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Asymmetric response and the reorientation of interfacial water with respect to applied electric fields
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Asymmetric response and the reorientation of interfacial water with respect to applied electric fields
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Content
Asymmetric Response and the Reorientation of Interfacial Water
with Respect to Applied Electric Fields
by
Angelo Montenegro
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 2022
Copyright 2022 Angelo Montenegro
Acknowledgments
Despite its many desirable attributes, a clean and robust graphene electrode is difficult to
fabricate and is admittedly an unforgiving tool to employ. The difficulty is further amplified by
the complexity that accompanies the utilization of a tunable and fully functional VSFG
spectrometer. To succeed in this endeavor required the collaborative and relentless efforts of
many persons, operating under the leadership and guidance of Professors Alexander V.
Benderskii and Stephen B. Cronin at the University of Southern California. I am forever
indebted to Professor Benderskii, who was truly an inspiration. Professor Benderskii allowed
me to work independently, and to learn at my own pace, though he was always there when I
needed his help. I would also like to acknowledge both Professor Benderskii and Professor Jahan
Dawlaty for being two of the best instructors I’ve ever had the pleasure of learning from.
Without Professor Cronin, there would be no graphene electrodes for my studies. Prof. Cronin
also deserves an abundance of credit for his many suggestions, for relentlessly pushing us to
publish our work, and for the thorough and valuable feedback he provided throughout the
development and manuscript stages. I acknowledge Haotian Shi for relentlessly fabricating the
graphene electrodes. Haotian very much walked along this treacherous path to success with
me, littered with the corpses of graphene electrodes. I would also like to thank my fellow
graduate students whom I worked with and provided an unforgettable and enjoyable
experience. Thank you Purnim Dhar, Sergey Malyk, Dhritiman Bhattacharyya, Gaurav Kumar,
Muhammet Mammetkuliyev, and Ariel Vaughn. Thank you, Chayan Dutta, for passing on much
ii
of your training and experience to me, this project would not have gone to the extent it has
without the foundation you provided. Most of all, thank you all, for being my friend.
The associated development and equipment costs are restrictive to the vast majority.
This project was financially supported by the University of Southern California, the Air Force
Office of Scientific Research (AFOSR) grant No. FA9550-15-1-0184 and FA9550-19-1-0115, the
Army Research Office (ARO) Award No. W911NF-17-1-0325, the United States Department of
Energy (DOE), Office of Science, Office of Basic Energy Sciences, under Award DE-SC0019322,
and the National Science Foundation (NSF) Award No. CBET-1512505. The aforementioned
sources that are entities of government, are in-turn financially dependent on the funds
surrendered by tax-paying citizens of the United States. Thus, I would like to express my
deepest gratitude to all the aforementioned entities for the financial support in this endeavor,
and to the countless and nameless individuals from which that support was derived.
I would also like to thank Vartan Ter-Mikirtychev. Vartan is my manager at Coherent
(Budd Lake, NJ), the company under which I am currently employed as a senior R&D engineer.
He provided a wealth of advice. I would also like to thank all my co-workers who made me feel
at home, taught me much, and helped me find the confidence to pursue my degree. Special
thanks is reserved for Hikmat Najafov, Nicholas Kearns, Alexander Goldgirsh, Jeongho Yeon, and
Ivo Nikalov.
The completion of this document and this chapter of my life is a testament to my
mother, who tirelessly pushed me in the right direction and shaped the person I am today, who
is a reservoir of infinite love. To my father, who provided encouragement, advice, and support.
To my siblings, who were a source of inspiration. To all of my extended family: to my
iii
grandparents, aunts, uncles, and cousins who all taught me important lessons. To my wife who
enriches every dimension of my life, and provides a wealth of love and support. To my son, who
somehow inherited very little from his mother and is almost an exact copy of me; who inspires
me to better myself every day. Experiencing the world again through his eyes has enriched my
life beyond measure.
Thank you
iv
Table of Contents
Acknowledgments..........................................................................................................................ii
List of Tables...................................................................................................................................vi
List of Figures................................................................................................................................vii
Abstract..........................................................................................................................................ix
Preface...........................................................................................................................................xi
Chapter 1: Introduction ...................................................................................................................1
The Electrical Double Layer.........................................................................................................2
The Graphene Electrode: An “Ideal” Interface...........................................................................4
SFG Spectroscopy of Water at Charged Interfaces......................................................................8
Miller’s Rule...............................................................................................................................20
Orientational Analysis of Water and the “Free-OH” .................................................................24
References.................................................................................................................................30
Chapter 2: Methodologies.............................................................................................................39
Fabrication of the Graphene Electrode: ....................................................................................40
The Electrochemical Cell...........................................................................................................41
Raman Spectroscopy.................................................................................................................43
VSFG Spectroscopy....................................................................................................................44
Spectro-electrochemical Measurements..................................................................................51
Spectral Decomposition into Surface and Bulk Contributions ..................................................56
Orientation Analysis ..................................................................................................................58
Control Experiments..................................................................................................................67
References.................................................................................................................................72
Chapter 3: Discussion of Results....................................................................................................75
Asymmetric Response of Interfacial Water to Applied Electric Fields......................................76
Measurements of the Free Energy Orienting Potential ............................................................86
Promising Preliminary Measurements and Future Studies......................................................99
References...............................................................................................................................102
Appendix......................................................................................................................................105
Matlab Script of Orientational Analysis ..................................................................................105
v
List of Tables
Table 1: Fitting results for the decomposition of surface and bulk responses. .............................83
Table 2: Spectral fitting results of the field-dependent free-OD response (PPP and SSP) ............92
vi
List of Figures
Figure 1: Sum frequency generation from a medium in reflection and transmission geometry . .10
Figure 2: Energy state diagram for the sum frequency generation process ..................................11
Figure 3: Time domain picture, inducing a second-order polarization ..........................................11
Figure 4: Real and imaginary parts of the Lorentzian lineshape function .....................................15
Figure 5: SSP and PPP VSFG spectra of the air-water interface.....................................................28
Figure 6: The Graphene Electrode.................................................................................................40
Figure 7: A schematic of the electrochemical cell (3-terminal configuration). .............................42
Figure 8: Schematic of the VSFG setup ..........................................................................................46
Figure 9: A schematic of the electrochemical cell, including an index-matched CaF2 prism to
enhance the VSFG signal................................................................................................................47
Figure 10: The Al
2
O
3
layer influences the graphene-D
2
O VSFG spectrum.....................................50
Figure 11: "Mushrooming" effect, with a TiO
2
adhesion layer (between CaF
2
and Graphene).....51
Figure 12: The G-band Raman shift is linear with respect to the applied voltage........................52
Figure 13: Charge carrier concentration plotted, derived from the extent of the Raman G-band
shift................................................................................................................................................53
Figure 14: The electrochemical current is linearly proportional to the voltage, defining a so-
called “safe range of operation”. ....................................................................................................55
Figure 15: Prediction of SSP and PPP amplitudes based on Wang's orientational analysis
formalism.......................................................................................................................................59
Figure 16: Experimental field-dependent VSFG spectra and the best-fit to the Free-OD response
.......................................................................................................................................................62
Figure 17: Field-dependent reorientation ; extrapolation of the fit ..............................................64
Figure 18: The free-energy orienting potential vs. the orientation angle. ....................................65
Figure 19: Extracting the distribution width through agreement of the orientational analysis
with the free-energy orienting potential .......................................................................................66
Figure 20: The minimum error between the two methods that extract orientation ....................67
Figure 21: The air-water VSFG spectrum of clean water vs. contaminated water........................68
Figure 22: Raman spectrum of good quality, monolayer graphene..............................................69
Figure 23: Microscope image (50 μm scale) of the graphene electrode.......................................69
Figure 24: Measurement of the same voltage periodically throughout an experiment to check
for reproducibility..........................................................................................................................70
Figure 25: VSFG spectrum of the "dry" graphene-air interface in the D
2
O-streching region........71
Figure 26: Isotopic dilution of D
2
O with H
2
O suppressed the free-OH stretching response.........71
Figure 27: Example of an organic (CH-stretch peak at ~3000 cm
-1
) contaminant observed at the
graphene-water interface..............................................................................................................72
Figure 28: Voltage-dependent VSFG spectra of D2O at the graphene interface...........................76
Figure 29: Doping concentration is calculated from the G-band shift. The G-band shift is linearly
dependent on the applied voltage.................................................................................................78
Figure 30: Field-dependent VSFG spectra of the graphene-water interface.................................79
vii
Figure 31: Spectral Decomposition of the field-dependent VSFG spectra (Fig. 28) of the
graphene-water interface into surface and bulk contributions. ....................................................82
Figure 32: Electric-Field dependent SFG spectra of the graphene-D2O interface collected in the
SSP and PPP configurations ............................................................................................................87
Figure 33: Electron Doping of Graphene.......................................................................................88
Figure 34: Applied voltages are within the range of electrochemical stability.............................89
Figure 35: The distribution of free-OD angles at the graphene-water interface is not consistent
with a decaying exponential. .........................................................................................................90
Figure 36: The calculated average orientation angle depends on the orientational distribution
width..............................................................................................................................................95
Figure 37: The free-energy orienting potential shifting with the applied field .............................96
Figure 38: Determination of the orientational distribution width ................................................97
Figure 39: The sum of the difference between the two complementary methods to determine
the average orientation .................................................................................................................98
Figure 40: Stark shift of the free-OD response in the PPP and SSP polarization configurations. . .99
Figure 41: Voltage-dependent spectra near the onset of the Free-OD response in PPP and SSP
configurations. .............................................................................................................................100
Figure 42: Voltage dependent SPS spectra of the graphene-D
2
O interface................................101
Figure 43: SPS spectrum of H
2
O at the graphene-water interface (in the OD-stretch frequency
region)..........................................................................................................................................102
viii
Abstract
Aqueous interfaces play a crucial role in areas ranging from life sciences and environmental
chemistry to heterogeneous catalysis, electrochemistry, and energy conversion applications. The
solvation properties of interfacial water dictate chemical equilibria and reaction rates. Our basic
understanding of water as a dielectric medium (polar solvent) relies on the assumption of linear
response, i.e. that an external perturbation (electric field) induces a linearly proportional response
(polarization) in the medium. Explicit in this assumption is antisymmetry with respect to the sign of the
external field: the response must be of the same magnitude and opposite sign for positive vs. negative
applied field of a given strength. We measured surface-selective vibrational sum frequency generation
(VSFG) spectra of water (D
2
O) near a monolayer graphene electrode, to study its response to an external
electric field under controlled electrochemical conditions. The graphene Raman G-band frequency is
used as an internal gauge of the surface charge density. VSFG spectra of the OD-stretch show a
pronounced asymmetry for positive vs. negative electrode charge. At negative charge (below 510
12
e
-
/cm
2
), a 2700 cm
-1
peak corresponding to the “free” (non-hydrogen-bonded) OD groups pointing
towards graphene surface is observed. At neutral or positive electrode potentials, the “free-OD” peak
disappears in an abrupt nonlinear fashion, and the spectra are dominated by the broad peaks of the
hydrogen-bonded OD-species (2300-2650 cm
-1
). Evolution of VSFG spectra as a function of the external
electric field is related to the linear susceptibility (and the dielectric constant) by Miller’s rule.
The
experimentally observed deviation from the linear response to electric fields of the order of 3×10
8
V/m
calls into question the validity of treating interfacial water as a simple dielectric medium. The
orientational distribution of the free-OD moiety is consistent with a Gaussian distribution, with σ =15 .
ix
We present a model of field-induced reorientation and extract an expression for the free-energy
orienting potential that is tested against experiment. Free-OD reorientation is measured with respect to
applied electric fields: it is linear with respect to fields up to 2×10
9
V/m, reorienting from about 45° to
30° relative to the surface normal. A linear relationship between the free-OD stark shift and the applied
field is presented, rendering the free-OD capable of serving as an interfacial field-sensing probe.
x
Preface
The work presented in this dissertation is based on the foundational works of countless others.
An attempt to express ample credit, appreciation, and respect for these countless contributors, will most
certainly end in failure.
In this body of work, the graphene electrode was employed to study effects that are applicable
to all aqueous interfaces, in general. The accuracy of the presented evidence and the validity of the
conclusions that are meant to follow are subject to peer review; if invalidated at any time, and found to
be false or impossible to reproduce, it should be purged from the public record. I believe that a study is
a success, not only when it yields answers to pressing questions, but when it inspires further inquiry. I
can only hope that this study is capable of such, and that my part in this endeavor will be looked upon by
my peers as productive toward that end.
What was deemed to be the most pressing background information is provided in the
Introduction. Due to the complexity and multidisciplinary nature of this project, the sheer immensity of
the background subject matter, surely capable of filling volumes, demands that a mere subset be
explored here. References are provided as an attempt to guide the reader down the rabbit hole, if so
desired. The details of the methods employed are provided in the methodology section. Many of the
methods were developed through trial and error, through a relentless desire to succeed. The results and
the interpretation of the results are provided in the results section. Hoping that they should stand the
test of time would most assuredly be an exercise in futility. Rather, I hope that the results, methods, and
arguments presented here should generate further interest worthy of confirmation or effort toward
invalidation. None would be more pleased than I, with whatever the outcome may be.
xi
Chapter 1: Introduction
The survival and proliferation of life depends deeply on water, and so its perceived
significance echoes through the ages. Ancient peoples of numerous cultures independently
surmised it to be one of a few substances from which all other things are composed, a
fundamental element of nature. Water was and is incorporated into mythology; personified
and deified. Yet, the story of water that has been constructed through the relentless application
of the scientific method is arguably the most complex and imaginative epic thus far.
In this body of work, spectroscopic techniques are frequently appealed to. Matter, it
seems, communicates through a complex language based on light, the manifestation of charges
in motion. The phonetics of this figurative language became much more accessible upon the
advent of the laser, a system capable of producing coherent light through stimulated emission.
1
Advances in spectroscopy are often realized through clever distillation or manipulation of light
into an effective probe or tool, capable of inducing a response in a material that is relevant to
the physics of interest and can be analyzed effectively. The interrogating light, and the light
produced by a medium in response, may be tailored or filtered with respect to its (e.g.)
frequency, bandwidth, directionality, and polarization. By shaping light into short pulses, the
material of interest can be made to experience intense peak fields that are conducive to
observing nonlinear effects. Multiple interactions with two or more pulses of light that are
shaped and spaced appropriately in time can yield dynamical information. The phase of a
response can be utilized to infer structural information, or to separate a surface response from a
1
bulk response. To extend the light-language analogy, spectroscopy is the art of interrogating a
material. Ask a witness or suspect in a criminal case the right questions, and they may “sing like
a canary”.
In general, with increasing complexity with respect to the number of interactions within
and between molecules, so too does it become increasingly difficult to communicate with the
material in the vernacular of light-matter interactions. The computational cost of theoretical-
based studies rises rapidly with the complexity of the system.
2
Herein lies the fundamental
difficulty in constructing physical models that accurately represent water. Water’s broad
absorption bands hint at its complexity, afforded by its strong dipole moment and its ability to
form networks of hydrogen bonds that dynamically vary in strength and extent.
3–5
Water’s
unique phase diagram, its high specific heat, high surface tension, and its excellent solvation
properties, are just some of the physical manifestations of this awesome complexity.
This dissertation, formulated (in-part) from original experimental research on the
graphene-water interface, aims to advance current models with respect to water’s structure,
orientational distribution, and its nonlinear response at charged interfaces. Given its ubiquity,
accurate models of aqueous interfaces are valuable to practical problem solvers operating over
a wide range of disciplines.
6–12
Charged aqueous interfaces are relevant to the environmental
sciences
13–15
, to drug design
16–18
, to energy storage and production.
19–30
The Electrical Double Layer
The interface is a source of asymmetry with respect to charge; it is the source of surface
effects which are distinct from the bulk. All chemical reactions must be realized via a shared
2
interface. Conceptually, distinguishing the surface from the bulk may seem trivial. One would
perhaps be tempted to define the surface to be the first, topmost atomic or molecular
monolayer—all sublayers being the bulk. Experimentally, however, the surface may not be
easily distinguished from the bulk. Separating the surface response from the bulk is a
commonly faced source of confusion and contention. The effect of the surface can extend over
many monolayers (on the order of ~1 µm for very weakly ionic solutions), the extent of which
depends on the details of the system of interest. For water, the electrostatics of the surface can
be described through models of the so-called electrical double layer (EDL).
31,32
In the late nineteenth century, Helmholtz introduced the concept of the electrical
double layer (EDL).
33,34
When an interface to water is charged, oppositely charged ions in
solution migrate to the surface because of the electrostatic force that attracts them. The
interfacial charge is screened by these ions and so the potential drops with distance from the
interface. The Debye length is a figure related to the depth by which the electrostatic effect of
the surface persists, after which thermal effects dominate, and the solution starts to become
bulk-like. The Debye length defines the plane of the so-called diffuse layer, which marks the
extent of the charged interface. Helmholtz modeled this system as a parallel plate capacitor,
where the two “plates” of the capacitor are the planes defined by the charged surface and the
center of the nearest fully solvated ions. The center of the nearest fully solvated ions defines
the outer Helmholtz plane (OHP) and the edge of the so-called Helmholtz (or Stern) layer: the
region between the interface and the OHP . The potential decreases linearly over the Helmholtz
layer, from the interface to the OHP . Grahame contributed to the EDL model by including
partially solvated ions, which are adsorbed to the interface and define a compact double layer,
3
known as the inner Helmholtz plane (IHP).
35
Gouy and Chapman describe the equilibrium ionic
distribution of the diffuse layer using the Poisson-Boltzmann equation, yielding an exponential
decay of the potential with distance from the interface (infinitely far from the interface, the
potential is defined to be zero).
36,37
Under this model the charge on the interface is taken to be
spatially homogeneous, the charged surface ends abruptly, ions are point charges that only
interact through the Coulombic force, there are no ion-ion correlations, and the dielectric
permittivity is constant throughout the double layer. To describe highly charged interfaces for
which the Gouy-Chapman model fails, Stern combined the Gouy-Chapman model of the diffuse
layer with the Helmholtz’s model of the double-layer.
38
Debye and Hückel linearized the
nonlinear Poisson-Boltzmann equation, reproducing the exponential drop of potential for
weakly-charged interfaces.
39
Conway, Bockris, Ammar, Devanathan, and Müller contributed to
the EDL description by accounting for changes in the dielectric constant of water with distance
from the charged interface.
40,41
Despite the many refinements and the usefulness of these
models to describe macroscopic behavior, these classical models can fail to describe processes
that are governed by mechanisms on the microscopic, molecular scale.
35,42,43
For example, water
splitting at the interface of an electrode is dependent on the structure and orientation of water
molecules, and is poorly described by classical EDL models.
The Graphene Electrode: An “Ideal” Interface
The number of unique aqueous interfaces are practically infinite. It is often the case that
preparing a faithfully representative system in the laboratory is a major barrier to progress. This
is especially true of biological and environmental systems, where molecules and their
4
environments are extremely complex and only a simplified subset of such systems can be
realized in the laboratory. The ideal interface is thus a subjective matter, naturally dictated by
the subject of interest and practical constraints. However, there is immense value to
constructing a real-world aqueous interface for study wherein complicating factors are
minimized, especially to theoreticians who wish to test the accuracy of their models. One might
imagine such an interface to be a chemically inert plane of charge, so that electrostatic effects
could be studied in the absence of counterions
44
or surfactants, i.e., in the absence of non-
generalizable local interactions and irregular surface morphology. The substance that
approximates this plane should also be conductive and electrochemically robust, so that its
charge density can be tuned at will. Additionally, the plane of charge should be optically
transparent, so that the interface is directly accessible to interrogating light. At this interface,
the electrostatic effect would be generally applicable to all charged interfaces, and thus it is
“ideal” from this perspective. Armed with such an interface, the effect of an applied charge on
molecular orientation and hydrogen bonding can be studied on a fundamental level.
31,45–47
The
work presented in this thesis was constructed with this goal in mind, wherein a graphene
electrode was employed, and meant to approximate an “ideal” interface from which
generalizations can be formulated. Despite its many desirable attributes, a clean and robust
graphene electrode is difficult to fabricate and is admittedly an unforgiving tool to employ. The
difficulty is further amplified by the complexity that accompanies a tunable VSFG setup. Thus,
experimental data of the graphene-water interface is scarce and in demand.
48,49
Surfactants with charged head groups or the exposed hydroxyl moieties of a mineral
surface have served well as charged interfaces subject to spectroscopic interrogation.
44,45,50–
5
52
However, charge tunability via these methods are unavoidably accompanied by the addition
of counterions and/or the addition of surfactants. Applying charge to the interface via these
methods are challenging, and the charge density is fundamentally limited by steric/packing
constraints. To estimate the electrostatic field of the interface, the pH or the surface coverage
must be known, and an appropriate model of the electrical double layer must be employed.
Additionally, only either a positively charged or negatively charged interface can be prepared at
a time, for a single experiment. Adopting a planar metallic electrode to study charged
interfaces demands that the interrogating light pass through the bulk of water to reach the
interface, then back out to a detector. Thin-cell experiments have been carried out to mitigate
absorption loss, however multiple reflections of light from the interfaces of a thin layer can lead
to complex interference effects, which must be considered and accounted for. Furthermore,
interactions with image charges of the electrode potentially complicates the analysis.
53–55
Graphene’s suitability to serve as a general charged interface stems from its simplistic,
repetitive, and planar structure. To its advantage over the metal electrode, graphene is
practically transparent, exhibiting a nearly wavelength-independent absorption of πα (2.3%) for
visible and near-infrared light.
56
This transparency allows light to access the aqueous interface
from the graphene side, in the reflection geometry, and so the problem of bulk absorption is
circumvented entirely. Additionally, interactions with image charge is minimized, since the
electrode is only one atomic layer thick.
Like a metal electrode, the graphene electrode can be doped with charge by “turning a
dial” on a potentiostat—by applying a voltage to the graphene electrode with respect to a
reference electrode. In this way, charge at the interface can be tuned at will from negative, to
6
neutral, to positive (and back again), in a single experiment. The charge concentration can be
tuned as high as 10
13
cm
−2
.
57–60
Neutral graphene is hydrophobic, whereas charged graphene is
hydrophilic, thus differences between a hydrophobic and hydrophilic interface can be readily
explored as well.
61
Graphene’s conductivity can be understood in terms of the unhybridizedp
z
valence electrons of its carbon atoms, which are oriented orthogonal to the atomic plane. The
p
z
electrons form an extended (delocalized) network of π -type ( π and π *) interactions. In
energy-momentum space, two inverted (Dirac) cones representing the valence and conduction (
π and π *) bands meet at their apex, at the K-point, such that there is no gap between the
bands.
59
Here, charge carriers experience a manifold of states that can be emptied/filled, that
can accessed upon being accelerated by an external field.
Raman spectroscopy is a quick and nondestructive method by which the quality and
charge density of graphene can be ascertained. Raman scattering is an electron-mediated
process where electromagnetic radiation exchanges vibrational quanta (phonons) with a
crystal.
62,63
The Raman spectrum of monolayer graphene (532 nm excitation) is characterized by
two main peaks, the G (1580 cm
-1
) and 2D bands (2690 cm
-1
).
64,65
The G-band is assigned to an
in-plane vibration and the 2D-band is assigned to an overtone of a different in-plane vibration.
When defects are present in graphene, a D-band (1350 cm
-1
) is found in its Raman spectrum,
assigned to the breathing modes of six-atom rings; in pristine graphene, the D-band is forbidden
by symmetry.
65–68
For single layer graphene, the 2D band is well described by a single Lorentzian,
and the ratio of intensities of the 2D to G-band correlates well with the number of layers (~2:1
for single layer graphene).
69
For greater than two layers, this 2D to G-band ratio is lost.
7
Additional interactions that are realized upon stacking of two or more graphene planes causes
the 2D band to split.
64
The charge density of graphene can be determined from the extent of the G-band shift
in the Raman spectrum of graphene, which is at a minimum for a neutral interface and (under
the right conditions) shifts linearly to higher frequency with increasing charge (electron or hole)
density.
57,60,70
Doping graphene with charge shifts its Fermi energy, decreasing the probability of
excited charge carrier recombination.
71
This causes photon perturbations to be non-adiabatic,
removing the Kohn anomaly and increasing the phonon energy for the G-peak, increasing its
frequency.
62,72
SFG Spectroscopy of Water at Charged Interfaces
Polarization, the dipole per unit volume, depends on the strength of the incoming field.
Driven by the electromagnetic field of light, charges in the material are forced to oscillate
rapidly, and thus a rapidly oscillating polarization is induced. This time-varying polarization can
act as a source for new components of the electromagnetic field, yielding an optical signal that
can be measured.
73,74
Δ
2
E–
n
2
c
2
∂
2
E
∂t
2
=
1
ϵ
0
c
2
∂
2
P
∂t
2
(1)
When the electromagnetic field of light oscillates in resonance with a material, dictated by its
electronic structure, the magnitude of the oscillations and thus the polarization is greatly
enhanced. The polarization can be expressed in the form of a power series, which depends on
the strength of the applied optical field.
P(t)=ϵ
0
[χ
(1)
E(t)+ χ
(2)
E
2
(t)+ χ
(3)
E
3
(t)+...+ χ
(n)
E
(n)
(t)] (2)
8
The optical susceptibilities, χ
(n)
,relate the optical field to the induced polarization. It should be
noted that this treatment assumes that the material responds instantaneously to the applied
field, which implies that the material is lossless and dispersionless, and so the susceptibilities
are given as constants in equation 2. In general however, the nonlinear susceptibility is not a
constant, it is a frequency-dependent complex quantity that relates the complex amplitude of
the polarization to that of the applied electric field.
74
The susceptibilities are tensorial in nature
(where χ
(1)
is a second-rank tensor, χ
(2)
is a third-rank tensor, and so on), allowing for the
polarization to possess directional components that are orthogonal to the driving field.
Microscopically, one source of this effect is charge-charge correlations. For weak incoming
fields, the polarization is often well approximated by the first, linear term (n=1) . For strong
fields, higher order terms become significant. Exposing a material to strong fields is analogous
to driving the motion of a spring past its intended limit, such that its motion is no longer well
described through a simple application of Hooke’s law, by a harmonic potential.
The surface may extend over several monolayers, the extent of which depends on the
parameters that affect the Debye length. Even-ordered (n=2, 4,6,...) nonlinear spectroscopies
have proven as powerful techniques, wherein the physics of an interface can be studied through
careful, clever control over the interrogating light. In this study of charged aqueous interfaces,
broadband vibrational sum frequency generation (VSFG) was routinely employed. SFG is a
second-order (n=2) nonlinear technique wherein two optical fields (E
1
,E
2
) of non-identical
frequencies overlap spatially and temporally at the interface.
1,75,76
P
SFG
(2)
(t)=ϵ
0
χ
(2)
(t)∘E
1
(t)E
2
(t) where ∘ denotes a convolution (3)
9
The signal that is generated in response travels in the phase-matched direction(k
SFG
=k
1
+k
2
) ,
carrying a frequency that is the sum of the two incident frequencies (ω
SFG
=ω
1
+ω
2
) . As a
result, the SFG signal is easily separated/filtered (spatially/spectrally) from the incident beams.
Figure 1: Sum frequency generation from a medium
in reflection and transmission geometry
For the broadband VSFG technique, several vibrational modes are excited simultaneously with a
short pulse that carries a broad range of frequencies, to induce a first-order polarization. A
second pulse that is relatively long and carries a narrow range of frequencies, “upconverts” the
first-order polarization to a second-order polarization.
10
Figure 2: Energy state diagram for the sum frequency generation process
The upconversion is efficiently achieved when the visible pulse is broad enough in the time
domain to overlap with the vibrational response (which typically decays on the order of a few
picoseconds).
Figure 3: Time domain picture, inducing a second-order
polarization
11
The visible upconversion pulse can be delayed slightly from the vibrational pulse (typically about
100 – 300 fs), such that the nonresonant response, which is nearly instantaneous and dies off
much faster than the vibrational response, is not efficiently upconverted and thus suppressed in
the SFG spectrum.
77
Another strategy to suppress the nonresonant response is to shape the
visible upconversion pulse in time, e.g., via an etalon, such that it is asymmetrically shaped: the
intensity rises sharply, then decreases gradually with time.
78
Some materials are rotationally
anisotropic with respect to the nonresonant contribution, and so yet another strategy to
minimize the nonresonant response is to adjust the orientation of these materials relative to the
polarized field of an incoming beam, such that the nonresonant signal is
minimized.
77,79,80
Employing one or more of these strategies can practically extinguish the
nonresonant component, relative to the resonant response.
For the broadband VSFG technique, The visible pulse is prepared such that it carries a
relatively narrow range of visible frequencies, relative to the vibrational pulse. This greatly
simplifies the SFG response, which can be modeled via the frequency-domain response
function. When the IR pulse carries a relatively broad range of frequencies, such that the visible
frequency distribution can be approximated by a δ -distribution, the convolution (∘) between
them returns the broad vibrational (infrared) frequency distribution.
81
I
SFG
(ω
SFG
)∝ϵ
0
|P
(2)
SFG
(ω
SFG
)|
2
=ϵ
0
|χ
(2)
(ω
SFG
,ω
IR
,ω
VIS
)E
IR
(ω
IR
)∘E
VIS
(ω
VIS
)|
2
∝ϵ
0
|χ
(2)
(ω
SFG
,ω
IR
,ω
VIS
)E
IR
(ω
IR
)|
2
=ϵ
0
|χ
(2)
(ω
SFG
,ω
IR
,ω
VIS
)|
2
I
IR
(ω
IR
)
(4)
However, since the visible pulse is not a δ -function in practice, the effect is that the SFG
spectrum is broadened by the upconversion. Typically, this broadening limits the spectral
12
resolution that can be achieved, which is dictated by the width of the visible pulse in the
frequency domain.
By choosing the upconversion pulse to be in the visible region of the electromagnetic
spectrum, the SFG signal is also visible (ω
SFG
=ω
VIS
+ω
IR
≈ω
VIS
) . Detection of a visible signal is
much less susceptible to noise, relative to detection of an infrared signal. Detectors that
operate in the visible regime, e.g., silicon detectors, are not sensitive to ambient light and
thermal noise due to the large band gap ( 1.12eV ≫k
b
T) which must be overcome in order to
convert the optical signal to an electrical one. In addition, the detector is typically cooled to
reduce the noise even further. A sensitive detector and a low signal-to-noise is essential
because the SFG signal, being a second-order response that is driven by the relatively few
number of molecules at the surface, is potentially extremely weak.
The sensitivity of the SFG technique to surfaces can be explained through an analysis of
the symmetries of the bulk and surface susceptibilities. The bulk phase of water is
centrosymmetric; the dipoles of water are, on average, randomly oriented and thus the bulk
susceptibility must be symmetric with respect to inversion.
χ
ijk,Bulk
(2)
=i χ
ijk,Bulk
(2)
(5)
In this notation, the subscripts i, j, k are dummy indices that represent the components of the
SFG, IR, and visible electric fields respectively, each of which can independently assume the x, y,
or z direction; i is the inversion operator. However, applying the inversion operator on a third-
rank tensor negates its value.
i χ
ijk,Bulk
(2)
=χ
−i−j−k,Bulk
(2)
=−χ
ijk,Bulk
(2)
(6)
13
Equations 5 and 6 can only be satisfied for χ
ijk,Bulk
(2)
=0 , thus the second-order SFG signal from
bulk water must be zero due to its centrosymmetry. Furthermore, the argument can be
extended to show that any even-ordered response must be zero for centrosymmetric media
(under the electric-dipole approximation).
82,83
An SFG signal is possible from the interface, or
wherever centrosymmetry is broken. An interface is fundamentally asymmetric, which
manifests as net ordering; water molecules at the surface necessarily lack intermolecular
hydrogen bonds and experience charge asymmetry.
The vibrational resonant response,χ
R
(2)
, can be modeled as a damped oscillator and
thus a Lorentzian line shape whereq indexes over the resonant vibrational modes, A
q
is the
amplitude, ω
0q
is the resonant frequency, γ
q
is the phase, and Γ
q
is the damping constant
(HWHM line width) of the resonant vibration. χ
NR
(2)
is the second order nonresonant response
and its phase is ϕ .
χ
(2)
(ω)=χ
NR
(2)
+χ
R
(2)
(ω)=| ( χ
NR
(2)
)|e
iϕ
+
∑
q
A
q
ω−ω
0q
−iΓ
q
e
iγ
q
(7)
The Lorentzian resonant response is complex and can be expressed in terms of its real
(dispersive) and imaginary (absorptive) components. The imaginary part of the SFG response,
due to its absorptive line shape, is much simpler to visualize and analyze. However, the real and
imaginary components are capable of interfering and contributing to the spectral intensity in a
nontrivial way, and so a spectral analysis at the intensity level must be wary of
oversimplification. In fact, a valid analysis may require that the relative phases be already
known through prior theoretical and/or experimental means.
14
χ
R
(2)
(ω)=χ
R,Real
(2)
(ω)+ χ
R,Imag
(2)
(ω )=
A(ω−ω
0
)
(ω−ω
0
)
2
+Γ
2
+i
AΓ
(ω−ω
0
)
2
+Γ
2
(8)
Figure 4: Real and imaginary parts of the Lorentzian lineshape
function
The optical heterodyne detection technique can be employed to extract the real and imaginary
parts through experimental means, wherein the phases are extracted via a Fourier analysis of
the interference fringes generated from the superposition of the SFG signal and a reference
signal of known phase.
50,84
In the homodyne detection scheme, only the intensity (modulus
square) of the signal field is measured, and thus the real and imaginary parts can not be
obtained without prior experimental or theoretical knowledge of the relative phases in the
response.
46–48,85
Interactions (interference) between vibrational modes are modeled through
their phases, γ
q
. The resultant superposition between densely packed vibrational modes is not
typically trivial to predict.
46,47
It should be noted, that the line shape is best represented by a
Voigt profile, which is a line shape obtained from the convolution between a Lorentzian and
Gaussian profile, allowing for homogenous and inhomogeneous broadening, respectively.
86–88
In
15
some cases, a Lorentzian line shape approximates the response reasonably well, allowing for
the physics of interest to be extracted simply and faithfully.
48,89,90
Two-dimensional SFG can be
applied to assess the degree of inhomogeneity based on an analysis of the two-dimensional line
shapes.
87,91
In VSFG, the IR excitation is in resonance with the medium, promoting the system to an
excited vibrational state. Thus, for the medium to be VSFG active, the vibrational selection rule
must be fulfilled: there must be a change in the dipole moment,μ , with respect to a change in
the vibrational coordinate. The IR excitation is followed by a visible nonresonant excitation,
which promotes the system to a virtual excited state. This step imparts a dependency of the
VSFG process on the Raman selection rule: that the Raman polarizability,α , must change with
respect to the vibrational coordinate. In fact, the amplitudeA
q
of the response is proportional
to the product of the IR transition dipole moment and the Raman transition probability.
92,93
A
q
∝
∂μ
∂q
×
∂α
∂q
(9)
In other words, to generate a VSFG signal, the vibration must be simultaneously IR and Raman
active. By the mutual exclusion rule, which states that the vibrational normal modes of
molecules that posses inversion symmetry can not be both IR and Raman active,
centrosymmetric systems are not SFG active.
94
Charge at the interface manifests as net ordering that persists into the bulk, the extent
of which is quantified by the Debye length. For pure water, which lacks the ionic strength to
shield the interfacial field effectively, net ordering can persist up to ~1 μm.
47
Thus, many
monolayers can contribute to the VSFG signal, complicating the analysis significantly. The first
16
group to observe and report this effect was Eisenthal’s in 1992: they noticed an increase of the
SHG signal at the water-silica interface, when the pH of the solution was tuned (-SiOH/-SiO
-
)
such that the interface was increasingly charged.
95
To account for this effect, they included a
third-order contribution to the signal (for the case where the static orienting interaction μE
0
is
less than the thermal energykT ):
95,96
P
2ω
(3)
=χ
(3)
E
0
(z)E
ω
E
ω
(10)
WhereE
0
(z) is the static electric field due to the interface, andz is the spatial coordinate that
extends into the bulk. Effectively, the static field emanating from a charged interface breaks
centrosymmetry deeper into the bulk, resulting in a third-order polarization that contributes to
the total SHG signal.
95
Integrating from the surface(z=0) to infinitely deep into the bulk of water(z=∞) , where the
potential atz=∞ is defined as zero(Φ(∞)=0) yields:
95
P
2ω
(3)
=χ
(3)
E
ω
E
ω
Φ(0) (11)
Where Φ(0) is the potential at the interface(z=0) .
Thus, the total second harmonic field can be expressed as:
95
E
2ω
∝P
2ω
=χ
(2)
E
ω
E
ω
+χ
(3)
E
ω
E
ω
Φ(0) (12)
Shen and Tian et al., carried out a set of phase-sensitive measurements on the water-
fatty acid interface (a lignoceric acid monolayer, C
23
H
47
COOH). For this interface, like the silica
interface, interfacial charge was tuned by adjusting the pH of the solution (-COOH/-COO
-
). Shen
and Tian model the effective SFG response,χ
S,eff
(2)
, as a summation of the so-called bonded-
17
interface layer (BIL) and a diffuse layer (DL). The BIL layer encompasses the first few monolayers
of the surface, where water forms strong interface-specific bonding networks; this is the surface
response of interest, χ
S
(2)
. The diffuse layer (DL) lies below the BIL, its effective length is
characterized by the Debye length. In the DL, water adopts a bulk-like configuration, which can
be influenced by the long-range DC field of the surface charge and by screening ions. The
response from the DL, χ
S,DL
(2)
, is typically an undesirable component that muddies the analysis
of an interface; it must be known in order to extract the second-order response of the interface
from the effective response.
χ
S,eff
(2)
=χ
S
(2)
+ χ
S,DL
(2)
(13)
χ
S,DL
(2)
=
∫
0
∞
χ
B
(3)
⋅^ zE
0
(z')e
iΔk
z
z'
dz'=χ
B
(3)
⋅^zψ
(14)
Δk
z
is the phase-mismatch of the reflected SFG wave
For variously charged interfaces, they isolated χ
B
(3)
and showed that it was always the same.
Moreover, this response (broad, double-humps at ~3220 and 3450 cm
-1
) is reminiscent of the
OH-stretching response observed in the IR and Raman spectra of (bulk) water, lending support
to the notion that a bulk-like ensemble is responsible for this component.
85,97
Additionally, a
molecular dynamics study carried out by Nagata et al., of the silica-water interface predicts that
the bulk-component is linearly dependent on the applied potential.
98
With contributions such as those from Shen and Tian et al.,
85
Nagata et al.,
98
and a
formalism of absorptive-dispersive mixing recently developed by Geiger et. al.,
46,47
the
interfacial-specific response can be disentangled from the deeper, bulk-like part of the
response. The formalism of absorptive-dispersive mixing allows for mixing between the second-
order and the field-induced third-order responses. Absorptive-dispersive mixing is
18
accomplished through a phase factor that depends only on experimental parameters (which, for
pure water, can be readily obtained), namely the Debye length and the phase mismatch.
I
SFG
=
|
χ
NR
(2)
+
∑
ν=1
n
χ
res,ν
(2)
e
iγ
ν
+
κ
√
κ
2
+(Δk
z
)
2
e
iϕ
χ
(3)
Φ(0)
|
2
(15)
ϕ =arctan(Δk
z
/κ )
Where Δk
z
and κ are the inverse coherence length and the inverse Debye length, respectively
44
(16)
The phase factor and the formalism of absorptive-dispersive mixing can be understood as a
means by which optical interference from multiple resonances originating from several
molecular layers are taken into account. Under conditions of resonance, such as when an
excitation source is in resonance with the OH-stretching vibration water, the second and third-
order imaginary (absorptive) components are nonzero; as such, they can interfere with the real
(dispersive) components of the response and with each other. In this scenario, absorptive-
dispersive mixing is crucial to reconstructing real-world line shapes from theory, or for isolating
the interfacial component of the response from experimental spectra. To isolate the interfacial
χ
S
(2)
response from graphene-water SFG spectra, a fitting procedure utilizing the absorptive-
dispersive formalism and knowledge of the χ
B
(3)
component from prior experimental and
theoretical sources have been employed. The details of this procedure are provided in the
methodology section. In summary, with the absorptive-dispersive phase factor known,
47
with
an estimate of the bulk component
85
which is expected to scale linearly with the applied
potential, and with knowledge (from prior research efforts) of the relative phases of the various
19
Lorentzian components, the interfacial-specific component of the response is that which yields
the best fit to the VSFG spectrum.
Miller’s Rule
Novel experimental evidence (provided in the results section of this thesis) calls into
question the validity of treating interfacial water as a simple dielectric medium. This is based
on an observed asymmetry in the response of interfacial water to applied charge, and a failure
to satisfy Miller’s rule.
99
The addition of an anharmonic potential to the damped oscillator of the Lorentz model
of the atom yields a classical description of the second-order nonlinear optical susceptibility (for
noncentrosymmetric media) that is useful to introduce, and provide a reasonable basis for
Miller’s empirical rule. The cost of treating the system classically is that the anharmonic
oscillator will only resonate a single frequency. The following arguments, which provide a
reasonable basis for Miller’s rule, are a distillation from a chapter in Boyd’s text.
74
The equation
of motion for an electron that is bound to the nucleus by a spring can be solved via a
perturbative expansion:
¨
~
x+2γ
˙
~
x +ω
0
2
~
x +a
~
x
2
=
−λe
~
E(t)
m
(17)
~
x is the charge position, γ is the damping constant, ω
0
is the resonance frequency, a
quantifies the anharmonicity of the potential, m is the mass of the electron (the reduced mass
of the electron-nucleus system),e is the electron charge, and λ is the parameter of the
perturbative expansion which ranges continuously from zero to one and characterizes the
20
strength of the interaction. The
~
denotes that the quantity varies rapidly with time.
~
E(t) is
the applied field of the form:
~
E(t)=E(ω
1
)e
iω
1
t
+E(ω
2
)e
iω
1
t
+c.c. (18)
If the applied field is sufficiently weak, the nonlinear term is much smaller than the linear term
for a displacement
~
x , and the solution to equation 17 can be expressed in the form of a power
series (perturbative expansion):
~
x=λ
~
x
(1)
+λ
2
~
x
(2)
+λ
3
~
x
(3)
+… (19)
Inserting equation 19 into equation 17, and grouping terms by powers of λ , yields the following
equations:
λ :
¨
~
x
(1)
+2γ
˙
~
x
(1)
+ω
0
2
~
x
(1)
=
−e
~
E(t)
m
(20)
λ
2
:
¨ ~
x
(2)
+2γ
˙ ~
x
(2)
+ω
0
2
~
x
(2)
+a[
~
x
(1)
]
2
=0 (21)
Note that the above groupings of terms are shown up to (but go beyond) λ
2
, since that is all
that is required to sufficiently describe the second-order response. In order for equation 19 to
be a solution to equation 17, equations 20 and 21 must satisfy the equation separately. The
solution to equation 20, which is simply the linear Lorenz equation, is known as:
~
x
(1)
(t)=x
(1)
(ω
1
)e
−iω
1
t
+x
(1)
(ω
2
)e
−iω
2
t
+c.c. (22)
Where the amplitudesx
(1)
(ω
j
) are the familiar Lorentzian functions:
x
(1)
(ω
j
)=
−e
m
E(ω
j
)
ω
0
2
−ω
j
2
−2iω
j
γ
=
−e
m
E(ω
j
)
D(ω
j
)
(23)
21
Squaring
~
x
(1)
(t) and substituting the sum frequency term,x
(1)
(ω
1
)x
(1)
(ω
2
)e
−i(ω
1
+ω
2
)t
, into
equation 21 yields the following equation:
¨
~
x
(2)
+2γ
˙
~
x
(2)
+ω
0
2
~
x
(2)
=−a(
e
m
)
2
E(ω
1
)e
−iω
1
t
D(ω
1
)
E(ω
2
)e
−iω
2
t
D(ω
2
)
(24)
The solution to equation 24 is:
~
x
(2)
(t)=x
(2)
(ω
1
+ω
2
)e
−i(ω
1
+ω
2
)t
(25)
Substitution of equation 25 into equation 24 yields the amplitude of the sum-frequency
response:
x
(2)
(ω
1
+ω
2
)=
−2a(
e
m
)
2
E(ω
1
)E(ω
2
)
D(ω
1
+ω
2
)D(ω
1
)D(ω
2
)
(26)
The linear and nonlinear (SFG) susceptibility is defined by:
P
(1)
(ω
j
)=ϵ
0
χ
(1)
(ω
j
)E(ω
j
) (27)
P
(2)
(ω
1
+ω
2
)=2ϵ
0
χ
(2)
(ω
1
+ω
2
,ω
1
,ω
2
)E(ω
1
)E(ω
2
) (28)
The linear and nonlinear (SFG) contribution to the polarization by the damped oscillator is given
by:
P
(1)
(ω
j
)=−Nex
(1)
(ω
j
) (29)
P
(2)
(ω
1
+ω
2
)=−Ne x
(2)
(ω
1
+ω
2
) (30)
WhereN is the number density of atoms.
22
Setting equation 27 equal to equation 29, substituting
x
(1)
(ω
j
)
E(ω
j
)
for
−e
mD(ω
j
)
via equation 23
yields an expression for the linear susceptibility; setting equation 28 equal to equation 30 and
substituting
x
(2)
(ω
1
+ω
2
)
E(ω
1
)E(ω
2
)
for
−2a(
e
m
)
2
D(ω
1
+ω
2
)D(ω
1
)D(ω
2
)
via equation 26 yields an expression for
the nonlinear (SFG) susceptibility, respectively:
χ
(1)
(ω
j
)=
−Nex
(1)
(ω
j
)
ϵ
0
E(ω
j
)
=
Ne
2
ϵ
0
mD(ω
j
)
(31)
χ
(2)
(ω
1
+ω
2
,ω
1
,ω
2
)=
−Ne x
(2)
(ω
1
+ω
2
)
2ϵ
0
E(ω
1
)E(ω
2
)
=
Ne
3
a
m
2
ϵ
0
D(ω
1
+ω
2
)D(ω
1
)D(ω
2
)
(32)
Inserting equation 31 into equation 32 to restate the complex denominator functions,D(ω
j
) ,
in terms of the linear susceptibility, and rearranging leads to the following equation:
χ
(2)
(ω
1
+ω
2
,ω
1
,ω
2
)
χ
(1)
(ω
1
+ω
2
)χ
(1)
(ω
1
)χ
(1)
(ω
2
)
=
aϵ
0
2
m
N
2
e
3
(33)
Millers rule was formulated from the experimental observation that the ratio in equation 33 is
nearly constant for all noncentrosymmetric crystals. This is reasonable because ϵ
0
,m , ande
are fundamental constants, andN is about the same for all condensed matter (~ 10
22
cm
−3
).
The magnitude ofa can be estimated by setting the linear and nonlinear restoring forces equal
to each other; which are expected to be comparable when the displacement of the electron
from its equilibrium position is approximately equal to the size of the atom, or the lattice
constantd :
mω
0
2
d=mad
2
⇒a=
ω
0
2
d
(34)
23
ω
0
2
andd are approximately the same for many crystals, which explains Miller’s observation
that the ratio of the nonlinear to linear susceptibilities were approximately constant.
Orientational Analysis of Water and the “Free-OH”
An interface is responsible for asymmetry with respect to the forces that water
molecules at the interface experience. This asymmetry manifests as net ordering of dipoles at
the interface. At the air-water interface, a narrow distribution of orientation angles (with
respect to the surface normal) of less than 15° has been reported by Wei Gan, et al. based on a
thorough orientational analysis of VSFG spectra of water, collected in a variety of experimental
configurations (for various incoming beam angles and polarization combinations of the SFG,
visible, and IR beams).
100
In addition to this contribution, a detailed resource for the (molecular
to lab frame) transformation required to carry out an orientational analysis is provided by Chiaki
Hirose, et al.
101
The orientational analysis carried out in this thesis is based heavily, though not
entirely, on these and other contributions.
100–107
Since the optical field must drive charges at resonance to elicit an efficient VSFG
response, this creates a dependency of the VSFG signal on the components of the optical field
that are compatible with the tensorial susceptibility of the material. As a result, the spectral
response can depend dramatically on the incoming angles of incidence and the polarizations of
each of the beams.
100,101
For an assumed orientational distribution and point-group symmetry of
the vibrational species of interest, with the appropriate elements of the hyperpolarizability
tensor known, with knowledge of the experimental optical parameters (e.g., incoming beam
24
angles and polarizations) and the refractive indices for the various frequencies of interest, a
transformation (from the molecular frame) to the laboratory frame can be carried out to yield a
plot of SFG intensity versus the ensemble-averaged orientation of water at the interface.
101
This
procedure allows for assumptions of the orientational distribution and the symmetry to be
tested against experimental data. The orientational distribution of water at the interface, and
how it may evolve with charge is still a subject of ongoing study and contention.
100,108,109
The hyperpolarizability β
i
’
j
’
k
’
(2)
is the molecular-level second-order electric susceptibility.
In other words, the hyperpolarizability is the microscopic analogue of the macroscopic
susceptibilityχ
ijk
(2)
. The hyperpolarizability can be obtained through a combination of Raman
depolarization measurements, the bond polarizability derivative model, and through ab initio
calculations.
100,102,104,110–115
Being that χ
ijk
(2)
is a third rank tensor, there are 27 elements of the
nonlinear susceptibility. The indices of the susceptibility refer to the polarizations of the SFG
signal, the visible beam, and the IR beam, respectively. Fortunately, it is often the case that the
susceptibility tensor can be simplified significantly based on the symmetry of the system. With
the plane of the surface defined by the xy-plane, the orthogonal xz-plane i.e., the plane of
incidence, is defined by the surface normal and beam propagation vectors. By the same logic
applied in section 2.3, where the bulk (isotropic) second-order susceptibility was shown to be
necessarily zero, each tensor element of the susceptibility can be evaluated via equations 5 and
6 to determine which are necessarily zero. The result of this evaluation forC
∞v
symmetry is
that only the nonlinear susceptibility elements which contain an even number of x or y
components can possibly be nonzero. Thus, for an azimuthally isotropic surface (C
∞v
) , there
are only four unique elements of the susceptibility tensor.
25
χ
xxz
(2)
=χ
yyz
(2)
(35)
χ
xzx
(2)
=χ
yzy
(2)
(36)
χ
zxx
(2)
=χ
zyy
(2)
(37)
χ
zzz
(2)
(38)
Elements of the hyperpolarizability tensor (β
i’j’k’
) in the molecular frame (i’,j’,k’=a,b,c)
are related to the macroscopic susceptibility tensor elements(χ
ijk
) in the laboratory frame
(i,j,k=x,y,z) through an Euler transformation.
101,102,104
χ
ijk
(2)
=N
s ∑
i'j'k'
⟨R
ii'
R
jj'
R
kk'
⟩ β
i'j'k'
(2)
(39)
N
s
is the number density of the vibrational species of interest, the rotational matrices,R , are
ensemble-averaged ⟨ ⟩ over the molecular orientational distributionf (θ,ϕ,ψ) :
100
⟨R⟩=
∫
0
π
∫
0
2π
∫
0
2π
R(θ,ϕ,ψ )f (θ,ϕ,ψ)sinθdθdϕdψ
∫
0
π
∫
0
2π
∫
0
2π
f (θ,ϕ,ψ )sinθdθdϕdψ
(40)
A simplified expression for the tilt angle θ (with respect to the surface normal) is obtained
when the response is assumed to be anisotropic with respect to the remaining two Euler angles,
though this is not always a valid simplification that can be made.
101,102,104
The VSFG spectrum of water in the SSP and PPP polarization configurations (co-
propagating, reflection geometry) can be related to the laboratory-frame nonlinear
susceptibilities through the following equations:
χ
eff,SSP
(2)
=L
yy
(ω
SFG
)L
yy
(ω
VIS
)L
yy
(ω
IR
)sin(β
IR
)χ
yyz
(41)
26
χ
eff,PPP
(2)
=−L
xx
(ω
SFG
)L
xx
(ω
VIS
)L
zz
(ω
IR
)cos(β
SFG
)cos(β
VIS
)sin(β
IR
)χ
xxz
−L
xx
(ω
SFG
)L
zz
(ω
VIS
)L
xx
(ω
IR
)cos(β
SFG
)sin(β
VIS
)cos(β
IR
)χ
xzx
+L
zz
(ω
SFG
)L
xx
(ω
VIS
)L
xx
(ω
IR
)sin(β
SFG
)cos(β
VIS
)cos(β
IR
)χ
zxx
+L
zz
(ω
SFG
)L
zz
(ω
VIS
)L
zz
(ω
IR
)sin(β
SFG
)sin(β
VIS
)sin(β
IR
)χ
zzz
(42)
L
ii
(ω
i
) are the tensorial Fresnel factors
92,102,116
and β
i
are the angles of incidence/reflection.
Note that based on the equations above, the behavior of the PPP response with changing
experimental conditions may not be trivial, since it is a complex summation of four terms. In
fact, the experimental configuration can be tailored such that the response is optimally sensitive
to orientational changes.
100
In the VSFG spectrum of the air-water interface, a narrow peak at approximately 3700
cm
-1
for H
2
O (2700 cm
-1
for D
2
O) is observed. This narrow peak has been assigned to the so-
called “free-OH” (or “free-OD”, respectively); it is a single vibrational stretching mode belonging
to an -OH moiety which points outward from the water phase, protruding into the air phase and
rendering it unable to hydrogen bond.
117–121
This is in contrast to the broad response originating
from the relatively red-shifted non-free OH-stretching modes, observed from approximately
3000 to 3600 cm
-1
. The non-free response is red-shifted since hydrogen bonding weakens its
internal OH-bond, and is energetically broad because the number and strengths of hydrogen
bonds vary over a broad continuum in liquid water. The “free” or non-hydrogen-bonded
stretching mode can only be observed at the surface, where the OH-moiety is abundant
because the interface is unable to provide a hydrogen-bonding interaction. This ensures that
the spectral response from the free-OH originates from molecules at the topmost monolayer,
where approximately 30% of water molecules at the interface are thought to be
“free”.
121
Analysis of the free-OH is relatively much simpler compared to its hydrogen-bonded
27
analogue, since its response is spectrally isolated and can be modeled faithfully with a single
Lorentzian function.
Figure 5: SSP and PPP VSFG spectra of the air-water interface
At mineral or surfactant interfaces, the free-OH response is lost entirely, due to hydrogen
bonding with the interface. For the graphene-water interface, the “free” response is observed
when the interface (the graphene electrode) is negatively-charged. In the same spirit as the
experimental configuration analyses carried out by Gan et. al.,
100
orientational information was
extracted from the graphene-water interface, accomplished through analyses of VSFG spectra
that differ with respect to the interfacial field that was applied (instead of changing the optical
angles of incidence) when they were collected. Essentially, the ensemble-averaged orientation
28
of water shifts in response to an applied interfacial field; the evolution of the spectral response
(in both the SSP and PPP experimental configurations) is observed for a range of applied fields
(various orientations) and compared to a calculated prediction. Since the calculated
orientational response depends on the chosen orientational distribution function, various
distributions can be tested and potentially invalidated, provided that the predicted change in
the SFG intensity with respect to orientation angle does not conform to experimental evidence.
By interacting with the permanent dipole of water(μ⋅E) , the static field can induce
molecular reorientation via torque. The orientational free energyG(θ ) is given in the following
expression:
e
G(θ )/k
B
T
=f (θ )
Wheref (θ ) is a normalized orientational distribution function of the ensemble
(43)
The free energy orienting potential,O(θ ) , is an orienting potential that takes into account the
field-induced torque.
O(θ )=G(θ )−μ⋅E(z)
Where μ is the permanent dipole moment and E is the static electric field
(44)
The minimum of the free energy orienting potential corresponds to the most energetically
stable orientation angle of the ensemble. As an example, a Gaussian orientational distribution
leads to a harmonic orientational free energy. Theμ⋅E term imparts anharmonicity to this
potential, and the width of this potential can be correlated with the susceptibility of the
ensemble to reorientation. For example, a very narrow potential describes an ensemble that is
quite rigidly oriented. Intuitively, the distribution is expected to narrow as the magnitude of the
static field is increased, though the extent of this effect is currently unknown. Between the
29
graphene electrode and the water phase, theoretical studies suggest the presence of a ~3
Angstrom gap.
61,122
With this suggestion, the field at the interfaceE(0) can be estimated by
treating the graphene layer as an infinite plane of charge.
E(0)=
σ
2ϵ
0
ϵ
With ϵ=1 , and σ is the charge density cm
−2
(45)
In the studies presented here, fields up to about - 0.2 V/Angstrom were applied, corresponding
to an electron charge density of about 2×10
13
cm
−2
. Several orientational distributions were
tested, and the distribution width was determined via a self-consistent procedure, the details of
which are provided in the methodology section.
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Interfacial Water is Exponential’. Phys. Rev. Lett. 123, (2019).
110. Guyot-Sionnest, P ., Hunt, J. H. & Shen, Y . R. Sum-frequency vibrational spectroscopy of a Langmuir
film: Study of molecular orientation of a two-dimensional system. Phys. Rev. Lett. 59, 1597 (1987).
111. Hirose, C., Akamatsu, N. & Domen, K. Formulas for the analysis of surface sum-frequency
generation spectrum by CH stretching modes of methyl and methylene groups. J. Chem. Phys. 96,
997–1004 (1992).
112. Wu, H., Zhang, W. K., Gan, W., Cui, Z. F. & Wang, H. F. An empirical approach to the bond
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113. Zhang, D., Gutow, J. & Eisenthal, K. B. Vibrational spectra, orientations, and phase transitions in
long-chain amphiphiles at the air/water interface: Probing the head and tail groups by sum
frequency generation. J. Phys. Chem. 98, 13729–13734 (1994).
37
114. Bell, G. R., Li, Z. X., Bain, C. D., Fischer, P . & Duffy, D. C. Monolayers of
Hexadecyltrimethylammonium p-Tosylate at the Air−Water Interface. 1. Sum-Frequency
Spectroscopy. J. Phys. Chem. B 102, 9461–9472 (1998).
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116. Feller, M. B., Chen, W. & Shen, Y . R. Investigation of surface-induced alignment of liquid-crystal
molecules by optical second-harmonic generation. Phys. Rev. A 43, 6778 (1991).
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Phys. Rev. Lett. 72, 238 (1994).
118. Brown, M. G., Raymond, E. A., Allen, H. C., Scatena, L. F. & Richmond, G. L. The Analysis of
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38
Chapter 2: Methodologies
The following subsections of this chapter details the experimental methods relevant to this
particular study of the graphene-water interface, the results of which are provided in the subsequent
chapter. Achievements were realized via the collaboratory efforts of two research groups at the
University of Southern California, led by Alexander Benderskii and Stephen Cronin. Briefly, this project
demanded the successful fabrication of the graphene electrode, and the application of electrochemical
and nonlinear spectroscopic techniques. Like most tasks worth carrying out, it is much easier said than
done. There were in fact many failures; moving the project forward to the point where the entire project
came together to yield intriguing experimental evidence that was reproducible, required the
development and application of several interdisciplinary methods, control experiments, and practical
“tweaks”. Every control or investigatory experiment supported the notion that we were indeed
influencing interfacial water by doping graphene with charge, the manifestation of which was observable
through spectroscopic means. Further efforts are underway by my colleagues, to better understand and
improve the processes detailed here. Some of the mathematical methods employed here can surely be
improved by adding complexity, or by including theoretical data that may become available in the future;
in some cases, the methodologies given below can be viewed as a first-order attempt to extract physical
meaning from the data, or is provided to demonstrate a potential method that may prove fruitful with
better or more background information. However, the methodologies employed here were in fact
tweaked many times based on control experiments and on the their ability to yield reproducible results
that were compatible with literature. I would not dare to presume that the collection of methods
detailed here are optimal, they are just the best that we have been able to achieve so far.
39
Fabrication of the Graphene Electrode:
Graphene must be stabilized on a substrate to prevent it from folding-in on itself. The substrate
also provides the rigidity needed to secure the graphene electrode in a sealed electrochemical flow-cell.
The spectroscopic dimension of this endeavor demands that the substrate be transparent to the
wavelengths of light that are of interest. Thus, CaF
2
was chosen as the substrate, though none others
were tested for viability.
Prior to transferring the graphene, two gold strips (50 nm thick) were deposited onto a
transparent CaF
2
window (25.4 mm diameter × 1 mm thickness, OptoCity Inc.) by electron-beam
evaporation using a shadow mask. The gold strips provide macroscopic contacts through which voltage is
applied, and the resistance is measured across the graphene electrode (typically 1 – 2 kΩ). Monolayer
graphene was grown by chemical vapor deposition (CVD) on copper foil at 1000
o
C in methane and H
2
gas at a reduced pressure of 1-1.5 Torr.
1
After growth, the copper foil was spin-coated with PMMA-A6 at
2000 rpm for 45 seconds and then baked at 150 ℃ for 5 minutes. The copper foil was etched away, the
graphene (1 cm × 1.5 cm) with PMMA was “scooped” out, rinsed with 10% HCl and DI water, and
transferred to the CaF
2
window.
2
Adhesion of graphene to CaF
2
was accomplished by baking the
electrode at 120 °C for 5 minutes.
3
The electrode must be fabricated as cleanly as possible, since VSFG
40
Figure 6: The Graphene Electrode
measurements are extremely sensitive to contaminants. The residual PMMA layer was removed by
placing the sample in an acetone bath for five minutes. After extracting the sample from the acetone
bath, it was rinsed profusely with isopropyl alcohol and then doubly-distilled water. Newton’s rings were
observed on the sample when it was not soaked or rinsed well enough to sufficiently remove PMMA. It
was also noticed that the reproducibility of the sample degraded in all measurable aspects and appeared
to correlated with the state of the quartz tube that houses the growth process; over time the quartz
tube would become yellowish due to the deposition of copper. Though cleaning the quartz tube was
attempted, reproducibility was restored only when the quartz tube was completely replaced.
The Electrochemical Cell
The monolayer graphene electrode, supported on a CaF
2
substrate, forms the top window of the
electrochemical flow-cell, with graphene facing the water (D
2
O). D
2
O was chosen over H
2
O because the
OH-stretch frequencies were not accessible via the tunable IR source of our VSFG setup. A glassy carbon
counter electrode (SPI Supplies) formed the bottom of the sandwich-type flow-cell, held together by
friction between two circular aluminum plates. The glassy carbon counter electrode was chosen
because it is known to be reasonably inert, chemically and electrochemically. The top and bottom
electrodes are separated by an 8 mm thick cylindrical Teflon spacer (Fig. 1a, left panel). The Teflon
spacer contains two (input and output) ports that can mate with tubing, providing a channel for water
flow. At both ends of the Teflon spacer, machined grooves house Teflon-encapsulated Silicone O-rings
(The O-ring Store, TES018); the Silicone cores provide the flexibility needed to serve as a sealing gasket,
while the outer Teflon is robust and can be cleaned aggressively. The top aluminum plate has an opening
of about 0.8” in diameter, which permits light to pass into and out of the cell. No electrolyte was added
to D
2
O in our experiments. The Teflon spacer and O-rings were cleaned with piranha solution, a 3:1 (by
volume) concentrated sulfuric acid to 30% H
2
O
2
. In the two-terminal configuration, the graphene and
41
glassy carbon electrodes were connected to the positive and negative terminals of a voltage source
(Keithley Instruments, Model 2400), respectively. In the three-terminal configuration the graphene,
glassy carbon, and Ag/AgCl electrodes served as the working, counter, and reference electrodes
respectively, and were connected to a potentiostat (Gamry Instruments, Reference 600). Thin (0.0005”)
ribbon wire (Omega, Chromel/Alumel) serve as leads to the electrodes, that are clamped in place by
frictional forces provided by the sandwich mechanism of the cell. A thicker ribbon wire, or cylindrical
wire, would otherwise create leaks in the cell. To minimize voltage drops across the graphene strip,
leads from the positive terminal were in contact with both gold strips on the sample. The reference
electrode was inserted through the side wall of the Teflon spacer, immersed in D
2
O between the working
and counter electrodes.
A peristaltic pump was incorporated to continuously flow water through the electrochemical
cell. The peristaltic pump minimizes the potential for contamination since no part of the pump is in
direct contact with water. A cautionary tale: employing the wrong tubing or the degradation of the
42
Figure 7: A schematic of the electrochemical cell (3-terminal configuration).
tubing (which can be accelerated via the pumping action of the peristaltic pump) can lead to the leaking
of contaminants into the water. Fresh tubing was utilized every experiment (9449K41, McMaster-Carr,
high-purity Versilon soft tubing). About 500 mL of doubly-distilled water was allowed to flow through
the cell and the tubing to rinse them, then that water was discarded. The cell was then filled with fresh
D
2
O and the voltage was set to the highest (positive and negative voltage) value, such that the
electrochemical current was below ±300 μA, typically at about ±5 V vs. glassy carbon (for about 15
minutes at each voltage). The strategy behind this step is to electrochemically drive any contaminants
off the electrodes, into the water which is then discarded, though admittedly the efficacy of this step has
not been proven and it may not be necessary. Electrochemical currents that exceeded ±500 μA tended
to irreversibly affect the electrodes, such that subsequent measurements were not reproducible or there
was no difference in measurements that were collected at variously applied voltages. Additionally,
following high electrochemical currents, a brownish residue could be found on the surface of the glassy
carbon electrode. Prior to each experiment, the glassy carbon electrode was polished with alumina
powders of various grit in figure-eight patterns, in accordance with instructions that accompanied an
electrode polishing kit (CHI120, CH instruments Inc), to manually remove any electrochemically induced
residues, and to expose a fresh surface.
Raman Spectroscopy
Raman spectra of the graphene electrode under applied electrochemical potentials were
collected using a Renishaw micro-Raman spectrometer. The measurement was conducted using a
backscattering geometry with a 50 µW, linearly-polarized 532 nm laser beam focused to 1 μm in
diameter. The collected Raman scattered light was dispersed onto a charged-coupled device (CCD) array
detector by a single-grating monochromator with a spectral resolution of approximately 0.5 cm
-1
.
Voltage-induced shifts in the Raman frequency of the G-band were collected using both two-terminal
43
and three-terminal configurations. In these electrochemical measurements, the graphene electrode was
in contact with D
2
O (99.9% purity, Cambridge Isotope Laboratories Inc.), and a 40X lens was immersed in
a DI-water reservoir above the sample. To protect the lens from electrolyte, a 13 µm thick Teflon sheet
(American Durafilm Inc.) was used to cover the lens.
4
VSFG Spectroscopy
A regeneratively-amplified Ti:sapphire laser system (Coherent Legend Elite Duo; 14 W, 5 kHz) was
pumped by an Nd:YLF laser system (Coherent Evolution; 10 ns, 60 W, 532 nm, 5 kHz) and “seeded” by a
femtosecond Ti:sapphire laser system (Coherent Micra; ~50 fs, 400 mW, 809 nm, 80 mHz) that was
stretched, amplified, and split into two paths. In one path the 809 nm light (8 W) was recompressed by a
pair of gratings to ~50 fs (measured via a home-built single-shot autocorrelator) and delivered to an
optical parametric amplifier (TOPAS-C Light Conversion) and noncollinear difference frequency generator
(NDFG Light Conversion) assembly, yielding tunable femtosecond mid-IR pulses. The other path of light
(6 W) was compressed externally and delivered to a 4f-stretcher. At the focal plane of the 4f-stretcher, a
narrow band region (806 nm centered, FWHM = 6-8 cm
-1
, ~2 ps) was selected spatially using a
mechanical slit. The pulsed visible (~25 mW, FWHM = 6-8 cm
-1
, ~2 ps) and IR beams (~12 mW, FWHM =
300-375 cm
-1
, ~50 fs) co-propagated in the plane of incidence, were focused to 250 μm and 200 μm
respectively, and overlapped (spatially and temporally) at the graphene-water interface to generate VSFG
signal. The average powers and incoming angles of the visible and the IR beams were 25 mW and 12
mW, and 68
°
and 60
°
from the surface normal, respectively. The IR beam path was purged of
atmospheric CO
2
via a purge-gas generator (Parker Balston, Model: 75-62). The polarizations of the
visible, IR, and SFG beams were adjusted using half-wave plates (Visible: zero-order quartz half-wave
plate, 800 nm, CVI Melles Griot; IR: zero-order CdSe half-wave plate, 1000-19000 nm, 5 mm thick,
Alphalas; SFG: zero-order quartz half-wave plate, 670 nm, CVI Melles Griot). An analyzer (polarizing
44
beamsplitter cube, extinction ratio > 500:1) blocked P-polarized SFG signal to eliminate polarization
contamination. The SFG signal was focused at the entrance slit of a single-grating monochromator
(Princeton Instruments Acton SP2500 monochromator), which was almost fully shut such that the signal
could pass unobstructed into the monochromator, while also restricting entry of background ambient
light. The signal was dispersed onto a liquid-nitrogen-cooled charged-coupled device (CCD) array
detector (Roeper Scientific, Spec-10:100B, 1340×100 pixels). The SFG spectra were relatively background
free, but a small spectrally-flat background from dark current is subtracted from the raw SFG spectra
(with the IR beam blocked), shifting its baseline close to zero. Background light was also minimized with
strategically placed pinholes and with a box (with small/thin entrance/exit slits) placed at the entry to
the detector. The nonresonant PPP spectrum of either GaAs or gold was used to divide-out the spectral
shape of the IR pulse from the SFG spectrum of the D
2
O-graphene interface.
45
Figure 8: Schematic of the VSFG setup
Since the PPP signal of the graphene-water interface was found to be extremely weak, it was not
practical to carry out a voltage-dependent quantitative orientational analysis, which requires spectra in
at least two different polarization configurations, at each voltage of interest (the more, the better). A 60°
equilateral CaF
2
prism was placed on top of the electrochemical cell, and an index matching fluid
46
(dimethylformamide) matched the CaF
2
substrate to the prism. The prism enhanced the signal quite
dramatically through total internal reflection and by affecting the angles of incidence. The critical angle
for total internal reflection is ~59° (n(D
2
O) ≈ 1.2, n(CaF
2
) ≈ 1.2). With a 60° equilateral prism, the
refraction is small since the incoming beam is nearly parallel with the surface normal of the prism face;
without the prism, the flat sample refracts the beam and changes its incoming angle significantly. In this
configuration, the PPP spectrum was dominant to SSP . With the prism in play, quantitative voltage
(electric field) dependent orientational analysis became practical, since much shorter acquisition times
could be employed, and many more spectra could be collected in a reasonable span of time (~2 – 3
minutes per spectral acquisition).
Figure 9: A schematic of the electrochemical cell, including an index-
matched CaF2 prism to enhance the VSFG signal
Tightening of four bolts, that pass through the top aluminum plate of the electrochemical cell
and thread into a bottom aluminum plate (The aluminum plates and two out of four of these bolts are
shown in Fig. 2). These bolts provide the force (via a “sandwiching” mechanism) that clamps the cell,
holding it together through friction and keeping it from leaking. To not crack the sample, the bolts were
tightened sequentially and repeatedly, carefully (small turns each time), in a crisscross pattern, much like
47
changing a tire on an automotive vehicle. After the sample was placed on the stage, a bubble-level tool
was placed on the electrochemical cell so that the appropriate bolts could be tightened to level the cell.
To align the incoming beams so that they pass through the prism, and through the CaF2
substrate, to achieve spatial and temporal overlap (to generate SFG in the reflection geometry) at the
graphene-water interface requires several steps. First, the sample stage should be level. The sample
stage can be leveled with a bubble leveling tool. Another method is to use a dish filled with water that is
placed on the sample stage. The dish should be sufficient in diameter so that the water at the center of
the dish is flat, and not curved due to interactions with the sides of the dish. Even if the stage is not flat,
the water surface adjusts under the force of gravity to always ensure a flat surface. A laser beam
originating from a vertically-mounted and angled laser pen is reflected off the water surface, and the
spot on the ceiling where the beam terminates is marked. Then a flat piece of gold is placed on the
sample stage, and the tilt of the stage is adjusted so that the alignment beam terminates to the same
place as marked on the ceiling. Then the PPP gold signal is routed and dispersed onto the CCD detector.
The routing mirrors to the detector are adjusted such that the SFG signal from gold is not tilted on the
CCD chip, i.e., when the signal is imaged well onto the detector, 1-3 rows of pixels are illuminated by the
SFG light and these rows of illumination are not tilted. A flip-mirror (placed in the path of the visible
beam following its reflection from the sample) is used to reroute the visible beam to a far-field screen
where its position is marked; it is engaged to set a reference height corresponding to the scenario when
the visible and IR are spatially and temporally overlapped at the surface of gold. The flip mirror is re-
engaged whenever the height of the interface needs to be checked or matched to this reference height.
Then the graphene electrode sample is placed on top of a flat gold-coated wafer, and the height of the
stage is adjusted so that the visible beam returns to the reference spot at the far field. At this point, the
signal should be weaker due to refraction of the incoming beams which degrade spatial overlap. The
signal is re-maximized by adjusting the spatial and temporal overlap of the incoming beams slightly.
48
Then the sample is mounted in the electrochemical cell as described in the previous paragraph, placed
on the sample stage, and the incoming beams are allowed to reflect from one of the gold strips on the
sample. Again, the height of the stage is readjusted accordingly, so that the visible beam reflected from
the gold strip is exactly at the mark on the far-field screen. If necessary, minor tweaks are again made to
the overlap of the beams to maximize the signal. Then a few drops of index matching fluid is placed on
the top window of the cell, and the prism is placed over the index fluid, eliminating the air gap. A drop
of index fluid should be placed on the top window (the sample) and near the prism edge, every 1-2
hours to prevent the loss of index fluid through evaporation, additional drops will seep under the prism
through capillary action. A loss of index fluid has an obvious effect on the signal and various aspects of
the alignment, and so there is no danger that the experiment could be carried out without not knowing
that the index fluid has depleted. Again, the beams are allowed to pass through the prism, through the
sample, and reflect off a gold strip. The height of the sample stage is adjusted accordingly so that the
visible beam is routed to the far-field reference mark, and the spatial and temporal overlap is adjusted to
maximize the signal. When done correctly, whenever a step is carried out that requires the height and
spatial overlap to be readjusted, the row of pixels that are illuminated by the SFG signal should never
drift relative to the way they were in the first step when only a sample of gold was used to generate a
SFG signal on the detector. The gold PPP spectrum is generated from one of the gold strips on the
sample, and utilized later for normalization of the raw data. Finally, the stage is shifting horizontally so
that the beams are moved away from the gold strip, to the center of the sample where the graphene-
water interface can be accessed. To check that the experimental setup has been prepared correctly, a
free-OD peak should clearly emerge corresponding to about ~2700 cm
-1
in the raw spectrum within 10-
30 seconds of acquisition time for negative voltages (typically easiest to see with about -4 to -5 V vs.
Glassy Carbon). Then the free-OD should clearly disappear with positively applied voltages. This is a
fully reversible process, provided that the graphene electrode is sufficiently robust; water will “dance” in
49
response to a changing voltage. The IR beam is blocked and a background spectrum is collected for
background subtraction.
To process the data, the background spectrum is subtracted from the raw spectrum. Then this
background-subtracted spectrum is divided by the gold PPP spectrum (normalization), to cancel out the
effect of the frequency dependence carried by the IR pulse itself. The intensity scale is not calibrated to
a reference, and thus is expressed in “arbitrary units”. Then the frequency scale is shifted to the IR
accordingly, by subtracting the visible central frequency from the SFG frequency.
A graphene electrode was fabricated with a thin layer of TiO
2
or Al
2
O
3
(of various thicknesses),
placed between graphene and the CaF
2
substrate to improve adhesion, but both had an undesirable
effect on the interfacial response and so this strategy was abandoned. With the Al
2
O
3
adhesion layer, the
graphene-water interfacial response was reminiscent of the CaF
2
-Al
2
O
3
-water response (in the absence of
graphene), suggesting that the Al
2
O
3
component was influencing the graphene-water spectrum.
With the TiO
2
adhesion layer, the VSFG signal was enhanced with increasing voltage, and the signal
tended to spread out more over the vertical dimension of pixels of the CCD detector, which would
normally correspond to signals generated from multiple surfaces, of various vertical heights. A.
Benderskii (hilariously) termed this strange but potentially interesting effect “mushrooming”. This effect
was reproducible and quite dramatic, but we could not identify the source of this effect.
50
Figure 10: The Al
2
O
3
layer influences the graphene-D
2
O VSFG spectrum
It was later found that the adhesion of graphene to CaF
2
was sufficient by baking the sample, and so the
adhesion layer strategy was abandoned as it seemed to complicate the system unnecessarily.
Spectro-electrochemical Measurements
VSFG experiments were carried out using the two-terminal configuration of the electrochemical
cell, since the electrochemical currents were lower when the reference electrode was absent. Opting to
forego the reference electrode eliminates this potential source of contamination. The voltage applied to
graphene in the two-terminal configuration (vs. a glassy carbon counter-electrode) was converted to a
three-terminal voltage (vs. the Ag/AgCl reference electrode) so that the applied voltages in the two-
terminal configuration could be reported without the effect of voltage-drops across the D
2
O at the
graphene and glassy carbon interfaces and with respect to a standard reference potential. The
conversion was achieved via Raman spectroscopic measurements of graphene’s G-band, which shifted
51
Figure 11: "Mushrooming" effect, with a TiO
2
adhesion layer (between CaF
2
and Graphene).
linearly with respect to an applied voltage in both two-terminal and three-terminal configurations. Given
a two-terminal voltage, the corresponding three-terminal voltage is that which yields the same G-band
shift.
Figure 12: The G-band Raman shift is linear with respect to the
applied voltage
The frequency shift of the G-band Raman mode of monolayer graphene provides an intrinsic
measure of the excess charge density via a well-established relationship. In situ Raman spectra of the
graphene electrode were collected under applied electrochemical potentials. The G-band frequency of
the graphene, around 1585 cm
-1
, reaches a minimum at the charge neutral point around +0.1 V vs.
Ag/AgCl. The G-band Raman frequency blue-shifts linearly as a function of the applied potential. From
the G-band frequency shift
∆ω
G
, the Fermi energy
E
f
and doping concentration n were calculated
through the following relations in the literature:
5,6
52
Electrons :E
f
=21Δω
G
+75 [cm
−1
] (46)
Holes :E
f
=−18Δω
G
−83 [cm
−1
] (47)
n=(
E
f
11.65
)
2
10
10
[cm
−2
] (48)
The surface charge density σ =ne was confirmed by independent electrode capacitance
measurements.
2
Figure 13: Charge carrier concentration plotted on the right, derived from the
extent of the Raman G-band shift (left)
Theoretical studies predict the presence of a 3 Å gap between graphene and water, and is
consistent with the sudden appearance of the free-OD stretch peak in the VSFG spectrum at sufficiently
negative applied voltages.
7–9
Assuming this gap between graphene and water, we can estimate an upper
53
limit of the electric field experienced by the top-most layers of water at the electrode surface as that of
an infinitely charged plane:
E
0
=
σ
2ϵ
0
ϵ
(49)
Where ϵ=1 , and σ is the surface charge density obtained from G-band shift measurements and the
application of equations 46, 47, and 48.
To discourage contamination of D
2
O by the dissolution of atmospheric H
2
O, and to discourage
acidification of water upon the dissolution of atmospheric CO
2
, the water reservoir and the
electrochemical cell was sequestered in a purged environment of gaseous CO
2
and H
2
O (Parker Balston,
Model: 75-62) at all times.
Although some of voltages applied in this study lie outside the range of electrochemical stability
of water (1.23 V), graphene and glassy carbon are inert electrodes, and the rate of the water splitting is
slow, as indicated by the relatively small electrochemical current flowing through the cell. Additionally,
there was no visual indication of the formation of bubbles in the cell for the voltages that were applied.
For 100 μA (at 2.7 V), and with a graphene electrode area of 1.5 cm
2
,
one electron is transferred per area
occupied by a single water molecule (~10 Å
2
) every 2 seconds, on average. In contrast, the time scale of
the spectroscopic measurement is shorter than 1 ps (vibrational dephasing time of the OD-stretch
modes). In fact, provided the water was extremely pure, and contaminants were minimized, water-
splitting at an appreciable rate was quite difficult to achieve.
10
The electrochemical current was linearly proportional to the applied voltage within a safe range
of operation.
54
Figure 14: The electrochemical current is linearly proportional to
the voltage, defining a so-called “safe range of operation”.
The graphene electrode must be sufficiently robust to survive a series of spectro-electrochemical
measurements. Both the laser beam and the application of voltage are capable of degrading the
graphene electrode. Laser damage was suppressed by constantly flowing D
2
O (Cambridge Isotopes
Laboratories Inc., 99.9% purity) through the electrochemical cell via a peristaltic pump (Fisher Scientific,
Model: 13-876-2), thereby continuously co oling the electrode. In addition, laser damage experiments
were roughly carried out beforehand wherein the sample was exposed to the beams of interest for
extended periods of time, followed by a visual survey of graphene with a Raman microscope. Voltages
were kept within a safe range of operation, such that the electrochemical current was linear with respect
to the applied voltage, and approximately below ±500 μA. It should be noted that the safe range of
operation (linear regime) varied somewhat, with the sample that was tested, but it was never observed
to be “safe” for applied voltages that led to electrochemical currents beyond 1 mA. No correlation could
55
be identified with respect to details in the fabrication process, or the procedural setup of the system for
experimentation, with the safe range of operation.
The in-plane resistance of graphene was measured repeatedly (through gold contacts on the
sample), following an application of voltage to graphene. After a voltage was applied, then halted, it
could take several minutes for the in-plane resistance of graphene to stabilize. It was observed that the
in-plane resistance across graphene was initially higher or lower than the steady-state resistance,
depending on whether the applied voltage was negative or positive with respect to the reference
electrode, respectively. A jump in the steady-state in-plane resistance (over three times the original
resistance, which is typically 1-2 kΩ) of graphene appeared to correlate with an electrode that developed
defects in the Raman spectrum, would no longer induce a reproducible response in interfacial water, or
there would be no difference in the response for variously applied voltages.
Once a voltage was applied, the electrochemical current took about two minutes to stabilize.
Thus, an equilibration time of about two minutes was allowed to elapse at each voltage to ensure the
measurements were performed in the steady state.
Spectral Decomposition into Surface and Bulk Contributions
Given Shen and Tian’s discovery that the SFG response of sub-surface water molecules
influenced by the DC-field of a charged interface is reminiscent of bulk water and is not affected by the
application of charge at the interface,
11
we used their results to disentangle the surface
χ
(2)
response of
D
2
O at the graphene interface through the following spectral fitting procedure . Adopting the
nomenclature of Shen and Tian, it is useful to define χ
S,DL
(2)
, which is the surface response of the diffuse
layer:
11
χ
S,DL
(2)
=
κ
√
κ
2
+(∆k
z
)
2
e
itan
−1
(
∆k
z
κ
)
(
B
χ
(3)
,1
ω−ω
χ
(3)
,1
+iΓ
χ
(3)
,1
+
B
χ
(3)
,2
ω−ω
χ
(3)
,2
+iΓ
χ
(3)
,2
)
e
iφ
χ
(3)
Φ (0) (50)
56
Our fits include F. Geiger’s formalism of absorptive/dispersive mixing and are based on his readily
accessible Mathematica code of three coupled oscillators.
12
The extent of mixing depends purely on
experimental parameters: refractive indices, incoming beam angles, and ionic strength. The refractive
index of D
2
O in the IR region of interest was obtained from a publication by Williams et al.,
13
and the
ionic strength is that of pure water. The following equation was used to fit our data:
(51)
Where κ is the inverse Debye length, ∆k
z
is the inverse coherence length,
Φ (0) refers to the voltage we
applied relative to the voltage at which graphene is neutral (graphene is neutral at about 0.1 V vs.
Ag/AgCl, Fig. 1), B
i
/Γ
i
is the amplitude, Γ
i
is the HWHM, ω
i
is the central frequency, and φ
i
is the phase
of the i’th Lorentzian. Note that our fitting equation differs slightly from what is found in F. Geiger’s
Mathematica code,
14
ours includes a nonresonant response, the phases of the twoχ
(3)
Lorentzians are
not independent, and we included a “scaling factor”, m. In our fits, the
χ
(3)
Lorentzian parameters (
B
i
,
Γ
i
and, ω
i
were frozen in accordance with estimates made by Geiger, which originates from Tian and Shen’s
experimentalχ
B
(3)
component.
11,12
Essentially the strategy to disentangle the surface
χ
(2)
contribution was
to freeze all the known parameters and allow the
χ
(2)
parameters to float such that our spectra were fit.
Since the central frequencies were given for the OH-stretch and not the OD-stretch, they were scaled by
assuming that the force constants for OH and OD are the same. To be consistent with the literature, the
free OD peak was forced to be positive by restricting and locking its amplitude and phase, respectively.
The phases of the twoχ
(2)
hydrogen-bonded OD stretch peaks were restricted to ±0.2 radians from the
phase at which they were purely absorptive in the imaginary spectrum, since lineshapes that are purely
absorptive are simpler to interpret. The phase,
φ
χ
(3)
, was allowed to freely float in the fit of the 1.0 V
57
spectrum, and its post-fit value was frozen in subsequent fits. The 1.0 V SFG spectrum was fit first
because its hydrogen-bonded peaks were relatively pronounced, and it tended to yield consistent results
with respect to changing of the initial guesses of the floating parameters. Qualitatively our χ
(3)
component is consistent with the literature:
11,15,16
its spectral shape is “bulk-like” and its amplitude is
positive for positive fields and negative for negative fields. The scaling factor, m, effectively served to
scale Shen and Tian’s χ
S,DL
(2)
spectra to our arbitrary scale. Assuming the χ
S,DL
(2)
/χ
S
(2)
ratio in our spectra
should be comparable to Tian and Shen’s, and by also considering the differences in our charge densities,
we estimated m to be about 30. We found that our choice in m yielded χ
S
(2)
responses that were
reasonable. The sensibility of our fits were assessed in the following ways: (1) the χ
S
(2)
spectra should be
flat on the blue side of the free-OD peak; (2) χ
S,DL
(2)
should not interfere with the free-OD peak to a
significant extent; (3) the goodness of the fit; (4) through comparison with a theoretical study carried out
by Morita et. al.
16
wherein the surface response increases in intensity as the field is increasingly made
negative, and at positive fields the hydrogen-bonded χ
S
( 2)
and χ
S,DL
(2)
components interfere destructively.
The decomposition into surface and bulk contributions, as well as the fit to the SFG spectra (each plotted
with respect to the applied electric field) is given in the “results” chapter.
Orientation Analysis
With knowledge of the appropriate optical and microscopic parameters of the system,
(e.g. the hyperpolarizability, the incoming angles, the refractive indices), a transformation based
on the works of Hirose and Wang et al.
17,18
is carried out to link the PPP and SSP response (the
amplitude) of the free-OD stretch to its ensemble-averaged orientation angle. A plot is
generated by this calculation to predict the PPP and SSP amplitudes, and the ratio of these
amplitudes, with respect to the average free-OD orientation.
58
Figure 15: Prediction of SSP and PPP amplitudes
based on Wang's orientational analysis formalism
Since the experimental data is expressed in arbitrary units of intensity, the trend in the change
of the PPP or SSP intensities relative to the average orientation can be evaluated, but the
experimental intensities and the predicted intensities are not directly quantitatively compatible.
However, the PPP to SSP ratio is directly and quantitatively applicable to the experimental data.
The free-OD amplitude is extracted from a (Lorentzian) best-fit to this response in the
experimental spectra, in the PPP and SSP polarization configurations, for variously applied
voltages. Then the PPP to SSP ratio of the response is fed into the orientation plot to determine
the average orientation angle of the ensemble. A Matlab script to carry out this analysis was
constructed by A. Benderskii and M. Mammetkuliev, the code is provided in the appendix. The
average orientation angle in this script represents the average angle between the surface
normal and the free-OD moiety, note that it is not the angle between the surface normal and
the permanent dipole. The interfacial refractive index was calculated using an analytical
expression provided by Zhuang, Miranda, Kim and Shen.
19
The refractive indices for of D
2
O is
59
obtained from data provided by Bertie, Ahmed, and Eysel and Sethna, Palmer, and
Williams.
13,20
The refractive index of CaF
2
is obtained from data provided by Li.
21
For
orientational calculations carried out in this thesis on the D
2
O-graphene interface, the
hyperpolarizability of the OD-stretch was taken to be β
aac
=β
bbc
=0.26, β
ccc
=1 , though a range
of 0.23 to 0.28 has been reported.
22
To carry out the orientational analysis requires that an assumption of the orientational
distribution be made. If the experimental PPP and SSP amplitudes are not consistent with the
orientational plot, the distribution that was assumed to generate the orientational plot is
falsified. This was in fact found to be the case when the exponential distribution was tested,
suggesting that the exponential distribution is not reflective of water at the graphene interface.
f (θ)=
1
Z
e
(−θ/θ
0
)
(52)
The Gaussian distribution was found to be compatible with the experimental data, though the
comparability was insensitive the distribution width, and thus a self-consistent procedure was
developed to find the optimal Gaussian distribution width.
f (θ)=
1
Z
e
−(θ−θ
0
)
2
(2σ
2
)
(53)
Where 1/Z is the partition function (normalization constant). This analysis posits that
reorientation is the dominant mechanism for the observed field dependence in the SFG
response. The width of the orientational distribution can be interpreted as a susceptibility to
reorientation, since narrower widths describe a more rigid ensemble. Intuitively the
distribution is expected to narrow as the electric field magnitude increases, though the extent
60
of this effect is currently unknown. Thus, this analysis assumes a static distribution width with
respect to the applied field, which is valid if the extent of the narrowing is negligible with
respect to the range of fields that were applied in this study. G (θ) is the orientational free
energy for a Gaussian distribution, centered at the orientation angle of the free-OD with respect
to the surface normal, at the point of zero charge (pzc).
O(θ)=G(θ)−μ∙E=kT
[
ln(σ √2π)+
(θ−θ
pzc
)
(2σ
2
)
]
2
−μEcos(θ
0
) (54)
θ
0
is the angle between the permanent dipole of water and the surface normal. The additional
term,μ∙E, is the potential energy of a dipole in a DC-field, which imparts anharmonicity onto
the orienting potential and shifts its minimum to narrower orientation angles, representing the
effect of the field-induced reorientation of water. (1) Assuming a Gaussian distribution with
various widths, (σ = 5
o
, 10
o
, 15
o
, 20
o
, 25
o
, and 30
o
were tested), PPP and SSP amplitudes and the
PPP/SSP ratio are calculated via H. F. Wang’s method, as a function of the average free-OD
orientation angle (several plots like that of Fig. 15 were generated, one for each width ranging
from 5° to 30°; 5° step). (2) Experimental free-OD peak amplitudes were obtained from a
spectral fit of the field dependent free-OD responses in the PPP and SSP polarization
configurations.
61
Figure 16: Experimental field-dependent VSFG spectra and the best-fit (solid line) of the Free-OD
response
To fit the PPP spectra, a nonresonant component was mixed with a single Lorentzian function:
I
SFG
=
|
B
NR
e
iϕ
+
B
ω−ω
1
+iΓ
|
2
(55)
The nonresonant phase, φ, was allowed to float in the fit of the spectrum corresponding to the most
negatively charged interface, then the phase was frozen in subsequent fits. This was to ensure that the
extracted amplitude from the fits would not be sensitive to a floating nonresonant phase. In the SSP
spectra, a nonresonant component was mixed with two Lorentzian functions. A component that
resembles a tail is present in the SSP spectrum, presumably originating from the hydrogen-bonded free-
OD stretching response. Thus, two Lorentzian functions were utilized to extract the best-fit parameters
that model the SSP response, one representing the free-OD response, and the other a broad hydrogen-
bonded response (centered at ~2500 cm
-1
, ~150 cm
-1
HWHM) that is characteristic of water:
62
I
SFG
=
|
B
NR
e
iϕ
+
B
1
ω−ω
1
+iΓ
1
+
B
2
ω−ω
2
+iΓ
2
|
2
(56)
Γ is the half-width half-max, ω
ν
is the central frequency of the ν
th
component in wavenumbers, φ
is the phase, and the Lorentzian amplitude is
B
Γ
. (3) The average orientation angle is
determined (vs. the applied field, obtained from G-band shift measurements, Figs. 12 and 13)
by locating the angle in the orientation plot (Fig. 15) that corresponds to the experimentally
determined PPP to SSP amplitude ratio, for each distribution width ( σ = 5
o
, 10
o
, 15
o
, 20
o
, 25
o
,
and 30
o
). Although the free-OD response is absent for neutral graphene, an estimate of the
free-OD angle at this point,
θ
pzc
, is obtained by extrapolation of the linear fit of this data to
E=0 . Here, again, the nonresonant phase, φ, was allowed to float in the fit of the spectrum
corresponding to the most negatively charged interface, then the phase was frozen in
subsequent fits. Additionally, the central frequency and the width of the hydrogen-bonded
component were frozen for every fit, to ensure that these parameters would not have a major
effect on the extracted free-OD amplitude.
63
Figure 17: Field-dependent reorientation; θ
pzc
is obtained
by extrapolating the fit to E=0 .
(4) The free energy orienting potential is plotted for each distribution width ( σ = 5
o
, 10
o
, 15
o
,
20
o
, 25
o
, and 30
o
) of the Gaussian orientational distribution function, and for each applied field,
E. To compute the orienting potential, the angle in the μ⋅E term is
θ
0
= θ + 52.5
o
,
where θ is
the angle between the surface normal and the free-OD moiety, and
θ
0
is the angle between the
surface normal and the permanent dipole moment of interfacial water, 2.5 D.
18, 19
64
Figure 18: The free-energy orienting potential (for σ =15 ) vs. the
orientation angle.
(5) Minima of the field dependent free-orienting potentials were located, which correspond to
the average free-OD orientation angles. These (most stable) orientation angles were plotted
against the applied field and superimposed onto the plots generated in step (3), organized by
the width of the orientational distribution (Fig. 19).
65
Figure 19: Extracting the distribution width through agreement of the orientational analysis
with the free-energy orienting potential
(6) Consistency between the two complementary methods, namely the PPP/SSP amplitude
orientational analysis and the orienting potential method, was evaluated by calculating the sum
of the squared difference between the two orientations for each applied field, and for each
distribution width. The distribution width that led to the most consistency between the two
methods to determine orientation, was about 15
o
(FWHM ≈ 2.355 × 15
o
≈ 35
o
). Thus, this is the
distribution width that is reported and utilized to determine the average orientation angles of
the free-OD with respect to the applied field (Fig. 17). (7) A plot of the sum of the squared
differences vs. the distribution width is fit with a polynomial to get an improved estimate for the
distribution width which would yield the greatest consistency between the two methods.
66
Figure 20: The minimum error between the two
methods that extract orientation
Control Experiments
Since the VSFG spectrum of the air-water interface is extremely sensitive to contaminants, a
sense of whether a sample of water has been contaminated can be qualitatively discerned. This can be
done through a comparison of the VSFG spectra, collected from the air-water interface, for two samples
of water where one is known to be very pure and the other is suspect because it began as a pure sample,
but was potentially exposed to a contaminating source. In other words, if the sample of water under
question reasonably matches the VSFG air-water spectrum of pure water, and matches with itself before
potentially being contaminated, then the water is reasonably contaminant-free. It was by this method
that it was found, by process of elimination, that the tubing of the peristaltic pump had degraded and
was leaking contaminants into the water. Water for rinsing the apparatus was obtained by doubly-
distilling it, first with a millipore filtration system, then followed by a distillation using a home-built
distillation apparatus; the purified water was immediately placed in a piranha-cleaned glass flask (the
67
flask was profusely rinsed with millipore-filtered water following piranha-cleaning). To minimize
contaminants, every part of the cell that could conceivably be a source of contamination was
meticulously cleaned and rinsed profusely (with doubly-distilled H
2
O, followed by a rinse with D
2
O), or
removed and replaced if necessary. Then (99.9% pure, Cambridge Isotopes) D
2
O was pumped through
the flow-cell and the air-water VSFG spectrum of this sample was compared to itself before it was
pumped through the electrochemical cell. Employing a new and more robust formulation of tubing in
the peristaltic pump, yielded water at the output of the electrochemical cell that was spectrally identical
to the “unexposed”, clean sample, and thus reasonably contaminant free.
The quality of the graphene electrode was routinely verified, before and after experimentation
concluded, through Raman spectroscopy: good quality graphene lacks the presence of the defect-
induced D band, the 2D band is well represented by a single Lorentzian peak, and the 2D to G band
amplitude ratio is about 2:1.
23–25
A large jump (greater than 3x) in the in-plane resistance of graphene
correlated with the degradation of the 2:1 amplitude ratio, and the emergence of the D-band (~1345 cm
-
1
).
68
Figure 21: The air-water VSFG spectrum of clean water vs. contaminated water
Figure 22: Raman spectrum of good quality, monolayer
graphene
Since the Renishaw-Raman system is equipped with a microscopic imaging system, obvious
defects on the order of tens to hundreds of microns were routinely checked for, before and after the
experiment. The image on the left in Fig. 23 was collected before the beginning of a measurement, the
image on the right was collected after the measurement had failed. Presumably, the black spots on the
image on the right is dirt and/or laser induced burns.
Figure 23: Microscope image (50 μm scale) of the graphene electrode
69
The applied voltages were randomly staggered (instead of stepping the voltage in a single
direction) to rule out any effects associated with irreversible changes to the electrode, and the VSFG
spectrum at one chosen voltage (e.g., 0.3 V was chosen in the figure below) was periodically re-
measured to ensure that there was no drift in the signal over time.
Figure 24: Measurement of the same voltage
periodically throughout an experiment to
check for reproducibility
To test whether water was trapped between CaF
2
and graphene, the water was allowed to flow
through the cell, then the cell was emptied and a VSFG spectrum of the “dry” graphene-air interface was
collected. The dry, empty cell did not yield an appreciable frequency-dependent SFG response in the
OD-stretch region.
70
Figure 25: VSFG spectrum of the "dry" graphene-air interface in the
D
2
O-streching region.
The VSFG signal of the free-OD vanished upon isotopic dilution with H
2
O, confirming that this
signal originates from D
2
O.
Figure 26: Isotopic dilution of D
2
O with H
2
O
suppressed the free-OH stretching response
71
50x10
-3
40
30
20
10
0
SSP
2700 2600 2500 2400 2300
30x10
-3
25
20
15
10
5
0
PPP
SSP
PPP
Organic contaminants at the interface, if present, can potentially be identified in the VSFG
spectrum, in the C-H stretch region (~3000 cm
-1
). The IR source was tuned to the C-H stretch, to check
the VSFG spectrum for organic contaminants, prior to committing to collecting data at the graphene-D
2
O
interface. With the CH signature present in the VSFG spectrum, the experiment would not be carried
out; the sample would be discarded and every component of the electrochemical cell would be
profusely cleaned or replaced before restarting with a new sample.
Figure 27: Example of an organic (CH-stretch peak at ~3000 cm
-1
) contaminant
observed at the graphene-water interface.
References
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Nanotechnology 24, (2013).
72
2. Shi, H. et al. Sensing local pH and ion concentration at graphene electrode surfaces using
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Ohmic/Schottky contacts. Appl. Phys. Lett. 101, 223113 (2012).
4. Shi, H. et al. Monitoring Local Electric Fields at Electrode Surfaces Using Surface
Enhanced Raman Scattering-Based Stark-Shift Spectroscopy during Hydrogen Evolution
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5. Froehlicher, G. & Berciaud, S. Raman spectroscopy of electrochemically gated graphene
transistors: Geometrical capacitance, electron-phonon, electron-electron, and electron-
defect scattering. Phys. Rev. B - Condens. Matter Mater. Phys. 91, 205413 (2015).
6. Das Sarma, S., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two-dimensional
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Graphene. J. Phys. Chem. B 118, 530–536 (2014).
8. Ohto, T., Tada, H. & Nagata, Y. Structure and dynamics of water at water-graphene and
water-hexagonal boron-nitride sheet interfaces revealed by: Ab initio sum-frequency
generation spectroscopy. Phys. Chem. Chem. Phys. 20, 12979–12985 (2018).
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Nat. 2021 5947861 594, 62–65 (2021).
10. Wang, Y., Narayanan, S. R. & Wu, W. Field-Assisted Splitting of Pure Water Based on
Deep-Sub-Debye-Length Nanogap Electrochemical Cells. ACS Nano 11, 8421–8428 (2017).
11. Wen, Y.-C. et al. Unveiling Microscopic Structures of Charged Water Interfaces by Surface-
Specific Vibrational Spectroscopy. Phys. Rev. Lett. 116, 016101 (2016).
12. Ohno, P . E., Wang, H. & Geiger, F. M. Second-order spectral lineshapes from charged
interfaces. Nat. Commun. 2017 81 8, 1–9 (2017).
13. Sethna, P . P ., Palmer, K. F. & Williams, D. OPTICAL CONSTANTS OF D2O IN THE INFRARED.
J Opt Soc Am 68, 815–817 (1978).
14. Ohno, P . E., Wang, H., Paesani, F., Skinner, J. L. & Geiger, F. M. Second-Order Vibrational
Lineshapes from the Air/Water Interface. J. Phys. Chem. A 122, 4457–4464 (2018).
15. Nihonyanagi, S., Yamaguchi, S. & Tahara, T. Direct evidence for orientational flip-flop of
water molecules at charged interfaces: A heterodyne-detected vibrational sum frequency
generation study. J. Chem. Phys. 130, (2009).
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16. Joutsuka, T., Hirano, T., Sprik, M. & Morita, A. Effects of third-order susceptibility in sum
frequency generation spectra: A molecular dynamics study in liquid water. Phys. Chem.
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17. Hirose, C., Domen, K. & Akamatsu, N. Formulas for the Analysis of the Surface SFG
Spectrum and Transformation Coefficients of Cartesian SFG Tensor Components. Appl.
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18. Wang, H. F., Gan, W., Lu, R., Rao, Y. & Wu, B. H. Quantitative spectral and orientational
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19. Zhuang, X., Miranda, P . B., Kim, D. & Shen, Y. R. Mapping molecular orientation and
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74
Chapter 3: Discussion of Results
A collection of results pertaining to the graphene-water interface are organized into the
following subsections. Additionally, the physical significance of the results are discussed. This study of
the graphene-water interface has indeed led to several intriguing findings.
Namely, the asymmetry of the free-OD response, with respect to the applied field, calls into
question the validity of treating interfacial water as a simple dielectric medium. This result was well
received by Nature and published in June of 2021.
1
The orientational analysis of the field-dependent PPP and SSP graphene-water VSFG spectra, the
free-energy orienting potential and the methodology to extract the orientational distribution width, and
the vibrational Stark shift of the free-OD with respect to the applied field has been submitted to the
scientific community for peer review. These results and/or arguments are thus more susceptible to
future modifications, based on reviewers’ responses. The electrostatic effects due to the field of a planar
charged surface is generally applicable to all charged interfaces. Additionally, a novel method to falsify
an assumed orientational distribution, and self-consistently find the optimized distribution width for an
assumed given distribution is explored by this study. Finally, the Stark shift of the free-OD is reported
relative to the applied field (the Stark shift of the hydrogen-bonded response is a potential future
project); the central frequency of the free-OD response can serve as a probe, to determine the electric
field at the interface.
Additional preliminary efforts have been carried out, though the reproducibility of the results
have not yet been demonstrated. The results of these preliminary efforts have not yet been submitted
for review, and may be verified and further explored by my colleagues at the University of Southern
California. This includes the SPS graphene-water VSFG spectrum, and an attempt to smoothly observe
75
what may perhaps be interpreted as a field-induced phase transition in interfacial water, for applied
fields very near the onset of the free-OD response in the VSFG spectrum.
Asymmetric Response of Interfacial Water to Applied Electric Fields
Voltage-dependent VSFG spectra of D
2
O at the graphene interface were collected using the SSP
polarization combination (SFG, visible, and IR beams, respectively).
Figure 28: Voltage-dependent VSFG spectra of D2O at the graphene
interface
Applying a negative/positive bias dopes the graphene with electrons/holes, yielding
negatively/positively charged interfaces (Fig. 28). The asymmetry in the observed spectra with respect
to positive vs. negative applied fields is striking. At 1.6 V (vs. Ag/AgCl) and below, the VSFG spectra of
76
the graphene-D
2
O interface exhibits one relatively narrow peak (FWHM: 30 cm
-1
) at 2697 ± 3 cm
-1
. We
assign this feature to the free-OD stretch, a local mode of water in the topmost monolayer, where one
OD-group points away from the bulk, toward the graphene surface, and into a gap of about 3 Å
(suggested by molecular dynamics studies).
2,3
It is therefore unable to hydrogen bond with other water
molecules, and is blue-shifted and narrow relative to the broad peaks of the hydrogen-bonded species,
similar to the air-water interface.
4,5
It should be noted that, although liquid bulk water has a fraction of
broken H-bonds, the free-OD peak is absent in the spectrum of bulk water, and only the surface species
contribute to that peak. Additionally, the free-OD species is absent in the spectra of other, previously
studied charged interfaces,
6–9
where the free-OD signal is suppressed due to hydrogen-bonding
interactions with those surfaces. For voltages of 1.0 V and above, the free-OD feature is absent and only
broad hydrogen-bonded peaks are observed in the 2300 to 2650 cm
-1
region.
10,11
Near the charge-
neutral point, the free-OD feature is absent, consistent with the experimental work of Singla et al.,
12
who
measured VSFG spectra of H
2
O in contact with graphene surface in an open circuit configuration.
However, this observation contradicts theoretical studies of the graphene-water interface, which predict
the presence of a free-OD feature at the neutral potential.
2
The range of applied potentials corresponds to the surface charge densities, σ , on the
graphene electrode from -1.0×10
13
cm
-2
to +5.0×10
12
cm
-2
.
77
Figure 29: Doping concentration is calculated from the G-band shift.
The G-band shift is linearly dependent on the applied voltage.
Taking into account the gap between the graphene and water, we can estimate an upper limit of
the electric field experienced by top-most layers of water the at the electrode surface as that of an
infinitely charged plane:E
0
(0)=
σ
2ϵ
0
ϵ
(with ϵ=1 ), giving the maximum E-field of -0.092 V/Å. The
field is expected to be weaker for deeper layers of water.
78
Figure 30: Field-dependent VSFG spectra of the graphene-water interface.
Although VSFG (ω
SFG
=ω
1
+ω
2
) is nominally a second-order nonlinear optical process, the
static electric field (E
0
,ω
3
=0) at a charged interface results in a third-order contribution to the signal:
E
SFG
=χ
(2)
:E
ω
1
E
ω
2
+ χ
(3)
:E
ω
1
E
ω
2
E
0
(57)
It is generally accepted that the χ
(2)
contribution originates from a few top-most monolayers of
water
5,9,13
(beyond which the isotropic orientational distribution of bulk water is restored, resulting in
zero SFG signal). On the contrary, the region contributing to theχ
(3)
signal may extend into the liquid as
far at the static field E
0
(z) penetrates, which decays over the Debye screening length.
13,14
Inspired by
79
Shen and Tian,
9
we spatially separate theχ
(3)
contribution into the ‘surface’ part originating from the
same interfacial region as χ
(2)
, and a ‘bulk’ part (Fig. 3a). The surface contributionχ
(3)
can be thought
of as the change in the interfacial second-order susceptibility due to the static field E
0
(z) estimated
above:
χ
s
(2)
(E
0
)=χ
2
(2)
(0)+ χ
s
(3)
E
0
(58)
The bulk contributionχ
b
(3)
is integrated over the depth (z), which results in the celebrated
Eisenthal relationship of the surface potential Φ
0
(0) .
15
When the Debye screening length is comparable
to the wavelength of light, phase retardation effects become important in the interference of the bulk
χ
b
(3)
contribution and the surface signal,
9
for which a formal expression was recently derived:
13,14
(59)
where κ is the inverse of the Debye screening length and Δk z = k SFG,z - k 1,z - k 2,z is the inverse of the
coherence length of the SFG process. In our case of pure D 2O (no electrolyte added), the Debye length is
of the order of 1 μm.
Recent studies of several charged aqueous interfaces (various lipid monolayers and mineral
surfaces) have concluded that the bulk contribution – the second term in Eq. 59, which we denote
Χ
b
(E
0
)≡
κe
iϕ
√
κ
2
+(Δk
z
)
χ
b
(3)
Φ
0
(0) , has nearly the same spectral line shape regardless of the chemical
nature of the surface, and follows the linear response, i.e., is proportional to the static field (and the
80
potential) of the surface.
2,15,16
We used this spectral shape of the bulk contribution
9,11,13
in fitting our VSFG
spectra to Eq. 59, allowing us to extract the spectra of the interfacial water as a function of the surface
field,χ
s
(2)
(E
0
) .
The results of the spectral decomposition are presented below in Fig. 31b,c, where the
imaginary parts of the bulk and surface contributions are shown.
81
Figure 31: Spectral Decomposition of the field-dependent VSFG spectra (Fig. 28) of the
graphene-water interface into surface and bulk contributions.
Consistent with the previous studies in both shape and sign, the assumed bulk contribution
Imag[χ
b
] , represented by two broad Lorentzians at 2365 cm
-1
and 2510 cm
-1
(FWHM = 150 cm
-1
),
resembles the linear absorption spectrum of bulk water and scales linearly with the applied fieldE
0
(0) .
82
The extracted surface contributionχ
s
(2)
(E
0
) does not follow the linear response behavior,
showing a pronounced asymmetry with respect to positive vs. negative surface charge. We fit (Table 1)
the χ
s
(2)
(E
0
) spectra using three Lorentzians: one narrow peak at 2697 cm
-1
representing the “free-OD”
species, and two broader red-shifted peaks at ~2350 cm
-1
and ~2500 cm
-1
representing H-bonded
structures.
Table 1: Fitting results for the decomposition of surface and bulk responses.
83
The amplitudes of these spectral components as a function of the applied field are shown in Fig. 31d-f.
The non-linearity implies that the surface signal does not behave according to Eq. 58. Note that
although our VSFG measurements were performed at the intensity level, the signs of the extracted
spectral components are consistent with all previous studies that used optical heterodyne
detection.
5,8,9
If we define the sign of Imag[χ
(2)
] for the free-OD feature as positive (free-OD groups
always point up), then the bulk contributionImag[χ
b
] is positive at negatively charged surfaces and
negative at positively charged surfaces. For negative fields, the sign of the hydrogen-bonded part of the
surface contribution also is negative.
The well-established Miller’s rule in nonlinear optics
17
is a proportionality relationship between a
nonlinear susceptibility and a product of the first-order (linear) susceptibilities at constituent
frequencies. It works well for off-resonant responses and therefore for DC fields, as was already pointed
out in Miller’s original paper. A straightforward extension of Miller’s rule to our case suggests that the
change of the second-order susceptibility in response to the static field of a charged surface, Eq. 58, is
proportional to the linear DC susceptibility of the interfacial layer,
χ
2
(3)
(ω
1
,ω
2
, 0)∝χ
s
(2)
(ω
1
,ω
2
)χ
s
(1)
(0) (60)
(Note that we only consider the off-resonant zero-frequency component for the proportionality
relationship; the proportionality does not imply that the second-order susceptibility χ
s
(2)
(ω
1
,ω
2
) is
related to the residual spectrum at zero field, χ
s
(2)
(0) in Eq. 58). The linear susceptibility is connected
to the dielectric constant of the interfacial layer, ϵ
s
=1+4 π χ
s
(1)
(0) . Thus, our experimental
demonstration that interfacial water responds nonlinearly to applied electric fields suggests that the
assumption of a linear dielectric response in attempts to better understand the behavior of this surface
layer may be invalid. The deviation of the electrostatics of interfacial water from the linear response
84
behavior has been suggested by multiple theoretical and computer simulation studies and has important
consequences for practical applications.
16,18–21
Recent studies of nanoconfined water have also shown
anomalous behavior of the dielectric response effected by surface interactions.
22
At the surface charge densities explored in our study (from -1.0 ×10
13
e
-
/cm
2
to +5.0×10
12
e
-
/cm
2
,
i.e., -0.016 to +0.008 C/m
2
), the electric field strengths are of the order of ±0.03 V/Å at the interface and
decay into the bulk. Dielectric saturation in bulk water manifests itself as a simple monotonic decrease
of the effective dielectric constant (defined as a derivative of the induced polarization vs. applied static
electric field) which begins to deviate from theϵ≈80 value at E-fields on the order of 10
9
V/m (0.1
V/Å).
23
The bulk contributionχ
b
(E
0
) obeys the linear behavior, consistent with this limit, since the
deeper water layers experience the static field weaker than at the interface, well below the dielectric
saturation limit. However, the response of interfacial water deviates from linear behavior at much
weaker fields, and in a non-monotonic fashion. We also note that the average surface charge density in
many commonly occurring systems, such as phospholipid monolayers and bilayers, can be as high as one
elementary charge per 60 Å
2
, while here it is less than one elementary charge per 1000 Å
2
. Additionally,
the local fields are expected to be even stronger around discrete charged head groups. The order of
magnitude of the dielectric saturation field in liquid water, ~10
9
V/m, can be qualitatively understood as
being comparable to the field imposed by the nearest neighbor molecules. From this standpoint, it
makes sense that the interfacial water should tend to exhibit non-linear effects at weaker fields, due to
the smaller average number of nearest neighbors.
It is interesting to consider possible molecular mechanisms responsible for the nonlinear
behavior of interfacial water,
16,21,24
whose polarization is largely due to re-orientation of the molecular
dipoles. Evolution of the VSFG spectra as a function of the applied field offers molecular-level insight
into the re-orientation and rearrangement of H-bonds. One obvious clue is the disappearance of the
free-OD feature at neutral or positive potentials. At a negatively charged interface (applied potentials,
85
below -1 V vs. Ag/AgCl), the free-OD signal abruptly appears as a narrow blue-shifted peak in the VSFG
spectra, indicating that the free-OD moiety likely points towards the graphene, into the gap. As the
surface becomes neutral or positive, the free-OD species orient away from graphene and towards bulk
water, where they are more likely to find H-bonding partners and no longer contribute to the free-OD
peak. This suggests a sudden rearrangement of the structure of the interfacial layer. Such asymmetric
response may be one of the mechanisms of the linear response breakdown. Recent surface enhanced
Raman experiments have been interpreted in this way.
25
Molecular re-orientation and interconversion
between different hydrogen-bonding classes leading to large-scale structural rearrangement of the
surface layer can be viewed as a field-induced phase transition of interfacial water, which was first
suggested based on temperature-jump relaxation measurements in 1980’s.
26
Measurements of the Free Energy Orienting Potential
Electric-field dependent VSFG spectra of the graphene-water (D 2O) interface were collected in
both the PPP and SSP configurations (Fig. 32). The voltages applied ranged from -2 V to -7 V (vs. Glassy
Carbon), or -1 V to -4 V (vs. Ag/AgCl).
86
Figure 32: Electric-Field dependent SFG spectra of the graphene-D2O interface collected in the
SSP and PPP configurations
A tunable electric field is readily applied to the interface by doping the graphene electrode with
excess charge via an adjustable voltage source (Fig. 33).
87
Figure 33: Electron Doping of Graphene
A safe range of voltages were applied and led to observed electrochemical currents that were low (< -
150 μA) and linearly proportional with the voltage (Fig. 34).
88
Figure 34: Applied voltages are within the range of
electrochemical stability
The narrow and spectrally isolated peak at 2690-2700 cm
-1
is assigned to a local OD-stretch vibration that
is not hydrogen bonded (i.e., the “free-OD”).
1,4,5
Its vibrational response is observable when even-
ordered, surface-selective spectroscopies are applied; it exists in the top monolayer, where the break in
symmetry permits a hydrogen-bond deficiency, and is much simpler to interpret
27
relative to the broad
hydrogen-bonded OD-stretch peaks spanning from approximately 2200 to 2600 cm
-1
.
2,27
The “free”
species is absent at typical charged interfaces, since water hydrogen-bonds with these interfaces (e.g.
surfactants with charged head groups; mineral surfaces). Remarkably, the application of sufficient
negative charge (corresponding to an electric field magnitude of approximately 0.02 V/ Å) to interfacial
water via the (relatively inert) graphene electrode led to the sudden onset of a free-OD response. This
free-OD response was found to be asymmetric with respect to the applied field, and absent when the
graphene electrode was neutral and doped with holes (positively charged). The asymmetry was
rationalized through a mechanism of field-induced molecular reorientation.
1
For negative DC fields (as
defined for negatively charged graphene), the dipole orients toward the graphene interface and into a ~3
89
Å gap,
2,3
rendering it unable to hydrogen bond. On the contrary, for positive fields, the OD is thought to
orient toward the bulk phase of water, forming hydrogen-bonds and leading to the suppression of the
free-OD signal.
8,28,29
Two commonly utilized orientational distributions were considered in this analysis: the Gaussian
and decaying exponential distributions.
f (θ)=
1
Z
e
−(θ−θ
0
)
2
(2σ
2
)
(61)
f (θ)=
1
Z
e
(−θ/θ
0
)
(62)
Where Z is the partition function (normalization constant). Although the exponential distribution may be
attractive from a thermodynamic perspective,
30
due to its restrictive orientational freedom, we believe
that it does not faithfully represent water at the graphene interface. Selecting the exponential
distribution in the orientation analysis led to predicted PPP to SSP amplitude ratios that were always
greater than 1.3, inconsistent with experimentally measured amplitude ratios that were found to lie
within a range of about 1 to 1.4 (Fig. 35).
Figure 35: The distribution of free-OD angles at the graphene-water interface is not consistent
with a decaying exponential.
90
An increase in the magnitude of the applied field was accompanied by a stronger free-OD
response; the transition dipole moment more effectively interacts with P-polarized light as the Free-OD
is forced to align with the DC field, and a stronger signal is observed.
Near the point of zero charge, the PPP and SSP amplitudes of the free-OD peak are
approximately equal, which translates to an average free-OD orientation of about 45
o
with respect to the
surface normal. Note that this deviates from the average orientation of the free-OD species at the air-
water interface, which orients at 30-40
o
with respect to the surface normal,
30–32
and may be due to the
hydrophobic nature of the neutral graphene interface.
5
The distribution width has a greater influence on
orientation angles as the magnitude of the applied field is increased (Fig. 36), which demonstrates the
importance of an accurate theoretical model for the orientational distribution at charged interfaces.
To fit the PPP spectra, a nonresonant component was mixed with a single Lorentzian
function:
I
SFG
=
|
B
NR
e
iϕ
+
B
ω−ω
1
+iΓ
|
2
In the SSP spectra, a nonresonant component was mixed with two Lorentzian functions. A component
that resembles a tail is present in the SSP spectrum.
I
SFG
=
|
B
NR
e
iϕ
+
B
1
ω−ω
1
+iΓ
1
+
B
2
ω−ω
2
+iΓ
2
|
2
Where, Γ is the half-width half-max, ω
ν
is the central frequency of the ν
th
component in wavenumbers, φ
is the phase, and the Lorentzian amplitude is
B
Γ
.
91
Table 2: Spectral fitting results of the field-dependent free-OD response (PPP and SSP)
2T voltage vs.
Glassy Carbon
(V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-7 -3.9 -0.171 Amp1 -10.2 0.8 Amp 40.8 0.5
Amp2 28.7 0.4 ω 1 2696
.1
0.4
ω 1 2500 0 Γ 19.4 0.4
ω 2 2691.4 0.5 B NR 8.5 0.3
Γ 1 150 0 φ -5.37 0.05
Γ 2 18.3 0.6
B NR -6.4 0.2
φ -2.7 0.1
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-6 -3.3 -0.129 Amp1 -8.7 0.2 Amp 36.9 0.2
Amp2 26.3 0.2 ω
1
2695.3 0.3
ω
1
2500 0 Γ 18.8 0.4
ω
2
2690.7 0.5 B
NR
7.5 0.2
Γ
1
150 0 φ -5.37 0
Γ
2
19.1 0.6
B
NR
-5.7 0.2
φ -2.7 0
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-5 -2.7 -0.092 Amp1 -9.2 0.1 Amp 33.0 0.5
Amp2 27.3 0.2 ω
1
2691.8 0.5
ω
1
2500 0 Γ 15.9 0.6
ω
2
2691.2 0.4 B
NR
4.6 0.4
Γ
1
150 0 φ -5.37 0
Γ
2
17.8 0.4
B
NR
-5.1 0.2
φ -2.7 0
92
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-4.5 -2.4 -0.077 Amp1 -9.7 0.2 Amp 30.8 0.3
Amp2 28.1 0.2 ω
1
2692.4 0.4
ω
1
2500 0 Γ 18.1 0.5
ω
2
2690.8 0.5 B
NR
6.6 0.2
Γ
1
150 0 φ -5.37 0
Γ
2
18.5 0.5
B
NR
-6.2 0.2
φ -2.7 0
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-4 -2.1 -0.062 Amp1 -8.5 0.1 Amp 31.2 0.3
Amp2 25.1 0.2 ω
1
2692.0 0.4
ω
1
2500 0 Γ 17.5 0.5
ω
2
2690.3 0.5 B
NR
5.7 0.3
Γ
1
150 0 φ -5.37 0
Γ
2
19.3 0.5
B
NR
-4.9 0.2
φ -2.7 0
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-3.5 -1.8 -0.049 Amp1 -9.1 0.1 Amp 25.9 0.2
Amp2 24.8 0.2 ω
1
2688.6 0.5
ω
1
2500 0 Γ 18.5 0.6
ω
2
2689.2 0.6 B
NR
6.0 0.2
Γ
1
150 0 φ -5.37 0
Γ
2
19.3 0.6
B
NR
-5.8 0.2
φ -2.7 0
93
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-3 -1.5 -0.038 Amp1 -9.2 0.1 Amp 27.8 0.3
Amp2 24.2 0.2 ω
1
2689.8 0.5
ω
1
2500 0 Γ 17.4 0.7
ω
2
2690.4 0.5 B
NR
5.7 0.3
Γ
1
150 0 φ -5.37 0
Γ
2
19.1 0.5
B
NR
-5.5 0.2
φ -2.7 0
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-2.5 -1.2 -0.028 Amp1 -9.4 0.1 Amp 24.1 0.2
Amp2 24.2 0.2 ω
1
2687.4 0.5
ω
1
2500 0 Γ 18.5 0.7
ω
2
2689.4 0.5 B
NR
6.4 0.2
Γ
1
150 0 φ -5.37 0
Γ
2
20.3 0.5
B
NR
-5.8 0.1
φ -2.7 0
2T voltage
vs. Glassy
Carbon (V)
3T Voltage
vs. Ag/AgCl
(V)
E-Field
(V/Ang)
Parameters SSP Error Parameters PPP Error
-2 -0.9 -0.02 Amp1 -9.5 0.1 Amp 22.7 0.2
Amp2 22.6 0.2 ω
1
2687.6 0.6
ω
1
2500 0 Γ 21.1 0.8
ω
2
2693.1 0.7 B
NR
6.5 0.2
Γ
1
150 0 φ -5.37 0
Γ
2
20.2 0.6
B
NR
-5.8 0.1
φ -2.7 0
Contrary to the exponential distribution, the assumption of a Gaussian orientational distribution yielded
plots that were in fact consistent with experimental PPP to SSP ratios. Additionally, qualitative trends in
the calculated amplitudes were found to be consistent with experiment (Fig. 35). (1) both PPP and SSP
94
amplitudes increase monotonically, (2) the PPP amplitude increases faster than the SSP amplitude as the
free-OD is aligned to steeper angles with respect to the surface normal, and (3) the experimental field-
dependent PPP to SSP amplitude ratio, ranging from 1 to 1.4, exists in the calculated orientation curves
and correspond to a unique orientation (Fig. 35a, b). These qualitative features consistently emerge for
variously selected Gaussian distribution widths, though the exact free-OD orientation angles that are
determined through this method are sensitive to the distribution width (Fig. 36).
Figure 36: The calculated average orientation angle depends
on the orientational distribution width
The width of the orientational distribution can be interpreted as a susceptibility of the free-OD to
reorientation with respect to the applied field; narrower distribution widths describe a more rigidly
oriented ensemble.
95
O(θ ) is the free energy orienting potential, G(θ ) is the orientational free energy for a
Gaussian distribution, centered at the orientation angle of the free-OD with respect to the surface
normal, at the point of zero charge (pzc).
O(θ)=G(θ)−μ∙E=kT
[
ln(σ √2π)+
(θ−θ
pzc
)
(2σ
2
)
]
2
−μEcos(θ
0
) (63)
θ
0
is the angle between the permanent dipole of water and the surface normal. The μ∙E term
in the orienting potential , is the potential energy of a dipole in a DC-field, which imparts
anharmonicity onto the orienting potential and shifts its minimum to narrower orientation
angles, representing the effect of the field-induced reorientation of water (Fig. 37a).
Figure 37: The free-energy orienting potential for σ =15 , shifting with the
applied field in accordance with μ⋅E
Minima of the field dependent free-orienting potentials were located, corresponding to the average
free-OD orientation angles, then plotted against the applied field (Fig. 38; orange data points).
96
Repeating this procedure and superimposing this result with the one obtained from the amplitude
orientational analysis (Fig. 38, blue data points) leads to the following set of plots.
Figure 38: Determination of the orientational distribution width
The greatest consistency between the two methods to determine orientation was achieved for a
Gaussian distribution with σ ≈15 (Fig. 39), thus this distribution was utilized to determine the field-
dependent orientation (Fig. 37b) for the fields that were applied. Near the pzc, the free-OD moiety is
tilted to 45° (on average) with respect to the surface normal; for an applied field of about -0.17 V/ Å, the
free-OD is tilted to about 30° (on average) with respect to the surface normal (Fig. 37b). The free-OD
points outward toward graphene and thought to exist in a gap between graphene in water; the other
97
OD-bond extends into the bulk of water. To convert the free-OD tilt angle provided above to the angle
with respect to the permanent dipole of water, add the angle of
104.5°
2
(half the bond angle of water).
Figure 39: The sum of the difference between the two
complementary methods to determine the average
orientation
The central frequency of the free-OD shifts with respect to the applied DC electric field at the
interface (Fig. 40). This is due to a modulation of the spring constant of the free-OD bond
through interaction with the DC field. Since the DC field is effectively P-polarized, and the free-
OD ensemble is aligned and tilted by the field with respect to the surface normal, it is this
component of the free-OD dipole that experiences a Stark shift. A clear Stark shift is observed
for the PPP polarization configuration, since all the optical fields are compatible with the
polarization of the DC-field, however the Stark shift in the SSP configuration is much less
apparent. Although in both cases (PPP and SSP) a P-polarized DC field is applied, and the
vibration is excited with a P-polarized IR pulse, the dipole component in the S-polarized
98
direction is upconverted by the visible pulse and the SFG response is S-polarized in the SSP
configuration, and thus the Stark shift is still trending in SSP but is suppressed relative to PPP .
Figure 40: Stark shift of the free-OD response in the PPP and SSP
polarization configurations.
Promising Preliminary Measurements and Future Studies
The following results are deemed “preliminary” because they are the result of a single
effort which has not yet demonstrated to be reproducible. As such, they are good starting
points for future studies carried out by my colleagues at the University of Southern California,
the results of which would certainly generate much interest among the community.
As mentioned previously, m olecular re-orientation and interconversion between
different hydrogen-bonding classes leading to large-scale structural rearrangement of the
surface layer can be viewed as a field-induced phase transition of interfacial water, which was
first suggested based on temperature-jump relaxation measurements in 1980’s.
26
For applied
voltages near the onset of the free-OD response, an interesting trend was observed that may be
99
linked to such a phase transition. A shoulder at ~2720-2750 cm
-1
, which is increasingly more
pronounced as the voltage is made more positive, is found near the free-OD response in both
the SSP and PPP spectra (Fig. 41). Note that the data in each spectrum was acquired in two
steps, with the IR centered at nonidentical but adjacent frequencies in order to capture the
entire spectral range of D
2
O. Then the spectra were spliced together (the data is noisy at ~2500
cm
-1
where they were spliced, because the IR intensity was weaker there).
Figure 41: Voltage-dependent spectra near the onset of the Free-OD response in PPP and SSP
configurations.
Additionally, voltage-dependent SPS spectra were collected (Fig. 42). SPS spectra
provide an additional perspective, and an additional polarization configuration by which the
results of the orientational analysis can be verified and confidence can be strengthened. The
SPS spectra of water is notoriously difficult to obtain, since it is typically is a very weak signal.
100
Figure 42: Voltage dependent SPS spectra of the graphene-D
2
O interface
The SPS experiment concluded with an isotopic dilution (Fig. 43). The hydrogen-bonded and
free-OD features were lost upon isotopic dilution (Fig. 43, black curve, -3 V vs. glassy carbon),
suggesting that they originate from D
2
O. Interestingly, at positive voltages (Fig. 43, red curve, +3
V), with H
2
O in the electrochemical cell, a novel peak emerged. If verified, this response which
potentially originates from H
2
O may be a fortuitous and novel discovery at the graphene
interface that would be of significant interest in the community. Admittedly, it could also be
that this response is related to the presence of contaminants in the cell. This experiment should
therefore be repeated with extreme care, and the presence of contaminants must be evaluated
carefully, before and after the experiment is carried out.
101
0.30
0.25
0.20
0.15
0.10
0.05
0.00
2800 2700 2600 2500 2400 2300 2200
Free-OD SPS
-3 V
-2.5 V
-2.25 V
-2 V
-1.5 V
Figure 43: SPS spectrum of H
2
O at the graphene-water interface (in the
OD-stretch frequency region).
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104
Appendix
Matlab Script of Orientational Analysis
clear all;
close all;
% Dec 27, 2017 note
% this code uses two layer model
% which was used by Hong-fei and the
% n` is calculated using analytical expression given by
% Shen and Miranda but I modified to the expression so the n1 not equal to
% 1
%Zhuang, X.; Miranda, P . B.; Kim, D.; Shen, Y . R. Mapping Molecular Orientation
%and Conformation at Interfaces by Surface Nonlinear Optics. Phys. Rev. B 1999, 59,
%12632-12640
%Import n and k data
D_n_ir = importdata('path to n (IR frequencies) data');
D_k_ir = importdata('path to k (IR frequencies) data');
D_n_vis = importdata('path to n (Vis frequencies) data');
D_k_vis = importdata('path to k (Vis frequencies) data');
C = importdata('Path to k, n (VIS & IR) CaF2 data');
%imported n and k data to arrays
xC = C(:,1); yC = C(:,2);
xD_n_ir = D_n_ir(:,1); yD_n_ir = D_n_ir(:,2);
xD_k_ir = D_k_ir(:,1); yD_k_ir = D_k_ir(:,2);
xD_n_vis = D_n_vis(:,1); yD_n_vis = D_n_vis(:,2);
xD_k_vis = D_k_vis(:,1); yD_k_vis = D_k_vis(:,2);
%hyperpolarizability
beta_aac = 0.26; beta_bbc = 0.26; beta_ccc = 1;
%wavelengths and conversions of vis, IR, SFG
IR_cm1 = 2700;
vis_um = 0.8; %our vis wavelength is 800 nm
IR_um = 10^4 / IR_cm1;
c = 3 * 10^8;
cm1toGHz = 100 * c / 10^9;
omega1 = c / (vis_um * 1000) ; %GHz, visible
omega2 = IR_cm1 * cm1toGHz; %GHz, infrared
omega = omega1 + omega2; %sfg
sfg_um = c/(omega * 1000);
105
%angles of incidence
vis_angle = 68*pi/180;
ir_angle = 60*pi/180;
%set distribution parameters (see expect.m file)
dist = 15;
dist_type = 2; %1 = step; 2 = gaussian, 3 = sigma, 4 = exponential
i=1;
%Interpolate refractive index data
%CaF2
n0_omega1 = (interp1(xC,yC,vis_um));
n0_omega2 = (interp1(xC,yC,IR_um));
n0_omega = (interp1(xC,yC,sfg_um));
n1_omega1 = (interp1(xC,yC,vis_um));
n1_omega2 = (interp1(xC,yC,IR_um));
n1_omega = (interp1(xC,yC,sfg_um));
%D2O
n2_omega1 = (interp1(xD_n_vis,yD_n_vis,vis_um))+1i*interp1(xD_k_vis,yD_k_vis,vis_um);
n2_omega2 = (interp1(xD_n_ir,yD_n_ir,IR_um))+1i*interp1(xD_k_ir,yD_k_ir,IR_um);
n2_omega = (interp1(xD_n_vis,yD_n_vis,sfg_um))+1i*interp1(xD_k_vis,yD_k_vis,sfg_um);
% n' (interfacial n)
%J.Phys.Chem.Lett. 2016, 7, 2597-2601
% Yamaguchi, S.; Hosoi, H.; Yamashita, M.; Sen, P .; Tahara, T. Physisorption Gives
%Narrower Orientational Distribution than Chemisorption on a Glass Surface: A
%Polarization-Sensitive Linear and Nonlinear Optical Study. J. Phys. Chem. Lett. 2010, 1,
%2662-2665.
%Zhuang, X.; Miranda, P . B.; Kim, D.; Shen, Y . R. Mapping Molecular Orientation
%and Conformation at Interfaces by Surface Nonlinear Optics. Phys. Rev. B 1999, 59,
%12632-12640
ni_omega1 = ((n1_omega1^2 + n2_omega1^2 + 4)/(2*(1/n1_omega1^2 + 1/n2_omega1^2 + 1)))^0.5;
ni_omega2 = ((n1_omega2^2 + n2_omega2^2 + 4)/(2*(1/n1_omega2^2 + 1/n2_omega2^2 + 1)))^0.5;
ni_omega = ((n1_omega^2 + n2_omega^2 + 4)/(2*(1/n1_omega^2 + 1/n2_omega^2 + 1)))^0.5;
%beta is the incidence/replection angle from the interface normal
beta1 = (90-(180-(45+90-asin(sin(45*pi/180-vis_angle)/n1_omega1)*180/pi)))*pi/180; % visible
beta2 = (90-(180-(45+90-asin(sin(45*pi/180-ir_angle)/n1_omega2)*180/pi)))*pi/180; % IR
beta = asin((omega1*sin(beta1) + omega2*sin(beta2))/omega); %radians
% Reflection intensity at air/caf2 for vis and IR, and caf2/air for sfg
% This does not change the analysis at all because when PPP/SSP intensity
% ratios are taken, surface reflections are cancelled
[Rs_sfg, Rp_sfg, R_sfg] = intrc(n0_omega, 1, 0,15*pi/180);
106
[Rs_vis, Rp_vis, R_vis] = intrc(1, n0_omega1,0,vis_angle-45*pi/180);
[Rs_IR, Rp_IR, R_IR] = intrc(1, n0_omega2,0,ir_angle-45*pi/180);
%fresnel coeff
Lxx_omega = fresnel_factor('xx', n1_omega, n2_omega, ni_omega, beta );
Lxx_omega1 = fresnel_factor('xx', n1_omega1, n2_omega1, ni_omega1, beta1);
Lxx_omega2 = fresnel_factor('xx', n1_omega2, n2_omega2, ni_omega2, beta2);
Lyy_omega = fresnel_factor('yy', n1_omega, n2_omega, ni_omega, beta );
Lyy_omega1 = fresnel_factor('yy', n1_omega1, n2_omega1, ni_omega1, beta1);
Lyy_omega2 = fresnel_factor('yy', n1_omega2, n2_omega2, ni_omega2, beta2);
Lzz_omega = fresnel_factor('zz', n1_omega, n2_omega, ni_omega, beta );
Lzz_omega1 = fresnel_factor('zz', n1_omega1, n2_omega1, ni_omega1, beta1);
Lzz_omega2 = fresnel_factor('zz', n1_omega2, n2_omega2, ni_omega2, beta2);
%angle range and step for orientation plot
theta_start = 0;
theta_end = 90;
theta_step = .1;
%initialize array for orientation plot
angle = zeros(1, floor((theta_end-theta_start)/theta_step) +1);
ssp_r = zeros(1, floor((theta_end-theta_start)/theta_step) +1);
pss_r = zeros(1, floor((theta_end-theta_start)/theta_step) +1);
sps_r = zeros(1, floor((theta_end-theta_start)/theta_step) +1);
ppp_r = zeros(1, floor((theta_end-theta_start)/theta_step) +1);
%lab frame response equation 13 HF Wang c and d parameters
R = beta_aac/beta_ccc;
% SSP; equation 6 HF Wang
sspC = (1-R)/(1+R);
sspD = Lyy_omega * Lyy_omega1 * Lzz_omega2 * sin(beta2) * beta_ccc * (1+R) * 0.5;
%SPS
spsC = 1;
spsD = Lyy_omega * Lzz_omega1 * Lyy_omega2 * sin(beta1) * beta_ccc * (1-R) * 0.5;
%PSS
pssC = 1;
pssD = Lzz_omega * Lyy_omega1 * Lyy_omega2 * sin(beta) * beta_ccc * (1-R) * 0.5;
%PPP
pppA = Lxx_omega * Lxx_omega1 * Lzz_omega2 * cos(beta) * cos(beta1) * sin(beta2);
pppB = Lxx_omega * Lzz_omega1 * Lxx_omega2 * cos(beta) * sin(beta1) * cos(beta2);
pppC = Lzz_omega * Lxx_omega1 * Lxx_omega2 * sin(beta) * cos(beta1) * cos(beta2);
pppD = Lzz_omega * Lzz_omega1 * Lzz_omega2 * sin(beta) * sin(beta1) * sin(beta2);
pppC1 = 0.5 * beta_ccc * (-pppA * (1+R) - pppB * (1-R) + pppC * (1-R) + 2 * pppD * R);
pppC2 = 0.5 * beta_ccc * (1-R) * (pppA+pppB-pppC+2*pppD);
pppC = -pppC2/pppC1;
pppD = pppC1;
% Amplitude
Const = 1;
for theta=(theta_start:theta_step:theta_end)*pi/180
107
anglea(i) = theta*180/pi;
ssp_ra(i) = ((1-Rs_sfg)*(1-Rs_vis)*(1-Rp_IR))*real(sec(beta)*sspD*(expect(dist_type, dist, 'cos', theta) -
sspC*expect(dist_type, dist, 'cos3', theta)));
sps_ra(i) = ((1-Rs_sfg)*(1-Rp_vis)*(1-Rs_IR))*real(sec(beta)*spsD*(Const * expect(dist_type, dist, 'cos',
theta) - spsC*expect(dist_type, dist, 'cos3', theta)));
pss_ra(i) = ((1-Rp_sfg)*(1-Rs_vis)*(1-Rs_IR))*real(sec(beta)*pssD*(Const * expect(dist_type,dist, 'cos', theta)
- pssC*expect(dist_type, dist, 'cos3', theta)));
ppp_ra(i) = ((1-Rp_sfg)*(1-Rp_vis)*(1-Rp_IR))*real(sec(beta)*pppD*(expect(dist_type, dist, 'cos', theta) -
pppC*expect(dist_type, dist, 'cos3', theta)));
i=i+1;
end
% Plots
figure(2);
h1=plot(anglea, ppp_ra,'k', anglea, ssp_ra, 'r', anglea, sps_ra,'b--');
%h1=plot(angle, ppp_ra./ssp_ra, 'r');
xlim([0 90]);
tt = title('CaF2 prism-Graphene/D2O');
tt.FontSize = 15;
lg=legend('PPP', 'SSP', 'SPS');
lg.FontSize = 15;
ylabel('Amplitude', 'FontSize',15);
xlabel('Orientation angle', 'FontSize',15);
set(gca, 'FontSize', 16);
set(h1 ,'linewidth',2);
grid on;
%fclose(fid);
figure(3);
ratio=ppp_ra./ssp_ra;
h2=plot(anglea, ratio);
%h2=plot(angle, ppp_ra./ssp_ra, 'r');
xlim([0 90]);
tt = title('CaF2 prism-Graphene/D2O');
tt.FontSize = 15;
ylabel('PPP/SSP Ratio', 'FontSize',15);
xlabel('Orientation angle', 'FontSize',15);
xt = get(gca, 'XTick');
set(gca, 'FontSize', 16);
set(h2 ,'linewidth',2);
grid on;
%fclose(fid);
108
Abstract (if available)
Abstract
Aqueous interfaces play a crucial role in areas ranging from life sciences and environmental chemistry to heterogeneous catalysis, electrochemistry, and energy conversion applications. The solvation properties of interfacial water dictate chemical equilibria and reaction rates. Our basic understanding of water as a dielectric medium (polar solvent) relies on the assumption of linear response, i.e., that an external perturbation (electric field) induces a linearly proportional response (polarization) in the medium. Explicit in this assumption is antisymmetry with respect to the sign of the external field: the response must be of the same magnitude and opposite sign for positive vs. negative applied field of a given strength. We measured surface-selective vibrational sum frequency generation (VSFG) spectra of water (D2O) near a monolayer graphene electrode, to study its response to an external electric field under controlled electrochemical conditions. The graphene Raman G-band frequency is used as an internal gauge of the surface charge density. VSFG spectra of the OD-stretch show a pronounced asymmetry for positive vs. negative electrode charge. With sufficiently applied negative charge, a 2700 wavenumber peak corresponding to the “free” (non-hydrogen-bonded) OD groups pointing towards graphene surface is observed. At neutral or positive electrode potentials, the “free-OD” peak disappears in an abrupt nonlinear fashion, and the spectra are dominated by the broad peaks of the hydrogen-bonded OD-species (2300-2650 wavenumbers). Evolution of VSFG spectra as a function of the external electric field is related to the linear susceptibility (and the dielectric constant) by Miller’s rule. The experimentally observed deviation from the linear response to electric fields of the order of 0.3 V/nm calls into question the validity of treating interfacial water as a simple dielectric medium. The orientational distribution of the free-OD moiety is consistent with a Gaussian distribution, with. ❧ We present a model of field-induced reorientation and extract an expression for the free-energy orienting potential that is tested against experiment. Free-OD reorientation is measured with respect to applied electric fields: it is linear with respect to fields up to 2 V/nm, reorienting from about 45° to 30° relative to the surface normal. A linear relationship between the free-OD stark shift and the applied field is presented, rendering the free-OD capable of serving as an interfacial field-sensing probe.
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Montenegro, Angelo
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Asymmetric response and the reorientation of interfacial water with respect to applied electric fields
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Chemistry
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2022-05
Publication Date
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Defense Date
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