 5.4/6.5 16.3 267 5.4/5.7 8.82 10.6 35 1.8 5.4/6.0 10 56.0 2.3.7. Conclusions Despite the qualitative trend of the pulse counting results to the absolute values obtained previously 10 , several factors are currently limiting a more quantitative agreement. As discussed earlier, we observe the M = 8 ion fragment signal by detection using an electron multiplier. Due to the slow response time of the amplifier, we cannot resolve individual events from each droplet. As a result, we observe a broad pulse 33 containing all events from the droplet in which the integrated area of the pulse is representative of the droplet size. However, the presence of background pulses in the absence of droplets produces difficulty in accounting for smaller droplets correctly. As a result, counts obtained at lower signal are less reliable. Furthermore, the intensity distributions of the background counts indicate different levels of amplification. This distribution most likely originates from the different multiplier plates from which the electron can spontaneously emit from as well as velocity distribution of the background gas present. Nevertheless, the observation of single electron pulses indicates we currently cannot account for small droplet sizes correctly based on the intensity. For example, Fig. 2.5 shows that obtained pulse intensities between droplets and background are similar. This implies that only one pulse event due to small droplets was observed. If the background counts are due to single electron events with comparable intensity to droplets, these low signal levels do not differentiate between droplet sizes. In order to distinguish pulse counts with respect to droplets, multiple events from a single droplet must be generated. In addition, the reduction in ionization probability for smaller droplets implies that some droplets may not be detected at all which may bias our obtained average droplet size to larger droplets. As a result, this work is still in progress. 34 Chapter 2 Bibliography 1 P. Sindzingre, M. L. Klein, and D. M. Ceperley, Physical Review Letters 63 (15), 1601 (1989); M. V. R. Krishna and K. B. Whaley, Journal of Chemical Physics 93 (9), 6738 (1990); M. V. R. Krishna and K. B. Whaley, Physical Review Letters 64 (10), 1126 (1990). 2 J. Harms, J. P. Toennies, and E. L. Knuth, Journal of Chemical Physics 106 (8), 3348 (1997); H. Buchenau, E. L. Knuth, J. Northby, J. P. Toennies, and C. Winkler, Journal of Chemical Physics 92 (11), 6875 (1990); M. Hartmann, F. Mielke, J. P. Toennies, A. F. Vilesov, and G. Benedek, Physical Review Letters 76 (24), 4560 (1996); A. R. W. McKellar, Y. J. Xu, and W. Jager, Physical Review Letters 97 (18) (2006); S. Grebenev, J. P. Toennies, and A. F. Vilesov, Science 279 (5359), 2083 (1998). 3 J. P. Toennies and A. F. Vilesov, Angewandte Chemie-International Edition 43 (20), 2622 (2004); M. Y. Choi, G. E. Douberly, T. M. Falconer, W. K. Lewis, C. M. Lindsay, J. M. Merritt, P. L. Stiles, and R. E. Miller, International Reviews in Physical Chemistry 25 (1-2), 15 (2006). 4 D. R. Miller, Atomic and Molecular Beam Methods. (Oxford, New York, 1988); Jet Spectroscopy and Molecular Dynamics, edited by J. M. Hollas and D. Phillips (Chapman & Hall, Bishopbriggs, 1995). 5 E. L. Knuth, Journal of Chemical Physics 66 (8), 3515 (1977). 6 J. Harms, J. P. Toennies, and F. Dalfovo, Physical Review B 58 (6), 3341 (1998). 7 M. Lewerenz, B. Schilling, and J. P. Toennies, Chemical Physics Letters 206 (1- 4), 381 (1993). 8 G. Tejeda, J. M. Fernandez, S. Montero, D. Blume, and J. P. Toennies, Physical Review Letters 92 (22) (2004). 9 E. L. Knuth and U. Henne, Journal of Chemical Physics 110 (5), 2664 (1999). 10 L. Gomez, E. Loginov, R. Sliter, and A. F. Vilesov, In Preparation (2011). 11 U. Henne and J. P. Toennies, Journal of Chemical Physics 108 (22), 9327 (1998). 35 Chapter III. Pulsed Helium Droplets 3.1. Introduction The He apparatus used in this work is a pulsed molecular beam apparatus, which is different from conventional continuous (cw) nozzle schemes used in our own group as well as in other research groups. 1,2 The outcome of the pulsed valve, such as average droplet size, is in general more difficult to characterize as compared with cw nozzles because it has additional parameters such as pulse width and repetition rate as well as moving mechanical parts such as the poppet. As a result, the temperature may be very different from the actual temperature of the expanding gas. In addition, the use of pulse nozzles has only recently been adopted in the last 10 years and the fundamentals of He droplet formation by pulsed nozzles are still not understood completely. As a result, this chapter is dedicated to detailing our current work and knowledge of pulsed nozzles for He droplet formation as well as discussing the outlook of pulsed nozzles to its continuous counterparts. This chapter is organized as follows: 1) general description of the current pulsed nozzle setup with modifications for different experiments detailed in their corresponding chapters, and 2) characterization of He droplets as produced by our pulsed valve. Finally, 3) we compare the mass spectra of the pulsed and cw nozzles in order to provide a convenient in-situ secondary standard for determining average droplet sizes. 36 3.2. Continuous vs. Pulse He Droplet Formation Despite the wide range of average cluster sizes available using continuous nozzles, several limitations arise. First, the continuous-flow source, due to the p 0 2 d scaling for cluster formation, requires a large capacity pumping rate in order to maintain appropriate vacuum conditions. Secondly, for spectroscopy experiments, pulsed lasers are necessary to study low concentrated species in the matrix. As a result for pulsed lasers and continuous nozzle sources, a significant portion of the beam is wasted. Therefore, it is desirable to improve experimental conditions by changing the constant low density beam of helium droplets to that of short pulsed droplets. A pulsed source can then be matched with a corresponding pulsed technique such as laser-induced fluorescence (LIF), laser photolysis, time-of-flight (TOF) mass spectroscopy, thereby providing enhancements to the field. The first low temperature pulsed He droplet source was produced in our group by Mikhail Slipchenko, utilizing a commercial electromagnetic valve with a customized faceplate. 3 Several additional attempts have been made following similar nozzles 4 as well as custom designs. 5 Although pumping constraints are lower for these pulsed setups, limitations exist in their shot-to-shot stability as well as limited characterization on droplet size and size distributions. Due to the limited information available, sufficient details and discussion are provided in Chapter 3 on the characterization of the current pulsed nozzle in the Vilesov lab. 37 3.3. Experimental Setup of Pulsed He Droplet Apparatus The schematic of the setup is shown in Fig. 3.1. The apparatus consists of 3 vacuum chambers (1 - 3). Chamber (1) contains the pulsed helium droplet source (B), which is mounted on a closed cycle cryostat (A). The source chamber is pumped by a 3000 L/s diffusion pump (P1) backed by a blower pump and rotary pump. Chamber (2) is an interaction chamber that can house smaller pickup cells if necessary. A nitrogen trap (D) serves as a cryopump. This chamber is pumped by a 400 L/s turbo-molecular pump (P2). Chamber (3) contains a time-of-flight (TOF) reflectron mass spectrometer (F) and a quadrupole mass spectrometer (E). This UHV chamber is pumped by two 170 L/s turbo molecular pumps (P3 & P4). The pressures achieved with typical experimental conditions are listed in Table 3.1. 38 (1) (2) (3) A B C D F E G P1 P2 P3 P4 FIG. 3.1. He apparatus. Table 3.1. Typical pressures achieved at a stagnation pressure of 20 bar and stagnation temperatures ranging from room temperature to about 15 K for pulsed valve operation at 200 μs duration. Chamber Ultimate Pressure w/o pulsed He beam Pressure w/ pulsed He beam 1 4x10 -8 – 2x10 -7 mbar 1x10 -5 – 1x10 -4 mbar 2 4x10 -7 – 1x10 -6 mbar 8x10 -7 – 4x10 -6 mbar 3 1x10 -9 – 5x10 -9 mbar 2x10 -8 – 1x10 -7 mbar The experimental setup is mounted on two steel rails, which are parallel to the apparatus axis. Each chamber can slide along these rails independently. By separating chambers, this flexible construction allows one to easily introduce or change parts as needed. In the following, each component marked by a letter in Fig. 3.1 will be described in detail. 39 (A) The pulsed nozzle assembly is cooled by a closed cycle refrigerator (Sumitomo Cryocooler, SRDK–408 DW), and its temperature is controlled by resistive heating. The pulsed nozzle is attached to a copper block with apiezon grease which is subsequently attached to the second stage of the closed cycle refrigerator, see Fig. 3.2. In addition, the stainless steel housing of the valve is wrapped in a copper sheet, which is in turn in thermal contact with the cold head for additional cooling of the valve (Not shown in current picture). An aluminum radiation shield is attached to the first stage of the cryostat in order to avoid radiation heating of the nozzle. An additional, detachable plate housed on the radiation shield covering the nozzle itself is used for enhanced cooling. Due to its restrictions, the plate is removed when performing experiments close to the nozzle, such as CARS experiments, see Chapter 4. The temperature of the pulse nozzle setup is obtained with two silicon diodes placed on the copper block (T C ) and on the copper sheet attached to the pulsed valve body (T V ). The T C sensor is located in the lower right hand side of Fig. 3.2 while the T V sensor is not shown. We found that because of the extensive heating due to the operation of the valve, T V is a more accurate description of the temperature of the expanding gas. However, due to the stainless steel housing, knowledge of the actual temperature of the expanding gas is not known accurately. 40 FIG. 3.2. Attachment of pulsed valve to second stage of closed cycle refrigerator. The current setup contains a copper sheet fitted around the pulsed valve housing (not shown) which is then attached by copper wires to the copper stage. (B) For the production of a pulsed He droplet beam, a modified pulsed valve (Parker inc., 99 series) was used. The modified construction of the pulsed valve is described in details in Appendix I. (C) A 2 mm skimmer (Beam Dynamics Inc.) is needed to collimate the pulsed He droplet beam. Skimmers ≥ 2 mm are necessary for pulsed He droplet production. (D) The liquid nitrogen trap serves as a cryopump and is used only when necessary. (F) In chamber (3), a Jordan Inc. time-of-flight mass spectrometer (TOF-MS) is installed in a vertical configuration and is equipped with an electron gun. However, it is possible to install a window instead of the electron gun for laser ionization. The TOF is 41 equipped for linear or reflectron TOF measurements each with MCP detection. This mass spectrometer is based on pulsed operation and can be used for analyzing the pulsed He droplet beam. (E) The second mass spectrometer installed in chamber (3) is a quadrupole mass spectrometer (Extranuclear Laboratories) equipped with an electron beam ionizer. This mass spectrometer is installed on-axis and scans continuously with a mass filter in the range of 0 – 300 amu. (G) A BaF 2 window is installed at the end of He apparatus as an entrance window for IR laser radiation. Experimental details describing laser systems and detection schemes for specific projects will be described in their corresponding chapters. 42 3.4. Characterization of He Droplets using Pulsed Nozzle This section is devoted to the characterization of He droplets formed by a pulsed helium droplet source employed in our lab that was used for all molecular and cluster spectroscopy work in He droplets performed in the current thesis. This section is organized into several parts focusing on 1) details of the experimental setup of the pulse nozzle itself, 2) characterization and optimization of the produced pulsed droplets as studied by mass spectrometry, and 3) estimation of droplet sizes based on ionization in helium droplets and comparison with cw nozzle results. 3.4.1. Pulsed Nozzle Operation The original pulse valve is shown in Fig. A1.1. It consists of the body (C), the head or faceplate (D), and a tube fitting (B). The valve is connected to the driver IOTA-1 by wire (A). The body and the faceplate have threads which can be tightened to one another with small copper gaskets between them. As shown in Fig. 3.2, the stainless steel pulsed nozzle assembly is attached to the second stage of a closed cycle refrigerator. The pulsed valve is an electromechanical device that operates by energizing a solenoid by a pulsed source pulling a small magnetic rod located inside the body thereby opening the valve. The rod is connected to a poppet (Kel-F material) for sealing. In the absence of electrical power, the rod and poppet are returned to the sealing point by a pusher spring. Upon opening, the IOTA-1 pulse driver at trigger time generates a 300 V electrical pulse 43 of approximately 180 μs duration time in order to open the valve and then maintains an approximate 28 V to hold the valve open for the allotted time period (pulse duration) as controlled by the driver. This operation of the valve produces heat at approximately 5 mJ/pulse (at 200 μs pulse duration) and is the predominate source of heating of the gas in the valve during operation. He droplets formed during the gas expansion from the pulsed nozzle are collimated using a 2 mm skimmer (C), pass through a high vacuum chamber (2) and enter into the quadrupole mass spectrometer chamber (3). For characterization purposes, the signal from the mass spectrometer was acquired using an oscilloscope triggered at the opening time of the pulsed nozzle by means of a delay generator. As a result, time-of- flight measurements were readily performed. The estimated distance between the pulsed nozzle and the ionizer was approximately 1.13 ± 0.03 m. A typical mass spectrum of pure helium is shown in Fig. 3.3 as obtained at T V = 16 K and P 0 = 20 bar. The mass peak with the largest signal associated with He is M = 4 due to atomic He. The large, broad peak near M = 17 – 19 is due to monomer and dimer water molecules trapped in He droplets. As observed, helium clusters up to M = 36 are present for the shown scan. Larger masses up to M = 70 are typically observed but not shown. Since (He 2 ) + is the dominant feature in the mass spectra, which undoubtedly stems from He droplets, M = 8 signal has been used to characterize the droplet beam. 44 -5 0 5 10 15 20 25 30 35 40 45 50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 File: 09-06-11_1815 Pure H e expansion Pulse D uration: 200 μs Back Pressu re: 20 b ar Sensitivity of BW pre-am p: 2*100 nA/V Ionizer: 5 m A Electron M ultiplier: 2.5 kV Tem perature: 10 K Signal, V m/z FIG. 3.3. Mass spectrum obtained via pulsed gas expansion of pure helium and detected by quadrupole mass spectrometer. The signal was recorded using a boxcar integrator set at delay of 3.2 ms and Δt = 3 μs. The large intensity peak in the range of M = 17 – 19 stems from water molecules and dimers trapped in He droplets. Examples of the temporal profiles of the mass spectrometer signal set at m/z = 4 and 8 at P 0 = 15 bar and T V = 16 K are shown in Fig. 3.4. The observed time delay is corrected due to the approximately 350 μs delay of the pulse valve with respect to the electrical trigger pulse. As a result, all timing schemes in this section have been corrected for the approximate time delay and refer to the beginning of the gas pulse. The profiles show a strong feature comprised of several narrow peaks at approximately 3.15 ms after the opening time of the valve. The observation of several narrow peaks around 3.15 ms imply some form of interference produced by droplet formation creating a 45 distribution of clusters which have different velocities or a secondary pulse of the valve. For m/z = 4, a weak and broad feature is observed around 2.6 ms and is indicative of fast He gas not formed in droplets as observed previously in continuous nozzles. 6 An additional feature only observed for M = 4 at 3.45 ms indicates possible interference at the skimmer generating He gas production, as this feature is not observed for M = 8. 2.02.53.03.54.04.55.0 -0.2 -0.1 0.0 Signal, V Time, ms -0.4 -0.3 -0.2 -0.1 0.0 M = 8 M = 4 File: 08-11-2010_1200 FIG. 3.4. Temporal profile of the droplet signal as measured at m/z = 4 and 8. T V = 16 K, P 0 = 15 bar at 200 μs nominal pulse duration and 20 Hz repetition rate. Both profiles show a feature seen at ~ 4.0 ms time delay in Fig. 3.4 which is only observed at T V < 21 K, indicating it originates from large clusters. However, this weak peak is not mass selected as is the prominent peak at 3.15 ms. At attempt to analyze the 4.0 ms peak with the mass spectrometer revealed that it represents a broad unresolved signal having maximum at M = 0 and extending towards M ~ 50. Therefore, this peak was assigned to large ionized droplets which remain relatively unaffected by the RF field 46 of the mass-filter. Thus these droplets propagate along the beam axis until attracted by the large negative potential of the cathode of the electron multiplier. 3.4.2. Optimization of He Droplet Formation Fig. 3.5 illustrates the temperature dependence of the dominant peak observed in Fig. 3.4 at t = 3.15 ms as measured at M = 8 at typical operating conditions (P 0 = 20 bar, nominal pulse width of 200 μs, repetition rate = 20 Hz). The onset of clustering occurs at temperatures beginning at about T V < 30 K. With decreasing temperature, the droplet signal increases, reaches a maximum at T V = 17 – 18 K and subsequently decreases at lower temperature. These results compare reasonably to previous results using the same pulsed valve. 3 The behavior of the cluster signal with temperature produced using the pulsed valve is also comparable to that in continuous systems in which a gradual rise in droplet size is observed with decrease of temperature. 1 As a result, decreasing the temperature of the expanding gas must lead to an increase of the degree of clustering. 47 12 14 16 18 20 22 24 26 28 30 32 0 100 200 300 400 500 File: 09-06-09_temperature Pulse Duration: 200 μs Back Pressure: 20 bar Sensitivity of pre-amp: 1*100 nA/V Ionizer: 5 mA Electron Multiplier: 2.5 kV Mass: 8 m/c Intensity, mV T V , K FIG. 3.5. Temperature dependence (T V ) of m/z = 8 signal using pulsed nozzle at a repetition rate of 20 Hz and nominal pulse width of 200 μs. Fig. 3.6 shows a similar temperature dependence of the delayed signal at t = 4.0 ms, which appears at T V < 22 K. The intensity of the delayed signal increases with decreasing temperature, which indicates shift of the droplet size distribution towards larger sizes. It is seen that at low temperature the signal is larger at lower repetition rate, which indicates the actual nozzle temperature is higher than nominal, and that the deviation is larger at higher repetition rate. 48 10 12 14 16 18 20 22 0 50 100 150 200 250 300 20 Hz 10 Hz 1 Hz Signal, mV T V , K FIG. 3.6. Temperature dependence (T V ) of time-delayed signal at t = 4.0 ms for M = 8 at P 0 = 15 bar, 200 μs pulse duration and various pulse repetition rates. Time delay of the droplet pulse is inversely proportional to the velocity of the beam. The distance between the nozzle and center of the ionization region is approximately 1.13 ± 0.03 m. As a result, velocities of the clusters as a function of temperature can be determined and compared to known results for continuous nozzles. Fig. 3.7 summarizes the measured velocities of the M = 8 cluster signal for several conditions as noted in the legend. Velocities from measurements obtained by continuous nozzles 7 are also shown as well. Based on the obtained velocities, measurements between T V = 10 – 14 K for both 1 Hz and 20 Hz repetition rates are in good agreement 49 with that obtained from a cw nozzle in the range of 300 m/s. However, the pulsed nozzle measurements begin to deviate from the cw results at higher temperatures starting at T V = 16 K and show slower velocities. Estimated velocities for an ideal gas indicate that the temperature of the clusters is higher than the nominal temperature due to heating of the nozzle. 4 6 8 1012 14 1618 202224 26 2830 32 150 200 250 300 350 400 450 500 550 600 pulsed - 1 Hz pulsed - 20 Hz cw - 20 bar Velocity, m/s T V (Kelvin) FIG. 3.7. Temperature dependence on the velocity of the droplets for pulsed and continuous nozzles at several operating conditions for M = 8 amu. Solid line indicates estimated velocity of ideal gas as calculated using gas kinetic theory. Beyond the temperature dependence, several systematic studies were performed on the droplet signal as a function of other parameters dictating droplet formation, i.e., backing pressure, pulse duration, and repetition rate. Fig. 3.8 illustrates the dependence of the cluster signal as a function of the nominal pulse duration, i.e., the width of the electric driving pulse. All measurements here were performed at T V = 16 K. Based on Fig. 3.8, the most efficient pulse duration is 200 μs. Further increase of the valve 50 opening time leads to destruction of the beam as shown by a drop in signal as well as observed interference in the peak profile. As discussed previously, a smaller peak at longer delay is observed at all duration times due to the low temperature at T V < 22 K. Three temporal profiles of the signal at M = 8 at different pulse openings are shown below in Fig. 3.9. 140 160 180 200 220 240 260 280 300 0 100 200 300 400 500 600 700 Pure Helium Mass: 8 m/c Temperature: 10 K Back Pressure: 20 bar Sensitivity of highBW pre-amp: 2*100nA/V 100 kHz low pass filter Ionizer: 5 mA Electron Multiplier: 2.5 kV Signal, mV Pulse Duration, μs FIG. 3.8. m/z = 8 signal dependence vs. nominal pulse duration at T V = 16 K, P 0 = 20 bar, and 20 Hz repetition rate. 51 23 -0.016 -0.014 -0.012 -0.010 4 Signal, mV Time, s c) t = 160 μs -0.6 -0.4 -0.2 0.0 b) t = 200 μs -0.2 0.0 a) t = 290 μs FIG. 3.9. m/z = 8 temporal profiles at various pulse durations (a – c) at T V = 16 K, P 0 = 20 bar, and 20 Hz repetition rate. Note the widths of the peaks with different pulsed valve openings in Fig. 3.9. The opening time of 200 μs provides sufficient resolution so as to distinguish multiple peaks whereas the other two are broadened. Upon comparison of all 3 profiles, the intensity of the delayed peak around t = 3.70 ms is larger at the longest pulse opening, which shows more efficient formation of larger droplets and possibly less influence on large droplets from skimmer interference. In addition, the increase in pulse duration shows a slight increase in arrival time from approximately 2.90 ms at a pulse duration of 160 μs to around 3 ms at a pulse duration of 290 μs. 52 140 160 180 200 220 240 260 280 300 0.0 2.0x10 -4 4.0x10 -4 6.0x10 -4 Nozzle QMS Pure Helium Mass: 8 m/z Temperature: 10 K Back Pressure: 20 bar Sensitivity of highBW pre-amp: 2*100nA/V 100 kHz low pass filter Ionizer: 5 mA Electron Multiplier: 2.5 kV Pressure, mbar Pulse Duration, μs FIG 3.10. Pressure in nozzle and QMS chambers vs. pulse duration at T V = 17 K, P 0 = 20 bar, and 20 Hz repetition rate. QMS pressure is factored by 10 3 for scaling purposes. Fig. 3.10 shows the dependence of the pressure rise inside the nozzle chamber and quadrupole mass spectrometer (QMS) chamber upon nominal pulse duration, which is proportional to the amount of gas in the pulse. It is seen that beyond 200 μs, the nozzle is fully opened and the flux depends approximately quadratically with opening time. The QMS pressure is factored by 10 3 for scaling purposes. Operation of the system with pressures in the nozzle chamber over 10 -3 mbar is limited by the pumping rate of the diffusion pump. As a result, no experiments were performed above 5·10 -4 mbar in the nozzle chamber. The parameters of the droplet beam are also influenced by the supplied backing pressure as shown in Fig. 3.11. Fig. 3.11 shows the signal of M = 8 as a function of helium backing pressure in which optimal droplet signal is achieved around 20 – 30 bar. 53 The decrease in signal with P 0 > 30 bar may indicate the effect of scattering of the intense pulsed beam on the skimmer or incomplete nozzle opening at high backing pressure. 5 1015 20 253035 40 0 200 400 600 800 1000 1200 Pure Helium Mass: 8 m/c Pulse Duration: 200 μs Temperature: 10 K Sensitivity of highBW pre-amp: 2*100nA/V 100 kHz low pass filter Ionizer: 5 mA Electron Multiplier: 2.5 kV Signal, mV Back Pressure, bar FIG. 3.11. m/z = 8 signal vs. He backing pressure at T V = 20 K, 200 μs pulse duration, and 20 Hz repetition rate. Fig. 3.12 shows the results of the pressure rise in the nozzle and QMS chambers as a function of He backing pressure. The QMS pressure is scaled by 2·10 2 for convenience. It is seen that the nozzle pressure reaches a maximum at ~ 20 bar. The subsequent drop in pressure above 20 bar is an additional indication that the pulsed valve may not be opening properly at such high pressures, as indicated in Fig. 3.11. 54 5 1015 2025 3035 40 3.5E-5 4E-5 4.5E-5 5E-5 5.5E-5 6E-5 Nozzle QMS Pressure, mbar Backing Pressure, bar FIG. 3.12. Dependence of the pressure rise in the nozzle and QMS chambers vs. nozzle He backing pressure at T V = 20 K, 200 μs pulse duration, and 20 Hz repetition rate. The QMS pressure is scaled by 2·10 2 for comparison. We found that the repetition rate affects the effective temperature of the He gas expansion. Figs. 3.13 and 3.14 show the m/z = 8 signal and velocity, respectively, vs. repetition rate of the nozzle up to 80 Hz heated at T V = 16 K. From Fig. 3.13, it is seen that the droplet signal is largest at repetition rates from 1 – 5 Hz and decreases monotonically afterward up to 80 Hz. Apparently at higher repetition rates, the heat released due to the increase in mechanical motion as well as the driving current pulses begin to increase the effective temperature of the nozzle. The temperature of the valve vs. repetition rate is shown in Fig. 3.15. For comparison, the temperature as measured at the second stage of the refrigerator (T C ) is much lower and shows a much smaller increase with the repetition rate. As a result, no cluster signal was observed at repetition rates greater than 80 Hz. 55 0 2040 6080 0 100 200 300 400 500 600 700 800 Pure Helium Mass: 8 m/c Pulse Duration: 200 μs Temperature: 10 K Sensitivity of highBW pre-amp: 2*100nA/V 100 kHz low pass filter Ionizer: 5 mA Electron Multiplier: 2.5 kV Signal, mV Repetition Rate, Hz FIG. 3.13. M = 8 signal vs. repetition rate as heated at T V = 16 K. 0 2040 6080 350 360 370 380 390 400 410 420 430 Pure Helium Mass: 8 m/c Pulse Duration: 200 μs Temperature: 10 K Sensitivity of highBW pre-amp: 2*100nA/V 100 kHz low pass filter Ionizer: 5 mA Electron Multiplier: 2.5 kV Velocity, m/s Repetition Rate, Hz FIG. 3.14. Velocity of M = 8 signal vs. repetition rate as heated at T V = 16 K. 56 0 204060 80 100 4 6 8 10 12 14 16 18 20 T C T V Temperature, K Repetition Rate, Hz FIG. 3.15. Temperature of the pulsed valve (T V ) and cold head (T C ) as a function of repetition rate of pulsed nozzle at 15 bar and 200 μs pulse duration. Fig. 3.16 shows measurements of the pressure rise in the nozzle and QMS chambers as a function of repetition rate. The QMS pressure is scaled by 2·10 2 for convenience. For the nozzle chamber, a monotonic rise in pressure is observed with increasing repetition rate while the pressure in the QMS chamber rises and subsequently saturates around 70 – 80 Hz. As droplet signal is not observed at higher repetition rates due to sufficient heating of the valve, the saturation in the QMS chamber most likely results from the diffusive gas beam. Typical operations use 20 Hz which provides pressures below 10 -4 mbar and is required to reduce interference in the temporal profile of the QMS signal. 57 0 2040 6080 0.0 1.0x10 -4 2.0x10 -4 Nozzle QMS Pure Helium Mass: 8 m/c Pulse Duration: 200 μs Back Pressure: 20 bar Temperature: 10 K Sensitivity of highBW pre-amp: 2*100nA/V 100 kHz low pass filter Ionizer: 5 mA Electron Multiplier: 2.5 kV Pressure, mbar Repetition Rate, Hz FIG. 3.16. Pressure rise in nozzle and QMS chambers vs. repetition rate at T V = 16 K, P 0 = 20 bar, and 200 μs pulse duration. QMS pressure scaled by 2·10 2 for comparison. 3.4.3. Large Ionized Droplets To further test the presence of large ionized clusters, as shown by a delayed signal in the temporal profile as shown in Fig. 3.4, we have studied the time appearance of the delayed signal as a function of the ion energy as determined by the corresponding setting of the quadrupole mass spectrometer. The ion energy dictates the acceleration of the ions into the QMS and therefore can be related to the mass by standard linear equations of motion. Fig. 3.17 shows the temporal profiles of the M = 8 signal vs. ion energy at T V = 20 K. Positive energy corresponds to acceleration and negative to deceleration of the ions. Two distinct features are present at positive potentials. The shorter delayed peak 58 corresponds to the He 2+ ions whereas the longer delayed peak is due to large clusters relatively unaffected by mass selection as discussed earlier. Upon application of deceleration (negative) potential, small masses such as m/z = 8 are retarded. However, the large droplet feature persists, although there is some shift towards longer time delays. The magnitude of the peak is also about a factor of five lower at high retarding potentials. Apparently, the kinetic energy of the clusters is so large that they cannot be retarded by applied potentials. Using the velocity of the beam of 325 m/s, the mass of the delayed droplets can be estimated to be about 30,000 He atoms at T V = 15 K for 20 Hz repetition rate. Droplets on the order of 80,000 He atoms can be achieved at T V = 10 K at 1 Hz repetition rate. These estimates imply singly charged droplets. 3.0x10 -3 3.5x10 -3 4.0x10 -3 4.5x10 -3 5.0x10 -3 0.0 0.2 0.4 0.6 0.8 1.0 Signal, mV Time, s +49.2 +25.0 +10.0 +0 -10.0 -25.0 -49.3 FIG. 3.17. Temporal profiles of m/z = 8 at T V = 15 K, P 0 = 5 bar, 200 μs pulse duration, and 20 Hz repetition rate for various ion energies. 59 3.5. Mass Spectroscopic Characterization of He Droplet Sizes In the case of cw nozzle expansion, the average size of the droplets is predominantly controlled by the source pressure and temperature. Fig. 2.1 shows the average droplet size from previous measurements as obtained by deflection of a continuous beam of He droplets upon capture of Xe atoms from a secondary beam or by the deflection of negatively charged droplets in an electric field for N He < 10 4 and 10 5 < N He < 10 8 , respectively. 8 However, less is known for expansion near the critical point due to the instability of cluster production as well as unreliability of the discussed deflection experiments in the corresponding range. In addition, it is unclear how average sizes measured by previous experiments correspond to other He droplet systems at varying conditions. As a result, a more accessible parameter for cluster sizes is needed. Nevertheless, it was observed back in 1990 that the mass spectra of He droplet beams changed upon passing from the sub-critical to supercritical expansion regime, 6 with the most noticeable effect being a large increase in the relative intensity of mass 16 due to He 4 + . Fig. 3.18 illustrates the intensity ratio of M = 16 to M = 8 for both continuous and pulsed nozzles as a function of temperature and different source conditions as obtained in our laboratory. For continuous nozzles above T 0 = 10 K, the ratio is approximately constant at 0.03. However, upon decreasing the temperature, a sharp rise is observed and appears to saturate at around I 16 /I 8 = 0.55 at temperatures below about 6 K. For pulsed nozzles, a similar trend is observed in which the ratio is approximately constant down to T V = 13 K at I 16 /I 8 = 0.08. Below T V = 13 K, a sharp 60 rise is seen up to 0.40 at T V = 10 K. Due to the current cooling arrangement of the pulsed nozzle, temperatures below T V = 10 K could not be achieved. Nevertheless, it is obvious that the intensity ratio depends on the average size of He droplets in the beam. As a result, this allows for estimates of the average droplet size in the pulsed source based on the measured intensity ratio and comparison with known results for well characterized continuous sources. However, it is important to note that measurements obtained by the pulsed nozzle were performed with a different mass spectrometer than that for the cw nozzle. Comparison of the measurements obtained with the pulsed valve shows that they have similar structure and lay on the same curve within scattering of the points. A similar trend is observed upon comparison between the M = 16 and M = 12 ratio, as shown in Fig. 3.18. Therefore we can estimate the sizes of the droplets in the pulsed expansion, which are shown in Fig. 3.20. 61 4 6 8 10 12 14 16 18 20 22 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 20 Hz 10 Hz 1 Hz cw, 20 bar I 16 / I 8 Temperature, K FIG. 3.18. Ratio of (He) 4 + /(He) 2 + signals at various temperatures for continuous (T 0 ) and pulsed nozzles (T V ). The pulsed nozzle was operated at P 0 = 15 bar and 200 μs pulse duration for various repetition rates. 4 6 8 1012 141618 2022 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 pulsed - 1 Hz pulsed - 10 Hz pulsed - 20 Hz cw - 20 bar M 16 /M 12 Temperature, K FIG. 3.19. Ratio of (He) 4 + /(He) 3 + signals at various temperatures for continuous (T 0 ) and pulsed nozzles (T V ). The pulsed nozzle was operated at P 0 = 15 bar and 200 μs pulse duration for various repetition rates. 62 For comparison, mass spectra are shown in Fig. 3.20 for cw and pulsed nozzles with similar I 16 /I 8 ratio. Here, the spectrum for the cw nozzle was measured at T 0 = 9.5 K while the pulsed nozzle spectrum was obtained at T V = 16 K. Here, peaks for the pulse operation are slightly broader than the cw counterparts. This can be attributed to the different mass spectrometers that were used and their corresponding settings. However, it is important to note that despite the broadening and similar I 16 /I 8 ratio, helium clusters produced by the pulsed valve are generally more intense than those produced by cw nozzles. This observation is not fully understood currently. 0 5 10 15 20 25 30 35 40 0 1 2 3 4 Normalized Intensity for Mass 8 Temperature, K Continuous Pulsed FIG. 3.20. Mass spectra for cw nozzle (T 0 = 9.5 K, P 0 = 20 bar) and pulsed nozzle (T V = 16 K, P 0 = 20 bar, 200 μs pulse duration, 20 Hz repetition rate) with comparable I 16 /I 8 ratio. Mass spectra are normalized with respect to their corresponding M = 8 value. 63 3.6. Electron-Impact Ionization of He Droplets In order to understand the enhancement of M = 16 signal upon increase of the droplet size, the mechanism for electron impact ionization and excitation must be considered. In small droplets, an ionizing collision produces a He + ion in the droplet with ejection of both electrons, followed by relaxation of the droplet to produce He 2 + or larger ions. The energy relaxation and subsequent ejection of He + ions allows detection of the charged species. In large droplets, it is believed that electronically excited atoms (He * ) become important. In bulk helium it is known that, upon excitation, He * species will capture another atom in approximately 15 μs forming metastable a 3 ∑ u + (He 2 * ) excimer molecules in vibrationally excited states. 9 If this formation takes place near the surface of the droplet, the energy released could be significant to eject the vibrationally excited He 2 * . Upon ejection, the neutral excitations could produce positive ions by collision with metal surfaces, as observed in bulk helium. 10 In addition, a collision of the free He 2 * with a second electron is also possible. In large droplets two He 2 * excimers can be produced. Upon collision they may yield He 4 + ions, which are then ejected. As obtained by our current work in pulsed nozzles, previous studies 6,11 have observed a delayed cluster feature unaffected by either the accelerating or quadrupole fields of the mass spectrometer. This delayed feature was attributed to very large ionized clusters or excited neutral clusters. In bulk helium, He 2 * can be formed in the ground vibrational state by the relaxation of an excited He 2 + ion and its subsequent recombination with an electron. 9 This process of cluster-electron recombination is likely 64 considering that an ejected electron with almost zero kinetic energy has the highest probability of being formed. 12 If a similar process occurs in droplets, the resulting ground vibrational state He 2 * may remain in the cluster for a time period longer than its vibrationally excited counterpart discussed previously. Due to the estimated binding energy 13 of He 2 * to that of surface atoms (~7 K), the excimer may evaporate from the droplet as it cools followed by collision with the multiplier emitting electrons. 3.7. Model of He Ionization and Excitation in He Droplets Bulk electronic excitations occur when incoming electron energies exceed ~ 21 eV. 14 In previous work, the efficiency of the He 4 + production by electron impact has been studied at different electron energies. It was obtained that the M = 16 signal has a threshold at energies of about 41 eV, indicating the occurrence of two separate excitations taking place. 11 The two He 2 * generated can then collide on the surface of the droplet producing He 4 + ions which subsequently detach from the droplet. The I 16 /I 8 ratio can be modeled by considering the ionization and excitation events as occurring by Poisson statistics. Based on energy conservation, no more than 4 ionization/excitation events can occur at the used electron impact energies of 100 eV. In addition, as discussed previously 11 , the dominate formation of He 4 + occurs by the creation of two excitons by the same electron. A schematic of electron impact events is shown in Fig. 3.21 in which an electron impact on a He atom creates either He + or He * . Accordingly, the electron loses 65 approximately 25 eV of energy for either event. Based on the previous discussions, M = 16 is a predominant product of collision between two metastable He 2 * species. As a result, for the consideration of two electron impact events, only one pathway exists which give rise to two He 2 * particles (D). A Poisson distribution can be applied to each event as shown in equation 3.1 3 .1 here λ is proportional to the event cross section, He number density, and droplet ! k e P k x λ λ − ⋅ = w diameter. k is equal to the number of events occurring. For the production of M = 8, two ionizations may occur (A). In addition, two pathways exist to create one ionization and one excitation, (B) and (C), both of which are assumed to create only M = 8. As a result, the sum of the different pathways to generate signal for M = 8 and M = 16 for 2 events is shown in equation 3.2, where P x refers to the Poisson probability for either ionization (i) or excitation (e) to occur. Additional summations are included for both masses for completeness in which the probability of ionization is about a factor of 3 larger than excitation at 100 eV. ( ) ( ) ( ) () () () ( ) ∑ = − = ⋅ + ⋅ + = 50 3 3 ! 8 03 . 0 2 ) 16 ( ! j j e e j e e j I P I j λ λ ∑ − ⋅ + ⋅ + + + = 150 2 2 2 1 1 8 j i e i i e i i e P P P P P I λ λ 3.2 66 He * He + e - (100 eV) He e - (75 eV) e - (50 eV) He + He + (C) He * (D) He * (B) (A) He * He * He + He + e - (100 eV) He He e - (75 eV) e - (50 eV) He + He + He + He + (C) He * He * (D) He * He * (B) (A) FIG. 3.21. Illustration of possible outcomes (A – D) for the multiple scattering of an electron in He droplet. E 2 shows the cross sections for the ionization and excitation of He atoms Fig. 3.2 with varying electron energy. As observed in the figure, the maximum cross section for both ionization and excitation occur around 100 eV, a typical energy used to ionize helium droplets in our experiments. However, probability for ionization to occur is more 67 than a factor of three larger than that for excitation. In addition, upon ionization or excitation, an electron loses approximately 25 eV of its energy. As a result, after the first event, the probability of ionization or excitation should be calculated for 75 eV electrons, which is comparable to that at 100 eV. However, probability for ionization to occur upon the third scattering event (50 eV) decreases by more than 30% whereas excitation probability has decreased by a little more than 10%. Probabilities for scattering events occurring at 25 eV are dramatically reduced and have been neglected. 10 100 1000 10000 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Excitation Ionization σ (10 -16 cm 2 ) Electron Energy (eV) FIG. 3.22. Cross-sections for electron impact ionization 12,15 (solid squares) and excitation 16 (open squares) for atomic He as a function of electron energy. 68 Fig. 3.23 shows the estimated intensity ratio of the M 16 /M 8 peaks as a function of the average He droplet size based on 2 electron scattering events. The solid line is a scaled ratio based on probabilities for ionization or excitation as described by equation 3.2. Solid squares are experimental values obtained in a cw nozzle beam expansion. We have included an offset due to the constant 0.03 ratio observed at high temperatures for cw experiments as shown in Fig. 3.18. Here, a comparable trend is observed for small and very large cluster sizes. However, deviations occur for droplets in the 10 5 – 10 7 atoms/droplet range in which our model does not predict an increase in M = 16 until 10 6 atoms/droplet. However, the onset of saturation does occur at comparable droplet sizes around 10 8 . 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 0.0 0.1 0.2 0.3 0.4 0.5 0.6 I 16 /I 8 <N He > FIG. 3.23. Ratio of (He) 4 + /(He) 2 + signals as obtained by experiment using cw nozzle (solid squares) and theory (solid line) as obtained by our modeling of ionization and excitation probabilities in helium droplets. 69 The origin of the saturation in the M 16 /M 8 ratio relates to the fact that there is a mited li number of scattering events of three based on the total initial electron energy of 100 eV. Based on the ionization cross-section for an electron at 100 eV and density of liquid He, the electron has a mean free path on the order of 10 nm. Therefore for small droplets, this mean free path allows only one scattering event at most, see Fig. 2.1. With increasing droplet size, additional scattering events will occur. As a result, the electron will lose all of its energy before escaping large droplets such that saturation is expected for very large droplets. Despite the qualitative agreement between experiment and theory, more detailed calculations would be necessary to fully describe the system, such as involving the third scattering event in eq. (3.2). 70 Chapter 3 Bibliography 1 J. P. Toennies and A. F. Vilesov, Angewandte Chemie-International Edition 43 (20), 2622 (2004). 2 F. Stienkemeier and A. F. Vilesov, The Journal of Chemical Physics 115 (22), 10119 (2001). 3 M. N. Slipchenko, S. Kuma, T. Momose, and A. F. Vilesov, Review of Scientific Instruments 73 (10), 3600 (2002). 4 S. F. Yang, S. M. Brereton, and A. M. Ellis, Review of Scientific Instruments 76 (10) (2005); F. Bierau, P. Kupser, G. Meijer, and G. von Helden, Physical Review Letters 105 (13) (2010). 5 D. Pentlehner, R. Riechers, B. Dick, A. Slenczka, U. Even, N. Lavie, R. Brown, and K. Luria, Review of Scientific Instruments 80 (4) (2009). 6 H. Buchenau, E. L. Knuth, J. Northby, J. P. Toennies, and C. Winkler, Journal of Chemical Physics 92 (11), 6875 (1990). 7 B. Schilling, Georg-August-Universitat zu Gottingen, 1993. 8 U. Henne and J. P. Toennies, Journal of Chemical Physics 108 (22), 9327 (1998); M. Lewerenz, B. Schilling, and J. P. Toennies, Chemical Physics Letters 206 (1- 4), 381 (1993). 9 J. W. Keto, F. J. Soley, M. Stockton, and Fitzsimm.Wa, Physical Review A 10 (3), 872 (1974); J. W. Keto, M. Stockton, and Fitzsimm.Wa, Physical Review Letters 28 (13), 792 (1972). 10 C. M. Surko and F. Reif, Physical Review 175 (1), 229 (1968). 11 H. Buchenau, J. P. Toennies, and J. A. Northby, Journal of Chemical Physics 95 (11), 8134 (1991). 12 Y. K. Kim, W. R. Johnson, and M. E. Rudd, Physical Review A 61 (3) (2000). 13 Arrighin.Gp, F. Biondi, and C. Guidotti, Physics Letters A A 48 (5), 385 (1974). 14 K. Martini, J. P. Toennies, and C. Winkler, Chemical Physics Letters 178 (4), 429 (1991). 71 15 Y. K. Kim and M. E. Rudd, Physical Review A 50 (5), 3954 (1994). 16 P. M. Stone, Y. K. Kim, and J. P. Desclaux, Journal of Research of the National Institute of Standards and Technology 107 (4), 327 (2002). 72 Chapter IV. Coherent Anti-Stokes Raman Scattering (CARS) of H 2 Molecules and Clusters 4.1. Introduction This section is devoted to the description of the experimental CARS process employed in our lab for both the vibrational and rotational Raman spectroscopy study of H 2 molecules and clusters. A more complete detailed description on CARS theory 1 and setup can be found elsewhere. 2 As a result, limited theoretical discussion is provided and a more technical description is employed. 4.2. Principles of CARS Technique The CARS (Coherent anti-Stokes Raman Spectroscopy) process is a non-linear four-wave mixing technique in which two incident waves of frequency ω 1 and wave vector k 1 ( ω 1 , k 1 ) interact with the medium to produce two output waves ( ω 2 , k 2 ) and ( ω 3 , k 3 ). A schematic of the CARS process is shown in Fig. 4.1 which describes CARS as consisting of two coherent Raman processes. The first Raman process involves the inelastic scatter of ω 1 , referred to as the pump beam, off of the molecule in the ground state. This inelastic scatter leaves the molecule in the excited state and produces an outgoing wave of smaller frequency at ω 2 = ω 1 - ν, known as the Stokes frequency where ν is the frequency of the Raman transition. Simultaneously, an additional ω 1 wave 73 scatters inelastically off of the molecule in the excited state, thereby returning the molecule to the ground state and emitting a wave of higher energy at ω 3 = ω 1 + ν, and is known as the anti-Stokes signal. The overall CARS signal will occur spontaneously at high enough intensity of the pump laser, ω 1 . However, the combination of the two spontaneous processes occurring generates very weak anti-Stokes signal. In order to obtain a spectrum as well as enhance the intensity of the CARS process, a ω 2 Stokes wave can be added externally in addition to that produced spontaneously. The external Stokes wave acts as a seeder thereby generating a single mode for the emitted ω 2 photons to fall into. This amplification occurs only on resonance according to ω 2 = ω 1 - ν. In order to achieve resonance at ω 2 , a tunable laser is generally used where once the external Stokes frequency is on resonance, thereby amplifying the Stokes process, the subsequent anti-Stokes process is amplified. Thus, by scanning the ω 2 frequency laser and applying energy conversation laws, one can obtain a spectrum by collecting the photons generated by the CARS signal at frequency ω 3 . 74 ν = 0 ν = 1 ω 1 ω 1 ω 2 ω 3 FIG. 4.1. Energy diagram of vibrational CARS process. Two incident waves (ω 1 ) and two outgoing waves ( ω 2 ) and ( ω 3 ) are shown by solid arrows. Ground and vibrationally excited states are denoted by ν = 0 and ν = 1, respectively as solid lines. Virtual levels are shown by dashed horizontal lines. It can be shown 1 that the intensity of the CARS anti-Stokes signal (I 3 ) is given by equation 4.1 .1 where n i refers to the index of refraction of H 2 at the corresponding frequency, I i is the intensity of the pump ( ω 1 ) and Stokes ( ω 2 ) waves, χ CARS is the third order nonlinear susceptibility of H 2 , Δk is the phase matching parameter, as satisfied by conservation of momentum Δk = 2k 2 – k 1 – k 3 , and L is the interaction length. For exact phase matching () ( ) 2 2 2 2 1 2 4 3 2 2 1 2 3 4 3 3 2 / 2 / sin 256 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ Δ ⋅ Δ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = L k L k L I I c n n n I CARS χ ω π ω 4 75 ( Δk = 0), the sin term goes to unity and intensity is maximized. For clusters, refraction of light is reduced from that in the bulk medium such that the index of refraction in air is suitable. Equation 4.1 can be simplified according to equation 4.2 assuming Δk = 0 4.2 ( ) ( ) ( ) 2 2 2 1 1 2 3 3 ω ω ω I I N I ⋅ ⋅ ∝ where N is the molecular number density. The quadratic dependence of the CARS signal on pump intensity demonstrates the need for high power pulsed lasers while the quadratic dependence on the number density limits the concentrations of samples available for study. For reference, ro-vibrational CARS spectra have been previously measured for H 2. 3 4.3. CARS Optical Setup The experimental layout of the helium droplet apparatus used for CARS experiments has already been described in Chapter 3. However, only Chamber (1) is employed in CARS studies, see Fig. 3.1. A schematic of the optical setup for CARS is shown in Fig. 4.2. Two lasers are required for CARS experiments in order to produce the pump and Stokes beam as discussed in section 4.2. The pump beam is provided by a pulsed Nd:YAG laser (Continuum Inc. Powerlite Precision II 8020). The Nd:YAG laser generates an approximately 8 ns pulse with a maximum output of 1000 mJ/pulse, 425 mJ/pulse, and 215 mJ/pulse for the fundamental (1064 nm), second (SHG – 532 nm), and 76 third harmonic generation (THG – 355 nm) wavelengths, respectively, when operated at a repetition rate of 20 Hz. The Nd:YAG laser is equipped with injection seeding allowing for nominal laser linewidths of about 0.003 cm -1 . The linewidth of the laser without injection seeding is on the order of 1 cm -1 . The Stokes beam is generated from a tunable dye laser (Lambda Physik NPD 3000) and is pumped by either SHG or THG of a Nd:YAG laser depending on the dye and wavelength required. The dye laser was originally equipped to be pumped by a rectangular-shaped beam from an excimer laser. As a result, a telescope is installed before the entrance of the dye laser that modifies the circular beam from the Nd:YAG laser. The dye laser can be equipped with an intra-cavity etalon which can reduce the linewidth from about 0.25 cm -1 down to about 0.05 cm -1 . For vibrational CARS, Pyridin 1 dye (Exciton) is used and has a maximum emission at 692 nm for 532 nm pump lasers and a working range from 670 – 710 nm where conversion efficiency is at least 50% that of the maximum. For rotational CARS, either Coumarin 540A pumped by THG or Fluorescein 548 pumped by SHG has been used. Coumarin 540A has a working range of 516 – 590 nm with a lasing wavelength maximum around 540 nm when using methanol. Fluorescein 548 has a lasing range around 536 – 567 nm with a max at 550 nm. Unfortunately, Fluorescein 548 has a large absorption and fluorescence around 532 – 540 nm, which makes pumping by SHG less advantageous. However, pumping of the dye laser by THG has been found to be more damaging to the dye cells than that by SHG due to unintended self focusing of the Nd:YAG laser pump beam on the face window of the dye cells. 77 A C B Nd:YAG Dye Laser P M T FIG. 4.2. CARS optical setup. The outer frame of the illustration denotes the borders of the optical table. The pump and Stokes laser beams are depicted by solid and dotted lines, respectively. Arrows correspond to the beams traveling to and from the pulsed cryogenic jet (not pictured here). The returning anti-Stokes signal is shown by a dashed line and is detected by a PMT. For optical setup, the 532 nm pump beam (solid line) is initially split (A) in order to pump the dye laser in which 10% is used for CARS generation. For proper temporal overlap between the pump and Stokes beams, a delay line (B) is used for the 532 nm 78 pump beam. In order to reduce background noise generated by the intense pump and Stokes beams, a folded boxcars technique has been employed, see Fig. 4.3. 4 As a result, the 532 nm pump beam is divided equally where each split beam is on the order of 3 – 5 mJ. The Stokes beam (dotted line) is expanded by means of a telescope (C) which can be adjusted on the optical axis of the Stokes beam for proper focusing together with the pump beams into the helium droplet machine, as shown in Fig. 4.4. Y X Z k 1 k 1 k 2 k 3 FIG. 4.3. Diagram illustrating folded BOX CARS geometry. k 1 vectors are in the horizontal plane whereas k 2 and k 3 vectors are in the vertical plane. The vector sum of Δk = 0 satisfies momentum conservation. Fig. 4.4 shows a schematic of the vacuum part of the experimental setup. The two pump and Stokes beams are focused into the axis of the nozzle beam inside the vacuum chamber using a 50 cm focusing length positive cemented doublet achromatic lens with 79 an anti-reflection coating for the range of 450 – 750 nm. Due to the folded BOX CARS technique employed, the anti-Stokes signal is generated at some angle to the pump or Stokes beams. As a result, an aperture is placed behind the output window of the vacuum apparatus to block the intense pump and Stokes beams. However, due to scattering of light from the clusters, the 532 nm light still penetrates behind the aperture. In order to reduce (and ideally eliminate) the intensity of the scattered 532 nm light, a diffraction grating (1800 grooves/mm), 532 nm notch filter, and interference filter are used. In addition, a small focusing lens (A) is used to focus the signal beam through a pinhole in front of the PMT. 80 ( ) PMT L (B) Neutral Filters nozzle (F) (C) (A) (D) (H) (E) Interference Filters FIG. 4.4. Schematic of helium droplet machine. Pump (solid lines) and Stokes (dotted line) beams are focused onto the expanding jet. An anti-Stokes signal (dashed line) is generated which is isolated by means of an aperture (A), a diffraction grating (B), and interference filters (C). In the case of high intensity, additional neutral filters (D) have been added to avoid saturation of the PMT (E). A lens (F) is placed after the first turning mirror to compensate for the divergent anti-Stokes signal generated while an additional lens (G) is used to focus the signal into a pinhole (H) located in the housing of the PMT (C). For initial alignment of the CARS set up, a thin piece of metal with a pinhole of 81 approximately 100 μm diameter, as prepared by focused laser burning and installed on a custom mount, was inserted at the focal point of the 50 cm achromatic lens inside the machine at the nozzle beam axis. Because of the contraction of the cold head and nozzle with decreasing temperature by about 1 – 2 mm, the nozzle shifts upwards as compared to its position at room temperature during operation. To account for this discrepancy, the system was cooled to operating conditions at which the nozzle was aligned using a telescope. Afterward, the custom pinhole was installed at room temperature at the noted position by the telescope. From here, the pump and Stokes beams can be aligned individually through the pinhole in which the throughput intensity was maximized using a power meter. Upon this initial alignment, a 26-cm long, 5-cm diameter copper gas cell filled with 0.5 atm of n-H 2 gas and equipped with 3 mm thick BK7 windows was installed inside the helium droplet apparatus on the beam path. The pre-aligned pump and Stokes beams usually produced sufficient CARS signal visible to the naked eye and was used for fine tuning of the optical setup. The CARS signal generated from this gas cell was then used to align into the PMT. Upon alignment, the gas cell was removed and CARS signal from the pulsed nozzle could be observed. The remaining chapter discusses the optimization and characterization of the CARS signal of clusters at various compositions of the expanding gas containing different fractions of H 2 and He. 82 4.4. H 2 Cluster Formation via Supersonic Co-expansion of H 2 and He. In general, He droplets formed by supersonic expansion are doped with atomic or molecular species in a pickup chamber. As it follows from eq. (4.2), CARS signal depends as a square of the number density signifying a 4 th power dependence on the CARS signal with increasing distance from the nozzle. Therefore, besides expansion of a liquid jet of neat H 2 , experiments can only be performed at distances no more than 5 cm away from the nozzle. Using a pickup cell is not practical, as it must be accommodated in the high density range of the expansion and thus will interfere with the expansion. As a result, for CARS experiments, we perform either a supersonic co-expansion of H 2 seeded in He or an expansion of neat H 2 . 4.5. Sample Preparation Parahydrogen was mixed with He in a 1 gal. stainless steel sampling cylinder. p- H 2 having o-H 2 content of less than 0.01% was prepared by passing liquid n-H 2 (research grade) over a paramagnetic material at temperature of about 16 K. 5 Sample mixtures were prepared by first purging the sample cylinder with helium gas. Afterward, known amounts of p-H 2 were added and subsequently filled up with He gas to pressures no higher than 40 bar. Total pressures of 40 bar were necessary to perform experiments for multiple days, typically never exceeding 3 days use to ensure purity of the p-H 2 . Samples were left overnight to ensure complete mixing. For experiments concerning mixtures of different isotopes of H 2 , i.e. p-H 2 /o-H 2 or p-H 2 /D 2 , the less concentrated species was 83 added first, followed by the other. 4.6. Electronics and Computer Interfacing The temporal overlap of the pulsed nozzle and lasers were synchronized by a pulse generator. The pulse generator controlled the triggering for both the flash lamps and Q-switching for optimal output. Typically, the laser pulse was delayed by about 350 μs with respect to the trigger of the pulsed nozzle due to an inherent time delay of the electronics and mechanical operation of the valve. Additional delay was necessary when probing the clusters at farther distances from the nozzle due to the finite velocity of the droplets. Time delay was also used to study different regions of the gas pulse, such as in the head and tail, as will be discussed in section 4.7. A schematic of the timing diagram is shown in Fig. 4.5. Trigger t = 0 Nozzle t = 350 μs Laser FIG. 4.5. Schematic of pulse nozzle timing diagram. A TTL trigger pulse signals for pulse valve to open. Nozzle valve opens approximately 350 μs after initial trigger. The laser is triggered to temporally overlap with the gas expansion at the focal point, as illustrated by the delay between laser pulse and nozzle, which is exaggerated for clarity. The intensity of the anti-Stokes CARS signal is collected using a Photo- 84 Multiplier Tube EMI 9789QA. The voltage supplied to the PMT can be varied from 0 – 2000 V. However, to avoid saturation in the CARS spectra, the voltage was set typically at 700 V. In addition, the CARS signal was amplified by a fast pre-amplifier and recorded by a Boxcar Integrator. The trigger signal for the Boxcar is supplied by a photodiode exposed to the scattered light of the pump laser. Neutral filters were used at the entrance of the PMT to avoid saturation effects. The averaged CARS signal supplied by the Boxcar was recorded using a data acquisition card (PCI-MIO E card from National Instruments) and controlled by a LabView application. During the scanning mode of the dye laser, a 0 – 10 V linear ramp was supplied from the dye laser corresponding to the starting and ending points of the scan. As a result, the obtained average signal can be associated with the corresponding wavelength. Calibration of the dye laser is obtained by comparison to the known Raman spectrum of H 2 gas. 6 4.7. Vibrational CARS of H 2 Molecules and Clusters in He Droplets A typical spectrum of n-H 2 expanded at T V = 300 K is shown in Fig. 4.6. The spectrum was calibrated based on the known line positions in the gas phase. 6 In Fig. 4.6, the ν = 1, J = 1 ← ν = 0, J = 1 o-H 2 transition, Q 1 (1), is observed around 4155.30 cm -1 while the p-H 2 Q 1 (0) transition ( ν = 1, J = 0 ← ν = 0, J = 0) is blue-shifted at 4161.17 cm -1 . The intensity ratio of the two lines was found to be 8.7 ± 0.5 which corresponds to an ortho-para ratio (OPR) of approximately 3:1, in accordance with the known ratio at 85 room temperature. 7 This indicates that ortho- and para-H 2 molecules relax into the lowest rotational level of the corresponding manifold without inter-conversion. 4150 4152 4154 4156 4158 4160 4162 4164 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Signal, V Wavenumbers, cm -1 FIG. 4.6. Vibrational CARS spectra of H 2 molecules obtained upon expansion of 0.5% n-H 2 in He at T V = 300 K and P 0 = 20 bar. The spectrum is calibrated against known position of the lines in the gas phase. Several experimental parameters, such as nozzle alignment, pulse delay, nozzle temperature, and observation distance from the nozzle were necessary to characterize and optimize to obtain the best CARS signal. As discussed in Chapter 3, the pulsed nozzle platform is allowed to move in the Y-Z horizontal plane of the apparatus. Here, the Y-position describes the axis parallel to the incoming laser beams while the Z- position describes the axis of the gas expansion and is perpendicular to the laser beam axis. As a result, the pulsed nozzle can be aligned for optimal signal. Fig. 4.7 shows the dependence of the CARS signal as measured on the o-H 2 gas 86 line upon expansion of pure n-H 2 at T V = 300 K as a function of distance, Y, parallel to the incoming beams, at two distances from the nozzle of Z = 6 mm and 45 mm in panels (a) and (b), respectively. Due to the copper block cover over the pulsed nozzle faceplate, the closest distance between the nozzle throat and the focal point of the lasers is approximately 6 mm (Z). At short distance (a), the signal intensity demonstrates a Gaussian type beam profile with a maximum at approximately 38 mm (Y) and width of about 4.3 mm. Here, the Y-position of the nozzle is given as the distance between the edges of the chamber housing platform to the small, adjustable positioning blocks holding the cold head platform. Please see arrows in Fig. 4.8 for illustration. A similar description is used to define the Z-direction. This assigned Y-position is essentially a reference point for laser focusing. Re-alignment of the laser beams through the pinhole defines the focal point. As a result, coarse adjustments for re-alignment change the optimal Y-position slightly. What is more important from Fig. 4.7 is the shape of the profile as it describes the profile of the expanding gas beam. Panel (b) in Fig. 4.7 illustrates the beam profile as measured at Z = 45 mm downstream from the nozzle. Here, a similar Gaussian profile is observed with Y max = 36.5 mm and width of about 9 mm. The shift in the Y dependence indicates either that the pulsed valve is not centered exactly perpendicular to the laser focal point or expansion from the nozzle is angled. Measurements from day to day experiments imply that the optimal position of the nozzle changes somewhat but re-alignment to obtain optimal CARS signal is usually minor. In addition, the expansion at distances farther from the nozzle is broader due to geometric expansion of the beam and shows some 87 larger scattering of the data points. 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 0 100 200 300 400 500 600 700 Z = 6 mm a) b) File: 08-11-18_1717 Signal, mV Y- Position, mm 0 50 100 150 200 250 300 Z = 45 mm File: 08-11-19_1511 FIG. 4.7. CARS signal dependence as a function of nozzle position parallel to pump and Stokes beam, Y, at T V = 300 K for Z = 6 mm (a) and Z = 45 mm (b). Expansion of n-H 2 at P = 20 bar. 88 Cold Head Y-Position Cold Head Platform Nozzle Chamber Z-Position FIG. 4.8. Schematic of nozzle chamber housing cold head from top-view. The cold head is installed on a platform which is then inserted into the nozzle chamber. The cold head can be positioned by using small steel blocks with mounted, threaded bolts. The Y- and Z-positions are defined from the edge of the nozzle chamber platform to the edge of the corresponding small blocks used for adjustments, as shown by arrows. An additional parameter for optimizing the CARS signal is the pulse delay, which ensures proper temporal overlap of the incoming laser beams with the expanding gas at position Y. For this purpose a delay generator was used to control the Nd:YAG laser and the driver of the pulsed nozzle. Fig. 4.9 illustrates the dependence of the CARS signal on the laser pulse delay with respect to the trigger point of the pulsed nozzle driver for nominal pulse duration of 200 μs at Z = 45 mm. Here, the maximum signal is achieved at a pulse delay of t = 375 μs with a width of about 50 μs. 89 320 340 360 380 400 420 440 0 100 200 300 400 500 600 700 Signal, mV R^2 = 0.90772 y0 36.78963 ±71.29488 xc 375.0753 ±2.18096 w 51.41409 ±9.41779 A 34332.45446 ±9552.439 nH 2 expansion T = 300 K Average: 100 Samples Sensitivity: 0.2 V Filters: No filters PMT: 700 V Z-Position @ #1: 45 mm Y-Position @ #4: 38 mm Frequency: 683.264 nm Pulse duration: 200 μs Pressure: 2*10 -4 mbar Pulse Delay, μs FIG. 4.9. CARS signal dependence vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver. n-H 2 expansion at T V = 300 K, P = 20 bar, nominal pulse duration: 200 μs, and Z = 45 mm. Measurements were obtained at the maximum of the o-H 2 gas line. Upon cooling the gas down to T V = 60 K, a larger laser pulse delay is required for similar Z-positions, as shown in Fig. 4.10 in panel (a) for a 1% n-H 2 mixture in He at Z = 6 mm. This delay is mostly due to some delay in opening of the nozzle at lower temperature. Panel (b) in Fig. 4.10 shows that an additional delay of about 23 μs is necessary to optimize the signal at Z = 27 mm, which is due to the lower speed of the beam at lower temperature. Based on the differences in arrival times and distances, the velocity of the beam is approximately 913 m/s at T V = 60 K, which is comparable to that obtained by gas kinetic theory at around 67 K. This result helps verify that the 90 temperature of the pulsed valve is generally higher than the temperatures listed on the sensors. 250 300 350 400 450 500 0 2 4 a) Signal, V Pulse Delay, μs File: 09-01-15_1530 0.0 0.5 1.0 b) File: 09-01-15_1616 FIG. 4.10. CARS signal dependence vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver. Expansion of 1% n-H 2 in He at T V = 60 K, P = 20 bar, nominal pulse duration: 200 μs, and at Z = 6 mm (a) and Z = 27 mm (b). Measurements were obtained at the maximum of the o-H 2 gas line. Fig. 4.11 shows vibrational CARS spectra of a 1% p-H 2 mixture in He upon cooling the gas mixture down to T V = 21 K. At temperatures below approximately 30 K, clusters begin to form. At T V = 21 K the spectra reveal only a single feature at 4150.49 cm -1 , red-shifted from the gas phase by approximately 10.7 cm -1 . Please see chapters 5 and 6 for further discussion on observed vibrational shifts. Laser pulse delay dependences of the cluster signal as measured at Z = 6 mm and Z = 24 mm, are shown in panels (a) and (b) of Fig. 4.12, respectively. At distances from the nozzle beyond Z = 24 mm for 1% mixtures, the signal was too weak to be measured. 91 4144 4146 4148 4150 4152 4154 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Signal, V Wavenumbers, cm -1 FIG. 4.11. Vibrational CARS spectra of 1% p-H 2 in He at T V = 21 K and P 0 = 20 bar. Fig. 4.12 shows the dependence of the cluster signal upon the delay of the laser pulse for a 1% p-H 2 mixture in He at Z = 6 mm (a), and Z = 24 mm (b) for T V = 21 K, P 0 = 20 bar. The time difference between the two distances of 18 mm is approximately 46 μs, providing a velocity of the cluster signal of 391 m/s or an effective He gas kinetic temperature around 24 – 25 K. 92 250 300 350 400 450 500 0 1 2 b) a) Signal, V Pulse Delay, μs File: 09-01-16_1130 Z = 6 mm 0 2 Z = 24 mm File: 09-01-16_1200 FIG. 4.12. CARS signal dependence vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver. Expansion of 1% p-H 2 mixture in He at T V = 21 K, P 0 = 20 bar, nominal pulse duration: 200 μs, and Z = 6 mm (a) and Z = 24 mm (b). Measurements were obtained at the maximum of the p-H 2 cluster line. As discussed earlier, an unfortunate aspect of the CARS experiments is the fast decrease in signal with increasing distance from the nozzle, Z, as 1/Z 4 . Fig. 4.13 shows a Log-Log plot of the CARS signal as a function of Z where the slope of the line represents the power dependence of about 4, as expected. It is important to note that the pulse delay must be corrected at each distance to maximize the CARS signal. 93 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Log (Signal) Log (Z) y = 7.53979 - 4.30538*X FIG. 4.13. Log-Log plot of cluster CARS signal vs. distance from nozzle, Z, for a 1% n- H 2 mixture in He at T V = 25 K and P 0 = 20 bar. 4.8. Rotational CARS of H 2 Molecules and Clusters in He Droplets According to selection rules for Raman spectra, only rotational levels having ΔJ = 2 can combine. Due to the large rotational constant (B 0 ≈ 59 cm -1 ) at low temperature, the spectrum consists of 2 ← 0 and 3 ← 1 transitions for p-H 2 and o-H 2 molecules, respectively. The degeneracy of the H 2 molecules in rotational state J is: g(J) = 2J + 1. In the solid, crystal field effects remove the degeneracy giving rise to a splitting, 7 i.e., the J = 2 rotational state splits into two and three levels for hcp and fcc lattices, respectively. 8,9 In liquid H 2 , due to the concomitant motion of the molecules, the anisotropy is averaged and only a single, broad feature is observed. 8 These characteristic spectra have also been observed in H 2 clusters, as described previously 10 and in the current work. 94 4.8.1. Experimental Setup of Rotational CARS In this work, rotational CARS of H 2 molecules and clusters have been measured. Rotational CARS is similar to that as described for vibrational CARS with only minor modifications. In the case of rotational CARS, a different dye is necessary to produce ≈ 545 nm Stokes beam to match the 2 ← 0 rotational transition. In previous experiments, Coumarin 540A and THG pumping must be employed. Another option includes using Fluorescein 548 as in this work, in which case no optical changes are required since it is pumped by SHG as in vibrational CARS. Due to the large difference in wavenumbers of the transitions, i.e., ≈ 354 cm -1 and 590 cm -1 in p-H 2 and o-H 2 molecules, respectively, spectra of both spin isomers cannot be obtained in the same scan using the current setup due to the large angle displacement of the corresponding beams generated by the diffraction grating, see Fig. 4.4. Practical experiments therefore require optical alignment for one spin isomer at a time in which the custom gas cell (discussed in section 4.3) was used for alignment. 4.8.2. Gas Phase Rotational CARS of H 2 Fig. 4.14 shows a typical rotational CARS spectra at T V = 300 K for a pure p-H 2 expansion without (a) and with (b) an intra-cavity etalon installed in the dye laser. Measurements were calibrated against known values in the gas phase. 8 Here, the ν = 0, J = 2 ← ν = 0, J = 0 p-H 2 transition is observed around 354.37 cm -1 . The width of the line 95 without the etalon is 0.5 cm -1 while the spectrum with the etalon has a sharper linewidth around 0.07 cm -1 , close to the resolution of the etalon at 0.05 cm -1 . Similar spectra are obtained at T V = 60 K and P 0 = 20 bar, as shown in Fig. 4.15 (a) and (b) without and with the etalon, respectively. 352 353 354 355 356 357 0 2 a) Signal, V Wavenumbers, cm -1 b) 0 1 FIG. 4.14. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of pure p-H 2 at T V = 300 K and P 0 = 5 bar without (a) and with (b) an etalon. The spectra are calibrated against the known position of the line in the gas phase. 8 96 352 353 354 355 356 357 0 2 4 (a) Signal, V Wavenumbers, cm -1 (b) 0 1 FIG. 4.15. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at T V = 60 K and P 0 = 20 bar without (a) and with (b) an etalon. 4.8.3. Rotational CARS of H 2 in Clusters Fig. 4.16 demonstrates the previously discussed splitting in solid obtained upon expansion of a liquid p-H 2 jet at T V = 26 K, P 0 = 20 bar which subsequently breaks up into droplets and freezes. Panels (a – f) show spectra at various pump and Stokes laser pulse energies. The pulse energies of each of the laser beams were measured before focusing. Dotted and dashed lines correspond to spectra obtained in hcp 8,9 and fcc 9 lattice structures for p-H 2 . Here, four bands are seen each with a width around 1 cm -1 . The waveform of the spectrum resembles a structure consisting of a combination of fcc and hcp lattices. 8,9 This is due to the fast nucleation of the clusters in which the molecules do not have sufficient time to sample lower energy structures. Thus the clusters have presumably mixed close packed structure. 97 Panels (a) – (f) in Fig. 4.16 demonstrate the effects of pump and Stokes laser pulse energy on the spectra. The total laser power is highest in panel (a) and decreases by approximately a factor of 100 in panel (f). The intensity of the spectra is controlled by neutral filters on the PMT. As a result, the spectrum in panel (f) was measured without any neutral filters while the spectrum in panel (a) was measured with filters reducing the intensity by a factor of 2·10 5 . Despite the reduced intensity, the spectra are comparable in their features except for an approximate factor of 2 reduction in linewidth from panel (a) to panel (f). 348 350 352 354 356 358 360 Wavenumbers, cm -1 E pump = 2 mJ E Stokes = 2.5 mJ a) b) E pump = 0.02 mJ E Stokes = 0.02 mJ E pump = 0.02 mJ E Stokes = 0.05 mJ E pump = 0.02 mJ E Stokes = 0.1 mJ E pump = 1 mJ E Stokes = 0.1 mJ E pump = 2 mJ E Stokes = 0.1 mJ c) d) e) f) FIG. 4.16. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of liquid p-H 2 at T V = 26 K and P 0 = 20 bar at various pump and Stokes laser energies. Dotted and dashed lines refers to p-H 2 spectra obtained in hcp 8,9 and fcc 9 crystal lattice structures. 98 4.8.4. Spectral Anomalies in Rotational CARS spectra of H 2 Clusters Fig. 4.17 shows a series of rotational CARS spectra similar to that in Fig. 4.16 but at slightly higher energies for both Stokes and pump beams for a 100% p-H 2 expansion at T V = 25 K. Here the signal was maximized with respect to the molecular line at T V = 60 K. Panels (a – d) represent spectra obtained beginning from highest Stokes pulse energy of 5 mJ (a) to 0.1 mJ (d) while the pump pulse energy is constant at 4 mJ. As compared to Fig. 4.16, panel (a) contains an additional dominant feature centered on the molecular line at 354.38 cm -1 . Upon decrease of Stokes pulse energy by approximately a factor of 15 in panel (b), this feature is reduced and is comparable to the peak at around 356 cm -1 . Upon further decrease in Stokes pulse energy in panel (d), the feature at 356 cm -1 is dominant and the spectrum resembles that at low energy in Fig. 4.16. The onset of this feature at the molecular line with high Stokes energy is reproducible yet not well understood. It is important to note that the onset of the gas line was never observed in vibrational CARS. It may imply that we are destroying the cluster. Due to the relatively larger width of rotational features to those observed in vibrational CARS by approximately a factor of 2 - 3, rotational excitation relaxes more efficiently and may explain the observation of gas features. 99 348 350 352 354 356 358 360 Wavenumbers, cm -1 E Stokes = 5 mJ E Pump = 4 mJ a) b) E Stokes = 0.3 mJ E Pump = 4 mJ c) E Stokes = 0.2 mJ E Pump = 4 mJ d) E Stokes = 0.1 mJ E Pump = 4 mJ FIG. 4.17. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of liquid p-H 2 at T V = 25 K and P 0 = 20 bar at various Stokes pulse energies and constant pump energy. Rotational spectra of clusters obtained upon expansion of 1% or 0.5% p-H 2 mixtures in He have previously been observed 10 to have only a single feature ( ν = 353.4 cm -1 , Δν ≈ 1.2 cm -1 ), indicating its fluid state. Fig. 4.18 shows a series of rotational CARS spectra for a 1% p-H 2 mixture in He as the temperature is reduced from T V = 60 K to T V = 21 K. The spectra were recorded at P 0 = 20 bar, Z = 5 mm, and without an etalon. The laser focal point in direction perpendicular to the molecular beam was at Y = 40 mm, as adjusted by highest signal at T = 60 K. The spectra obtained at T V = 60 and 50 K contain only a single gas phase line at 354.4 cm -1 see panels (e) – (f), respectively. However, upon cooling down to T V = 40 K and below, panels (a) – (c) contain spectra consisting of two peaks at 354.1 and 354.5 cm -1 with widths of 0.3 cm -1 and centered approximately around the gas line at 354.4 cm -1 . The observed splitting near the gas line 100 is believed to be due to a saturation dip in the CARS signal. In addition, despite the low temperature of T V = 21 K, we did not observe any feature which can be identified with clusters. 10 351 352 353 354 355 356 357 Wavenumbers, cm -1 a) T V = 21 K T V = 30 K b) T V = 40 K c) T V = 50 K d) T V = 60 K e) FIG. 4.18. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at various nozzle temperatures: P 0 = 20 bar, Z = 5 mm. Fig. 4.19 shows spectra obtained at T V = 40 K with (a) and without (b) a 70% optical transmission filter on the Stokes beam. Here the addition of a filter (a) to the Stokes beam provides a spectrum of a single feature at the gas line without a splitting, indicating the absence of power saturation. As a result, the addition of the filter was used for all measurements thereafter. 101 352 353 354 355 356 357 0.0 0.5 1.0 1.5 2.0 2.5 Signal, V Wavenumbers, cm -1 a) 0 1 2 3 4 5 6 b) FIG. 4.19. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at T V = 40 K, P 0 = 20 bar, Z = 5 mm. Panels (a) and (b) shows spectra with and without a 70% optical transmission filter, respectively. Fig. 4.20 (a) and (b) demonstrates the effect of shift of the observation point by 1 mm perpendicular to the beam axis in the case of a 1% p-H 2 mixture in He at T V = 20 K. The spectrum in panel (a) (Y = 38 mm) shows a single broad feature (~ 2 cm -1 ), indicative of fluid clusters as observed previously. 10 However, the spectrum measured upon minor shift of the laser beam focus to Y = 39 mm in panel (b) shows a much narrower and more intense peak at 354.2 cm -1 . In addition at T V = 60 K, the maximum signal in the gas phase occurs at Y = 39 mm for this series of experiments. Here, a 70% filter was added to the Stokes beam to reduce power saturation. This change in spectra upon probing different volumes of the expansion indicates large inhomogeneity of the expansion. However, it is important to note that upon returning to vibrational CARS, 102 such anomalies were not observed, and the signal of clusters was maximized at the same Y position as in the case of gas the line. This indicates that the discrepancies may originate from the differences in rotational and vibrational CARS processes. 346 348 350 352 354 356 358 360 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 b) Signal, V Wavenumbers, cm -1 a) 0 2 FIG. 4.20. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 1% p-H 2 mixture in He at T V = 20 K, P 0 = 20 bar, Z = 5 mm, and without an etalon. Panels (a) and (b) refer to spectra obtained at Y = 38 and 39 mm, respectively. Inhomogeneity in the expansion is also observed at other conditions such as the pulse duration. Fig. 4.21 illustrates the effect of pulse duration for a series of spectra of a 1% p-H 2 mixture in He at T V = 20 K. Panels (a – d) show spectra at pulse durations spanning differences less than 22 μs. However, the spectrum in panel (a) at pulse duration of 114 μs shows a broad feature centered around 354 cm -1 , indicating liquid structure. Upon further increase in pulse duration, additional features appear similar to those measured in solid, see Fig. 4.16 and Fig. 4.17. However, intensity is 103 predominantly located around 354 cm -1 , whereas solid features contain two dominant features at 354 and 356 cm -1 . In addition, a sharp feature is dominate at 354.2 cm -1 , implying the presence of gas. This may provide evidence of inhomegeneity in which in all three phases are present in different proportions. As shown in Fig. 4.21, the total signal increases with increasing pulse duration. Therefore, it is not immediately clear if the onset of additional features is due to changes in the expansion conditions or lack of signal in panel (a). 346 348 350 352 354 356 358 360 362 0.1 0.2 0.3 0.4 Pulse Duration = 114 μs Signal, V Wavenumbers, cm -1 a) 0.2 0.4 0.6 Pulse Duration = 119 μs b) 0.0 0.5 1.0 Pulse Duration = 128 μs c) 0 1 2 d) Pulse Duration = 136 μs FIG. 4.21. Rotational CARS spectra obtained at different pulse delays upon expansion of a 1% p-H 2 mixture in He at T V = 20 K, P 0 = 20 bar, Z = 5 mm, Y = 38 mm, and without an etalon. Despite the observed splitting and inhomogeneity in the clusters as shown in Fig. 4.21, spectra of a 2% p-H 2 mixture in He displays a liquid structure, as shown in Fig. 4.22 at T V = 23 K and several Z-positions from 5 – 15 mm (a – c). It is important to 104 point out all measurements in Fig. 4.22 were obtained at Y = 36 mm in which the molecular line became dominate at Y > 36 mm for these set of experiments, as shown in Fig. 4.24. It is also important to point out that the successful observation of liquid clusters shown in Fig. 4.22 was reproducible throughout the day of the experiment. Unfortunately the following day, no cluster signal was present at identical conditions. However, additional experiments were eventually able to reproduce the results at Z = 5 mm in Fig. 4.22, as shown in Fig. 4.23. 348 350 352 354 356 358 0.0 0.2 0.4 0.6 0.8 1.0 Z = 5 mm Signal, V Wavenumbers, cm -1 a) 0.0 0.2 0.4 0.6 Z = 10 mm b) -0.2 0.0 0.2 0.4 0.6 0.8 1.0 c) Z = 15 mm FIG. 4.22. Rotational CARS spectra obtained at different Z-positions upon expansion of a 2% p-H 2 mixture in He at T V = 23 K, P 0 = 20 bar, Y = 36 mm, and without an etalon. Fig. 4.23 demonstrates the reproducibility of experiments for a 2% p-H 2 expansion at T V = 23 K for different Y-positions. The difference in position of 1 mm between panel (a) and (b) at Y = 34 mm and Y = 35 mm, respectively, demonstrates the strong presence of the gas at low temperatures. Panel (c) shows etalon measurements in 105 which the width of the band is approximately the same as without the etalon, indicating the width of the clusters is not determined by the resolution of the laser and is broad. 350 351 352 353 354 355 356 357 Y = 35 mm Wavenumbers, cm -1 a) b) Y = 34 mm Y = 35 mm c) FIG. 4.23. Rotational CARS spectra obtained at different Y-positions upon expansion of a 2% p-H 2 mixture in He at T V = 23 K, P 0 = 20 bar, Z = 5 mm. Panels (a) - (b) were obtained without an etalon while panel (c) was obtained with an etalon. Fig. 4.24 shows the dependence of the CARS signal upon shift of the focal point along Y axis, i.e., perpendicular to the direction of the molecular beam for a 2% p-H 2 mixture in He at T V = 40 K (a) and T V = 23 K (b) as obtained at the maximum of the p- H 2 molecular line. Panel (a) shows that at T V = 40 K, the optimal CARS signal was observed at Y ≈ 35 mm, while the signal at T V = 23 K has two peaks at approximately 35 and 38 mm. The shift in optimal Y-position at T V = 25 K for the molecular line indicates that cluster formation effects the expansion. 106 26 28 30 32 34 36 38 40 42 44 46 48 T V = 40 K Y-Position, mm a) T V = 25 K b) FIG. 4.24. Rotational CARS signal dependence of 2% p-H 2 mixture in He at the gas line vs. Y -position at T V = 40 K (a) and T V = 23 K, respectively. Comparisons between Fig. 4.21 and Figs. 4.22 – 4.23 show slight differences in their spectra. These discrepancies between the 1% and 2% mixtures in terms of their waveforms indicate the transition from solid to liquid is not well defined and somewhat broad. This is confirmed by the vibrational CARS frequency dependence on p-H 2 fraction in helium, as shown in Fig. 4.25. Here, upper and lower horizontal lines represent vibrational Raman frequencies obtained in the liquid at T = 18 K 8 and in the solid at T = 4 K 11 , respectively. Previous results 10 , illustrated by solid squares, show a dramatic change in vibrational frequency upon decreasing the p-H 2 fraction from 1% and below. However, our current work, shown by open squares, demonstrates a more gradual shift in frequency. 107 0.01 0.1 1 10 100 4149.5 4150.0 4150.5 4151.0 4151.5 4152.0 Liquid bulk, 18 K Frequency, cm -1 % of pH 2 in He Solid bulk, 4 K FIG. 4.25. Vibrational CARS frequency of the Q 1 (0) line in clusters as a function of p-H 2 molecules in expanding He gas. Horizontal dashed lines show the Q 1 (0) frequencies in solid p-H 2 at 4 K 11 and in liquid p-H 2 at 18 K 8 . Solid squares are points from previous work 10 while open squares are from current work. The effect of the gas pulse duration is also prominent at higher temperatures. Fig. 4.26 shows the intensity of the CARS signal vs. laser pulse delay with respect to the trigger at different nominal gas pulse durations (a – d) for a 1% p-H 2 mixture in He at T V = 60 K. The time profile in panel (a) was obtained at a pulse duration of 126 μs, in which some form of bimodal distribution is seen. Increases in the gas pulse duration up to 146 μs leads to broadening of the pulse by approximately a factor of 2. The profiles also show some asymmetry. It is important to note that these features appear somewhat different from day to day. 108 250 300 350 400 450 500 550 600 0.5 1.0 1.5 Signal, V Pulse Delay, μs 126 μs a) 0 2 4 136 μs b) 0 2 4 6 146 μs c) FIG. 4.26. Rotational CARS signal dependence of p-H 2 gas line vs. laser pulse delay with respect to the trigger point of the pulsed nozzle driver for various pulse durations at T V = 60 K. Despite the discrepancies observed for 1% and 2% mixtures, measurements for a 0.5% p-H 2 mixture were obtained. In addition, it is currently unclear as to why this particular day provided working spectra in which measurements were obtained at Z- positions up to 15 mm, previously unattainable for 1% mixtures. Unfortunately, it must be pointed out that these measurements were not reproducible from day to day. Fig. 4.27 illustrates rotational CARS spectra for a 0.5% p-H 2 mixture in He at T V = 20 K. In order to achieve sufficient signal, the nominal gas pulse duration was set to 300 μs. Here a single feature centered around 353.8 cm -1 with a width of about 2 cm -1 is observed. Fig. 4.28 shows the intensity of the rotational CARS for the 0.5% p-H 2 mixture in He as a function of Z-position. Due to the weak signal, measurements could only be obtained up to distances of 15 mm from the nozzle. The Log-Log plot of signal vs. Z-position shows a slope of 1.6, whereas previous vibrational CARS measurements (Fig. 4.13) 109 demonstrated the predicted slope of 4. This discrepancy is currently not well understood. 350 352 354 356 0 1 2 Signal, V Wavenumbers, cm -1 FIG. 4.27. Rotational CARS spectra of p-H 2 molecules obtained upon expansion of a 0.5% p-H 2 mixture in He at T V = 20 K, P 0 = 20 bar, Z = 5 mm, Y = 37 mm, and without an etalon. 110 0.7 0.8 0.9 1.0 1.1 1.2 -0.8 -0.6 -0.4 -0.2 0.0 0.2 Log 10 (Signal) Log 10 (Z-Position) y = 1.13 - 1.6*Log 10 (Z) FIG. 4.28. Rotational CARS signal dependence of 0.5% p-H 2 mixture in He at the max of the cluster peak in Fig. 4.27 vs. Z-position at T V = 20 K. Large drop in rotational CARS signal was observed upon cooling during the formation of clusters as compared to that for vibrational CARS. For the current measurements, most rotational CARS spectra were measured with the complete removal of neutral filters from the PMT for 1% p-H 2 mixtures in He whereas filters suppressing the signal by as much as a factor of 10 were used for mixtures down to 0.5% p-H 2 for vibrational CARS. Laser powers from dyes used for vibrational and rotational CARS were comparable. Despite the rare anomalies for 2% and 0.5% mixtures observed occasionally, see Figs. 4.22 – 4.23 and 4.27, respectively, rotational CARS experiments could not be performed for 1% p-H 2 mixtures at distances beyond Z = 6 mm. Additional anomalies in the rotational CARS signal were also observed. As shown in Fig. 4.20, spectra at Y = 39 mm (b) shows the S 0 (0) line in the gas phase, 111 despite the low temperature at T V = 20 K. One explanation may be due to the faster relaxation of rotational excitations of molecules in the cluster which could cause sufficient evaporation of the cluster. However, expansion of liquid p-H 2 showed intense signal, despite the observed splitting. Unfortunately, the intensity disparity is currently not well understood. Measurements are currently underway to quantitatively measure the intensities of the rotational and vibrational Raman spectrum in the bulk. 112 Chapter 4 Bibliography 1 G. V. K. J.W. Nibler, Raman Spectroscopy of Gases and Liquids. (Springer- Verlag, Berlin, 1979). 2 K. Kujanovs, University of Southern California, 2007. 3 F. Moya, S. A. J. Druet, and J. P. E. Taran, Optics Communications 13 (2), 169 (1975). 4 W. Demtroder, Laser Spectroscopy, 3rd ed. (Springer-Verlag, Berlin, 2003). 5 K. E. Kuyanov, T. Momose, and A. F. Vilesov, Applied Optics 43 (32), 6023 (2004). 6 S. L. Bragg, J. W. Brault, and W. H. Smith, Astrophysical Journal 263 (2), 999 (1982). 7 I. F. Silvera, Reviews of Modern Physics 52 (2), 393 (1980); J. van Kranendonk, Solid Hydrogen: Theory of the Properties of Solid H 2 , HD, and D 2 . (Plenum Press, New York and London, 1983). 8 S. S. Bhatnagar, H. L. Welsh, and E. J. Allin, Canadian Journal of Physics 40 (1), 9 (1962). 9 G. W. Collins, W. G. Unites, E. R. Mapoles, and T. P. Bernat, Physical Review B 53 (1), 102 (1996). 10 K. Kuyanov-Prozument and A. F. Vilesov, Physical Review Letters 101 (20), 205301 (2008). 11 K. E. Kerr, T. Momose, D. P. Weliky, C. M. Gabrys, and T. Oka, Physical Review Letters 72 (25), 3957 (1994). 113 Chapter V . Structure of Cold, Mixed Para-H 2 – D 2 Clusters 5.1. Introduction Hydrogen may constitute a new class of molecular superfluids that are characterized by anisotropic interaction and rotational angular momentum of the particles. Normal hydrogen consists of two modifications: para-H 2 (p-H 2 ) and ortho-H 2 (o-H 2 ). p-H 2 molecules are spinless Bosons (I = 0) and at low temperature reside in the ground rotational state J = 0, which makes p-H 2 the prime candidate for observation of superfluidity. p-H 2 has a calculated superfluid transition temperature at ≈ 1 K in the bulk 1 and ≈ 2 K in small clusters. 2 However, superfluidity of hydrogen, although predicted three decades ago, 3 continues to elude experimental observation. Due to stronger intermolecular interactions, freezing of hydrogen at 13.8 K is the primary experimental obstacle. Although the rate of freezing is predicted to be very low at T ≤ 3 K, 4 numerous attempts at supercooling liquid hydrogen in macroscopic droplets, 5 clusters, 6 porous media, 7 or in the bulk 8 have proved unsuccessful. Recently, we have assembled clusters having about 10 4 p-H 2 molecules at low temperatures by free jet expansion of p-H 2 gas seeded in He. 9 Using rotational spectra measured via coherent anti-Stokes Raman scattering (CARS), we have shown that such clusters remain liquid at estimated T = 1 – 2 K, i.e., close to the predicted superfluid transition temperature. We have also found that the vibrational CARS frequency of the p-H 2 clusters is in agreement with that expected for super-cooled liquid at T < 5 K. 10 114 One of the unique properties of liquid He is the phase separation of 3 He/ 4 He mixtures at temperature below 0.87 K. 11 At very low temperatures, the mixture of 3 He and 4 He consists of nearly pure 3 He liquid on the surface and a mixture of 8% 3 He in a 4 He core. Phase separation has also been predicted in mixtures of p-H 2 and D 2 at temperatures ≤ 3 K 12,13 , where it derives from different zero point energies in neat and mixed substances. At these low temperatures, hydrogen is solid and thus no phase separation has been directly detected due to very slow diffusion rate in solid. 14 As a result, the goal of this work is to observe phase separation in cold liquid p-H 2 /D 2 clusters via vibrational CARS spectroscopy of p-H 2 molecules in the cluster. In H 2 condensed phases, vibrations form a band having width of about 3 cm -1 . 15 Dilution of p-H 2 with D 2 molecules leads to a decrease of the efficiency of the vibron hopping and thus smaller band width. Therefore, the measured vibrational frequency of the p-H 2 molecules is a direct probe of the fraction of the D 2 molecules in the p-H 2 liquid. 16 We have obtained that the mole fraction of D 2 in solid clusters is very close to that in the expanding gas mixture. On the other hand, D 2 content in liquid clusters is depleted by up to a factor of five with respect to that in the expanding gas. These results indicate phase separation into nearly pure p-H 2 and D 2 phases in the surface and interior of the cluster, respectively. 115 5.2. Experimental Technique Hydrogen (p-H 2 or mixed p-H 2 /D 2 ) clusters are formed by a pulsed free jet expansion of either a liquid or cold gas mixture of hydrogen in He at T 0 = 15 – 22 K and a stagnation pressure of P 0 = 3 and 20 bar, respectively. p-H 2 is produced by catalytic conversion of liquid n-H 2 (Praxair, research grade) with a residual o-H 2 content of less than 0.1%. 17 Normal D 2 was used as received. p-H 2 /D 2 /He mixtures were prepared in a 1 gal. stainless steel sampling cylinder. Mixtures were generally prepared the day prior to experiment to ensure sufficient mixing. The combined molar fraction of hydrogen and deuterium in the He mixture will be referred to as X. X = 100% indicates expansion of pure hydrogen/deuterium mixtures in the absence of helium. In this work we have studied clusters which have been prepared from mixtures having X = 1%, 8%, and 100%. For each X, the molar fraction of D 2 in the H 2 /D 2 gas is varied in the range of Y = 0 – 98%. The cryogenic molecular beam apparatus is described in detail elsewhere. 18 The pulsed valve assembly, used to form the jet expansion, consists of a Series 99 (General Dynamics Valves Inc.) valve equipped with copper sealing gaskets. The nozzle has a 1 mm diameter with a custom machined conical opening of about 90 º . The entire valve assembly is mounted onto a copper platform which is attached to the second stage of a closed-cycle helium refrigerator. The pulsed nozzle assembly can be moved in the horizontal plane. Thus, Raman spectra can be obtained at different distances from the nozzle – L up to about 50 mm. 116 The vibrational spectra of p-H 2 molecules in clusters were obtained via CARS 19 technique. In this four-wave mixing scheme, a 532 nm pump beam, generated from a Nd:YAG laser (Powerlite Precision II 8020), and Stokes beam (~ 683 nm) from a tunable dye laser (Lambda Physics, NPD 3000) were focused into the center of the expanding mixture by means of a 50 cm achromatic lens. Both pump and Stokes beams have vertical polarization. When the frequency difference of the pump and Stokes laser beams matches the vibrational frequency of the p-H 2 molecules, an anti-Stokes signal is generated, which is separated from the pump and Stokes beams by means of a diffraction grating and subsequently detected by a photomultiplier equipped with appropriate interference filters. The pump beam has a linewidth of about 0.003 cm -1 , whereas the Stokes beam has a linewidth of approximately 0.05 cm -1 and 0.25 cm -1 , respectively, with or without an intra-cavity etalon installed. Calibration of the absolute frequency of the spectrometer was achieved using Raman spectra of p-H 2 gas as measured previously at high resolution. 20 117 5.3. Results Fig. 5.1 shows typical CARS spectra of the vibrational Q 1 (0) line ( ν = 1, J = 0 ← ν = 0, J = 0) of p-H 2 molecules in clusters obtained upon gas expansion in He having different X and Y, as measured without an intra-cavity etalon. The lower panel of each column in Fig. 5.1 displays spectra in the absence of D 2 , i.e. Y = 0, while the upper panels show spectra at increasing values of Y studied for each series of experiments. Traces (a) – (c) show spectra of X = 1% p-H 2 /D 2 in He obtained upon expansion at T = 16 K while traces (d) – (f) show spectra of X = 8% in He at T = 20 K. Spectral line shifts of about 1.4 cm -1 and 0.5 cm -1 were observed in clusters obtained from mixed samples from X = 8% and X = 1% mixtures, respectively. Typical linewidths observed in spectra of clusters as obtained from the X = 1%, 8%, and 100% samples were about 1.1, 0.9, and 0.8 cm -1 , respectively, as measured without an intra-cavity etalon. Much narrower lines in bulk solid down to 1 MHz at 4.2 K were observed previously in pure p-H 2 solids using high resolution cw laser systems, 21,22 while linewidths of about 0.115 cm -1 were observed in bulk liquid 10 . 118 Y = 58% D 2 X = 1% T = 16 K a) d) b) Y = 85% D 2 X = 8% T = 20 K Y = 37% D 2 X = 8% T = 20 K Y = 0% D 2 X = 8% T = 20 K Y = 0% D 2 X = 1% T = 16 K Y = 27% D 2 X = 1% T = 16 K e) 4145 4150 4155 c) Wavenumbers, cm -1 4145 4150 4155 f) Wavenumbers, cm -1 FIG. 5.1. CARS spectra of the Q 1 (0) transition of p-H 2 molecules in clusters obtained upon expansion of gas having X = 1% p-H 2 /D 2 (a - c) and X = 8% (d - f). The fraction of D 2 in the expanding gas (Y) as well as nozzle temperature is shown in each panel. The spectra were measured at L = 10 mm without an intra-cavity etalon. Fig. 5.2 shows a series of spectra for the Q 1 (0) line of p-H 2 molecules in clusters obtained upon expansion of a liquid hydrogen/deuterium mixture (X = 100%) at indicated values of Y and at a nozzle temperature of T = 22 K. Upon expansion, the liquid breaks into large clusters which freeze before the observation point. 9 Fig. 5.2 shows that upon increase of D 2 content in the expanding liquid, the Q 1 (0) line shifts towards higher frequency. Beginning at Y = 60% D 2 , a broad feature appears to form at higher frequency. At Y = 80% D 2 , the additional feature has a frequency of about 0.8 cm -1 higher than the main feature. Further increase in D 2 content to Y = 92% shows a similar doublet structure; however, it has a smaller splitting of about 0.5 cm -1 and larger intensity. Finally, the two peaks appear to merge at Y = 98%, see panel (f) of Fig. 5.2. The line is 119 again a singlet having frequency of 4152.25 cm -1 , i.e., has a shift by approximately 2.6 cm -1 from that in spectrum (a) at Y = 0. The frequency of the Q 1 (0) line in clusters obtained upon expansion of neat p-H 2 liquid is in agreement with previous results obtained in solid clusters 9 and in bulk solid. 10,21,22 4146 4148 4150 4152 4154 a) Y = 0% D 2 Wavenumbers, cm -1 b) Y = 31% D 2 c) Y = 80% D 2 Y = 60% D 2 d) e) Y = 92% D 2 f) Y = 98% D 2 FIG. 5.2. CARS spectra of the Q 1 (0) line of p-H 2 clusters at X = 100% with varying D 2 content, Y, obtained upon expansion at T = 22 K and P = 3 bar and measured without an intra-cavity etalon. Traces (e) – (f) were measured with intra-cavity etalon. All spectra represented were obtained at L = 10 mm. Fig. 5.3 shows the results of all measurements of the frequency of the Q 1 (0) line of p-H 2 in clusters at different D 2 content and X = 1%, 8%, and 100%. Solid shapes indicate frequencies obtained at a distance of L = 10 mm, while open shapes represent frequencies measured at larger distances as specified. Solid and open triangles represent high frequency peaks observed from split features for X = 100% at L = 10 and 35 mm, respectively, as shown in Fig. 5.3 (a). Each point represents the frequency average 120 obtained from three to five spectra. Error bars are included to account for the scattering of the results observed for each sample studied. The dashed line in each panel represents the dependence expected in the bulk solid. Panels (a) – (b) show the results of solid clusters at X = 100% and 8%, respectively, while panel (c) shows results obtained from liquid clusters at X = 1%. For solid clusters, the frequency rises approximately linearly with increasing D 2 composition. Frequencies obtained at distances of L ≥ 25 mm and 35 mm for 8% and 100% mixtures, respectively, are the same as spectra obtained at L = 10 mm. Linear fits for X = 1%, 8%, and 100% at L = 10 are shown in equations (5.1) – (5.3), respectively. Note that equation (1) for X = 1% is determined from Y = 0 – 58%. However, the linear fit for X = 1% is somewhat arbitrary depending on points used and should be considered less quantitative. X = 1%: ν = 4151.02 ± 0.04 cm -1 + (1.0 ± 0.1 cm -1 ) ⋅Y% 5.1 X = 8%: ν = 4150.28 ± 0.04 cm -1 + (1.62 ± 0.07 cm -1 ) ⋅Y% 5.2 X = 100%: ν = 4149.54 ± 0.03 cm -1 + (2.73 ± 0.03 cm -1 ) ⋅Y% 5.3 Fig. 5.3 shows that for X = 1%, a linear rise in frequency is observed with D 2 content up to about Y = 35%. At higher Y, the frequency of the line is approximately independent of D 2 content up to Y = 70% at approximately 4151.52 ± 0.02 cm -1 . As the intensity of the CARS signal decreases rapidly with increasing Y, cluster spectra could not be obtained at Y > 70% for X = 1%. Fig. 5.3 (c) also shows that, at each Y for X = 1%, increasing the observation distance, L, leads to a decrease of the slope of the 121 dependence to about 0.6, as shown by open squares and lower solid line in panel (c). Again, the spectra could not be recorded at L > 10 mm at Y = 70% due to the quadratic drop in number density upon expansion and subsequent quadratic dependence of number density on CARS signal. 19 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 4149.5 4150.0 4150.5 4151.0 4151.5 4152.0 4152.5 D 2 Fraction 4149.5 4150.0 4150.5 4151.0 4151.5 4152.0 4152.5 L = 10 mm L > 18 mm L = 10 mm L = 25 mm c) X = 1% T = 15 K a) X = 100% T = 22 K b) X = 8% T = 20 K 4149.5 4150.0 4150.5 4151.0 4151.5 4152.0 4152.5 L = 10 mm L = 35 mm L = 10 mm L = 35 mm FIG. 5.3. Frequencies of the Q 1 (0) line in p-H 2 /D 2 clusters versus the deuterium content, Y , at X = 100%, 8%, and 1% in panels a), b), and c), respectively. Solid squares represent frequencies measured at distances of L = 10 mm while open squares indicate measurements obtained at longer distances as specified in each panel. Solid and open triangles indicate the higher energy peaks for L = 10 and 35 mm, respectively, in panel a) as observed from Fig. 2. The error bars represent mean square deviation of several measurements. Lines are linear fits according to eqs. (5.1 – 5.3). The dashed line represents the dependence expected in bulk. 122 5.4. Discussion It is important to review previous results regarding the physical origin of the vibrational frequency shift in condensed phase p-H 2 and its mixtures. 15,16,21,23,24 The frequency of the Q 1 (0) line in solid is about 11.4 cm -1 lower than that observed in the gas phase 20 at 4161.1687 cm -1 . The lowering of the frequency is mainly accounted for by an 8.7 cm -1 shift due to isotropic dispersion intermolecular interactions. 24 In addition, the vibron excitation is easily delocalized between p-H 2 molecules in the solid giving rise to a vibrational band which has width of about 3.6 cm -1 . 15,22 However, due to momentum conservation, which dictates the selections rules in the Raman spectrum 15 , only transitions to the lowest level of the vibron band are allowed, thereby producing a very narrow Q 1 (0) line. As a result, the frequency of the Q 1 (0) line has an additional 2.7 cm -1 downward shift. 24 Formation of the vibron band in liquid has been studied to a much lesser degree. Measurements of the intensity ratio of the Q 1 (0) and Q 1 (1) lines in liquid H 2 show the same intensity enhancement of the Q 1 (1) line as in solid indicating similar vibron band formation. 25 Our recent study of the temperature dependence of the frequency of the Q 1 (0) line in pure pH 2 shows that the frequency change of the Q 1 (0) line in liquid and in solid can be accounted for by the same function of density, indicating similar origin of the line shift in solid and in liquid. As a result, we assume that the magnitude of the vibron shift of the Q 1 (0) line in liquid is approximately the same as in solid. If we assume that the width of the vibron band scales with the total shift of the Q 1 (0) line from the gas phase, about 10% smaller band width is expected in low temperature liquid than in solid 123 based on results of our recent work. 10 Therefore, based on the previous discussion, the frequency of the Q 1 (0) line is a sensitive probe for the composition of the hydrogen solid. Replacing p-H 2 molecules by o-H 2 or D 2 molecules decreases the probability of the vibron hopping, and thus leads to a decrease of the vibron band width and concomitant upward shift of the frequency of the Q 1 (0) line. In bulk solid samples of mixed p-H 2 /o-H 2 , the frequency of the Q 1 (0) line shifts linearly with o-H 2 content to higher energy. Similarly, the frequency of the Q 1 (1) line shifts linearly to lower energy. 24 Similar effects have been observed upon replacement of D 2 molecules by H 2 molecules. In solid D 2 /H 2 samples, the frequency of the Q 1 (0) and Q 1 (1) lines of D 2 shift towards higher frequency upon increasing of the H 2 content. 16 Furthermore, the shift of the frequency of the Q 1 (J = 0, 1) lines of D 2 molecules in D 2 /HD mixtures were found to be nearly the same as in D 2 /H 2 mixtures of the same content. This indicates that a possible change of the interaction due to different masses of the substitute molecules is of minor importance. According to Ref. 16, the frequency of the Q 1 (0) line has a linear dependence on the fraction of the added foreign isotopomer molecules as well documented in mixtures of D 2 - T 2 and D 2 -H 2 . Although in the last case only the lines of D 2 molecules have been studied, the linear dependence must also hold for the frequency of the H 2 lines, based on the same physical mechanism of the shift. Therefore, Fig. 5.3 (a) shows the expected dependence of the frequency of the Q 1 (0) line of p-H 2 vs. the fraction of the D 2 molecules in the mixture. This dependence is based on the well studied dependence of the Q 1 (0) frequency upon the fraction of the o- H 2 molecules in the solid p-H 2 /o-H 2 mixture. 24 124 Clusters obtained upon expansion of neat p-H 2 /D 2 liquid (X = 100%), see Fig. 5.3 (a), provide the closest comparison to bulk material studied so far. Indeed, the frequency of the Q 1 (0) line in clusters of 4149.7 cm -1 obtained upon neat p-H 2 expansion (Y = 0) matches that in bulk solid, 10,21 suggesting comparable density between clusters and bulk. The addition of D 2 and subsequent blue shift of about 2.6 cm -1 from neat p-H 2 is similar to that obtained in bulk p-H 2 /o-H 2 samples 24 where a shift of 2.7 cm -1 is observed. The shift of 2.7 cm -1 corresponds to complete quenching of the vibron band. The frequency shift also scales linearly with Y , in agreement with previous solid phase observations. 24 The origin of the splitting in the spectra of Fig. 5.2 (d, e) obtained at high content of D 2 molecules of Y ≥ 80%, remains unclear. As observed in Fig. 5.3 (a) for Y = 80%, the low frequency peak is in line with the predicted position at 4151.50 cm -1 while the high frequency peak is blue shifted by almost 0.9 cm -1 . This may indicate partial phase separation in the solid, which contains p-H 2 in an extreme D 2 rich environment as well as regions where the composition is close to that in the expanding mixture. At Y = 92% in Fig. 5.2 (e), the two peaks have comparable intensity, which may indicate similar amount of molecules trapped in D 2 rich and D 2 poor phases. Prior to expansion for X = 100% at T = 22 K as discussed previously, the mixture is liquid. Upon expansion, the liquid breaks into large clusters which freeze before the observation point. Since phase separation in solid is considered extremely slow as well as the fact that phase separation has not been observed in bulk liquids 26 , incomplete phase separation must occur during the expansion and subsequently quenched by freezing. The results in clusters obtained upon gas expansion of X = 8% p-H 2 /D 2 in He are 125 qualitatively similar to those obtained from liquid expansion of the neat p-H 2 /D 2 liquid. The frequency of the Q 1 (0) line rises linearly with Y, but has somewhat smaller slope of 1.6 cm -1 as compared with 2.7 cm -1 at X = 100%. The discrepancy between observed slope of the frequency dependence at X = 8% and 100% is not completely understood. Comparison of panels (a) and (b) in Fig. 5.3 shows that neat p-H 2 clusters obtained at X = 8% have about 0.6 cm -1 higher frequency as compared with clusters obtained at X = 100%. This may indicate that clusters obtained at X = 8% have lower density than in the bulk, which will also result in lower rate of vibron hopping than in bulk hydrogen. It should be noted, that the frequency shift is not due to temperature dependence, as it is very weak. Previous high resolution measurements show that the frequency of the Q 1 (0) line in bulk crystalline solid rises approximately 0.13 cm -1 from 4.9 to 13.5 K. 21 Thus we conclude that clusters obtained at X = 100% and 8% may have somewhat different structure and density, such as polycrystalline and amorphous. Different structures of the clusters may also influence the width of the vibrational band, which is expected to be smaller in less regular clusters. Finally, the frequency may be influenced by some phase separation, as it will be discussed in more details in the case of X = 1%. We proceed with discussion of the results obtained at X = 1%. Fig. 5.3 (c) shows that for small L and increasing D 2 content, the frequency of the Q 1 (0) line first rises by about 0.4 cm -1 up to Y = 35%. At larger Y, the frequency of the line remains approximately constant at 4151.52 ± 0.02 cm -1 . At large L, the frequency is about 4151.29 ± 0.05 cm -1 , only slightly higher than in neat pH 2 clusters at 4151.01 ± 0.05 cm -1 . The saturation of the frequency dependence at Y ≥ 35%, in terms of vibron hopping, 126 implies that further increase of the D 2 content in clusters does not lead to a reduction of the number of nearest neighbor p-H 2 molecules in the vicinity of a given p-H 2 molecule. Therefore, the saturation of frequency with D 2 indicates the onset of the phase separation between isotopic mixtures. Furthermore, the fact that the frequency of the Q 1 (0) line is lower at larger L demonstrates that the phase separation is more pronounced at larger L. The time of flight of the gas from the nozzle throat to the observation point at L = 10 mm can be estimated to be about 25 μs. Phase separation may require some time for molecules to diffuse through the cluster, favoring more complete separation at larger distances. The temperature of the clusters is also expected to decrease downstream, favoring more complete phase separation as will be discussed later. Taking that the slope of the dependence of the frequency with Y in the liquid is still given by eq. (5.3), we can estimate the fraction of the D 2 molecules in the H 2 rich fraction to be around 20% at L = 10 and about 10% at L = 20 mm. According to this picture, H 2 molecules dissolved in the D 2 rich fraction of the cluster should give rise to a spectral peak at higher frequency. The fact that no such peak is observed in the spectrum in Fig. 5.1 (b – c) is consistent with a low content of H 2 in the D 2 rich fraction of less than 30%, producing a factor > 5 weaker CARS signal from the D 2 rich phase. Fig. 5.4 illustrates the concentration of D 2 in the p- H 2 rich phase as a function of D 2 fraction in the prepared gas mixture. It is seen that in the case of X = 1%, the concentration of D 2 molecules in the p-H 2 rich fraction levels of at about 0.2 and 0.1 for L = 10 mm and 20 mm, respectively. 127 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 X = 100% X = 8% X = 1%, L = 10 mm X = 1%, L = 20 mm D 2 fraction in p-H 2 phase D 2 fraction in prepared gas mixture FIG 5.4. Fraction of D 2 in the pH 2 rich phase as a function of the fraction of D 2 in the prepared gas sample. Solid shapes indicate points obtained at L = 10 mm while open circles represents points obtained at L = 20 mm for X = 1%. Isotopic mixtures of liquid helium ( 3 He and 4 He) is a textbook example of phase separation in quantum liquids. 11 In 3 He/ 4 He mixtures, the physical origin of the phase separation involves different mass and different spin statistics of the particles. In the case of H 2 /D 2 , it must be predominantly due to the effect of different masses giving rise to a larger zero point energy and somewhat lower number density in the H 2 liquid. Phase separation in H 2 /D 2 systems at temperatures below about 3 K have been predicted by Prigogine 13,27 and Simon and Bellemans 28 . Calculations of the phase-separation temperature yield values of 0.8 – 4 K. 12,29,30 In agreement with these calculations, no evidence has ever been seen in the liquid phases of H 2 /D 2 for anything but complete miscibility. 26 Mixtures of H 2 and D 2 have freezing points in the range of 14 - 19 K, 128 depending on the D 2 content. Observation of phase separation in solid is complicated by the low rate of diffusion. Nevertheless, phase separation in H 2 /D 2 solids at 16.4 K was indicated by results of Ref. 31 However, subsequent works found phase separation only at temperatures lower than 8 K. 12,29,32 Thermodynamically, phase separation derives from the non ideal behavior of mixtures. Non-ideality of mixtures is described in terms of its excess properties, where an excess property of a mixture A E can be defined as A E = A M – A Ideal 5.4 where A M is the property for the mixture, and A Ideal is the property for an ideal solution. Complete knowledge of the excess thermodynamic properties of a liquid mixture requires the excess Gibbs free energy, G E , and the excess heat of mixing, H E as a function of temperature. In the case of an ideal binary mixture, the change of the Gibbs free energy upon mixing, Δ m G Ideal , reads as: Δ m G Ideal = R ⋅T ⋅{x 1 ⋅ln(x 1 ) + x 2 ⋅ln(x 2 )} 5.5 where R is the gas constant and x i is the mole fraction of the corresponding species. According to eq. (5.5), ideal mixtures have zero heat of mixing such that only entropic terms dominate. Therefore no phase separation in ideal mixtures is forthcoming. Phase separation in a non-ideal mixture is a result of a competition between the change of 129 enthalpy and entropy of the liquid upon mixing. The P, T, and x relationships of liquid hydrogen isotopic mixtures have previously been studied in the temperature range of 18 – 28 K. 33 Lambert 34 measured the excess enthalpy, H E , for a number of compositions of p- H 2 /o-D 2 mixtures at 20.4 K. The excess enthalpy was expressed as: H E = α ⋅x(H 2 ) ⋅x(D 2 ) 5.6 where α = 11.8 cal/mol. A value of H E was also reported for an equimolar mixture of p- H 2 /o-H 2 at 20.4 K of 0.4 cal/mol, which is almost 8 times smaller. 34 Similar results for p- H 2 /o-D 2 mixtures were also observed by Knaap et al. 35 However, less agreement is observed between studies of the excess volume of H 2 /D 2 mixtures, in which the deviation from ideality was observed to be in the range of -0.6 to -1.2% at temperatures from 15 to 20.4 K 34,35 . This is in contradiction to the positive values of the deviation predicted by Prigogine. 13,28 In addition, as observed by Knapp 35 , a non-zero excess entropy implies that mixtures of H 2 /D 2 isotopes do not form “regular solutions” where both excess entropy and molar volume are equal to zero. 36 Clusters of about 10 4 molecules (X = 1 %) as studied in the present work differ from the bulk phase in that they have a large fraction of surface molecules of about 20%. 37 Molecular dynamics simulation of classical binary Lenard-Jones clusters show a broad phase diagram depending on the size of the particles involved and the relative depth of the potential wells. 38 For example, classical Lenard-Jones clusters with ε AA < ε AB < ε BB energy parameters and σ AA > σ AB > σ BB size parameters for species A and B are 130 expected to form spherically coated structures with the more weakly bound species preferentially located on the cluster surface. However, due to the low temperatures of the H 2 and D 2 components, quantum effects become important as the degree of delocalization of particles is different and is greater for particles with lower mass. Recent path integral Monte Carlo calculations on p-H 2 and p-H 2 /D 2 clusters with less than 40 molecules indicate that heavier D 2 molecules predominantly reside near the center of the cluster 39,40 , whereas the probability of finding H 2 peaks exists in the surface region of the cluster. 39 Here we present a simple calculation of the phase separation based on the measured values of H E at T = 20.4 K. 34 Unfortunately, the temperature dependence of H E has not been studied, and it remains unclear how this value extrapolates into the region of supercooled liquid. In the assumption that the value of α in eq. (5.6) is temperature independent, enthalpy of mixing reads as: ΔH = α ⋅x A ⋅(1 - x A ) + α ⋅x B ⋅(1 - x B ) 5.7 Here, A and B are labels for different phases. In each phase x i + (1 – x i ) = 1 holds. The Gibbs free energy of mixing can be obtained from the definition ΔG = ΔH – T ΔS, by insertion of eqs. (5.5) and (5.7). The solution gives two phases of symmetric composition at temperatures of less than about 3 K, as shown in Fig 5.5. Thus at temperatures of 2 K, calculations predict two phases: one having 10% D 2 and 90% H 2 and the second consisting of 10% H 2 and 90% D 2 . The prediction of phase separation in p-H 2 /D 2 mixtures at temperature lower than 3 K is in agreement with the present observations. A 131 larger degree of phase separation for L > 20 mm is in agreement with the lower temperature at larger expansion distances. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 1 2 3 4 Temperature, K D 2 Fraction FIG. 5.5. Phase diagram of p-H 2 /D 2 mixture at low temperature based on eqs. 5.5 and 5.6. Previous work studying Raman spectroscopy of p-H 2 clusters 9 has shown that clusters with X < 2% in He are liquid. In those measurements, frequencies of clusters with X ≥ 2% are comparable to that in bulk solid samples. In addition, a blue shift is observed with decreasing X down to 0.5% in He indicating a possible temperature dependence, as was later confirmed in bulk liquid p-H 2 10 . The local temperature of the clusters in He can be estimated based on the following considerations. Following the equation of state of adiabatic gas expansion 41 and observation point at L/d 0 = 10, collisions are still occurring such that the local temperature of the expanding gas can be 132 estimated by equation 5.8. 41 3 / 4 0 0 35 . 0 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × = L d T T 5.8 However, clustering of hydrogen in the droplet leads to an increase in temperature. The density of the He gas at the observation point, ρ He can be obtained by ideal gas expansion 41 at about 10 20 atoms/cm 3 . The density of the He gas is somewhat less than ρ He due to formation of He droplets. As a result, growth of He droplets is expected to continue at the observation point due to the relatively small L/d 0 and large ρ He . The increased condensation of He into droplets indicates that the system is supersatured and the temperature therefore must be lower than the temperature of the saturated vapor pressure at ρ He , which is about 2 K. As a result, previous results have estimated the temperature in the range of 1 – 2 K for liquid clusters 9 while the temperature dependence in the bulk provides a maximum temperature in the clusters of ≤ 5 K 10 . Temperatures further downstream of the jet are lower due to evaporative cooling and has been shown to be as low as T = 0.38 K. 42 Observation of phase separation in liquid pH 2 /D 2 clusters, therefore, supports our previous evidence 9 of super-cooled liquid. 133 5.5. Conclusions We have prepared large p-H 2 /D 2 clusters in a cryogenic pulsed nozzle beam expansion of neat and dilute p-H 2 /D 2 in He and studied their aggregate properties by CARS spectroscopy. We observed that in the expansion of neat p-H 2 /D 2 with increasing amount of D 2 , the vibrational Raman spectra shift follows the previously observed shift in mixed bulk samples and can be explained in terms of vibron hopping. The vibrational shift of liquid clusters obtained from highly diluted p-H 2 /D 2 gas saturate with increasing D 2 content indicating the onset of phase separation. In addition, the vibrational shift is reduced upon observation at longer distances downstream from the nozzle source indicating further phase separation. Our simplified model of phase separation requires a temperature lower than 3 K for phase separation to occur. 134 Chapter 5 Bibliography 1 S. M. Apenko, Phys. Rev. B 60, 3052 (1999); V. S. Vorob'ev and S. P. Malyshenko, J. Phys. Condens. 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Temperature dependence of the Raman spectra of liquid para-hydrogen 6.1. Introduction Superfluidity of hydrogen, predicted three decades ago, 1 continues to elude experimental observation. However, hydrogen may constitute a new class of molecular superfluids that are characterized by anisotropic interaction and rotational angular momentum of the particles. Normal hydrogen consists of two modifications: para-H 2 (pH 2 ) and ortho-H 2 (oH 2 ). pH 2 molecules are spinless Bosons (I = 0) and at low temperature reside in the ground rotational state J = 0, which makes pH 2 the prime candidate for observation of superfluidity. pH 2 has a calculated superfluid transition temperature at ≈ 1 K in the bulk 2 and ≈ 2 K in small clusters. 3 Freezing of hydrogen at 13.8 K is the primary experimental obstacle. Although the rate of freezing is predicted to be very low at T ≤ 3 K, 4 numerous attempts at supercooling liquid hydrogen in macroscopic droplets, 5 clusters, 6,7 porous media, 8 or in the bulk 9 have proved unsuccessful. Recently, we have assembled clusters having about 10 4 pH 2 molecules at low temperatures by free jet expansion of pH 2 gas seeded in He. 10 Using rotational spectra measured via coherent anti-Stokes Raman scattering (CARS), we have shown that such clusters remain liquid at estimated T = 1 – 2 K, i.e., close to the predicted superfluid transition temperature. On the other hand, we observed that the vibrational CARS frequency of the liquid pH 2 clusters is higher than that in solid, but lower than that in the bulk liquid at 18 K. 11 We have speculated that this change indicates a strong dependence of the vibrational frequency of the pH 2 liquid upon temperature, which may in turn be 138 used as a monitor of the temperature of the clusters. Surprisingly, we did not find any systematic study of the temperature dependence of the Raman spectra in the liquid, except for a single data point at 18 K dating back to 1962. 11 Therefore, this work is aimed at studying the temperature dependence of the vibrational and rotational spectra in liquid pH 2 . We have observed that the vibrational frequency of pH 2 liquid increases by about 2 cm -1 upon change of temperature from 14 K to 30 K. We have found that the frequency change, Δν, scales as the square of the density of the liquid, ρ L . The obtained scaling enables prediction of the vibrational frequency in the liquid below the freezing temperature. 6.2. Experimental Technique The cryogenic experimental apparatus is described in detail elsewhere. 12 The system consists of a Janis SHI-4 optical cryostat equipped with a Sumitomo RDK-408D closed-cycle refrigerator. The 3-cm long optical cell is made of stainless steel and has a 1 × 1 cm 2 optical clearance and two CaF 2 windows. The upper part of the cell has a copper post, which is directly attached to the second stage of the refrigerator through a copper heat conductor. The cell is screened from thermal radiation by an aluminum shield attached to the first stage of the refrigerator and is mounted inside a vacuum shroud, which is also equipped with CaF 2 windows. The cell temperature can be varied in the range of 4 to 30 K by resistive heating of the second stage of the refrigerator. The temperature of the liquid hydrogen inside the cell was calibrated via known saturated vapor pressure for hydrogen 13 as measured by means of a Wika TRONIC pressure 139 transmitter. Normal hydrogen (Praxair, research grade) was converted to pH 2 , with residual oH 2 content of less than 0.1%, by catalytic conversion of liquid H 2 at 17 K. A Brooks 5850i mass flow controller was used to ensure sufficient contact time with the catalytic material. Upon conversion, liquid pH 2 was continuously flowed into the optical cell at a temperature of 15 K. The procedure for preparing the solid crystalline sample follows that of Hakuta et. al. 14 The cell was first filled with liquid pH 2 , and gradually cooled down to 9 K under constant pressure of 24 bar. Upon cooling, the crystal grew from the upper copper surface downward until the entire cell was filled. Once solid, the cell can be further cooled down to 4 K. Due to the decrease of the molar volume of solid pH 2 with temperature, the internal pressure of the solid sample is expected to be close to zero, 14 but cannot be measured in this work. The spectra of the bulk liquid or solid were obtained via CARS 15 technique. In this four-wave mixing technique, a 532 nm pump beam generated from a Nd:YAG laser (Powerlite Precision II 8020) and Stokes beam from a dye laser (Lambda Physics, NPD 3000) were focused onto the center of the pH 2 sample by means of a 2 meter plano- convex lens. Both pump and Stokes beams have vertical polarization. When the frequency difference of the pump and Stokes laser beams matches the vibrational or rotational frequency of the pH 2 molecules, an anti-Stokes signal is generated, which is separated from the pump and Stokes beams by means of a diffraction grating and detected thereafter by a pyro-electric detector. The pump beam has a linewidth of about 0.003 cm -1 , whereas the Stokes beam has a linewidth of approximately 0.05 cm -1 and 0.25 140 cm -1 , respectively, with or without an intracavity etalon installed. Calibration of the absolute frequency of the spectrometer was achieved using Raman spectra of solid pH 2 as measured previously at high resolution 16 . 6.3. Results Fig. 6.1 shows the CARS spectra of the rotational S 0 (0) line ( ν = 0, J = 2 ← ν = 0, J = 0 ) in both solid and liquid pH 2 which have been measured at different temperatures as indicated and without an intra-cavity etalon. Traces (a) – (c) show that the S 0 (0) line in the crystal is split into a triplet having separation of the components by about 2 cm -1 . This splitting pattern is characteristic for the hcp crystal structure and results from the electric quadrupole-quadrupole and crystal field type intermolecular interactions between the pH 2 molecules in the crystal. 17,18 The observed spectra in the solid are in agreement with previous results obtained via conventional Raman spectroscopy 11,19 , but have different intensity distributions. The intensity distribution of the CARS spectrum depends on the orientation of the hcp crystal axis with respect to the polarization of the pump and Stokes laser beams. However, this effect was not studied in any detail in the present work. 141 348 349 35 0 35 1 35 2 35 3 3 54 3 55 3 56 3 57 358 a) Intensity, a.u. W av en u m b er, cm -1 T = 5 K T = 2 2 .3 K b) T = 9 K c) T = 13 K d) T = 15 K e) T = 1 8 .5 K f) FIG. 6.1. CARS spectra of the S 0 (0) transition in both solid (a) – (c) and liquid (d) – (f) pH 2 at different temperatures as measured without an intra-cavity etalon. Measurements in liquid were obtained at P = 2 bar. The frequency of the S 0 (0) line in the gas phase at 354.37 cm -1 is shown by a dashed vertical line. 20 The spectra of the S 0 (0) line in liquid pH 2 at different temperatures and at a pressure of 2 bar are shown in traces (d) – (f) of Fig. 6.1. The observation of the single line is consistent with the previously measured spontaneous Raman spectra in liquid pH 2 . 11 The absence of the splitting reflects the averaging of the anisotropic intermolecular interaction in the liquid. The S 0 (0) line has the same frequency of 353.0 ± 0.1 cm -1 and similar linewidths of approximately 1 cm -1 in the temperature interval of 15 K - 24 K. For comparison, the frequency of the S 0 (0) line in liquid pH 2 of 353.3 cm -1 has previously been measured at 18 K. 11 The frequency of the S 0 (0) line in the gas phase at 354.37 cm -1 is shown in Fig. 6.1 by a dashed vertical line. 20 Typical CARS spectra of the vibrational Q 1 (0) ( ν = 1 ← 0, J = 0 ← 0 ) line in 142 solid (traces a, b) and in liquid pH 2 (traces c - h) obtained at different temperatures are shown in Fig. 6.2. The frequency of the Q 1 (0) line in the solid shifts by approximately 0.07 cm -1 upon increase of temperature of the cell from 6 K to 11 K. Previous high resolution measurements show that the frequency increases by 0.13 cm -1 upon increase of the temperature of the solid from 4.9 K to 13.5 K. 21 The frequency increases by approximately 2 cm -1 upon melting. In the liquid, the frequency increases by about 2 cm -1 during the temperature change from 15 K to 26 K. 4148 41 49 4150 4151 41 52 4153 4154 Intensity, a.u. W avenum ber (cm -1 ) T = 6 K a) b) T = 11 K c) T = 15 K d) T = 16.7 K e) T = 18.5 K f) T = 24.3 K T = 20.4 K h) g) T = 26.3 K FIG. 6.2. CARS spectra of the Q 1 (0) line of pH 2 at different temperatures as obtained with an intra-cavity etalon. Traces (a) and (b) are in solid, whereas traces (c) – (h) are in liquid. All spectra in the liquid were obtained at a constant pressure of 3 bar except trace (h) which was measured at 9 bar and without an intra-cavity etalon. Because of the extensive boiling of liquid pH 2 in the cell at saturated vapor pressure (SVP) and concomitant disruption of the CARS signal, most of the measurements in this work have been done at elevated pressure. Thus, we have studied 143 the pressure dependence of the Q 1 (0) line at different temperatures, which are shown in Fig. 6.3. At each studied temperature, we found that the frequency of the Q 1 (0) line decreases linearly with applied pressure. Fig. 6.3 also shows the frequency of the Q 1 (0) line as a function of temperature at constant pressure of 3.0 ± 0.2 bar. 0 5 10 15 2 0 25 3 0 41 51. 0 41 51. 5 41 52. 0 41 52. 5 41 53. 0 1 5 .2 K 1 8 .5 K 2 1 .3 K 2 4 .3 K 3 b ar 2 4 .3 K 2 2 .3 K 2 0 .4 K 1 8 .5 K 1 6 .7 K 15 K Wavenumber (cm -1 ) P ress u r e (b a r ) 1 4 .2 K FIG. 6.3. Frequencies of the Q 1 (0) line in liquid pH 2 at different temperatures and pressures as indicated in the legend. Lines are linear fits to the results. Open circles show the results at constant pressure in the cell of about 3 bar and at indicated temperatures. Fig. 6.4 shows the results of all measurements of the frequency of the Q 1 (0) line at different temperatures in both liquid and solid. The values measured in solid are shown by triangles while those measured in liquid are illustrated by open squares and circles at 3 and 9 bar, respectively. The data points for the liquid were linearly extrapolated to SVP using results obtained at higher pressure, see Fig. 6.3. Previous high resolution measurements of the Q 1 (0) frequency in solid at SVP 21 are shown for 144 comparison by upside down triangles. Frequencies in liquid measured directly at SVP (solid squares) are also included for comparison. Previously, the frequency of the Q 1 (0) line in liquid at 18 K and SVP 11 was obtained at 4151.9 cm -1 (see star in Fig. 4) and is in good agreement with the results of the present work. For comparison, 4161.1687 cm -1 is the known frequency of the Q 1 (0) line in the gas phase. 22 0 5 10 1 5 20 2 5 30 4149. 5 4150. 0 4150. 5 4151. 0 4151. 5 4152. 0 4152. 5 4153. 0 4153. 5 4154. 0 Wavenumber (cm -1 ) T em p eratu r e (K ) FIG. 6.4 Frequencies of the Q 1 (0) line in both solid and liquid pH 2 . Results in liquid were obtained at a constant pressure of 3 and 9 bar, as shown by open squares and circles, respectively, and were linearly extrapolated to SVP based on the results shown in Figure 3. Frequencies in liquid measured directly at SVP (solid squares) are also included for comparison. The only previous measurement of liquid pH 2 at 18 K and SVP 11 is shown by a star. Frequencies obtained in solid in this work and at SVP are shown by regular and upside down triangles, respectively. The widths of the Q 1 (0) line were obtained from the spectra measured with an intra-cavity etalon. In the solid, a linewidth of about 0.06 cm -1 was obtained, which is comparable with the nominal resolution of the current laser system. Much narrower lines 145 in the solid, down to about 1 MHz at 4.2 K, have been obtained using high resolution cw laser systems. 21,23 In the liquid, constant linewidths of about 0.115 ± 0.005 cm -1 were observed over the temperature range of 14 K – 24 K. The Q 1 (0) line, obtained at T = 26 K in trace (h) in Fig., is broader as it was measured without an intra-cavity etalon. 6.4. Discussion Fig. 6.4 shows that, although the frequency of the Q 1 (0) line in the solid varies little with temperature, a large shift in the vibrational frequency of about 2 cm -1 occurs upon melting the solid pH 2 sample followed by a continuing blue shift in the temperature range of 14 – 26 K in the liquid. In order to obtain an insight into the physical origin of the shift versus temperature in liquid pH 2 , we will first review some previous results obtained in solid pH 2 . 17,19,21,24,25 The Q 1 (0) line in solid has about 11.4 cm -1 lower frequency as compared to that in the gas phase. A major contribution to the shift of about 8.7 cm -1 results from the isotropic dispersion intermolecular interaction. In addition, the vibron hops easily between the pH 2 molecules of the solid giving rise to a vibrational band of about 3.6 cm -1 wide. 18,23 Momentum conservation dictates the selection rules in the Raman spectrum, 18 where only transitions to the lowest level of the band are allowed, thereby producing a very narrow Q 1 (0) line. Thus, the frequency of the Q 1 (0) line in the solid has an additional shift of about 2.7 cm -1 . 25 In Refs. 18,26 , it was shown that the leading term in both vibron hopping and isotropic interaction contributions to the shift scale as R -6 , where R is the distance between the molecules in the crystal. Therefore, the 146 shift scales with the density as ρ 2 . 23 Liquid hydrogen has a much larger thermal expansion coefficient as compared to solid. The density vs. temperature in both liquid and solid pH 2 at SVP is plotted in Fig. 6.5. 13,27 It is seen that, in the solid, the density decreases slightly by about 1% upon increase of the temperature from 4 K to 13.5 K. This weak density decrease explains the observed weak increase of the frequency of the Q 1 (0) line in the solid with temperature. 21 On the other hand, the density decreases by 13% upon melting and decreases further by almost 30% upon increase of temperature from 14 K to 30 K, which correlates agreeably with the much larger shift of the frequency with temperature in the liquid. 0 5 10 1 5 20 2 5 30 0. 0 50 0. 0 55 0. 0 60 0. 0 65 0. 0 70 0. 0 75 0. 0 80 0. 0 85 0. 0 90 Density (g/cm 3 ) Te m pe ra ture (K ) FIG. 6.5. Density vs. temperature in solid 13 (squares) and liquid 27 (triangles) pH 2 . The dotted line indicates the fitted density of liquid hydrogen, which includes an extrapolation into the metastable range below the freezing temperature. 147 0 5 10 15 20 2 5 414 9 415 0 415 1 415 2 415 3 415 4 Wavenumbers, cm -1 Te m pe ra ture (K ) FIG. 6.6 Q 1 (0) frequencies measured in this work for solid and liquid pH 2 are shown by filled squares. The experimental points in liquid were obtained at 3 and 9 bar and extrapolated to SVP. Solid curves show the fits of both solid and liquid pH 2 results to Eq. (6.1) with identical parameters. The Q 1 (0) frequency in solid at SVP obtained by Kerr et. al 21 is shown by triangles. The dotted curve shows the estimated frequency in the liquid below the freezing point, which was obtained from Eq. (6.1) using the estimated density 4 of liquid pH 2 at low temperature as shown in Fig. 6.5. We found that the square dependence of frequency of the Q 1 (0) line vs. density as originally discussed for solid is well applicable in the liquid as well. Fig. 6.6 shows the result of the fit of the measured Q 1 (0) frequency to equation (6.1): ν = ν 0 - c ⋅ρ(T) 6.1 The results in liquid and in solid have been fitted with the same parameters, ν 0 = (4157.1 ± 0.1) cm -1 and c = (975 ± 28) cm -5 ·g -2 , using the density of solid 13 and liquid 27 pH 2 as 148 plotted in Fig. 6.5. It is seen that eq. (1) works equally well for solid and liquid over the entire studied temperature range of 5 – 26 K, indicating that the density is indeed the predominant factor in determining the frequency of the Q 1 (0) line in condensed phases. Based on the quadratic dependence of the density with temperature 4 , the Q 1 (0) frequency in the liquid can be fit as a function of temperature: ν = 4151.40 + 4.86 ×10 -3 ⋅T 2 – 8.83×10 -7 ⋅T 4 6.2 The good quality of the fit for the stable condensed phases of pH 2 suggests that Eq. (6.1) with the same parameters can be applied for a metastable liquid at lower temperature if the density of the liquid is known. Previously, the density below the triple point has been estimated assuming that the thermal expansion of hydrogen is proportional to the specific heat of the liquid. 4 The known density above the triple point was used to obtain the equation of state for liquid pH 2 to be: ρ L = 0.08277 – 3.01·10 -5 ·T 2 at T > 2.41 K and ρ L = 0.08260 at T < 2.41 K. 6.3 where ρ L is the density of the liquid in units of g/cm 3 . Eq. (6.3) is shown in Fig. 6.5 by a dashed line. The dotted curve in Fig. 6.6 shows the extrapolation of the frequency of the Q 1 (0) line in the liquid below the freezing point, using eq.(1) and density given by eq.(6.3). In 149 lieu of the actual data below the freezing point in hydrogen, it is instructive to review the temperature dependence of the density of liquid 4 He. 28 The density of 4 He liquid increases upon decrease of the temperature until it reaches superfluid transition temperature at T ≈ 2.17 K. Below this temperature, the density suddenly decreases from 1.462 g/cm 3 to 1.451 g/cm 3 and stays to within 0.1% of the latter value down to T = 0 K. If a similar drop in density is realized in the case of liquid hydrogen upon predicted transition to the superfluid state, the frequency of the Q 1 (0) line must have similar discontinuity, thus providing a convenient monitor of the phase transition. So far, substantial supercooling of macroscopic samples of liquid hydrogen could not be demonstrated. Recently, we have shown that supercooled pH 2 clusters of about 10 4 molecules can be prepared in a cryogenic expansion of pH 2 seeded in an excess of He. 10 Based on the equation of state of the adiabatic gas expansion, the temperature of the clusters was estimated to be in the range of T = 1 - 2 K. The frequency of the Q 1 (0) line of the liquid clusters was found to be 4150.4 ± 0.1 cm -1 . Using the extrapolated frequency in Fig. 6.6 will place the temperature of the clusters in the range of T < 5 K. Therefore, the temperatures of the clusters are indeed much lower than the freezing temperature of the pH 2 liquid at 13.8 K, which supports extensive supercooling. Unfortunately, in clusters, the temperature is not the sole cause of the frequency shift. Additional shift may also be caused by the finite size effects in the clusters. 7 Upon decrease of the cluster size, the Q 1 (0) frequency must approach its single molecule value, i.e., the frequency is expected to rise. Therefore, the frequency of the Q 1 (0) line in clusters at a given temperature is expected to have some upward shift with respect to that 150 in the bulk. The precise effect of the cluster size on the frequency of the Q 1 (0) line remains to be understood. As a result, a more detailed theoretical work for determining the density below the triple point as well as the role of the size effects are required in order to describe their effect on the Raman spectrum of the clusters. The fact that Eq. (6.1) provides a universal fit of the frequency in both liquid and solid is somewhat surprising. Apart from the larger thermal expansion coefficient, liquid differs from the solid in at least two other important respects: i) it lacks a long range order of the molecules, and ii) molecules in the liquid are in a state of Brownian motion, which causes faster de-phasing of the excitations than in solid. Nevertheless, relatively narrow widths of the Q 1 (0) lines in the liquid of about 0.1 cm -1 show that momentum of the vibrons remains a relatively good quantum number. The results also suggest that larger delocalization of the H 2 molecules in the liquid has a small effect on the frequency. Thus, our results indicate that the vibron hopping observed previously in the solid is also effective in the liquid. This is in agreement with previous conclusions based on the intensity ratio of the Q 1 (0) and Q 1 (1) lines in liquids consisting of mixed pH 2 and oH 2 . 29 6.5. Conclusions We have prepared bulk pH 2 in both solid and liquid phases and studied their vibrational and rotational Raman spectra at different temperatures. The vibrational frequency in the liquid increases with temperature by about 2 cm -1 from 14 to 26 K. The vibrational frequency was found to scale with the square of the density in the liquid. These results were used to extrapolate the vibrational frequency in the temperature range 151 below the freezing point and to confirm the supercooled state of liquid clusters obtained in our previous study. 10 The results indicate that the vibron hopping between the molecules is active in the liquid, similar to that previously found in the solid. 152 Chapter 6 Bibliography 1 V . L. Ginzburg and A. A. Sobyanin, JETP Letters 15 (6), 343 (1972). 2 S. M. Apenko, Physical Review B 60 (5), 3052 (1999); V. S. Vorob'ev and S. P. Malyshenko, Journal of Physics-Condensed Matter 12 (24), 5071 (2000). 3 P. Sindzingre, D. M. Ceperley, and M. L. Klein, Physical Review Letters 67 (14), 1871 (1991); F. Mezzacapo and M. Boninsegni, Physical Review Letters 97 (4), 045301 (2006); S. A. Khairallah, M. B. Sevryuk, D. M. Ceperley, and J. P. Toennies, Physical Review Letters 98 (18), 183401 (2007); F. Mezzacapo and M. Boninsegni, Phys. Rev. Lett. 100, 145301 (2008). 4 H. J. Maris, G. M. Seidel, and T. E. Huber, Journal of Low Temperature Physics 51 (5-6), 471 (1983). 5 H. J. Maris, G. M. Seidel, and F. I. B. Williams, Physical Review B 36 (13), 6799 (1987). 6 S. Goyal, D. L. Schutt, and G. Scoles, J. Phys. Chem. 97 (10), 2236 (1993). 7 G. Tejeda, J. M. Fernandez, S. Montero, D. Blume, and J. P. Toennies, Physical Review Letters 92 (22), 223401 (2004). 8 J. DeKinder, A. Bouwen, and D. Schoemaker, Physical Review B 52 (22), 15872 (1995); M. Schindler, A. Dertinger, Y. Kondo, and F. Pobell, Physical Review B 53 (17), 11451 (1996). 9 A. C. Clark, X. Lin, and M. H. W. Chan, Physical Review Letters 97 (24), 245301 (2006). 10 K. Kuyanov-Prozument and A. F. Vilesov, Physical Review Letters 101 (20), 205301 (2008). 11 S. S. Bhatnagar, H. L. Welsh, and E. J. Allin, Canadian Journal of Physics 40 (1), 9 (1962). 12 K. E. Kuyanov, T. Momose, and A. F. Vilesov, Applied Optics 43 (32), 6023 (2004). 153 13 P. C. Souers, Hydrogen Properties for Fusion Energy. (University of California Press, Berkeley, 1986). 14 M. Suzuki, M. Katsuragawa, R. S. D. Sihombing, J. Z. Li, and K. Hakuta, Journal of Low Temperature Physics 111 (3-4), 463 (1998). 15 W. M. Tolles, J. W. Nibler, J. R. Mcdonald, and A. B. Harvey, Applied Spectroscopy 31 (4), 253 (1977). 16 F. Le Kien, A. Koreeda, K. Kuroda, M. Suzuki, and K. Hakuta, Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers 42 (6A), 3483 (2003). 17 I. F. Silvera, Reviews of Modern Physics 52 (2), 393 (1980). 18 J. van Kranendonk, Solid Hydrogen: Theory of the Properties of Solid H 2 , HD, and D 2 . (Plenum Press, New York and London, 1983). 19 G. W. Collins, W. G. Unites, E. R. Mapoles, and T. P. Bernat, Physical Review B 53 (1), 102 (1996). 20 D. E. Jennings and J. W. Brault, Journal of Molecular Spectroscopy 102 (2), 265 (1983). 21 K. E. Kerr, T. Momose, D. P. Weliky, C. M. Gabrys, and T. Oka, Physical Review Letters 72 (25), 3957 (1994). 22 S. L. Bragg, J. W. Brault, and W. H. Smith, Astrophysical Journal 263 (2), 999 (1982). 23 K. Kuroda, A. Koreeda, S. Takayanagi, M. Suzuki, and K. Hakuta, Physical Review B 67 (18), 184303 (2003). 24 J. Vankranendonk, Physica 25 (11), 1080 (1959); J. van Kranendonk, Physica 25 (11), 1080 (1959). 25 V. Soots, E. J. Allin, and H. L. Welsh, Canadian Journal of Physics 43 (11), 1985 (1965). 26 H. M. James and J. van Kranendonk, Physical Review 164 (3), 1159 (1967). 27 B. A. Younglove, J. Phys. Chem. Ref. Data 11 (1), 1 (1982). 154 28 E. C. Kerr, Journal of Chemical Physics 26 (3), 511 (1957); R. D. McCarty, J. Phys. Chem. Ref. Data 2 (4), 923 (1973). 29 A. H. Rosevear, G. Whiting, and E. J. Allin, Canadian Journal of Physics 45 (11), 3589 (1967). 155 Chapter VII. Fast nuclear spin conversion in water clusters and ices 7.1. Introduction It is well known that H 2 exists in two forms, ortho and para, in which the total nuclear spin angular momentum is I = 1 and 0, respectively. Pure para-hydrogen, p-H 2 , is usually obtained via cryogenic conversion of liquid hydrogen on para-magnetic salts. 1 Previous studies demonstrated that gaseous p-H 2 is remarkably stable at room temperature and can be stored for days with negligible back conversion. 2 A number of other molecules such as H 2 O, NH 3 , CH 2 O, and CH 3 F having equivalent hydrogen atoms are known to have ortho and para nuclear spin isomers. 3 The possibility of separating nuclear spin isomers in water molecules has attracted considerable attention due to the fundamental atmospheric 4-6 and biological significance of water. At equilibrium and temperatures larger than 50 K, the abundance ratio of the ortho and para isomers, OPR, of H 2 O is very close to the statistical weight of 3:1. Therefore, practical spin conversion requires interaction of the water molecules with a low temperature bath of less than or equal to 10 K. However, the rotation of water molecules is quenched in ices, such that the energy difference between the nuclear spin isomers in ice is presumed to be negligibly small. Thus, single water molecules have been isolated in cryogenic rare gas solids, 7-13 where they continue rotating and demonstrate slow nuclear spin conversion at T = 4 K. Nevertheless, controversy remains if para-H 2 O molecules are stable in ice, liquid, or gas. Early works report on the short 156 lifetime of p-H 2 O molecules in Ar matrices at higher temperatures. 9 Very recently, however, enrichment of ortho- and para- water via gas phase chromatography has been reported with surprisingly long conversion times in liquid of about 30 min. 8,14 Infrared spectra of water molecules in cometary tails have indicated low OPR of about 2.5:1, which is consistent with a spin temperature of about 30 K. 4,5 As a result, it is generally believed that the obtained OPR could be a measure of the temperature of the primordial solar system. 15 Conversely, some recent works have questioned the enhancement of para-H 2 O due to its negligible vapor pressure at 30 K and the extent of which the temperature of the water vapor corresponds to the temperature of the comet ice. 16 In this work, we studied the feasibility of the formation of p-H 2 O ices. We began with the nuclear spin conversion of very diluted samples of water in Ar matrices that have been spin converted at T = 4 K in an enclosed cryogenic optical cell. The ice particles are formed from p-H 2 O molecules upon fast increase of the temperature and removal of the Ar constituency from the cell. Finally, infrared spectra of the gas in the cell have been obtained at T = 260 – 280 K. The acquired spectra are identical with those of unconverted water, showing that the lifetime of p-H 2 O in ice is less than about 30 min. In addition, our results indicate that spin conversion takes place already in water dimers. 157 7.2. Experimental Technique The general technique of matrix deposition has been described previously. 12 Our cryogenic system is based on a Janis SHI-4 optical cryostat equipped with a Sumitomo RDK-408D closed-cycle refrigerator. The schematic of the copper cell is shown in Fig. 7.1. The cell is directly attached to the second stage of the refrigerator. The gas is introduced through a stainless steel adaptor using copper tubing. The copper tubing is resistively heated to prevent freezing of the water mixture. The temperature of the cell was measured by silicone diodes and controlled by resistive heating. 10 cm FIG. 7.1. Schematic of cryogenic copper cell. The 3-cm long copper cell has an 18 mm diameter optical clearance enclosed by two 3-mm thick CaF 2 windows. The adjacent side of the cell provides a 9 mm clearance in which a stainless steel adapter with 1/16” thick copper tubing is attached for gas mixture introduction. Ar (Gilmore, 99.9999% purity)) was used without purification. Water was 158 filtered (Milli-Q) and degassed carefully. H 2 O:Ar mixtures ≤ 1:100 were prepared by standard manometric procedures. Due to adsorption of water onto the stainless steel walls of the gas handling system, the uncertainty in water content is estimated at 50%. The solid sample was prepared by slowing depositing the gas mixture onto the CaF 2 window at a nominal temperature of 4 K at a flow rate of approximately 10 mmol/hr. The typical deposition time was between 40 - 70 min. Absorption spectroscopy was performed using a Nicolet Avatar 360 FTIR spectrometer in the 1000 – 4000 cm -1 region with a maximum resolution of 0.5 cm -1 . The quality of the sample during deposition was monitored by recording scans periodically. 7.3. Results Fig. 7.2 shows a schematic of the relevant energy levels of water molecules in the ground and vibrationally excited states. Water is an asymmetric top molecule, and its ro- vibrational levels are labeled by J KaKc , where J is the total rotational angular momentum quantum number and K a and K c are quantum numbers of the components of the total angular momentum on the principal axes a and c, respectively. These levels are assigned in the ground vibrational state as well as in ν 1 and ν 2 vibrationally excited states to either para or ortho for even or odd K a + K c , respectively. 17 The notations are inverted in the anti-symmetric vibrational ν 3 state. Because the total wavefunction of water molecules must be anti-symmetric with respect to exchange of H-atoms, it follows that the ground state of water molecules, 0 00 , has a total nuclear spin I = 0, whereas the first excited 159 rotational state, 1 01 , (E = 23.8 cm -1 ) 18 has I = 1, which belong to para- and ortho- nuclear spin isomers, respectively. ν 1 / ν 2 ν 3 0 00 1 01 o p 2 12 1 10 1 11 1 01 0 00 o p o p o o 2 20 2 02 1 10 1 11 1 01 0 00 2 12 o p o p o FIG. 7.2. Energy level diagram of water molecules. Rotational level labels to the left of the lines represent J KaKc and correspond with the ortho- and para- labels on the right; o and p, respectively. Solid arrows indicate observed ro-vibrational transitions in ν 1 , ν 2, and ν 3 bands at low temperature. Fig. 7.3 shows the IR absorption spectra in the region of the ν 3 , ν 2 , and ν 1 bands of H 2 O as obtained immediately after a deposition of 70 min at 4 K was completed (a). No annealing has been used in order to avoid cluster formation. Fig. 7.3 (b) shows the spectrum measured after the matrix remained for 1400 min at 4 K. Spectrum (a) corresponds to transitions from the lowest rotational levels of the p-H 2 O and o-H 2 O molecules, 0 00 and 1 01 , respectively, in agreement with previous observations. 12,13 The 0 00 ← 1 01 , 1 01 ← 0 00 , and 2 02 ← 1 01 lines of the ν 3 band of single H 2 O molecules are assigned in the spectrum accordingly. The weak features at 3669.6 cm -1 and 3653.3 cm -1 160 have been assigned to 1 11 ← 0 00 , 1 10 ← 1 01 lines of the ν 1 band, respectively. It is seen that the spectrum contains virtually no bands due to water clusters, indicating single water molecules are indeed isolated in the Ar matrix. For comparison, the spectra obtained in this work at higher water concentration (see Fig. 7.9) in solid Ar have well resolved strong bands at 3574 and 3533 cm -1 due to hydrogen bond bridge vibrations on dimers 11,13 and trimers 13 . 1500 1550 1600 1650 1700 3500 3550 3600 3650 3700 3750 3800 3850 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Dimer Log 10 (I 0 /I) Wavenumbers, cm -1 1 11 ←0 00 0 00 ←1 01 1 10 ←1 01 1 11 ←0 00 0 00 ←1 01 1 01 ←0 00 2 02 ←1 01 1 10 ←1 01 1 11 ←0 00 2 12 ←1 01 a) t = 0 min Dimer 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ν 2 (b) t = 1400 min 1 01 ←0 00 2 02 ←1 01 1 10 ←1 01 1 11 ←0 00 ν 3 ν 1 FIG. 7.3. IR absorption spectra of the ν 1 , ν 2, and ν 3 regions of H 2 O of a 1:2000 H 2 O:Ar sample. Panels (a) and (b) refer to spectra obtained after completing ~ 70 min deposition at a nominal temperature of 4 K and after an additional 1400 min, respectively. Trace (b) in Fig. 7.3 was obtained after 1400 min time upon the completion of a ~ 70 min deposition, during which the matrix was kept at 4 K. It is seen that the same lines as in (a) are observed but with different intensities. Much weaker intensity of the lines from the 1 01 levels and simultaneous increase of the intensity of the lines from 0 00 levels 161 indicates spin conversion. The total intensity of the lines of the ν 3 band in spectrum (a) before the conversion was found to be the same as upon conversion within 20% accuracy. It should be noted that the OPR in spectrum (a) was found to be about 2 and not 3 as in the deposited water gas. This indicates that some conversion already proceeds during the deposition process. Similar spectra have been measured at intermediate times. From the time dependence of the spectra, the conversion time was obtained to be τ = 650 ± 50 min, which is comparable to what was previously observed in solid argon at 4 K. 8 From the intensity of the lines in trace (b), we have estimated the spin temperature of the water molecules to be approximately 6 K. This is somewhat higher than the measured temperature of the cell of 4 K due to the likely higher temperature of the optical window as well as slow rate of conversion. Spectra in the ν 2 region of H 2 O are shown in the low frequency range of Fig. 7.3 and are in agreement with the findings from the other bands. Assigned transitions originate from the 1 01 and 0 00 levels of the ground state as noted previously. 12,13 Some weak features are also seen at 1593 and 1611 - 1612 cm -1 which are likely due to overlapped bands from water dimers and H 2 O:N 2 complexes while features around 1600 and 1602 cm -1 originate solely from H 2 O:N 2 complexes. 13,19-21 Similarly, weak features around 3730 cm -1 can be assigned to the ν 3 band of H 2 O:N 2 complexes. 20-22 The weakness of the bands indicate that single water molecules are indeed the main constituency of the matrix while clustering is minimized. Previously, an additional weak band at 1589.1 cm -1 was assigned to non-rotating monomers. 13,23 However, this frequency coincides with a known band of the H 2 O:CO 2 162 complexes. 11 Overall, we did not detect any additional bands which could be assigned to non-rotating water molecules in the ν 1 and ν 3 ranges of the spectra. Thus, we concluded that if such sites containing non-rotating molecules are present their abundance is negligible under the conditions of the present work. Finally, a relatively intense and broad structure (10 cm -1 ) with two features centered approximately around 1661 and 1657 cm -1 is observed as noted previously. 11-13 Upon comparison between trace (a) and (b) in Fig. 7.3 and in Ref. 11 , spin conversion occurs favoring the red-shifted component at the expense of the blue-shifted feature. The frequency of these features are close to the expected frequency of the 2 21 ← 1 10 and 2 20 ← 1 11 lines. 13 However, at a temperature of about 6 K, the populations of the 1 11 and 1 10 levels are too small to explain their intensity in Fig. 7.3. As a result, Michaut et al. 12 have assigned these features to rotation- translation satellites of the 1 11 ← 0 00 line. Fig. 7.4 shows the evolution of the absorption spectrum upon a fast temperature increase of the matrix. Trace (a) in Fig. 7.4 is equivalent to the single molecule spectra of Fig. 7.3, i.e., at T = 4 K after conversion. Fig. 7.4 trace (b) shows a spectrum obtained upon heating of the sample to T = 50 K within about 2 min. Spectrum (b) shows a broad, strong absorption in the range of 3000 - 3600 cm -1 and a narrower band close to 3700 cm - 1 . These bands arise from the hydrogen bond bridge and free OH vibrations, respectively, in water clusters. 13,24 Based on analogy with the spectra of water clusters in He droplets, bands 25 at 3573.6 cm -1 , 3530 cm -1 , 3370 cm -1 , and 3320 cm -1 can be assigned to dimers, trimers, tetramers, and pentamers, respectively. Similar absorptions in solid Ar have also been attributed to small clusters. 21 The unresolved broad absorption in the range of 3000 163 – 3600 cm -1 must be due to larger water clusters. The total integral intensity of spectrum (b) is a factor of about 10 larger than that in trace (a), which reflects a large increase of the infrared intensity upon formation of hydrogen bonds in clusters. 26 The factor of 10 is in qualitative agreement with the increase of the total infrared intensity in ice in the range of 3100 - 3800 cm -1 of about 20 as compared with that in the ν 3 mode of free water molecules. 26 The lower factor in this work is likely due to the fact that, in clusters, there remains a large number of dangling OH bonds as indicated by the intense band around 3700 cm -1 . The precise measurement of the increment factor is also hindered by a larger contribution to the spectra from light scattering. 1500 1550 1600 1650 1700 3000 3250 3500 3750 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Log 10 (I 0 /I) Wavenumbers, cm -1 T = 6 K t = 1400 min a) (H 2 O) 2 1 01 ←0 00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 (b) T = 50 K t = 1402 min (H 2 O) 3 (H 2 O) 4 (H 2 O) 5 FIG. 7.4. IR absorption spectra of the ν 1, ν 2 and ν 3 regions of H 2 O in a 1:2000 H 2 O:Ar sample at 4 K (a) and 50 K (b). Timeline refers to spectra obtained after completing ~ 70 min deposition of mixture. 164 Similar changes in the spectrum occur upon heating in the ν 2 spectral range. Upon increase of temperature the lines of single molecules disappear. Simultaneously, a broad feature in the range of 1600 - 1700 cm -1 and a narrower band at 1593.4 cm -1 are observed. The total integral intensity of spectrum (b) is only a factor of 1.7 larger as compared with that in trace (a). This is in agreement with a small change of the infrared intensity of the bending ν 2 band of water upon clustering. 26 A summary of the observed single molecule peak positions in solid argon and assignments as well as comparison to gas phase 18 and previous work in argon 12 are provided in Table 7.1. Table 7.1: Frequencies (cm -1 ) and assignments of absorption lines of single H 2 O molecules in the ν 1 , ν 2 and ν 3 regions in solid argon at 4 K. Transition Spin Isomer Gas 18 In Ar, This Work In Ar, Ref. 12 ν 1 band 1 01 → 1 10 ortho 3674.697 3653.3 3653.38 0 00 → 1 11 para 3693.293 3669.7 3669.85 ν 2 band 1 01 → 1 10 ortho 1616.711 1607.7 1607.9 0 00 → 1 11 para 1634.967 1623.6 1623.8 1 01 → 2 12 ortho 1653.267 1636.7 1636.5 ν 3 band 1 01 → 0 00 ortho 3732.134 3710.8 3711.2 0 00 → 1 01 para 3779.493 3756.1 3756.49 1 01 → 2 02 ortho 3801.419 3775.9 3776.30 Previous works report fast decrease of the conversion time of the spin isomers of water molecules upon increase of temperature of the matrix. 8 Indeed, we have estimated the equilibration time of the nuclear spin isomers at 30 K to be about 5 min. Accurate measurements of the conversion time at higher matrix temperature are complicated by 165 clustering and concomitant appearance of multiple cluster spectral features. Fast spin inter-conversion impedes our ability to form water clusters entirely from p-H 2 O molecules. Panels (a) – (e) in Fig. 7.5 demonstrate the stages of clustering observed upon completion of ~ 40 min 1:1000 H 2 O:Ar sample deposition at 4 K (a) with an OPR of about 1.5:1, ~ 1730 min conversion at 4 K (b), annealing to 30 K for 1 min (c), continued annealing at T = 30 K for 5 min (d), and re-cooling back to 4 K (e). Upon immediate heating to 30 K, as observed in panel (c), the 0 00 → 1 01 para transition at 3756 cm -1 is dominant despite the onset of clustering. Thus we have concluded that small clusters are formed from predominantly p-H 2 O molecules. In addition, we observed the growth of 1 11 → 1 10 (para) and 1 10 → 1 11 (ortho) transitions at 3738.8 and 3725.0 cm -1 , respectively, as observed previously. 12 Upon continued annealing at T = 30 K for ~ 5 min (d), intensity growth of ortho and subsequent decrease of para transitions are observed. Re-cooling the sample to T = 4 K shows the return of 0 00 ← 1 01 and 2 02 ← 1 01 lines with OPR of about 1:1. In addition, the para AA band of the water dimer is observed at 3736.4 cm -1 as will be discussed below. 166 3500 3600 3700 3800 0.0 0.1 0.2 0.3 0.4 0 00 ←1 01 2 02 ←1 01 Log 10 (I 0 /I) Wavenumbers, cm -1 T = 4 K t = 0 min a) 1 01 ←0 00 0.0 0.2 0.4 0.6 b) T = 4 K t = 1730 min 0.0 0.1 0.2 0.3 1 01 ←0 00 T = 30 K t = 1731 min c) T = 30 K t = 1735 min 0.0 0.1 0.2 0.3 0.4 FD d) T = 4 K t = 1745 min 1 10 ←1 11 1 11 ←1 10 0.0 0.2 0.4 0.6 BD e) AA 2 02 ←1 01 0 00 ←1 01 FIG. 7.5. IR spectra in the ν 3 / ν 1 region upon completion of ~ 40 min. 1:1000 H 2 O:Ar sample deposition at 4 K (a), ~1730 min. conversion at 4 K (b), annealing to T = 30 K within 1 min (c), after constant heating for 5 min at 30 K (d), and after re-cooling the sample back to 4 K (e). Fig. 7.6 shows spectra of a 1:1000 H 2 O:Ar mixture after completing ~ 40 min deposition at 4 K (a), similar to that in Fig. 7.5, but upon immediate annealing to T = 30 K (b) without spin conversion, continued annealing at 30 K for ~ 5 min (c), and after re- cooling down to T = 4 K (d). Despite the lack of time for sufficient conversion to occur as compared to spectra in Fig. 7.5, similar features are observed. In particular, upon re- cooling to T = 4 K, panel (d) in Fig. 7.6, a single feature is observed associated with the para AA dimer band, as will be discussed in the following. 167 3500 3600 3700 3800 0.0 0.1 0.2 0.3 0.4 b) a) Log 10 (I/I o ) Wavenumbers, cm -1 T = 4 K t = 0 min 2 02 ←1 01 0 00 ←1 01 1 01 ←0 00 0.0 0.1 T = 30 K t = 1 min 2 02 ←1 01 0 00 ←1 01 2 02 ←1 01 2 11 ←1 10 1 10 ←1 11 1 11 ←1 10 0.0 0.1 c) T = 30 K t = 5 min FD 0.0 0.1 0.2 0.3 d) T = 4 K t = 15 min 2 02 ←1 01 0 00 ←1 01 1 01 ←0 00 AA BD FIG. 7.6. IR spectra of a 1:1000 H 2 O:Ar sample in the ν 3 / ν 1 region upon completion of ~ 40 min. deposition at 4 K (a), annealing to T = 30 K within 1 min (b), after constant heating for 5 min at 30 K (c), and after re-cooling the sample back to 4 K (d). We proceed with experiments designed to estimate the lifetime of para-ice clusters. In these experiments, clusters have been formed upon rapid (5 min) heating of the converted samples from 4 K to about 90 K. The matrix melts at about 90 K and the Ar constituency was then removed from the cell by pumping. The cell containing ice particles was then heated within about 60 min up to T = 250 K to ensure sufficient vapor pressure of water for infrared analysis. Spectra were recorded at interval times throughout the heating process. Gas spectra of water could first be observed at T ≥ 250 K as shown in Fig. 7.7 for the ν 3 / ν 1 region. Traces (a) – (c) represent spectra of water vapor above ice, ice/liquid, and liquid H 2 O at T = 260, 270, and 280 K, respectively. A spectrum of unconverted H 2 O at room temperature is provided in trace (d) in Fig. 7.7 for 168 convenience. All spectra were normalized for comparison. As observed, transitions originating from both ortho and para levels are present where intensities are equal within error bars to those obtained from an ordinary water sample. Fig. 7.8 shows a magnified part of the spectra which also contains identification of the lines originating from o- and p- water by solid and dashed lines, respectively. These observations indicate complete back-conversion of the p-H 2 O sample during the course of the experiments. 3500 3600 3700 3800 3900 4000 0.0 0.2 0.4 0.6 0.8 1.0 T = 260 K above ice Normalized Intensity Wavenumbers, cm -1 (a) 0.0 0.2 0.4 0.6 0.8 1.0 (b) T = 270 K above water/ice 0.0 0.2 0.4 0.6 0.8 1.0 (c) T = 280 K above liquid 0.0 0.2 0.4 0.6 0.8 1.0 (d) T = 295 K 1 mbar nH 2 O FIG. 7.7. Normalized IR absorption spectra of ν 1 / ν 3 region of H 2 O at various temperatures after conversion to p-H 2 O and subsequent fast annealing, (a) – (c). Panel (d) shows comparable spectra of normal H 2 O at 1 mbar and T = 295 K. 169 3750 3800 3850 0.0 0.2 0.4 0.6 0.8 1.0 Wavenumbers, cm -1 a) 0.0 0.2 0.4 0.6 0.8 1.0 (b) Normalized Intensity 0.0 0.2 0.4 0.6 0.8 1.0 (c) T = 270 K above water/ice T = 280 K above liquid T = 295 K 1 mbar nH 2 O FIG. 7.8. Magnified spectra of traces (b) - (d) from Fig. 7.7 in the range of 3750 – 3850 cm -1 . Solid lines represent o-H 2 O transitions while dashed lines represent p-H 2 O transitions. 18 Unlabeled lines represent overlaps of ortho and para transitions. Spectra of matrices obtained upon deposition of mixtures having larger content of H 2 O:Ar have also been studied. Fig. 7.9 shows spectra of a 1:100 H 2 O:Ar mixture after completing ~ 40 min deposition at 4 K (a) and after an additional ~ 1500 min at 4 K (b). The spectra show several new bands, which can be assigned to water dimers. The bands at 3573.6 cm -1 (I = 1), 3633.0 cm -1 (I = 0.02), 3708.1 cm -1 (I = 0.45), and 3735.4 cm -1 (I = 0.25) are assigned to OH stretching bands in water dimers having predominantly donor OH-stretch (BD), acceptor symmetric stretch (SA), donor free OH-stretch (FD) and acceptor asymmetric stretch (AA), respectively. The relative intensities of the bands are given in parenthesis. The band positions are in good agreement with previous Ar matrix studies. Our recent He droplet study 27 gives the positions of the BD, SA and FD bands to be 3597.4, 3654.2, and 3729.5 cm -1 , respectively, i.e., having about ~ 22 cm -1 blue shift 170 with respect to corresponding frequencies in Ar matrix. The relative intensities of the dimer bands are in good agreement those obtained in our He droplet study. 27 Fig. 7.9 shows that the AA band has two closely spaced components having frequencies of 3735.4 and 3737.5 cm -1 and full widths of about 3 cm -1 each. A similar splitting has been observed in solid Ar with better resolution, where it was assigned to AA features. 12 Previous studies in solid Ar have also observed similar features and have assigned it to the AA band. 20 For comparison in He droplets, the AA band has two intense sub-bands at 3752.5 cm -1 and 3759.9 cm -1 , assigned to transitions from higher and lower components of the acceptor switching doublet, i.e., having ortho- and para-H 2 O molecules as acceptors. 3500 3600 3700 3800 0.0 0.2 0.4 AA b) Log 10 (I 0 /I) Wavenumbers, cm -1 a) BD 0 00 ←1 01 2 02 ←1 01 0 00 ←1 01 1 11 ←0 00 1 10 ←1 01 0.0 0.2 0.4 T = 4 K t = 0 min T = 4 K t = 1500 min FIG. 7.9. IR absorption spectra of ν 1 / ν 3 region of 1:100 H 2 O:Ar samples at T = 4 K after ~ 40 min completed deposition (a) and after 1500 min conversion (b). The panels are scaled to illustrate dimer features. 171 7.4. Discussion Water is one of only a few molecules that rotate in solid matrices. The frequencies of the ro-vibrational lines of the ν 1 / ν 2 and ν 3 bands from Table 7.1 were fitted to the known expressions for the b- and a- type transitions of an asymmetric top, respectively, by employing effective rotational constants to account for the matrix environment. 28 Based on pure rotational spectral analysis by Perchard 13 , the ground state rotational constants, A 0 and C 0, were obtained experimentally while B 0 could not be determined directly because transitions between states of different symmetry are forbidden. Here, we assume the same values of the rotational constants in the vibrationally excited state as in the ground state. Rotational constants and band origins in solid Ar are compared to the corresponding values in the gas phase 18 as well as to previous work 12 in Table 7.2. Our data and the ones of Ref. 12 are comparable with differences attributed to the reduction in parameters employed. Due to the limited number of lines, the A rotational constant could not be obtained. All constants are about 10% smaller than those in the gas phase which is consistent with the effects of a hindered rotation in the argon cage. 172 Table 7.2. Band origins and rotational constants (in cm -1 ) of single water molecules in the ν 1 , ν 2 and ν 3 regions in solid argon at 4 K and in the gas phase. Constants Gas 18 In Ar, This Work In Ar, Ref. 12 ν 1 band ν 0 (sym) a 3657.049 3638.4 3638.5 C 9.105 8.2 8.25 ν 2 band ν 0 (sym) a 1594.752 1589.0 1589 C 9.134 8.0 8.11 ν 3 band ν 0 (asym) 3755.950 3733.5 3733.5 (B + C)/2 11.77 11.3 11.5 a For calculation of ν 1 / ν 2 band origins, positions of the 0 00 → 1 11 lines and C constant from current work as well as A from Ref. 12 were used. Spectra of low concentration H 2 O in Ar mixtures have demonstrated effective isolation of single H 2 O molecules in the matrix. The spectra have also illustrated ortho to para conversion with time. Previous work 8 studied the effect of atmospheric impurities, crystal quality, sample holder, and radiation on H 2 O nuclear spin conversion time. Effects on the conversion were negligible with the exception of double doping with O 2 due to its paramagnetic properties. However, effects with O 2 were only observed beginning with a concentration ratio of 1:2 H 2 O to O 2 , substantially higher than would be observed in the absence of doping. It can therefore be concluded that the nuclear spin conversion of H 2 O in H 2 O:Ar mixtures is essentially mediated by the argon matrix environment. Spin conversion in the gas phase due to the intramolecular mixing of ortho and para states of the molecule during collisions has been discussed 6,29,30 for several molecules such as CH 3 F 29 , CH 4 30 , CCH 4 31 , and H 2 O 30 . Ab initio calculations have 173 estimated that the nearest ortho and para states capable of coupling in the ground vibrational state are para 18 15,3 and ortho 17 10,7 , which have energies of about 6869 cm - 1 , 32 and thus inaccessible in a cryo- matrix. Of course resonances between the ortho and para levels may occur at lower energy in matrices where the rotational constants are different. Larger width of the rotational energy levels in the matrix will also facilitate the conversion. In addition, interaction with the matrix will facilitate conversion because the matrix can break the symmetry of the rotational wavefunction allowing for spin-rotation coupling. In the gas phase as well as in single water molecules isolated in matrix, relative stability of the spin isomers stems from the fact that ortho and para states belong to different rotational states, having splitting of about 24 cm -1 , see Fig. 7.2. However in ice, intermolecular hydrogen bonding quenches molecular rotation, in which splittings between ortho and para states are expected to be on the order of 10 -2 Hz. 16 As a result, spin-spin interactions become important and mediate nuclear spin relaxation. Model calculations have been done for relaxation in water dimers, 16 indicating conversion within about 100 μs. Figs. 7.7 – 7.8 illustrated that upon annealing to T = 260 - 280 K, the spectra of previously converted H 2 O is identical, within error limits to that of normal, unconverted H 2 O. This observation indicates that the back-conversion of para-H 2 O to thermal equilibrium occurs in less than 60 min as limited by the time required to heat the cell up to 260 K. This is at variance with the recent reports on gas-chromatographic preparation and storage of para-ice and para-water samples over a time period of a few months and 174 about 30 min time, respectively, without noticeable back conversion. 14 Other works have reported spin selectivity of H 2 O by its interaction with porous surfaces of inorganic and organic materials 33 as well as in biological solutions 34 . However more recent experiments by Chapovsky et. al 35 failed to reproduce earlier results. Present work suggests that spin conversion is fast in water clusters. Features due to different o-H 2 O and p-H 2 O compositions in larger clusters remain unresolved. However, some information can be gained from the asymmetric stretch vibration of the acceptor molecule (AA) in dimers. The water dimer is a nearly symmetric prolate top with gas phase rotational constants of about A = 7.6 cm -1 and (B + C)/2 = 0.205 cm -1 . 36 Hindered internal rotation of the acceptor molecule, commonly referred to as acceptor switching, results in the splitting of the dimer’s energy levels into and components of about 7 cm + 1 A − 2 A -1 . 37 At T = 4 K, only K a = 0 and K a = 1 states are populated such that four components are expected. According to Ref. 37 , the and components correspond to para-para and ortho-ortho dimers, respectively, while ortho-para dimers contribute to both and components. Previous work in He droplets + 1 A − 2 A + 1 A − 2 A 27,38,39 observed three of the four acceptor switching features indicating rotation of the dimer. The AA bands originating from pH 2 O-pH 2 O and oH 2 O-oH 2 O dimers have two prominent bands separated by about 7.5 cm -1 , as observed in He droplets. 27 It was also observed that the dimer having donor p-H 2 O and o-H 2 O acceptor molecules relaxes into the lower state (i.e., ortho-para) via interchange tunneling. However, due to the short timescale for the He droplet study of about 3 ms, nuclear spin conversion in single molecules as well as in dimers was not observed. + 1 A 175 Based on the shift of the ν 3 band origin of single H 2 O molecules in solid Ar with respect to that in He droplets 10,39 and the gas phase 18 , the sub-bands of AA molecules in solid Ar are expected to red shift by ~ 23 cm -1 . The observed feature at 3736 cm -1 is in accordance with predictions of the para transition. The observation of the single para dimer sub-band indicates either fast nuclear spin relaxation or quenching of the acceptor switching motion of the dimer in Ar matrix. However, taken that such motion mainly involves rotation of the water acceptor molecule around its C + = ← = 1 " ' , 0 1 A K K a a 2V axis, and the fact that rotational constants of single water molecules in Ar are very close to those in the gas phase, it is very likely that acceptor switching splitting in Ar remains comparable to that in the gas phase. Thus, observation of a single AA line indicates fast nuclear spin relaxation in water dimers. The relative intensities of the free (FD) and bonded (BD) OH-stretch of the donor in H 2 O dimers to the single AA band around 3736 cm -1 in solid Ar agrees to within 20% of the total intensity of the AA band obtained in He droplets. 27 The accuracy of the intensity estimates is limited due to the broad background in the vicinity of the AA band. The good agreement of the intensity measurements in Ar and in He droplets indicates that the band around 3736 cm -1 accounts for the total intensity of the AA band. As a result, the lack of an additional feature of similar intensity further indicates nuclear spin relaxation of the dimer in Ar matrix. The relative intensity of the two components of the AA band seems to be independent of annealing and conversion time, see Figs. 7.5, 7.6, and 7.9. Therefore, it is unlikely these components stem from different nuclear spin isomers in water dimers. It is more likely that the rate of conversion in dimers should be 176 greater than or equal to the conversion rate of single water molecules. Thus, we conclude that the splitting around 3736 cm -1 is a site effect due to the Ar matrix and that spin relaxation in the dimer is fast in the scale of a few minutes. A recent work has focused on water dimers in a variety of matrices. 40 For solid Ar, an indication of acceptor switching was observed in the ν 3 region based on the presence of split features at 3736.0 and 3737.7 cm -1 , similar to what was observed in the current work at 3735.4 and 3737.5 cm -1 . In addition, both these features are believed to originate from the ground state implying para-H 2 O dimers. However due to selection rules, as dictated by the nuclear spin wavefunctions, transitions originating from para- (H 2 O) 2 to anti-symmetric ro-vibrational states are forbidden. As a result at low temperature, if dimers have relaxed, only a single feature should occur as is observed in the current work. On the other hand, we have occasionally observed a second feature located around 3725 cm -1 which was attributed to dimer complexes with N 2 as observed previously. 21 However, the intensity of the feature decreased irreversibly over time indicating a conversion but without the subsequent increase of para features. With constant annealing at T = 30 K and subsequent re-cooling to T = 4 K, the irregular feature was not restored despite the onset of intensity from single molecule ortho lines. Upon stringent purification methods of the experimental setup, the feature was absent from later spectra indicating a possible impurity effect. Infrared spectra of water molecules in cometary tails have indicated low OPR of about 2.5:1, which is consistent with a spin temperature of about 30 K. 4,5 As a result, it is generally believed that the obtained OPR could be a measure of the temperature at which 177 cometary ice is formed. According to this theory, OPR in cometary ices is preserved over the time of 4.5 billion years, during which comets are mostly at 50 K or less, then heated briefly to temperatures higher than 180 K at which point they sublimate. However, our spectra of water vapor (at T = 260 K) above ice, originally prepared from para- water molecules, show thermal OPR. Unfortunately, due to the low vapor pressure of water below T = 250 K and concomitant insufficient optical density, we are unable to study the molecules subliming at 180 K, such as in outer space. Nevertheless, our matrix isolation results of single water molecules show that at temperatures as low as 30 K, spin conversion of single water molecules and dimers proceeds within minutes. As a result, long time stability of para- water molecules in ices at higher temperatures seems unlikely, and the conclusion that cometary formation temperatures can be probed using the OPR ratios is in doubt. 178 7.5. Conclusions In this work, we have studied the ro-vibrational spectra of single water molecules isolated in solid Ar matrices in the range of ν 1 , ν 2 , and ν 3 bands using FTIR spectroscopy. Using nuclear spin conversion at T = 4 K, we have prepared almost pure para-H 2 O. Upon fast annealing, we generated ice particles and studied their corresponding vapor from T = 260 – 280 K. By comparison to normal H 2 O, FTIR studies of the vapor indicate re-conversion of nuclear spins to equilibrium conditions. Subsequent experiments of water dimers in solid Ar have been performed in which all four OH-stretching bands (AA, FD, SA, and BD) were observed. The observation of a single AA feature indicates fast nuclear spin relaxation into the para-(H 2 O) 2 configuration. As a result, the preparation of concentrated samples of para-H 2 O, such as in ice or vapor is unfeasible. 179 Chapter 7 Bibliography 1 T. Momose and T. Shida, Bulletin of the Chemical Society of Japan 71 (1), 1 (1998); K. E. Kuyanov, T. Momose, and A. F. Vilesov, Applied Optics 43 (32), 6023 (2004). 2 A. Farkas, Orthohydrogen, Parahydrogen, and Heavy Hydrogen. (Cambridge Univ. Press, London, 1935). 3 G. Hertzberg, Molecular Spectra and Molecular Structure, II Infrared and Raman Spectra of Polyatomic Molecules. (Van Nostrand Reinhold Company, New York, 1945). 4 M. J. Mumma, H. A. Weaver, and H. P. Larson, Astronomy and Astrophysics 187 (1-2), 419 (1987). 5 N. Dello Russo, B. P. Bonev, M. A. DiSanti, M. J. Mumma, E. L. Gibb, K. 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Lindsay, G. E. Douberly, and R. E. Miller, Journal of Molecular Structure 786 (2-3), 96 (2006). 40 J. Ceponkus, P. Uvdal, and B. Nelander, Journal of Chemical Physics 133 (7) (2010). 183 Chapter VIII. Conclusions and Future Works 8.1. Conclusions In this work we have studied different molecular systems at ultra-cold temperatures, such as in Ar matrices, in He droplets and in hydrogen clusters. Para-H 2 clusters embedded in helium droplets have been studied via coherent anti-stokes Raman spectroscopy. Based on our Raman spectroscopy study in bulk p-H 2 , we have been able to determine an upper limit to the temperature of liquid p-H 2 clusters to ≤ 5 K. Furthermore, our bulk p-H 2 work has provided the first systematic study on the temperature dependence of the vibrational Q 1 (0) line and therefore provides a benchmark for future experiments and calculations. In addition, we have discovered phase separation in mixtures of p-H 2 /D 2 clusters. By employing a simple thermodynamic model of phase separation, we have estimated the temperatures of the mixed p-H 2 /D 2 clusters to be ≤ 3 K, providing additional verification on the supercooled liquid state of the H 2 clusters. A significant portion of this thesis is devoted to the characterization of helium droplets obtained in pulsed nozzle beam expansions, which is much less characterized as compared to its continuous nozzle counterpart. As a result, we have summarized the optimization of parameters dictating cluster formation. Based on a collaborative work using cw nozzles, we have been able to provide a method for determining droplet size and their corresponding size distributions. 184 In addition to the work in helium droplets, we have also studied water molecules using matrix isolation spectroscopy inside argon matrices. Here, this work was performed in order to address the much debated theory of nuclear spin conversion between para- and ortho-H 2 O in ices. Based on the results of our study, we have observed the fast nuclear spin conversion from ortho-H 2 O to para-H 2 in the timescale of less than one hour by comparing infrared intensities between the two spin isomers. Our results on the fast spin conversion of water hopefully will promote further studies of cometary ices where the ratio of ortho to para-H 2 O have previously been considered to be indicative of the temperatures in the primordial solar system. 8.2. Future Works 8.2.1. Superfluidity of Para-H 2 clusters Previous work 1 has observed liquid p-H 2 clusters and estimated their temperature at around 1 – 2 K. Our current work has verified the supercooled temperature of such clusters by several methods, indicating the validity of the work. However, superfluidity in such clusters has still not been observed. As a result, study of p-H 2 clusters is not complete. Based on previous work 1 , rotational Raman spectra provides the best indication of the fluid nature of H 2 . However, the previous work observed the liquid clusters at distances close to the nozzle, in which an accurate description of the temperature could not be made due to condensation of the H 2 clusters. An important study would be to perform the experiments at farther distances from the nozzle. This test would help verify that clusters are not liquid only at short distances as previously 185 observed. Furthermore, due to supersonic expansion in helium droplets, increased distances provide the additional cooling to ensure that the clusters are at the low temperature of T = 0.4 K as dictated by the helium droplet. Unfortunately, as discussed in Chapter 4, rotational CARS experiments could not be performed presently due to signal constraints. Nevertheless, attempts of rotational CARS should be made once corresponding issues have been addressed. An additional problem of probing the clusters at far distances from the expansion source is the subsequent decrease in number density. This issue can be addressed by lowering the temperature of the source to create larger clusters. However, operation of the pulsed valve generates sufficient energy to limit the temperature of the source to temperatures no lower than T V = 10 K at 1 Hz repetition rate, T V = 12 K at 20 Hz. Therefore, additional cooling of the pulsed valve is necessary to provide large helium droplets. For temperatures down to T V ≤ 6 K, recent work with continuous nozzles has indicated droplets on the order of 10 8 – 10 10 He atoms can be produced. Based on our current work with pulsed nozzles, it is likely that larger droplets at similar low temperature conditions can be achieved. For co-expansion of H 2 with He, this will undoubtedly freeze H 2 inside the nozzle. However, if such temperatures can be accomplished, then a pickup cell placed away from the nozzle may provide suitable means for doping. For determining superfluidity of H 2 clusters, several possible methods exist. For example, transitions from normal liquid to superfluid may be accompanied by significant decrease in the linewidth of the spectral lines. For comparison, the superfluid transition 186 in liquid He is accompanied by a dramatic decrease of the linewidth of via inelastic neutron scattering spectra. 2 The resolution of our current laser systems is limited to about 0.05 cm -1 . However, the linewidth of vibrational transitions in clusters from current experiments is more than 0.5 cm -1 . Our previous study of bulk liquid H 2 observed a temperature dependence on the vibrational transitions in p-H 2 . This temperature dependence was understood in terms of vibron hopping, which is dictated by density. For helium, a slight decrease in density is observed upon transitioning into the superfluid phase. Fig. 8.1 demonstrates the density change in 4 He with temperature, as measured previously. 3 If p-H 2 exhibits a similar density drop, this effect could be observed in the spectra. FIG. 8.1. Density of 4 He as a function of temperature. 3 187 8.2.2. Nuclear Spin Conversion in H 2 O Our recent FTIR matrix isolation study of water molecules in argon has provided an additional matrix isolation tool for our lab. The design of the cell allows it to be incorporated into our working p-H 2 Raman shifter. In addition, the cell provides capabilities to perform matrix isolation studies for time periods longer than the 3 ms flight time dictated by the helium droplet technique. As a result, this cell can be used for time-dependent studies for time scales orders of magnitude longer than by the helium droplet setup. Furthermore, this method can provide compatible support for future works in helium droplets. However, modifications should be made in order to allow matrix isolation using p-H 2 rather than argon due to the quantum nature of solid H 2 and its corresponding softer environment, comparable to that in helium droplets. 8.2.3. Vibrational Spectroscopy of Ions in Helium Droplets 8.2.3.1. Introduction Since the application of helium nanodroplet spectroscopy, a large body of neutral molecules have been studied. 4 From these studies, structures of important molecular systems 5 as well as insights into chemical reaction mechanisms 6 have been discovered. The general model for performing spectroscopy of molecules in helium droplets is based on the energy transfer from an excited chromophore to the helium bath. In this thermal process, the heated droplet will then cool by evaporation of individual helium atoms. Here, every evaporated He atom removes around 5 cm -1 of energy from the droplet. For 188 example, excitation of an OH-stretch in water around 3700 cm -1 should lead to the evaporation of about 740 He atoms. Based on the corresponding decrease in helium droplet flux with frequency, spectra can be obtained. Despite the numerous works of neutral molecules in helium droplets, less work has been performed for ion-containing helium droplets. 7,8 In addition, there is a current disparity in whether or not the cooling of ions in helium droplets is governed by thermal or non-thermal mechanisms. This idea of non-thermal cooling was first introduced by Gspann 9 who observed the formation of small, charged helium clusters following the electron impact ionization of large helium droplets. It was suggested that the ejection of these ionized clusters was generated due to the strong attraction of the helium atoms solvating the ion, leading to local heating and subsequent ejection of ions. Recent experiments on the electron impact ionization of molecules in helium droplets showed that the first several thousand helium atoms leaving the droplet can take away up to 22 cm -1 of energy per atom, indicating a non-thermal process. 10,11 Similar theoretical results 12 were obtained on the electron-impact ionization of neon clusters in helium droplets. In these experiments, the generated ions are created with a substantial amount of internal energy. As a result, it is unclear if ejection of ions is due to solvation of the ion by helium or if the internal energy of the ion and its subsequent energy transfer to the droplet is sufficient to promote ejection. Recently, a novel spectroscopic method was introduced to help address this issue based on the detection of ejected aniline cations from helium droplets following vibrational excitation. 8 Here, droplets containing single aniline molecules are photo- 189 ionized and subsequently excited using tunable IR radiation following a delay of several hundred nanoseconds. Following absorption of the IR radiation by the ions, the energy is efficiently transferred to the helium environment leading to the formation of bare or partially solvated aniline ions. The aniline ions resulting from IR excitation are then detected using time-of-flight mass spectrometry. By monitoring the aniline ion mass signal with laser frequency, background-free IR excitation spectra can be recorded. Despite the observation in this previous work that vibrational excitation does lead to the ejection of ions by a non-thermal process, problems still persist regarding whether or not the ejection of ions is solely due to vibrational excitation or ion solvation. In addition, it is important to determine whether or not vibrational induced ejection can be applied for different molecular systems or it is molecule specific. As a result, this section is devoted to describing a preliminary technique for observing ejection ions of water molecules in helium droplets. 8.2.3.2. Proposed Experimental Setup Previous work produced aniline cations by photoionization. 8 However, this approach is limited to molecules containing conjugated pi-systems in order for efficient photoionization to occur. Electron-impact ionization is a more general technique, as it is not molecule specific. More importantly, ionization of dopants in He droplets by electron-impact occurs indirectly. 11 However, ionization of doped helium droplets usually gives rise to a broad distribution of ion fragments. Thus, it will be difficult to 190 distinguish ions produced via direct ionization from those ejected upon vibrational excitation. This fragmentation induced background can be removed by employing electron-impact ionization at distances far away from the quadrupole and ion optics such that the unwanted ionized fragments are not mass selected. In addition, large enough droplets containing ions of interest must survive the fragmentation process for experiments to be performed. Fortunately, as discussed in Chapter 3, droplets obtained from our pulsed nozzle are sufficiently large that a fraction of ionized droplets are not deflected by the electric fields in the QMS, see Fig. 3.4. As a result, we can utilize these large ionized droplets for the proposed experiments. We have previously observed that He droplets can be ionized using an electron- gun (EGUN) installed on our TOF-MS, which is housed approximately 10 cm upstream from the entrance to the QMS. In addition, only the un-deflected large droplets containing ions will be able to reach the QMS region, while all lighter ions can be retarded by the electric field. As a result, installation of another ionizer is not necessary. For preliminary experiments, the simplest molecule to study for this project is water. Mass spectra of He droplets (see Fig. 3.3) indicate sizeable H 2 O + peaks, which originate from pickup of residual water gas. As a result, no pickup cell is necessary. Fig. 8.2 shows vibrational spectra for a variety of protonated water clusters, H + (H 2 O) N , for N = 2 - 11. For clusters larger than N = 3, the bands are significantly broadened. Due to the spectral broadening, water clusters should provide easier IR tuning in which the laser wavelength can be centered only approximately at the maximum. 191 FIG. 8.2. Argon predissociation spectra of (H 2 O) N ·H + for N = 2 – 11 with N decreasing down the figure. 13 For tunable IR radiation, we can utilize a pulsed OPO/OPA system (LaserVision) which allows for tunable IR radiation in the range of 1.35 to 5.0 microns. Maximum output on the order of 12 mJ exists in the 1.5 – 3.5 micron range. However, output energies of a few mJ should be sufficient to excite the ions. Upon vibrational excitation, the ions should efficiently transfer their energy to the droplet violently enough to produce ejection of the ion. Upon ejection, the molecules can then be detected using our QMS. Due to the pulsed operation of the nozzle, suitable temporal overlap is necessary to 192 vibrationally probe the molecules upon ionization. Fig. 8.3 illustrates a possible timing schematic. 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Chem. Ref. Data 11(1): 1 -11. 209 Appendix. Pulsed Valve Modifications and Assembly Design and Principals of Operation The original pulse valve is shown in Fig. A1.1. It consists of the body (C), the head or faceplate (D), and a tube fitting (B). The valve is connected to the driver IOTA-1 by wire (A). The body and the faceplate are threaded and can be tightened and sealed with a small copper gasket between them. The body contains a coil of wire, by which magnetic force drives the ferromagnetic rod inside. The rod is supported by two springs FIG. A1.1. The draft of the pulsed valve (099-0215-900 Solenoid Valve, Axial,28 V DC, SS body, conflat,0.039" orifice (1 mm),Kel-F poppet, copper gasket). (A) – wires to the driver, (B) – A-lock type tube fitting, (C) – body, and (D) – faceplate. 210 at both ends and is also connected to a poppet. The faceplate has a CF groove and in the middle it has a hole from 0.25 to 1.0 mm diameter depending on the part number. Without electrical power, the poppet is pressed against the nozzle orifice and the valve is closed. Upon triggering, the driver IOTA-1 generates a 300 V electrical pulse of approximately 180 μs duration time in order to open the valve and then maintains about 28V to hold the valve open. Poppet Changing Procedure Upon operation of the pulsed valve, the poppet strikes against the stainless steel faceplate with every pulse. This process causes a degradation of the poppet at which time the valve will eventually start to leak or the droplet flux may decrease due to a change of geometry of the poppet. In order to change the poppet, the pulsed valve should be taken out of the He apparatus. Once the valve is disconnected from the He apparatus, the pulsed valve is opened by inserting two nails into two opposite holes in the faceplate and holding the nails using a vice. With the pulsed valve engaged, which pulls poppet away from faceplate in order to prevent damage, the body is unscrewed from the faceplate using a wrench inserted in between the faceplate and the body. The driving rod and two springs are removed from the valve and the poppet is removed from the inside driving rod and changed for a new one. When assembling the pulsed valve, it is necessary to take special care in order to avoid scratching of the poppet surface upon screwing together the body and the faceplate. Following the driver manual, one should set the 211 driver IOTA1 for long (several minutes) pulse times and manually press the driving rod with the poppet completely into the body without putting stress of the poppet itself. If engaged properly, the driver will hold the driving rod with the poppet inside the body allowing the faceplate to be screwed back on without touching the poppet surface. In order to seal the pulsed valve, we usually use 4 copper gaskets (0.0125 mm thickness each) together; however depending on the particular valve 3 of 5 gaskets have been used. After the body is screwed back to the faceplate, the faceplate is held again in a vice using two nails and the body is securely tightened. Serious over tightening should be avoided so not to damage either the body or faceplate threads. Poppet Performance Check Once the poppet has been changed, the assembled pulsed valve is connected to the He gas line, in which, at a gas pressure of about 20 bar, a correctly assembled pulsed valve should not leak when closed. This can be checked by inserting it into a beaker with methanol. The valve should start to open at about 200 μs duration time and bubbles should be easily seen at 300 μs duration time. However, depending on the number of copper washers employed, the opening time varies. Also, the valve should be able to open completely at 20 bar pressure in the gas line. In order to check complete opening, the valve should be operated with pulse parameters set for long pulse duration times (at least several seconds). If everything is right, the valve should open completely and gas 212 should escape with loud noise. In addition, a similar loud noise should be heard at 200 μs duration. If the valve does not leak at room temperature, but cannot be opened completely, the amount of copper gaskets should be reduced. If the valve can be completely opened but leaks, it should be tightened more securely. If the tightening does not help, the poppet is, most probably, damaged and the changing poppet procedure should be repeated. If the valve does not leak and can be completely opened, an extra check can be done by inserting the pulsed valve connected to a high pressure gas line into liquid nitrogen. The valve should not leak at these conditions. It has been observed that leaks occur at the poppet orifice once placed in liquid nitrogen. However, if the poppet is allowed to run for an extended time at either room temperature or in liquid nitrogen, the leaking is removed entirely. 213 Modifications All modifications were designed by Mihail Slipchenko and affect only the faceplate and do not change the procedure for exchanging poppets described above. The faceplate has 3 factory modifications, which depend on the part number and result in different diameters of the nozzle orifice in the faceplate. The 0.25 mm modification has hole diameter of 0.5 mm from the inside of the faceplate and 0.25 mm outside, see Fig. A1.2 (a). The 0.5 mm and 1.0 mm modifications (b) have a constant sized orifice through the faceplate of 0.5 and 1.0 mm diameter respectively. The current setup uses a 1 mm faceplate with a 90 degree opening, see Fig. A1.2 (c). In addition, the thickness of the faceplate is reduced by custom machining in order to improve heat transfer. Drawings of both original 1 mm faceplate and modified faceplate FIG. A1.2. Three different faceplate orifice cross sections. 214 cross-sections are shown in Fig. A1.3. However, if custom machining of a new valve is necessary, the old valves can be used as a blueprint. FIG. A1.3. Final modification of pulsed valve faceplate.

Abstract (if available)

Abstract This dissertation covers several different aspects of spectroscopy of molecules and molecular clusters embedded in low-temperature matrices, such as helium droplets. First, details on the formation and optimization of He droplets will be discussed. A new method of measuring droplet sizes for cw nozzle expansions using mass spectrometry was developed. The results of the measurements of the sizes of the droplets in pulsed expansion as a function of temperature will be described. Details on the electron-impact ionization of He droplets will also be discussed as well as a simple method of modeling the ionization and excitation of He atoms in the droplet. In addition, preliminary measurements on the size distribution of He droplets produced at very low temperature of 5 – 7 K in continuous expansion will be addressed.

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Asset Metadata

Creator Sliter, Russell Thomas (author)

Core Title Infrared and Raman spectrosopy of molecules and molecular aggregates in helium droplets

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 04/26/2011

Defense Date 04/21/2011

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag clusters,helium droplets,laser spectroscopy,matrix isolation,OAI-PMH Harvest,superfluidity

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Vilesov, Andrey F. (committee chair), Kresin, Vitaly V. (committee member), Reisler, Hannah (committee member)

Creator Email sliter@usc.edu,sliterr@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3778

Unique identifier UC1142400

Identifier etd-Sliter-4404 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-468814 (legacy record id),usctheses-m3778 (legacy record id)

Legacy Identifier etd-Sliter-4404.pdf

Dmrecord 468814

Document Type Dissertation

Rights Sliter, Russell Thomas

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu