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Vibrational sum frequency spectroscopy of molecules on metal, semiconductor, and aqueous surfaces
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Vibrational sum frequency spectroscopy of molecules on metal, semiconductor, and aqueous surfaces
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Content
VIBRATIONAL SUM FREQUENCY SPECTROSCOPY OF MOLECULES ON
METAL, SEMICONDUCTOR, AND AQUEOUS SURFACES
by
Fadel Y. Shalhout
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMISTRY)
August 2013
Copyright 2013 Fadel Y. Shalhout
To my parents, Yousef and Muna Shalhout
ii
Acknowledgments
I am greatly indebted to my advisor, Alex Benderskii, who has given me the privilege
to be a part of his research group. It was truly an honor to know Alex throughout
these many years. I highly admire him for his unique scientic astuteness and ability
to elucidate and simplify the most unyielding questions. I thank him for giving me the
opportunity to transfer with him to USC from Wayne State University. The experience
I have gained during my four years at USC is something that I will never forget. I was
excited to be Alex's rst graduate student at USC and to be able to build the laser setup
from scratch in the newly renovated SSC 616 lab { a truly gratifying process once it was
nished and we found SFG signal for the rst time.
I would like thank Sergey Malyk, who has mentored me every day since coming to
USC. He is a great friend and has always oered to answer any naive question that I
threw at him. I thank him for his encouragement and guidance in these many years. He
taught me how to think not only like a scientist, but like a physicist.
I would also like to thank the members of the Benderskii group who have helped
me along the way: David Valley, Purnim Dhar, Sean Roberts, Ian Craig, and Misha
Vinaykin. David was particulary helpful with sharing his Mathematica, WinSpec, and
Igor Pro tricks and I enjoyed our enthusiastic conversations about baseball. Purnim was
especially kind for forfeiting some of his laser time to me to acquire the last measurments
of a long experiment. Sean and Ian were especially helpful during my preparation for
the qualifying exam and always had positive things to say to me. And of course, I would
iii
like to thank Misha, who I admired for his relentless determination, curiosity, humor,
and friendship.
I must not forget to thank my former lab mates from the Benderskii group at Wayne
State: Igor Stiopkin, Champika Weeraman, Himali Jayathilake, Achani Yatawara, and
Andrey Bordenyuk. They were the rst whom I met when I joined the group and who
all taught me, a true beginner at the time, about nonlinear spectroscopy.
I would like to thank my Ph.D. dissertation committee members Stephen Bradforth
and Mohamed El-Naggar. Their comments have always been thoughtful. I want to
particularly acknowledge Prof. Bradforth for always showing a sincere interest in my
research and my future prospects. Also, I want to acknowledge Prof. Bradforth's group
on the 7th
oor for being friendly neighbors.
I would like to thank our collaborators on the silicon project at Cal Tech, Prof. Nate
Lewis and Leslie O'Leary. I am grateful to Prof. Stephen Cronin and his group members
Wenbo Hou and Shermin Arab for sending samples our way. I thank John Curulli from
CEMMA for training me on the SEM instrument. Funding from the AFOSR, NSF,
Institute for Manufacturing Research, WSU, and USC were much appreciated, as well.
I want to thank my very talented summer REU student Joshua Hinman, who joined
us on the gold catalysis project and was great to have around to help work up data and
prepare samples.
I thank Prof. Hanna Reisler and Dr. Jessica Parr, who were both wonderful teaching
supervisors when I taught for their Advanced General Chemistry courses. I must also
acknowledge all of my brilliant undergraduate students, who made teaching chemistry
labs at 8 AM more enjoyable.
Of course, I cannot fail to thank the administrative sta for making graduate school
and all of the paperwork associated with it stress-free. Michele Dea, Valerie Childress,
and Katie McKissick were not only all extremely careful in making sure deadlines were
met, but that we felt like at home.
iv
Most importantly, I owe everything to my parents, Yousef and Muna, whose love,
encouragement, and support have guided me throughout my life. I thank my brothers,
Fuad and Fareed, and my sisters, Linda, Jowan, and Lisa, have all been inexplicably
patient with me. I thank my brothers-in-law, Ahmed and Ali, for their hospitality and
friendship. I thank my grandfathers, Fadel and Hamed, and my grandmothers Husseina
and Amna, who have always wished me the best. I must not forget to give the most
praise to my very smart nieces Dena, Layali, Zahraa, and Maram, and nephew Hadi,
who all make me feel 20 years younger when I am around them.
Fadel Shalhout
May 2013
Los Angeles, CA
v
Table of Contents
Dedication ii
Acknowledgments iii
List of Figures ix
List of Tables xiv
Chapter 1: Introduction 1
1.1 Surfaces 1
1.2 Background on Vibrational SFG 3
1.3 Nonlinear Spectroscopy 5
1.3.1 Second-Order Polarization 5
1.3.2 Second-Order Susceptibility
(2)
7
1.3.3 Sum Frequency Generation Spectroscopy 10
1.4 Thesis Outline 12
Chapter 2: Experimental Details of SFG Spectroscopy 14
2.1 SFG Spectrometer Setup 14
2.2 Appendix 20
2.2.1 Cross-Chirp Narrow-band 400 nm Generation 20
2.2.2 Homebuilt Single-Shot Autocorrelator 22
2.2.3 Plasma Technique for Compressing Pulses 26
2.2.4 Pinhole Technique for Finding Spatial Overlap 26
2.2.5 Fitting Code: Igor Pro 27
Chapter3: AzimuthalAnisotropyandRotationalDynamicsofCH
3
-Si(111)
Surfaces 29
3.1 Introduction 29
3.2 Experimental Details 32
3.2.1 SFG Setup 32
3.2.2 Sample Preparation and Handling 32
3.2.3 Orientational Anisotropy and Rotational Dynamics 34
3.2.4 Signal Processing 34
3.3 Results 34
vi
3.4 Discussion 46
3.4.1 Vibrationally Nonresonant Response of the Silicon 46
3.4.2 Resonant Response of the Surface-bound Methyl Groups 51
3.4.3 Rotational Dynamics of the Surface-bound Methyl Groups 56
3.5 Conclusion 58
3.6 Appendix 60
Chapter 4: Relative Phase Flip of Nearby Resonances in Temporally
Delayed SFG Spectra 66
4.1 Background on Time Delay SFG Techniques 66
4.2 Experimental Results 68
4.3 Time-Domain Description of SFG 71
4.4 Simulation of SFG Spectra 74
4.5 Phase of Vibrational Coherences 77
4.6 Conclusion 78
4.7 Appendix 79
Chapter 5: Reaction Intermediates on Plasmonic Photocatalysts 82
5.1 CO
2
Reduction on Au/TiO
2
Surfaces 82
5.1.1 Introduction 82
5.1.2 Experimental 85
5.1.3 Results and Discussion 86
5.1.4 Conclusions 95
5.2 Water-enhanced CO Adsorption on Roughened Gold Surfaces at Ambient
Conditions 96
5.2.1 Introduction 96
5.2.2 Experimental 97
5.2.3 Results and Discussion 99
5.2.4 Conclusion 108
5.3 Appendix 109
Chapter6: VibrationalCouplingandHydrogenBondingattheAir-Water
Interface 114
6.1 The Water Surface 114
6.2 Theory of Heterodyne-Detected SFG 117
6.3 Experimental Details 119
6.3.1 Heterodyne-detected SFG Setup 119
6.3.2 Sample Preparation 121
6.3.3 Data Processing 121
6.4 Results and Discussion 126
6.4.1 HD-SFG 126
6.4.2 Molecular Dynamics Simulations and Spectral Calculations 131
6.5 Conclusion 137
6.6 Appendix 137
6.6.1 H/D Isotopic Scrambling 137
vii
6.6.2 Normalization: Apparatus Function, f(!) 138
6.6.3 Amplitude and Phase 138
Bibliography 139
Autobiographical Statement 157
viii
List of Figures
1.1 Vibrational SFG energy diagram. The IR photon excites a vibrational
resonance in the molecule, and then a non-resonant interaction with a
visible photon leads to upconversion to a virtual state. The sum frequency
signal is emitted as the molecule returns to its ground state. 9
1.2 SFG interaction picture. An IR pulse induces a rst-order polarization
in the sample, followed by the visible pulse that induces a second-order
polarization in the sample. 11
2.1 Schematic of the vibrational SFG setup. Generated 800 nm light split
into two parts. 40% compressed, stretched with etalon. 60% split using
OPA and dierence taken in DFG to generate ngerprint region IR. Both
beams are focused on sample stage Detail of stage shown in Figure 2.3.
SFG signal is polarization selected and collected on CCD. 15
2.2 Spectra of the output from the Ti:sapphire oscillator (red line) and the
compressed pulse output from the Ti:sapphire regenerative cavity (blue
line). Black lines show ts to Gaussian pulse shape. 16
2.3 Detail of SFG stage. Purge box was lled with dry, CO
2
depleted air from
FTIR purge gas generator. 17
2.4 IR spectrum in CH stretch region taken on MCT detector. Black line is
tting with two gaussian line shapes. 18
2.5 (A) Frequency-resolved cross-correlation of femtosecond IR pulse and picosec-
ond visible pulse. (B) Temporal prole of visible pulse passed through the
etalon. (C) Freguency-domain spectrum of visible pulse. 19
2.6 Detail of the compressors used for 400 nm generation. Compressor 2
generally left in place between SFG and SHG setups. Compressor 1 used
for SFG and SHG and requires tuning. Tuning each compressor both
changes chirp and relative delay of the 800 nm laser pulses. After the
100 cm lens both pulses are summed though a BBO crustal to produce
transform limited picosecond 400nm pulse. 21
2.7 Layout of the single-shot auto-correlator (SSA). The optical path length
of Leg 1 and Leg 2 must be equal when they meet at the crystal. The
delay stage is used to compensate for Leg 1. The smaller the angle
between legs, the better the time resolution of the image (Fig. 2.8). BS
= beam splitter, HR = high re
ector. 23
ix
2.8 Schematic of achieving a single-shot autocorrelation of a femtosecond laser
pulse from the spatial intensity prole of the SFG signal from a nonlinear
crystal. Pulse length ct
p
, half-angle , and spatial fwhm x. 24
2.9 Spatial intensity distribution of SFG signal from nonlinear crystal obtained
by capturing image from screen using VGA web camera. 25
3.1 FTIR absorption intensity of the CH
3
symmetric stretch transition dipole
as a function of incident beam angle calculated for several CH
3
tilt angles. 31
3.2 SFG spectra of methyl-terminated Si(111) before (red) and after (blue)
baking at 450
C for 3-5 days in vacuum. 33
3.3 Temporal prole of the narrow-band visible pulse produced by passing a
femtosecond pulse through the etalon. 36
3.4 Eect of IR-visible time delay on the SFG signal for PPP polarization.
Spectra were recorded with zero delay (red line) and 300 fs delay (blue
line). 37
3.5 SFG PPP polarized spectra (0 fs delay) for rotation angles of 0
(brown
dots), 20
(blue), 40
(gray), 60
(green), 80
(red), 100
(purple), and
120
(orange). Only one rotational period is shown for clarity. Solid black
lines are ts to Eq. (3.6) 38
3.6 Polar plot showing the azimuthal dependence of the nonresonant ampli-
tude, A
NR
, on the in-plane rotation angle, ', changing counter-clockwise
from 0
to 360
, for PPP spectra (0 fs delay). 39
3.7 SFG PPP polarized spectra (300 fs delay) for rotation angles of 0
(brown
dots), 20
(blue), 40
(gray), 60
(green), 80
(red), 100
(purple), and
120
(orange). Only one rotational period is shown for clarity. Solid black
lines are ts to Eq. (3.6) 40
3.8 Polar plot showing the azimuthal dependence of the resonant amplitude
B(r
+
) of the PPP spectra (300 fs delay) normalized by (r
+
) on the
in-plane rotation angle, ', changing counter-clockwise from 0
to 360
41
3.9 Polar plot showing the azimuthal dependence of the resonant amplitude
B(r
) of the PPP spectra (300 fs delay) normalized by (r
) on the
in-plane rotation angle, ', changing counter-clockwise from 0
to 360
42
3.10 SFG SSP polarized spectra (0 fs delay) for rotation angles of 162
(red
dots), 182
(blue), 202
(green), 222
(gray), 242
(pink), 262
(purple),
and 282
(brown). Only one rotational period is shown for clarity. Solid
black lines are ts to Eq. (3.6) 43
3.11 Polar plot showing the azimuthal dependence of the nonresonant ampli-
tude A
NR
on the in-plane rotation angle, ', changing counter-clockwise
from 0
to 360
, for SSP spectra. 44
3.12 Polar plot showing the azimuthal dependence of the resonant amplitude
B(r
+
) normalized by (r
+
) of the SSP spectra (300 fs delay) on the in-
plane rotation angle, ', changing counter-clockwise from 0
to 360
45
x
3.13 Broadening of the line width for the CH
3
asymmetric stretch (r
) at
2976 cm
1
for the SPS spectrum (blue) compared to the PPP (red) polar-
ized SFG spectrum. Solid blue and red lines are ts of the SPS and PPP
spectra, respectively, to Eq. (3.6). 46
3.14 Geometry of SFG, surface coordinate system, orientation of the methyl
group on Si(111) surface, and the wave vectors and components for the
propagating visible eld. For the model we assume that is approximately
the same for !
1
and !
2
. The refractive index of Si is n and N at !
1
and
(!
1
+!
2
), respectively. 60
4.1 Experimental SFG spectra of CH
3
-Si(111) for IR-vis delay = 0 fs (a)
and = 300 fs delay (b). Solid black lines show ts to Eq. (4.3), and
dashed lines show decomposition of the t into a Gaussian (nonresonant)
envelope and two resonant Lorentzian terms, per Eq. (4.3), with resonant
amplitudes B
0
r
+ =1:0 and B
0
r
=0:63 (a.u.) for = 0 fs spectrum
(a) and B
0
r
+ = +0.38 and B
0
r
=0:28 (a.u.) for = 300 fs delay
spectrum (b). 69
4.2 (A) Frequency-resolved cross-correlation of the femtosecond IR and picosec-
ond visible pulses. (B) Temporal prole of the narrow-band visible pulse.
(C) Frequency-domain spectrum (red line) of the narrow-band visible
pulse produced by passing the compressed pulse through the etalon. Blue
line shows a Lorenztian t. 71
4.3 Temporally-delayed asymmetric visible pulseE
vis
(t) used to suppress non-
resonant signal produced by IR pulse E
IR
(t) at t = 0. 72
4.4 Simulated SFG spectra for IR-visible delay = 0 fs (a) and = 300 fs
(b). Solid black lines show ts to Eq. (4.3), and dashed lines show t
decompositions. 75
4.5 Picture depicting two vibrational coherences, who oscillate at slightly dif-
ferent frequencies, are in-phase at t = 0, and almost exactly out-of-phase
at300 fs delay. 77
5.1 Spectral distribution of solar photons (air mass = 1.5) (shown in red) and
absorption spectrum of TiO
2
(blue). Figure based on Seinfeld and Pandis,
1998. 83
5.2 SEM image of 5 nm of Au nano-island lm on TiO
2
. Image courtesy of
Prof. Stephen Cronin group, USC. 87
5.3 VSFG spectra of neat TiO
2
(blue) and TiO
2
covered with Au nano-islands
(red). 87
5.4 VSFG spectra showing CO stretch on Au/TiO
2
. Red: initial spectrum;
blue: annealed at 140
C; black: next day (left in air and light). PPP
polarization, 300 fs delay. 88
5.5 VSFG of controlled dosing experiments mimicking atmospheric condi-
tions. PPP polarization, 300 fs delay. 89
5.6 VSFG spectra of Au/TiO
2
before annealing (red), after annealing (blue),
after O
2
and light dosing (green), and after CO
2
and light dosing (green). 90
xi
5.7 VSFG spectra of unannealed 5 nm Au deposited on SiO
2
exposed to visible
laser beam in air (A) and an argon atmosphere (B). SEM images of non-
irradiated spot (C) and laser irradiated spot (D). 92
5.8 VSFG spectra of annealed 5 nm Au deposited on SiO
2
exposed to visible
laser beam of varying times in air (top) and argon atmosphere (bottom). 93
5.9 VSFG spectra of annealed 5 nm Au deposited on SiO
2
initially in argon
(red), after dosing with CO without (blue) and with (green) laser irradia-
tion, after dosing with CO and water with (pink) and without (black) laser
irradiation, and after
ash annealing sample to 100
C (spot 2 orange, and
spot 1 teal). Spectra were oset for clarity. 94
5.10 VSFG spectra of hydrogen
ame annealed (A), and non-treated (B) con-
tinuous vapor-deposited Au. Spectrum before dosing adsorbates (red
line), after dosing CO only (blue), and after co-dosing CO and H
2
O (green).101
5.11 VSFG spectra piranha-cleaned continuous vapor-deposited gold (sample
1). Spectrum before dosing adsorbates (red line), after dosing CO only
(blue), and after co-dosing CO and H
2
O (green). Black lines are ts to
Eq. (5.2). 102
5.12 VSFG spectra of electrochemically roughened continuous vapor-deposited
gold (sample 2). Spectrum before dosing adsorbates (red line), after dosing
CO only (blue), and after co-dosing CO and H
2
O (green). Black lines are
ts to Eq. (5.2). 103
5.13 (A) VSFG spectra after co-dosing CO and H
2
O vapor on non-treated
(green line), hydrogen
ame-annealed (black), piranha-cleaned (pink),
electrochemically roughened (blue), and electrochemically roughened then
piranha-cleaned (red) continuous vapor-deposited gold surfaces. SEM
images of hydrogen
ame-annealed gold (B), piranha-cleaned gold (C),
electrochemically roughened (D), and electrochemically/piranha-cleaned
gold (E). 104
5.14 VSFG spectra of piranha-cleaned Au (sample 3) acquired before dosing
adsorbates (red spectrum), after rst co-dosing of CO and H
2
O vapor
(green), after rst
ash annealing (black), after second co-dosing of CO
and H
2
O vapor (blue), after second
ash annealing (orange), and after
third co-dosing of CO and H
2
O vapor (purple). 106
5.15 VSFG spectra of piranha-cleaned continuous vapor-deposited gold. The
spectra in (a) are direct measurements of the SFG intensity upon dosing
H
2
O (blue) and co-dosing CO and H
2
O vapor (green), and (b) shows the
dierence in the intensity relative to the initial (red) spectrum from (a)
of dosing H
2
O (blue) and co-dosing CO and H
2
O vapor (green). The
same description follows for (c) and (d) except the gold sample was
ash
annealed at 120
C. 108
5.16 VSFG spectra of Au/TiO
2
initially in argon (red), after annealing (blue),
and after dosing oxygen in the dark (green), in the light for 30 min (pink)
and 60 min (black). 109
xii
5.17 VSFG spectra of unannealed Au/SiO
2
while dosing with oxygen (top) at
increasing times, and while oxygen is being purged from the sample at
increasing times (bottom). PPP polarization and 0 fs delay. 110
5.18 VSFG spectra of piranha-cleaned Au samples 4-7 (A-D). Sample 7 was
also electrochemically etched. 111
5.19 Scanning electron microscopy image of non-treated Au sample. 112
6.1 Heterodyne-detected SFG beam geometry. 120
6.2 The local oscillator (B) is subtracted from the HD-SFG interferogram (A)
to obtain the cross-term (C), assumingjE
LO
j
2
jE
SFG
j
2
. 122
6.3 The cross-term (A) is inverse Fourier transformed (IFFT) to obtain the
time domain amplitude (B). A square window is applied to lter out the
LO at t = 0, and then the spectrum is forward Fourier transformed (FFT)
to give the cleaned-up cross-term (C). 123
6.4 Principle of the phasing procedure. Phasing of spectra comprises of mul-
tiplying a spectrum by a phase factor e
i
. 124
6.5 Nonresonant (NR) background subtraction in HD-SFG. The NR back-
ground (100% H
2
O) (B) is subtracted from the 100% D
2
O spectrum (A)
to obtain the purely resonant spectrum (C). 125
6.6 HD-SFG spectra of the free OD stretch at the air-water interface. 127
6.7 Changes in vibrational spectra with isotopic dilution. 128
6.8 The vibrational coupling scheme of the free OD stretch at the air-water
interface. 130
6.9 Simulating and modeling the air-water interface. 134
xiii
List of Tables
3.1 Fitting parameters for PPP spectra recorded with 0 fs delay between IR
and visible pulses. 62
3.2 Fitting parameters for PPP spectra recorded with 300 fs delay between
IR and visible pulses. 63
3.3 Fitting parameters for SSP recorded with 0 fs delay between IR and visible
pulses. Amplitudes A
NR
and B(r
+
) are normalized with respect to PPP
0 fs delay amplitudes. 64
3.4 Fitting parameters for the rotational anisotropy in resonant and nonreso-
nant amplitudes for PPP and SSP spectra. 65
3.5 Nonresonant nonlinear susceptibilities of methyl-terminated Si(111) sur-
face obtained by tting the nonresonat SFG signal for PPP and SSP
polarization combinations to equations (3.19-3.21) 65
3.6 Vibrationally resonant nonlinear susceptibilities of CH
3
-Si(111) surface for
symmetric and asymmetric C-H stretch modes obtained by tting the res-
onat SFG signal for PPP and SSP polarization combinations to equations
(3.19-3.21). 65
4.1 List of parameters obtained by tting experimental PPP spectra at 0 fs
and 300 fs IR-visible delay (shown in Figure 4.1 in the main text) with
Eq. (4.3). Units for A
NR
, B(r
+
), and B(r
) are in arb. units,
NR
is in
rad., and !
g
,
g
, (r
+
), (r
), !(r
+
), !(r
) are in cm
1
79
4.2 List of parameters obtained by tting simulated PPP spectra at 0 fs and
300 fs IR-visible delay (shown in Figure 4.1 in the main text) with Eq.
(4.3). Units for A
NR
, B(r
+
), and B(r
) are in arb. units,
NR
is in rad.,
and !
g
,
g
, (r
+
), (r
), !(r
+
), !(r
) are in cm
1
80
4.3 Wavelength and pulse duration parameters used in Eqs. (4.10) and
(4.11) to simulate the electric elds of the visible and IR pulses. 80
4.4 The amplitudes B, line widths and central frequencies ! of the reso-
nant response for the symmetric (r
+
) and asymmetric (r
) CH
3
-stretch
vibrational modes, as well as the amplitude and phase of the nonresonant
background used in the simulations (Eq. (4.9) of the main text). Units
for A
NR
, B(r
+
), and B(r
) are in arb. units,
NR
is in rad., and (r
+
),
(r
), !(r
+
), !(r
) are in cm
1
81
5.1 Fitting parameters using Eq. (5.2) from main text. 113
6.1 H/D isotopic scrambling ratios for a given concentration, N. 138
xiv
Chapter 1
Introduction
1.1 Surfaces
The surface is where the bulk begins. It is the uppermost layer of molecules or atoms
in a medium. Molecules at the surface are surrounded by two bulk phases that they
separate, while bulk molecules all share a similar environment. In general, the percentage
of molecules at the surface is insigicant compared to the number of molecules in the
bulk. However, while there are comparatively few molecules at the surface, some of the
most important processes occur at surfaces or interfaces. The transport of ions, enzymes,
and other molecules across the membrane in a cell, the conversion of toxic combustion
byproducts into CO
2
and water by a vehicle catalytic converter, or the oxidation of iron
into rust are just some examples of processes that take place at the surface or interface.
The surface of a material can have very dierent properties than the bulk. For
example, because the symmetry is broken at the surface, molecular orbitals of surface
atoms are left exposed, which can render the surface highly reactive. This asymmetry
has intrigued scientists for several decades, and has oered a great challenge in describing
surface phenomena. Nobel prize-winning physicist Wolfgang Pauli had once guratively
proclaimed: "God created the bulk; the devil invented surfaces."
Surface chemistry encompasses many concepts such as heterogeneous catalysis,
1,2
semiconductor device fabrication, fuel cells, organic photovoltaics, adhesives, and self-
assembled monolayers.
3,4
With the emergence of these important surface processes, many
1
techniques have been developed to characterize and understand surface processes. Moti-
vated by the development of heterogeneous catalysts, the investigation of solid-gas inter-
faces advanced with the introduction of ultra high vacuum (UHV) in the mid-20th cen-
tury, which made it possible to study atomically clean surfaces. Methods such as inelas-
tic scanning tunneling spectroscopy,
5,6
high resolution electron energy loss spectroscopy
(HREELS),
7
helium atom scattering (HAS),
8,9
and X-ray scattering
10,11
are techniques
that employ the interaction of electrons, atoms, or x-rays with surfaces, all of which
require UHV conditions. Optical spectroscopic techniques have also been developed to
examine surfaces: attenuated total re
ection Fourier transform infrared (ATR-FTIR)
spectroscopy,
12,13
near eld scanning optical microscopy (NSOM),
14
surface-enhanced
Raman spectroscopy (SERS),
15
tip enhanced Raman spectroscopy (TERS)
16,17
and pho-
toacoustic spectroscopy
18,19
each oer a degree of surface-specicity. Scanning probe
microscopic techniques that oer information about surface structure and morphology,
such as scanning electron microscopy (SEM) and atomic force microscopy (AFM), have
also been invaluable in characterizing surfaces.
However, some disadvantages with most of these methods are that (1) they require
extreme environmental conditions (e.g., low temperatures or pressures) to analyze the
surface, (2) the method perturbs the system, (3) some methods are restricted in types of
samples they are able to measure or (4) the surface needs to be adjacent to or in contact
with the instrument.
Although linear optical spectroscopic techniques such as ATR-FTIR and SERS oer
structural information of molecules at surfaces, they lack surface-selectively and the
resulting spectra are often obscured by signal from the bulk. To overcome the limitation
of linear spectroscopic techniques, even-ordered nonlinear spectroscopies were developed
that are bulk forbidden (under the electric-dipole approximation) in centrosymmetric
media. However, at the surface the symmetry is broken, thus allowing the process to
yield a spectroscopic signal generated from only the surface. The two second-order
optical techniques that have been developed are second harmonic generation (SHG) and
2
sum frequency generation (SFG). Their key attribute is their ability to obtain surface-
selective molecular information without bulk signal contamination and with minimal or
no pertubation of the system. Additionally, these spectroscopies can provide information
about molecular orientation, vibrational modes, or electronic states, and are capable of
measuring time-dependent dynamics with femto- or picosecond resolution. Moreover,
the types of systems that can be probed with SHG and SFG are almost unlimited (e.g.,
liquid/solid, solid/solid, gas/solid, or liquid/liquid interfaces.)
1.2 Background on Vibrational SFG
The general case of second-order nonlinear spectroscopy is SHG, where an input beam
at frequency ! interacts nonlinearly with the material to produce the doubled output
signal of frequency 2!. The rst SHG measurements were performed on bulk non-
centrosymmetric media in the 1960s.
20
Around that time, Bloembergen and coworkers
developed the theoretical framework of SHG and SFG.
21
Experimental SFG is a relatively
young technique, pioneered by Shen and coworkers in the 1980s.
22,23
In an SFG experi-
ment, a vibrationally resonant IR pulse is overlapped temporally and spatially with an
o-resonant visible pulse used to upconvert the signal. Although SFG is experimentally
more complex than SHG, the attraction of the technique is its ability to probe vibrations
of molecules, thus allowing for the interrogation of molecular structure, orientation, and
dynamics.
Since the early SFG work on relatively simple dye molecules, the eld has expanded
vastly into more complex systems. The most popular system of study in SFG is the
aqueous surface, in particular the air-water interface. A number of studies have focused
on the free OH stretch
24{28
and more recently the bending mode of water,
29
to inves-
tigate hydrogen bonding structure at the surface. Substantial work has also been con-
ducted to understand water structure as it is aected by salts such as sodium halides,
30
3
ammounium,
31
and sulfates.
32
Moreover, the structure of water adjacent to a hydropho-
bic medium, e.g., organic-water interfaces, has been extensively studied.
33,34
Biological
interfaces have also been vigorously studied by SFG. The ability of SFG to probe buried
interfaces has shed some light on the understanding of biological processes in situ. Bio-
logical systems studied include lipid bilayer interfaces,
35
interfacial proteins,
36,37
and
chiral proteins structures.
38
Another active area of SFG research is on molecules physi- or chemisorbed to metal or
semiconductor surfaces. The properties of molecules on metal or semiconductor surfaces
are critical for a number of applications in areas in the elds of catalysis, electrochemistry,
and surface passivation. Vibrational SFG has provided valuable information for deter-
mining the molecular intermediates from catalytic surfaces, e.g., ethylene hydrogena-
tion or CO oxidation on Pt(111) surfaces.
39,40
Hydrogen
41
and octadecyl
42
terminated
Si(111) surfaces that feature ordered molecular layers, important as far as technological
applications are concerned, have been previously investigated using SFG. SFG is also
used extensively to study self-assembled monolayers (SAMs). SAMs take advantage of
the strong gold-thiolate bond to spontaneously form well-ordered organic domains that
are easily synthesized on gold substrates, both on
at and nanoparticle surfaces.
43,44
SAMs provide model surfaces for biomembrane mimetic studies, photoswitches,
45
and
are ideal candidates for chemical functionalization of surfaces. Moreover, the SFG signal
can be enhanced signicantly, in a similar electromagnetic enhancement mechanism to
surface-enhanced Raman scattering (SERS), if either the visible or SFG laser elds are
resonant with the nanoplasmon bands (gold520 nm, silver400 nm).
46
SFG spectroscopy can also be performed in the time domain, where temporal infor-
mation about the vibrational free induction decay can be studied through the analysis of
SFG line shapes.
47,48
In a time-domain SFG measurement, a femtosecond visible pulse
(required for time resolution) is used instead of a picosecond visible pulse (required for
frequency resolution). Although frequency and time domain measurements are equiv-
alent, in principle, it has been demonstrated that the two approaches are sensitive to
4
dierent aspects of a system and provide complementary information.
49
Time domain
SFG measurements have been used to investigate inter- and intramolecular coupling on
the C{O stretching vibration of CO adsorbed on Pt(111),
50
quantum beating,
48
and
vibrational energy relaxation at a metal surface,
51
to name a few. More recent develop-
ments in SFG spectrsocopy are heterodyne detection
52
and two-dimensional heterodyne
detected spectroscopy.
53,54
1.3 Nonlinear Spectroscopy
1.3.1 Second-Order Polarization
Spectroscopy is the study of the interaction between light and matter. When an elec-
tromagnetic wave interacts with a material, the electric eld component
~
E will exert a
force on the charged particles within that matter. In a dielectric medium the charges
are bound together and will begin to oscillate in the applied electric eld, and induce a
polarization
~
P in the medium, given by
55{57
~
P =
~
E (1.1)
At low intensity electric elds,
~
P responds linearly, and scales with the polarizability
of the medium. The polarizability of a medium is the ability for the molecules to be
polarized. Generally, the polarizability can be thought of as the volume occupied by the
electrons. Equation 1.1 may also be written as
~
P =
(1)
~
E (1.2)
where
(1)
is the linear suspectibility tensor of the medium. Linear processes such
absorption,
uorescence, and scattering, all depend on
(1)
.
With the advent of high power ultrashort laser pulses, where typical peak intensites
are on the order of 10
11
10
13
W/cm
2
, the assumption that the induced polarization is
5
linearly related to the electric eld strength can no longer apply, and the polarization
must be expressed as a Taylor expansion in the eld strength
~
P =
(1)
~
E +
(2)
:
~
E
2
+
(3)
:
~
E
3
+::: (1.3)
where
(n)
is the nth-order nonlinear susceptibility tensor.
In this dissertation, all nonlinear processes are second-order. Thus, let us consider
the case of two incoming electric elds with frequencies !
1
and !
2
such that E(t) =
E
1
e
i!
1
t
+E
2
e
i!
2
t
+c:c: (c.c. is complex conjugate), then the second-order polarization
P
(2)
can be expressed as
P
(2)
=
(2)
E
1
e
i!
1
t
+E
2
e
i!
2
t
+c:c:
2
(1.4)
=
(2)
E
1
2
e
2i!
1
t
+
(2)
E
2
2
e
2i!
2
t
+c:c: (1.5)
+ 2
(2)
E
1
E
2
e
i(!
1
+!
2
)t
+c:c: (1.6)
+ 2
(2)
E
1
E
2
e
i(!
1
!
2
)t
+c:c: (1.7)
+ 2
(2)
E
1
E
1
+ 2
(2)
E
2
E
2
(1.8)
A closer look at P
(2)
reveals that term 1.5 represents the second harmonic generation
(SHG) from each of the two incumbent electric elds. Term 1.6 represents the polariza-
tion oscillating at the sum of the two frequencies, i.e., sum frequency generation (SFG),
whereas term 1.7 is the dierence frequency of the two incumbent beams (a process
used to generate infrared pulses, see Chapter 2). The nal term (1.8) describes the
frequency-independent optical rectication (quasi-direct current polarization).
Now, let us examine how second-order nonlinear processes such as SFG are surface-
specic. For SFG,
(2)
is a third-rank tensor dened by a set of 27 elements
(2)
ijk
,
with i;j;k representing the three spatial coordinates. We can write the second order
6
polarization in terms of the two incoming beams, E(!
1
), E(!
2
), and the second order
nonlinear susceptibility
(2)
ijk
.
P
(2)
i
(!
s
) =
(2)
ijk
E
j;2
(!
2
)E
k;1
(!
1
) (1.9)
For a medium that possesses an inversion symmetry (centrosymmetric media), applying
the inversion operator i will change the sign of the electric elds, ^
~
E(!
1
) =
~
E(!
1
)
and ^
~
E(!
2
) =
~
E(!
2
), and will also change the sign of the polarization ^
~
P
(2)
=
~
P
(2)
.
However, in a centrosymmetric medium, opposite directions of the material are identical,
and ^
(2)
ijk
=
(2)
ijk
(the material properties are invariant under inversion). This now gives
us the expression,
P
(2)
=
(2)
(E(!
1
))(E(!
2
)) (1.10)
so that
(2)
E(!
1
)E(!
2
) =(
(2)
(E(!
1
))(E(!
2
)))
=(
(2)
E(!
1
)E(!
2
)) (1.11)
(2)
=
(2)
(1.12)
This condition can only be satised when
(2)
= 0. Thus, for centrosymmetric media,
within the electric dipole approximation, SFG is a forbidden process. At an interface or
surface, centrosymmetry is inherently broken and thus we can have a nite
(2)
.
1.3.2 Second-Order Susceptibility
(2)
The second-order (macroscopic) susceptibility tensor
(2)
ijk
of the surface is composed
from individual elements of the molecular (microscopic) hyperpolarizabilities
(2)
ijk
.
(2)
ijk
7
is calculated by transforming
(2)
ijk
from the molecular frame (a;b;c) (represented by
indices l;m;n) to the lab frame (x;y;z) (represented by indices i;j;k):
(2)
ijk
( ) =
*
X
lmn
R
ijk;lmn
( )
(2)
lmn
+
(1.13)
where R
ijk;lmn
( ) is the 6th-rank transformation tensor and represents the Euler
angles (; ;).
58
hi represents ensemble average over all molecules, since
(2)
lmn
are molec-
ular properties whereas
(2)
ijk
( ) is a macroscopic property of the sample.
(2)
lmn
generally consists of the resonant and nonresonant terms,
(2)
lmn
=
R
lmn
+
NR
lmn
,
where
R
lmn
was derived using pertubation theory:
59
R
lmn
=
X
v;g
hgj
lm
jvihvj
n
jgi
!
v
!
IR
i
v
v
(1.14)
Examining the hyperpolarizability tensor in Eq. 1.14 tells us that the SFG process
consists of an IR-active process (i.e., probability for IR transition dipole from ground
state g to rst vibrational state v,hvj
n
jgi), and an anti-Stokes Raman process (i.e.,
probability for Raman transition dipole fromv tog via virtual states,hgj
lm
jvi). Thus,
molecules must obey both IR and Raman spectroscopic selection rules to be SFG-active
(see Fig. 1.1).
8
Figure 1.1. Vibrational SFG energy diagram. The IR photon excites a
vibrational resonance in the molecule, and then a non-resonant interac-
tion with a visible photon leads to upconversion to a virtual state. The
sum frequency signal is emitted as the molecule returns to its ground
state.
For an azimuthally isotropic surface, i.e., symmetry about z-axis in the (x;y) plane,
of the 27 elements in the
(2)
ijk
tensor, only four independent non-zero elements survive,
namely
xxz
=
yyz
,
xzx
=
yzy
,
zxx
=
zyy
, and
zzz
. In an SFG experiment, the
polarization (direction of
~
E-eld) of the incident IR and visible laser beams and the
outgoing sum frequency signal can be individually controlled to probe particular tensor
elements of the susceptibility. The possible polarization combinations (for an azimuthally
isotropic surface) are PPP, SSP, SPS, and PSS (polarization of SFG-Visible-IR), and it is
possible to determine the orientation of molecules on surfaces or interfaces by measuring
the sum frequency signal strength as a function of these polarization combinations.
9
1.3.3 Sum Frequency Generation Spectroscopy
Let us now discuss what physically happens during an SFG experiment. An infrared
(IR) pulse, which is typically sent to the sample rst in time, excites an ensemble of
vibrational coherences in the molecule. If a single molecule was excited and was iso-
lated from its surroundings (bath), the vibration would oscillate without damping, so
the oscillation in time would be sinusoidal. However, in the condensed-phase, billions
of molecules are excited, and since each molecule has a slightly dierent energy (due to
dierent environment in the bath), they will all oscillate at slightly dierent frequencies.
At the initial excitation event (t = 0), we can assume that the oscillators, e.g., O-H
stretch at the water surface, will be in-phase. As time progresses, they will destruc-
tively interfere with each other since they are going to be out-of-phase. This is what
is dened as inhomogeneous vibrational dephasing. Therefore, when an IR pulse E
IR
excites vibrational coherences, it induces a rst-order polarization P
(1)
(t) in the mate-
rial, which decays in time. P
(1)
(t), or the free-induction decay (FID), not only contains
vibrational dephasing information, but also information about other physical processes
such as rotational dephasing
60,61
or energy transfer.
Formally, P
(1)
(t) is represented as
P
(1)
(t) =
1
Z
1
dt
1
S (t
1
)E
IR
(tt
1
) (1.15)
where S(t
1
) is the spectroscopic repsonse function of the surface, which contains all
the chemical information of the system. S(t
1
) contains both non-resonant and resonant
contributions. For example, for a surface-adsorbate interface such as carbon monoxide
adsorbed to gold (as in the system studied in Chapter 5), the resonant part ofS(t
1
) con-
tains the vibrational dephasing of the CO stretch, while the non-resonant part contains
the response mostly from the gold substrate. The non-resonant and resonant contribu-
tions to the response are discussed in more detail in Chapter 4.
10
Figure 1.2. SFG interaction picture. An IR pulse induces a rst-order
polarization in the sample, followed by the visible pulse that induces a
second-order polarization in the sample.
The next interaction in the SFG process involves the visible pulse. The visible pulse
E
vis
is said to be an upconversion pulse because it projects a second-order polarization
P
(2)
onto the sample. In other words, it will create a new polarization in the sample
after P
(1)
has been prepared. P
(2)
will now radiate an electric eld at the sum of the
frequency of the IR and the visible pulses.
P
(2)
(t) =
1
Z
1
dt
1
1
Z
1
dt
2
S
(2)
(t
1
;t
2
)E
IR
(tt
1
)E
vis
(tt
2
t
1
) (1.16)
Because the second interaction is nonresonant (i.e., instantaneous), the molecular
response is a-function with respect to the visible eld, S
(2)
(t
1
;t
2
) =S (t
1
)(t
2
), which
removes the second integration step in Eq. 1.16, and the second-order polarization is
expressed as
P
(2)
(t;) =P
(1)
(t)E
vis
(t) (1.17)
11
where is now the time delay between the IR and visible pulses. Figure 1.2 summarizes
the time-domain interaction picture of an SFG process.
In a frequency-domain SFG measurement, the signal is Fourier transformed by a
monochromator, and is given by time averaging the square of the polarization
I
SFG
(!
SFG
;)/
1
Z
1
P
(2)
(t;)e
i!
SFG
t
2
dt (1.18)
1.4 Thesis Outline
This thesis describes the implementation of the surface-specic vibrational sum frequency
generation spectroscopy to study the orientation, chemical structure, and dynamics of
molecules on various surfaces. The work shown here demonstrates the
exibility of the
SFG technique and how it could be used to understand systems having potential indus-
trial applications to systems of fundamental biological importance. Chapter 2 describes
the experimental details of the broad-bandwidth SFG spectrometer. In Chapter 3, vibra-
tional SFG was used to study the orientation and rotational dynamics of methyl groups
terminating a silicon(111) surface. The in
uence of the underlying silicon hyperpolariz-
ability on the hyperpolarizability of the methyl groups was found to be signicant, as
observed in the 3-fold azimuthal anisotropy in the vibrational SFG spectra. The rota-
tional dynamics of the methyl group was also determined from the analysis of SFG line
shapes.
Chapter 4 describes a fundamental and important phenomenon observed in
temporally-delayed SFG spectra. The SFG spectroscopy community relies on the anal-
ysis of SFG line shapes, particularly resonant amplitude ratios, to deduce orientations
of molecules on surfaces. However, spectal tting can sometimes be ambiguous, and
extracting correct amplitudes (and signs) of resonances is very important to obtain cor-
rect orientations. In this study, it was shown that when the nonresonant signal is not
fully suppressed by osetting the IR-visible delay, two nearby resonances may appear
12
in- or out-of-phase, depending on the time delay used for the measurement. This has
signicant implications since the phase of the SFG signal carries molecular information
such as a vibrational chromophore being oriented up versus down.
Chapter 5 demonstrates the potential of SFG to investigate heterogeneous catalytic
chemical reactions in situ and to identify intermediates. The chapter is divided into
two parts. Part one describes a phenomenological study of the carbon dioxide reduction
with water on a well-known photocatalyst of titania-supported gold nano-islands. Here,
we investigate the source of a pronounced CO adsorption peak that regenerates only
while the sample is in air and exposed to ambient light. In part two, CO adsorption
on continous gold lms was studied to elucidate the nature of the CO adsorption site
observed in part one. Quite interestingly, a new CO adsorption peak was observed
and could be enhanced when the gold surface was co-dosed with CO and water vapor,
indicating cooperativity in the adsorption behavior.
Finally, in Chapter 6, heterodyne-detected SFG (HD-SFG) was used to investigate
hydrogen bonding at the air-water interface. Here, the use of a local oscillator beam
to interfere with the SFG signal was able to provide sub-monolayer sensitivity as well
increased signal-to-noise ratio. The implementation of HD-SFG allows one to extract
both phase and amplitude of the spectroscopic signal, thus allowing to subtract the
nonresonant background signal. Subtraction of the nonresonant background signal allows
for the analysis of the true resonant line shapes. In this study, the question of just how
thin is the water surface, i.e., does the water surface have long-range eects into the
bulk, will be addressed.
13
Chapter 2
Experimental Details of SFG
Spectroscopy
In this thesis, all of the experiments were based on a femtosecond 800 nm Ti:sapphire
laser: the workhorse of our setup. In vibrational sum frequency generation spectroscopy,
two ultrashort pulses are required: a vibrationally resonant broad-bandwidth (100 fs)
IR pulse, which excites the molecule, and a nonresonant, spectrally-narrow picosecond
visible pulse, which acts as the up-conversion pulse. The Ti:sapphire regenerative ampli-
er is used to produce both of these pulses.
2.1 SFG Spectrometer Setup
The broadband vibrational SFG (BB-SFG) spectroscopy setup was based on a fem-
tosecond Ti:Sapphire laser system (Spectra Physics Spitre) that was retrotted with a
Coherent Legend regenerative amplier cavity, pumped with a Nd:YLF laser (18 W, 1
kHz, Evolution-30, Spectra Physics) and seeded with a Ti:sapphire oscillator (350 mW,
82 MHz, Kapteyn-Murnane Laboratories) centered at800 nm (full width at half max-
imum, fwhm50 nm). The oscillator was pumped with a Nd:YVO
4
laser (2.6 - 3.0
W, Millenia Vs J, Spectra Physics). Sixty percent of the 4 mJ fundamental pulse was
directed through a compressor that produced fwhm60 fs pulses (1.8 mJ,796 nm,
fwhm27 nm) that were used to pump an optical parametric amplier (TOPAS-C,
Light Conversion).
14
Figure 2.1. Schematic of the vibrational SFG setup. Generated 800 nm
light split into two parts. 40% compressed, stretched with etalon. 60%
split using OPA and dierence taken in DFG to generate ngerprint
region IR. Both beams are focused on sample stage Detail of stage
shown in Figure 2.3. SFG signal is polarization selected and collected
on CCD.
15
Figure 2.2. Spectra of the output from the Ti:sapphire oscillator (red
line) and the compressed pulse output from the Ti:sapphire regenera-
tive cavity (blue line). Black lines show ts to Gaussian pulse shape.
The signal and idler pulses ( = 1.1 - 2.6 m) that were produced from the TOPAS
were mixed in a dierence frequency generator (NDFG, Light Conversion), to yield
tunable IR pulses (500 - 4000 cm
1
). The mid-IR output was10 mW centered at
2900 cm
1
(C-H stretch region) with fwhm350 cm
1
(Figure 2.4). The remaining
40% of the uncompressed fundamental pulse was directed into a second compressor to
produce 55 fs visible pulses. These pulse were then sent into a high-power air-spaced
etalon (TecOptics; fwhm = 17 cm
1
, free spectral range480 cm
1
, and nesse65) at
11
incidence angle from the surface normal to produce a picosecond narrow-bandwidth
pulse that was centered near 796 nm.
Two separate lenses, a 10 cm focal length CaF
2
lens for the IR beam and 50 cm
BK7 lens for the visible lens, were used to focus the beams onto a200m spot on the
sample surface. The incidence angles of the IR and visible beams were 66
and 63
from
surface normal, respectively. The SFG stage beam geometry is shown in Figure 2.3.
16
Figure 2.3. Detail of SFG stage. Purge box was lled with dry, CO
2
depleted air from FTIR purge gas generator.
The laser power at the sample was typically 8 - 9J/pulse for IR. The intensity of the
visible was adjusted by a variable density lter before the sample (maximum power was
18-22 mW). The time delay between the two pulses was adjusted by a joystick-controlled
translation stage (Newport VX-25, 0.1 m (0.67 fs) accuracy). The SFG signal was
recollimated, spatially and frequency ltered, and focused onto the entrance slit of a 300
mm monochromator (Acton Spectra-Pro 300i). The signal was detected using a liquid
nitrogen-cooled CCD (Princeton Instruments, Spec-10:100B, 1340 100 pixels). PPP
(SFG-visible-IR), SSP, and SPS polarizations were used to obtain SFG spectra. The
polarization of the visible beam was controlled by using a zero-order quartz half-wave
plate (800 nm, CVI Melles Griot) while the IR beam polarization was controlled by using
a zero-order MgF
2
half-wave plate (150 - 6500 nm, 5 mm thick, Alphalas). The SFG
polarization was controlled by using a zero-order quartz half-wave plate (670 nm, CVI
Melles Griot). To eliminate polarization contamination, polarizers were used for the IR
(wire-grid holographic polarizer, extinction ratio > 300 : 1) and SFG beams (polarizing
beamsplitter cube, extinction ratio> 500 : 1). (The SFG polarization is rst selected by
the polarizer and then a half-wave plate is used to change the polarization to horizontal,
since the grating in the monochromator is approximately two times more ecient for
horizontal than vertical polarizations.)
17
The spectra of the narrow-band visible and broad band IR pulses were recorded
using the same signal collection optics and the same monochromator by replacing the
sample surface with a gold substrate (BioGold Microarray Slides, Thermo Scientic).
The spectra of the narrow-bandwidth visible pulse were recorded using the same grating
and CCD as for SFG detection. The spectra of the IR pulses were measured using an IR
grating blazed at 5 m and a liquid nitrogen-cooled mercury cadmium telluride (MCT)
detector (IR Associates).
Figure 2.4. IR spectrum in CH stretch region taken on MCT detector.
Black line is tting with two gaussian line shapes.
18
Figure 2.5. (A) Frequency-resolved cross-correlation of femtosecond IR
pulse and picosecond visible pulse. (B) Temporal prole of visible pulse
passed through the etalon. (C) Freguency-domain spectrum of visible
pulse.
The temporal proles of the compressed fundamental 800 nm pulses were determined
using a homebuilt single-shot autocorrelator to have fwhm55 fs. The compressed
fundamental pulses were then used to characterize the time width and chirp of the BB IR
pulses using a SFG cross-correlation on a nonresonant substrate (Au). Temporal proles
of the narrow-band picosecond visible pulses produced by the etalon were measured
by scanning the femtosecond IR pulse across the visible pulse and recording the SFG
cross-correlation signal from a nonresonant Au substrate.
19
2.2 Appendix
2.2.1 Cross-Chirp Narrow-band 400 nm Generation
The purpose of producing a picosecond narrowband 400 nm pulse was to pump our
multi-stage picosecond tunable visible OPA (not used in the work in this thesis). With
a tunable narrowband visible pulse, we can perform second harmonic generation (SHG)
studies on e.g., photovoltaic materials to study electronic states at the surface, or study
frequency-dependent surface plasmon enhancement on Au or Ag nanoparticles. To gener-
ate the narrowband picosecond 400 nm pulses, we used the method developed by Raoult
and coworkers
62
by summing oppositely chirped stretched femtosecond 800 nm pulses
in a nonlinear BBO crystal. To achieve a narrow, nearly transform-limited pulse, the
two pulses were tuned to give equal and opposite chirp (i.e., time dependence of the
instantaneous frequency of a pulse) through the frequency summing crystal such that
the sum frequency is narrowband.
We implemented this by splitting uncompressed fundamental output at 800 nm of
our Ti-Sapphire laser and compressing the two beams with a matched pair of grating
compressors (Newport), Fig. 2.6. The exact chirp of each the beams is not characterized,
although we believe the chirp for both pulses is nearly linear. However, optimization for
the conguration where the two beams have equal and opposite chirp can be achieved by
monitoring the SHG power output after doubling and minimizing the spectral width of
the doubled beam. This procedure does not yield a global optimum, but for each setting
of compressor 2 (top) there is a single optimum for compressor 1 and delay setting for a
transform limited picosecond pulse. The compressor 2 setting can be changed to adjust
the pulse duration and bandwidth of the resultant optimized 400 nm output.
Narrowband Generation Details
40% of the 800 nm fundamental pulse was split through a 50:50 beamsplitter and directed
into a pair of grating compressors (Newport) to stretch 6 ps chirped pulses (positive and
20
negative, respectively). Each stretched pulse was P polarized (vertical with respect to
table) with a zero-order quartz half-wave plate (800 nm, CVI Melles Griot). The two
stretched 800 nm pulses are focused (0.8
angle between beams) with a 100 cm lens and
temporally correlated through a 10 10 1 mm BBO crystal to generate300-340 mJ
(30-34% eciency) pulses of 4 picosecond, 7 cm
1
fwhm centered at 400 nm.
λ/2 plate
λ/2 plate
Delay
50:50 BS
100cm Lens
1
2
Figure 2.6. Detail of the compressors used for 400 nm generation.
Compressor 2 generally left in place between SFG and SHG setups.
Compressor 1 used for SFG and SHG and requires tuning. Tuning
each compressor both changes chirp and relative delay of the 800 nm
laser pulses. After the 100 cm lens both pulses are summed though a
BBO crustal to produce transform limited picosecond 400nm pulse.
21
2.2.2 Homebuilt Single-Shot Autocorrelator
Shown in Figure 2.7, the layout of our single-shot autocorrelator (SSA) is given (not
drawn to scale). A beamsplitter creates two copies of the same input femtosecond pulse,
which then are overlapped spatially and temporally onto a nonlinear crystal (type-I
BBO, 1 mm thick) to produce a SFG signal. The optical path lengths of both pulses
must be equal when they meet in the crystal, and a delay stage is used to adjust the
delay between the pulses. Leg 1 is transmitted through the beamsplitter while leg 2 is
re
ected. Therefore, since leg 1 accumulates group velocity dispersion (GVD) through
the medium, we must also compensate for this GVD in leg 2 by placing an optical
element of the same thickness (and material) of the beamsplitter. This is accomplished
by placing a 1 mm thick CaF
2
window in the path of leg 2.
22
Figure 2.7. Layout of the single-shot auto-correlator (SSA). The optical
path length of Leg 1 and Leg 2 must be equal when they meet at the
crystal. The delay stage is used to compensate for Leg 1. The smaller
the angle between legs, the better the time resolution of the image
(Fig. 2.8). BS = beam splitter, HR = high re
ector.
The intensity of the SFG signal depends on . When = 0, intensity is maximum.
Hence, by recording the intensity of the SFG signal as a function of the delay position
(which can be done with a translation stage with micrometer control), the pulse duration
t
p
(fwhm) can be measured (noting that the speed of light c = 2.99810
8
m/s) from
the autocorrelation function, given by
63
A () =
1
Z
1
I (t)I (t)dt (2.1)
23
As opposed to the above approach (which employs a multi-shot scanning operation
by introducing dierent delays), the duration of laser pulses from tens of femtoseconds
to a few picoseconds can be recorded in a single shot due to their small spatial extent.
63
Again, two identical laser pulses are made to cross each other at a small angle inside
a nonlinear crystal (Figure 2.8). At each point where the two pulses overlap, a SFG
signal is generated whose intensity is proportional to the product of local intensity in
each path.
Figure 2.8. Schematic of achieving a single-shot autocorrelation of a
femtosecond laser pulse from the spatial intensity prole of the SFG
signal from a nonlinear crystal. Pulse length ct
p
, half-angle , and
spatial fwhm x.
24
Figure 2.9. Spatial intensity distribution of SFG signal from nonlin-
ear crystal obtained by capturing image from screen using VGA web
camera.
As depicted in Figure 2.8, the direction of the signal is along the bisector of the
crossover angle. For any line parallel to the bisector, the SFG signal represents the time-
integrated intensity product. Since the beams cross at angle 2, dierent lines parallel to
the bisector correspond to overlap for dierent time intervals. Thus, the autocorrelation
function is mapped into a spatial intensity distribution of the SFG emission, which, in
our setup, is captured with a common VGA web camera. The fwhm x of the spatial
intensity distribution is related to the laser pulse duration as
t
p
= (k x sin)=c (2.2)
25
wherek is a numerical factor dependent on the pulse shape. For a Gaussian pulse shape,
k =
p
2.
2.2.3 Plasma Technique for Compressing Pulses
A quick way to compress an intense femtosecond pulse (> 1 mJ) is to place a lens in
front of the beam and look at the intensity of the plasma as you vary the delay on the
compressor. This method can be performed if you do not need to determine the actual
pulse duration (such as with an SSA), but need only to know that the pulse is compressed
as much as possible. Plasma is created by the electrical breakdown of air (ionization) at
the focal spot of the beam, where the intensity is the highest. The global maximum of
the plasma intensity is achieved when the plasma is the brightest (hottest), which can
be best observed by placing a white card after the lens and noting the change in color
as the pulse is being compressed.
2.2.4 Pinhole Technique for Finding Spatial Overlap
Finding SFG signal is sometimes tricky. A clever way to nd spatial overlap between
the IR and visible pulse is to cut out a hole no larger than the diameter of either beam
(in our case,300 m) in a thin piece of paper. To do this, fold a piece of paper (1
cm
2
) and cut a semi-ellipse along the crease, so when the paper is unfolded, an elliptical
hole is revealed. To nd spatial overlap at the sample stage:
1. with the visible beam blocked, re
ect the IR beam o a gold substrate and align
a thermal sensor to measure the power.
2. note the maximum IR power,
3. place the "pinhole paper" on the gold surface such that the crease is parallel to
the plane of incidence and the
aps are facing upward.
4. using a liquid crystal IR paper, roughly align the pinhole with the IR beam spot.
26
5. using the micrometers on the translation stage, make ne adjustments until the
pinhole is aligned with the IR beam. Alignment is accomplished when the power meter
shows a value near the maximum IR power (as noted in step 2).
6. unblock the visible beam, and align the visible beam onto the pinhole by adjusting
the lens translation stage. This step can be done with or without (by naked eye) a power
sensor.
2.2.5 Fitting Code: Igor Pro
Fitting code for SFG spectra: two Lorentzian functions for the resonant part and a
Gaussian function for the IR envelope. The code can be loaded into Igor Pro as a .ipf
le:
Function SFG_TwoLorentz_IRGaussian(w,x) : FitFunc
Wave w
Variable x
//CurveFitDialog/ These comments were created by the
//CurveFitDialog/ Curve Fitting dialog. Altering them will
//CurveFitDialog/ make the function less convenient to work
//CurveFitDialog/ with in the Curve Fitting dialog.
//CurveFitDialog/ Equation:
//CurveFitDialog/ f(x) = y0+magsqr(Anr*cmplx(0,phi)+b1/(cmplx(x-f1,G1))
+b2/(cmplx(x-f2,G2)))*exp(-((x-fg)/Wg)^2)
//CurveFitDialog/ End of Equation
//CurveFitDialog/ Independent Variables 1
//CurveFitDialog/ x
//CurveFitDialog/ Coefficients 11
//CurveFitDialog/ w[0] = y0
//CurveFitDialog/ w[1] = Anr
27
//CurveFitDialog/ w[2] = phi
//CurveFitDialog/ w[3] = b1
//CurveFitDialog/ w[4] = b2
//CurveFitDialog/ w[5] = G1
//CurveFitDialog/ w[6] = G2
//CurveFitDialog/ w[7] = f1
//CurveFitDialog/ w[8] = f2
//CurveFitDialog/ w[9] = fg
//CurveFitDialog/ w[10] = Wg
return w[0]+magsqr(w[1]*exp(cmplx(0,w[2]))+w[3]/(cmplx(x-w[7],w[5]))
+w[4]/(cmplx(x-w[8],w[6])))*exp(-((x-w[9])/w[10])^2)
End
28
Chapter 3
Azimuthal Anisotropy and
Rotational Dynamics of
CH
3
-Si(111) Surfaces
Polarization-selected vibrational sum frequency generation spectroscopy (SFG) has been
used to investigate the molecular orientation of methyl groups on CH
3
-terminated Si(111)
surfaces. The symmetric and asymmetric C-H stretch modes of the surface-bound methyl
group were observed by SFG. Both methyl stretches showed a pronounced azimuthal
anisotropy of the 3-fold symmetry in registry with the signal from the Si(111) substrate,
indicating that the propeller-like rotation of the methyl groups was hindered at room
temperature. The dierence in the SFG line widths for the CH
3
asymmetric stretch that
was observed for dierent polarization combinations (SPS and PPP for SFG, visible,
and IR) indicated that the rotation proceeded on a 12 ps time scale, as compared to the
100 fs rotational dephasing of a free methyl rotor at room temperature.
3.1 Introduction
Chemical functionalization of crystalline silicon surfaces is of interest for applications in
semiconductor technology, photovoltaics
64
, molecular electronics
65,66
, catalysis
67
, and
29
chemical and biological sensors.
68
Methyl-terminated Si(111) surfaces, in which essen-
tially all Si atop sites are terminated by methyl groups, have exhibited enhanced resis-
tance to air oxidation relative to the H-terminated Si(111) surface.
69,70
Studies of methyl-
terminated Si(111) surfaces using transmission infrared spectroscopy
71,72
, low temper-
ature STM
73
, and helium atom diraction
9
have indicated that the CH
3
groups are
oriented perpendicular to the substrate. This conclusion is also supported by theoret-
ical studies.
74{76
Low-temperature scanning tunneling microscopic (STM) studies have
shown that, at 4 K, CH
3
groups are immobile and are regularly oriented normal to the
unreconstructed Si(111) surface.
73,77
Although modeling indicates that the rotation of
neighboring closed-packed CH
3
groups might be inhibited due to steric interactions, the
rotational dynamics of such systems at room temperature are not well elucidated.
78
An azimuthal anisotropy of the second harmonic generation (SHG) signal has been
observed for silicon surfaces with various terminations.
79{81
However, the SHG signal is
dominated by the above-band-gap electronic resonances in silicon, so SHG probes the
symmetry of the silicon substrate (3-fold symmetry in the case of Si(111)) rather than
the surface-bound chemical species. Linear infrared (IR) spectroscopy has been used to
characterize the vibrations of the CH
3
- and C
2
H
5
-functionalized Si(111) surfaces.
71,72
While the C-H stretching and bending umbrella motions can be detected by IR absorp-
tion, the linear spectroscopy does not provide the sensitivity and information content
regarding the molecular orientation and conformation that is aorded by surface-selective
nonlinear spectroscopies, such as vibrational sum frequency generation.
3,23,44,56,82{87
For
example, infrared spectroscopic measurements are relatively insensitive to dierences
between zero and small tilt angles (on the order of 10
{20
) of the CH
3
group with
respect to the Si(111) surface normal, because such changes would result in only about
10% change in the magnitude of the IR transition dipole projection onto the surface
normal (Fig. 3.1.
30
Figure 3.1. FTIR absorption intensity of the CH
3
symmetric stretch
transition dipole as a function of incident beam angle calculated for
several CH
3
tilt angles.
In this work, we have used vibrational sum frequency generation (SFG) spectroscopy
to study the orientation of the methyl group of the CH
3
-Si(111) surface. Specically, two
of the methyl vibrational modes, the symmetric (r
+
) and asymmetric (r
) C-H stretches
have been investigated. A full description of the theory of nonlinear spectroscopy was
discussed in Chapter 1. Brie
y, SFG is a second-order surface-selective technique in
which two ultrafast laser pulses interact at the surface (or interface), to induce a second-
order polarization, P
(2)
(!):
P
(2)
(!) =
(2)
E
vis
(!)E
IR
(!) (3.1)
whereE
IR
(!) andE
vis
(!) are the electric elds of the infrared and visible laser pulses,
respectively, and
(2)
is the second-order susceptibility. This second-order polarization
acts as the source term for the radiation of the SFG signal, whose intensity is given by:
31
I
SFG
(!)/
P
(2)
(!)
2
(3.2)
The second-order nonlinear susceptibility,
(2)
, is a property of the material, and thus
contains both resonant
(2)
R
(vibrational transitions) and nonresonant
(2)
NR
(o- or on-
resonance electronic polarizability) contributions:
(2)
=
(2)
R
+
(2)
NR
(3.3)
(2)
R
is signicantly enhanced when the IR eld is resonant with a molecular vibrational
mode. In contrast,
(2)
NR
does not exhibit sharp vibrational resonances, and is typically
small for dielectric substrates but can be large for metal surfaces.
3.2 Experimental Details
3.2.1 SFG Setup
Detailed information about the SFG setup was discussed in Chapter 2. For this experi-
ment, the mid-IR output was centered at 2900 cm
1
(C-H stretch region) with a fwhm
350 cm
1
). The laser power at the sample was 8{9J/pulse for the IR. The intensity
of the visible was adjusted by a variable density lter before the sample stage so as not
to damage the sample, <10 J/pulse for CH
3
-Si(111) samples.
3.2.2 Sample Preparation and Handling
CH
3
-terminated Si(111) surfaces were prepared and characterized by the N. Lewis group
at Caltech as described previously.
71,88{90
After transporting to USC, the samples were
rinsed with water, acetone, methanol, and again with water. The samples were then
dried with inert gas, and heated at 450
C for 3-5 days, under vacuum, to remove
adventitious carbon (organic impurities) prior to SFG studies. To conrm the removal
of the impurities, a SFG spectrum was taken before and after the cleaning procedure.
32
Upon cleaning, the methylene (-CH
2
-) vibrational peaks from impurities could not be
detected, and only the CH
3
symmetric and asymmetric peaks remained (Fig. 3.2).
Additional heating of the sample did not alter the sample, as evidenced by a lack of
change in the CH
3
peaks. A SFG spectrum in the Si-H stretching spectral region (
2100 cm
1
) conrmed the absence of the H-terminated Si sites and was indicative of
100% methyl monolayer coverage of the Si surface.
Figure 3.2. SFG spectra of methyl-terminated Si(111) before (red) and
after (blue) baking at 450
C for 3-5 days in vacuum.
All SFG measurements were performed in dry air obtained from the FTIR purge
gas generator. Data acquisition was completed within 3 hours. The SFG spectra were
reproducible for dierent spots on the sample, indicating that there was no damage due
to the laser beams, and for dierent samples. The SFG spectra shown below represent
one of the samples, and the azimuthal dependences combine data collected for 3 samples.
Samples that were exposed to ambient air for longer than a few hours became contam-
inated with hydrocarbons, evidenced by the appearance of -CH
2
- vibrational peaks in
SFG spectra, indicating that the methyl-terminated Si surface is strongly lipophilic.
33
3.2.3 Orientational Anisotropy and Rotational Dynamics
The rotational anisotropy of the samples was determined for PPP and SSP polarization
combinations for 0 fs IR-visible delay (2 and 5 min exposure times, respectively). PPP
spectra for 300 fs delay were recorded with an exposure time of 5 min. A graduated
rotation stage (estimated accuracy0.5
) was used for azimuthal rotation of the sample
(in the plane of the sample surface). The rotational stage was aligned such that the
rotation axis coincided with the spot where the IR and visible beams overlapped on the
sample surface. This alignment procedure ensured that rotation of the stage would not
aect the position of the irradiated region of the sample.
To study the in-plane rotational dynamics of the methyl groups, several SFG spectra
were collected and averaged for PPP (5 min exposure times) and SPS (30 or 40 min
exposure times) polarizations combinations at a 300 fs IR-vis delay.
3.2.4 Signal Processing
The CCD image was processed using WinSpec (Roper Scientic). The SFG signal for all
experiments was focused onto 4 or 5 pixel strips in the vertical (Y) direction (pixel size,
20 m). A CCD pixel binning of 3X 4Y or 3X 5Y was used in all experiments. A
background correction was performed by subtracting a nonilluminated region of the CCD
(e.g., strip 16) from the SFG signal strip (e.g., strip 15). Spikes due to cosmic X-rays
were removed using an internal discriminator option within the WinSpec program. The
IR frequencies were calculated by subtracting the central frequency of the narrow-band
visible pulse from the SFG frequency.
3.3 Results
SFG spectra of the CH
3
-Si(111) surface were recorded at room temperature, for PPP
(SFG-vis-IR) and SSP polarization combinations, for a full 360
rotation in the plane of
the sample. The spectra covered the C-H vibrational stretch region from 2800-3000 cm
1
.
34
Two peaks, corresponding to the symmetric and asymmetric stretch, respectively, of the
methyl group were observed. All of the SFG spectra were tted to the relationship:
47
I
SFG
(!) =
(2)
eff
(!)E
IR
(!)E
vis
(!)
2
(3.4)
=
(2)
NR
+
(2)
R
E
IR
(!)E
vis
(!)
2
(3.5)
A
NR
e
i
+
N
X
j=1
B
j
!!
j
+i
j
2
e
(!!g)
2
g
2
(3.6)
which assumes a Gaussian spectral prole for the broad-band mid-infrared pulse with
central frequency !
g
and width
g
, and incorporates a convolution () with the narrow-
band visible pulse into the Lorentzian line shapes of the resonances. The vibrationally
nonresonant term,
(2)
NR
= A
NR
e
i
, with an amplitude A
NR
and a phase relative to
the resonant contribution, represents the electronically resonant response of the silicon
substrate, because both the visible and the VSFG photon energies are above the Si
band gap. Equation 3.5 assumes that this contribution to
(2)
NR
is spectrally
at within
the relatively narrow ( 200 cm
1
) frequency range corresponding to SFG wavelengths
between 645 nm and 654 nm. The resonant term
(2)
R
=
N
P
j=1
B
j
!!
j
+i
j
describes Bloch-
type (exponential) dephasing for each vibrational mode j, by a Lorentzian line shape
with a line width
j
, an amplitude B
j
=
j
, and a central frequency !
j
.
35
Figure 3.3. Temporal prole of the narrow-band visible pulse produced
by passing a femtosecond pulse through the etalon.
A time-delay technique introduced by Lagutchev et al.,
91
in which the asymmetry of
the visible pulse in the time-domain (Fig. 3.3) is used to up-convert mainly the slower
resonant contribution when the IR-visible time delay is judiciously chosen, was used to
decouple the nonresonant and resonant signals. As shown in Fig. 3.4, this technique
is particularly advantageous when a considerable nonresonant SFG signal is present, as
in the PPP spectra. However, a time delay was not used for the SSP spectra because
the signal was weaker at delayed times and longer exposure times were thus required to
obtain acceptable signal-to-noise.
36
Figure 3.4. Eect of IR-visible time delay on the SFG signal for PPP
polarization. Spectra were recorded with zero delay (red line) and 300
fs delay (blue line).
Figure 3.5 shows a series of PPP spectra at 0 fs IR-visible time delay, for azimuthal
angles ' varying from 0
to 120
. This pattern repeated itself for azimuthal angles
from 120
to 240
, and again from 240
to 360
, indicating a 3-fold in-plane symmetry.
The PPP spectra showed the CH
3
symmetric stretch (r
+
), at 2912 cm
1
, and the CH
3
asymmetric stretch (r
), at 2976 cm
1
. The solid black lines in Fig. 3.5 are the ts
using Eq. (3.6), with the tting parameters for each azimuthal angle listed in Table 3.1
of the Appendix at the end of this chapter.
37
Figure 3.5. SFG PPP polarized spectra (0 fs delay) for rotation angles
of 0
(brown dots), 20
(blue), 40
(gray), 60
(green), 80
(red), 100
(purple), and 120
(orange). Only one rotational period is shown for
clarity. Solid black lines are ts to Eq. (3.6)
.
Figure 3.6 shows the azimuthal rotational anisotropy of the nonresonant amplitude
A
NR
(red squares) for the full range of angles, ', from 0
to 360
, that were obtained
from the ts using Eq. 3.6. Also shown is the t (blue line) that describes the rotational
anisotropy:
38
Figure 3.6. Polar plot showing the azimuthal dependence of the non-
resonant amplitude, A
NR
, on the in-plane rotation angle, ', changing
counter-clockwise from 0
to 360
, for PPP spectra (0 fs delay).
A(') =
q
(a +c cos (3' +'
0
))
2
+k
2
(3.7)
where a and c are the isotropic and anisotropic contributions to the response, respectively,
k is a term to account for incoherent background (e.g., scattering), and' is the azimuthal
angle, with a phase correction of '
0
.
Because of the strong nonresonant signal at 0 fs delay observed in the PPP spectra,
the resonant amplitudes for the methyl stretches could not be determined accurately.
A 300 fs delay between the IR and visible pulses was used to suppress the nonresonant
background signal
(2)
NR
. Figure 3.7 shows the PPP spectra, at 300 fs delay, for the
same range of azimuthal angles as in Fig. 3.5, 0
<'<120
(again, the pattern repeated
39
itself twice more, for 120
<'<240
, and 240
<'<360
). The tting parameters for each
azimuthal angle are listed in Table 3.2 in the Appendix.
Figure 3.7. SFG PPP polarized spectra (300 fs delay) for rotation
angles of 0
(brown dots), 20
(blue), 40
(gray), 60
(green), 80
(red),
100
(purple), and 120
(orange). Only one rotational period is shown
for clarity. Solid black lines are ts to Eq. (3.6)
.
Figures 3.8 and 3.9 present the resonant amplitudes for the symmetric and asym-
metric CH
3
stretch,B(r
+
)=(r
+
) andB(r
)=(r
) (red squares), obtained from the ts
40
(Eq. 3.6) for each azimuthal angle. The model (shown as blue lines in Figs. 3.8 and 3.9)
that was used to describe the resonant amplitude anisotropy is:
B(') =a +c cos (3' +'
0
) (3.8)
where the denitions of the terms are the same as in Eq. 3.7.
Figure 3.8. Polar plot showing the azimuthal dependence of the res-
onant amplitude B(r
+
) of the PPP spectra (300 fs delay) normalized
by (r
+
) on the in-plane rotation angle,', changing counter-clockwise
from 0
to 360
.
41
Figure 3.9. Polar plot showing the azimuthal dependence of the res-
onant amplitude B(r
) of the PPP spectra (300 fs delay) normalized
by (r
) on the in-plane rotation angle,', changing counter-clockwise
from 0
to 360
.
42
Figure 3.10 shows a series of SSP spectra, at 0 fs delay, for one rotational period.
Only the CH
3
symmetric stretch (r
+
) at2912 cm
1
was observed in the SSP spectra.
Figure 3.10. SFG SSP polarized spectra (0 fs delay) for rotation angles
of 162
(red dots), 182
(blue), 202
(green), 222
(gray), 242
(pink),
262
(purple), and 282
(brown). Only one rotational period is shown
for clarity. Solid black lines are ts to Eq. (3.6)
.
43
The nonresonant, A
NR
, and resonant, B(r
+
)=(r
+
), amplitudes were obtained from
the ts to the spectra using Eq. (3.6), and are plotted in Figures 3.11 and 3.12, respec-
tively (the complete list of SSP spectral tting parameters is given in the Appendix,
Table 3.3). Equations (3.7) and (3.8) were used to describe the nonresonant and reso-
nant anisotropy in the SSP spectra. A list of the tting parameters used in Eqs. (3.7)
and (3.8) for both PPP and SSP spectra is provided in the Appendix, Table 3.4.
Figure 3.11. Polar plot showing the azimuthal dependence of the non-
resonant amplitude A
NR
on the in-plane rotation angle, ', changing
counter-clockwise from 0
to 360
, for SSP spectra.
44
Figure 3.12. Polar plot showing the azimuthal dependence of the res-
onant amplitude B(r
+
) normalized by (r
+
) of the SSP spectra (300
fs delay) on the in-plane rotation angle, ', changing counter-clockwise
from 0
to 360
.
Figure 3.13 shows the SFG spectra for the PPP (red dots) and SPS (blue dots)
polarization combinations, averaged over four sets of PPP and SPS spectra recorded with
a 300 fs delay. A broadening of the spectral line shape for the CH
3
asymmetric stretch
(r
) vibrational mode was observed for the SPS spectrum relative to the PPP spectrum.
The spectral ts that were performed using Eq. (3.6) are shown as solid lines. These
measurements were performed at a 120
rotational angle, for which the nonresonant
background was at its minimum. The asymmetric stretch line width for the PPP spectra
was
PPP
(r
) = 12:4 0:5 cm
1
and for the SPS spectra was
SPS
(r
) = 15:9 1:0
45
cm
1
. The dierence in the line widths, 3:5 1:5 cm
1
, was interpreted as rotational
dephasing, as discussed in detail below.
Figure 3.13. Broadening of the line width for the CH
3
asymmetric
stretch (r
) at 2976 cm
1
for the SPS spectrum (blue) compared to
the PPP (red) polarized SFG spectrum. Solid blue and red lines are
ts of the SPS and PPP spectra, respectively, to Eq. (3.6).
3.4 Discussion
3.4.1 Vibrationally Nonresonant Response of the Silicon
A phenomenological macroscopic theory of the second harmonic generation (SHG) elec-
tronic response of a surface of a cubic centrosymmetric crystal was developed by Sipe
et al.
80
This theory does not make any assumptions regarding the microscopic physical
46
properties of the surface or bulk response tensor. The theory is rigorous in the sense
that it is purely based on the macroscopic symmetry of the surface and of the bulk of
the crystal.
78
The approach provides a convenient framework with which to analyze the
SFG signals from the CH
3
-Si(111) surface. The key concepts and equations, specically
adapted for understanding the vibrational sum frequency response of the CH
3
-Si(111)
surface, are brie
y summarized below.
The eective second-order polarization P
(2)
(!) contains contributions from the sur-
face and from the bulk of Si crystal. Each of these contributions has isotropic and
anisotropic components, based on the crystal symmetry. The bulk contribution to the
eective polarization, in the case of a homogeneous medium excited by a single transverse
plane wave, consists of nonlocal electric quadrupole as well as magnetic dipole terms (the
lowest-order surviving multipole terms), and can be written as:
79,80,92,93
P
(2)
i
=
r
i
(E
IR
E
vis
) +
iiii
E
IR
i
r
i
E
vis
i
(3.9)
where
and are phenomenological constants. The rst term is isotropic with respect
to the crystal orientation, while the second term has both isotropic and anisotropic
components (here we neglect the term that is nonlocal in the IR eld). For a Si(111)
surface that has 3-fold rotation symmetry, the SFG elds that are generated outside of
the medium have a form:
79,80
E
SFG
= (a +c cos 3')E
vis
E
IR
(3.10)
where ' is azimuthal angle within the (111) plane; and a and c represent the isotropic
and anisotropic response, respectively.
We only consider the SSP and PPP polarization combinations that are relevant to
our experimental conditions. The SFG elds that are generated by the bulk response for
these two polarization combinations are:
47
E
SFG
p
=A
p
D
a
p
bulk
+c
p
bulk
cos 3'
+
F
S
E
vis
p
E
IR
p
(3.11)
E
SFG
s
=A
s
D (a
s
bulk
+c
s
bulk
cos 3')E
vis
s
E
IR
p
(3.12)
where a
s;p
bulk
and c
s;p
bulk
are bulk isotropic and anisotropic coecients, respectively. F
s
is
the sine of the angle of the SFG beam in the silicon, and A
p
, A
s
, and D are constants
that contain the angle of incidence and the optical properties (refractive indices) of the
interface.
80
Calculation of the isotropic and anisotropic bulk coecients,
80
a
s;p
bulk
and
c
s;p
bulk
, involves only the incident angles and the dielectric constant of the medium at
IR, visible, and SFG frequencies (details are presented in the Appendix at the end of
this chapter). Essentially, two adjustable parameters,
and , describe the nonlinear
response of the bulk medium and thus can change the bulk contribution to the signal.
The surface contribution to the SFG signal is primarily dipolar, because the inversion
symmetry is broken on CH
3
-Si(111) surfaces.
79,80
The symmetry of the SFG nonlinear
susceptibility tensor is assumed to be determined by the symmetry of the Si(111) sur-
face. If only the rst layer of Si atoms is taken into account, the symmetry is C
6v
;
79,80
however, the symmetry lowers toC
3v
if additional surface layers are considered.
79,80
The
nonlinear surface susceptibility tensor for the Si(111) surface should satisfy C
3v
symme-
try, and thus has four independent elements, comprised of three isotropic terms and one
anisotropic term.
79
The 2
nd
-order polarization for the Si(111) surface, when the z-axis
is perpendicular to the surface and the y-axis is perpendicular to the plane of symmetry,
can be written as:
79,80
48
P
(2)
x
P
(2)
y
P
(2)
z
=
@
11
@
11
0 0 @
15
0
0 0 0 @
15
0 @
11
=2
@
31
@
31
@
33
0 0 0
E
vis
x
E
IR
x
E
vis
y
E
IR
y
E
vis
z
E
IR
z
E
vis
y
E
IR
z
E
vis
x
E
IR
z
E
vis
x
E
IR
y
(3.13)
where @
15
;@
31
;@
33
are isotropic terms and @
11
is anisotropic term. As can be seen from
3.13, these constants are simply related to the elements of the 2
nd
-order SFG suscepti-
bility tensor
(2)
by:
(2)
zzz
=@
33
;
(2)
zxx
=@
31
;
(2)
xxz
=@
15
;
(2)
xxx
=@
11
(3.14)
The SFG surface responses for PPP and SSP polarizations have the form:
80
E
SFG
p
=A
p
a
p
surf
+c
p
surf
cos 3'
E
vis
p
E
IR
p
(3.15)
E
SFG
s
=A
s
a
s
surf
+c
s
surf
cos 3'
E
vis
s
E
IR
p
(3.16)
where, as outlined in the Addendum, the a
s;p
surf
and c
s;p
surf
are surface isotropic and
anisotropic coecients that contain the @ coecients dened in Eq. (3.13), the inci-
dence beam angles, and the dielectric constants.
80
The constants A
p
and A
s
are the
same as in Eqs. (3.11, 3.12).
Combining the bulk, Eqs. (3.11,3.12), and surface, Eqs. (3.15,3.16), expressions
the isotropic and anisotropic contributions to the total SFG signal for PPP and SSP
polarization combinations are thus:
49
E
SFG
p
=A
0
p
(1 +R
ppp
cos 3')E
vis
p
E
IR
p
(3.17)
E
SFG
s
=A
0
s
(1 +R
ssp
cos 3')E
vis
s
E
IR
p
(3.18)
where we have introduced the ratio R
ppp;ssp
of the anisotropic to isotropic components
that determines the modulation depth in the experimentally measured azimuthal angular
dependence of the SFG signal:
R
ppp
=
Dc
p
bulk
+c
p
surf
=
Da
p
bulk
+
F
s
+a
p
surf
(3.19)
R
ssp
=
Dc
s
bulk
+c
s
surf
=
Da
s
bulk
+a
s
surf
(3.20)
To compare the amplitudes of the PPP and of the SSP signals, we also dene the ratio
of the anisotropic parts for the SSP and PPP polarizations:
c
ppp
=c
ssp
=
Dc
p
bulk
+c
p
surf
=
Dc
s
bulk
+c
s
surf
(3.21)
The ratio of the isotropic parts of the PPP and SSP signals can be obtained from Eqs.
(3.19 { 3.21)
Figures 3.6 and 3.11 show the azimuthal dependence of the nonresonant amplitude
of the CH
3
-Si(111) SFG signal for the PPP and SSP polarization combinations. The
SFG amplitudes clearly showed a 3-fold dependence on the azimuthal angle, with the
same phase in both cases. The nonresonant SFG signal should be dominated by the
response of the silicon itself (not the surface methyls), and thus is expected to be well
described by the phenomenological model outlined above. Several groups have mea-
sured the azimuthal dependence of the second harmonic generation (SHG) for Si(111)
surface.
79{81
In particular, Mitchell et al.
81
studied the behavior of the isotropic a and
anisotropic c parameters as a function of the surface functionalization and of the probe
50
wavelength. H-Si(111) surfaces exhibit isotropic and anisotropic parameters with a ratio
R
ppp
changing from4.6 for 830 nm fundamental excitation to1.3 for 775 nm exci-
tation. For CH
3
-Si(111), an R
ppp
value of2.9 was obtained from the t of the PPP
nonresonant SFG amplitude for the 796 nm visible and the 650 nm SFG wavelength,
which is well in the range of values reported by Mitchell et al.
81
The nonresonant ampli-
tude for the SSP SFG signal (see Fig. 3.11) hadR
ssp
5.1 and had the same phase'
0
as
the PPP SFG anisotropic part. Additionally, the ratio of anisotropic parts c
ppp
=c
ssp
was
observed to be2.3. The parameters for the Si(111) surface and bulk nonlinear response
can be obtained from Eqs. (3.17 { 3.20), with a total of six independent parameters in
the model: four for the surface response, @
15
;@
31
;@
33
and @
11
, and two for the bulk
response,
and . However, only three independent parameters that characterize the
anisotropy can be obtained experimentally, Eqs. (3.19, 3.20) and (3.21). Thus, all of
the model parameters can not be determined, but the experiment can constrain some of
their ratios. One possible set of the model values is listed in Table 3.5 of the Appendix.
Overall, the obtained values are close to the ones reported by Mitchell et al.
81
3.4.2 Resonant Response of the Surface-bound Methyl Groups
The vibrationally resonant SFG signals contain information on the molecular orientation
and on the dynamics of the CH
3
groups at the Si(111) surface. Even without a detailed
analysis, the pronounced 3-fold azimuthal anisotropy of the CH
3
resonant signal (Figs.
3.8, 3.9, 3.12) observed in both the PPP and SSP spectra suggests that the methyl
groups are well oriented and preserve the azimuthal symmetry of the Si(111) surface, i.e.
they do not freely rotate at room temperature.
The standard SFG orientational analysis assumes a three-layer model for the inter-
face,
56,94
and calculates the resonant contribution to
(2)
by assuming a molecular
hyperpolarizablity tensor
(2)
for a given vibrational mode. The
(2)
tensor is then
converted from the molecular frame (a;b;c) into the lab frame (x;y;z), where the z-
axis is usually chosen to be normal to the sample surface.
56,58,95
This approach has
51
been applied to access the orientational analysis of the SFG spectra, in particular to
azimuthally anisotropic systems such as rubbed polymer surfaces.
96{98
The hyperpolar-
izablity tensors for the symmetric and asymmetric stretch modes of the methyl group
have been estimated from experimental SFG measurements on molecules with long alkane
chains,
23,48,82,87,97,99,100
and can be approximated by a bond-additivity model.
82,101
The
SFG hyperpolarizabilities of the C-H stretches of CH
3
OH have been rigorously modeled
computationally.
102,103
Because the methyl group C-H stretches are relatively weakly
coupled to other C-H stretching modes, the hyperpolarizablity tensors
(2)
are gener-
ally assumed to be similar for terminal methyl groups on long-chain alcohols, carboxylic
acids, and alkane thiols.
However, use of the literature values for
(2)
of the terminal methyl group did not
allow reproduction of the observed azimuthal dependence of the resonant SFG signal on
the CH
3
-Si(111) surface. Notably, the molecular hyperpolarizability tensor is a product
of the vibrational transition dipole moment and the Raman polarizability tensor:
i
lmn
/
@
lm
@q
i
@
n
@q
i
(3.22)
whereq
i
is the normal coordinate of i-th vibrational mode and the indices l;m;n repre-
sent the axes of the molecular frame (a;b;c), with thec axis usually chosen to be the main
symmetry axis. Because of the C
3v
symmetry of the methyl group, the IR transition
dipole for the symmetric stretch (ss) is along the C
3
axis (c), and the Raman polar-
izability tensor is isotropic about the symmetry axis, such that
ss
aac
=
ss
bbc
.
94
Hence,
if the C
3
axis of the methyl group is normal to the surface, no azimuthal anisotropy
of the symmetric stretch signal can exist, regardless of the in-plane orientation of the
methyl group (e.g., either isotropic random azimuthal orientation or locked orientation
in registry with the silicon substrate). Thus, only asymmetric stretch (as) anisotropy
can be present, for all anisotropic (e.g., 3-fold) azimuthal distributions of the methyl
52
group. This expectation is clearly contradicted by the experimental observations, Figs.
3.8 and 3.12.
We also considered a distribution of the methyl orientations along the Euler angles
(; ;') that dene the orientation of the molecular frame (a;b;c) relative to the lab
frame (x;y;z). The distribution along the azimuthal angle ' was taken to be a sum of
three delta functions shifted by 120
relative to each other, and no torsional motion was
allowed (delta-function distribution along the torsion angle ). Several distributions of
the tilt angle, including a delta-function centered at
0
, a Gaussian centered at
0
, and
a bi-modal distribution with two sub-populations centered at 0 and
0
, were tested. The
macroscopic susceptibility
(2)
was then calculated by rotating
(2)
from the molecular
frame to the lab frame, and averaging over the orientational distribution:
56,58,82,95
(2)
ijk
=N
S
X
l;m;n
hR
ijk;lmn
(; ;')i
;';
(2)
lmn
(3.23)
In all cases, as expected, no azimuthal anisotropy of the symmetric stretch was calculated
for CH
3
groups oriented normal to the surface (
0
= 0). A signicant tilt (
0
> 50
) of the
CH
3
groups was required to obtain any substantial amplitude of azimuthal anisotropy
for the simulated CH
3
symmetric stretch (r
+
) signal. Furthermore, the experimental
modulation depth in the azimuthal dependence of the r
+
signal in the PPP and SSP
spectra (Figs. 3.8, 3.12) could not be reproduced even for
0
= 50
, a situation for
which a substantial fraction of CH
3
groups would be lying
at on the surface. The 3-fold
azimuthal anisotropy of the methyl groups in the SFG spectra was observed previously
for octadecyl-terminated Si(111), the situation when the alkyl chain was proposed to lie
at 50
, and the terminal methyl group at 85
with respect to the surface normal.
42
Our experimental data could only be reproduced by radically changing the hyperpo-
larizablity tensor
(2)
of the CH
3
symmetric stretch mode, introducing a
(2)
aaa
component
and signicantly changing the ratio
(2)
aac
=
(2)
ccc
of the tensor elements, by a factor of >
20 compared to the range of values 1.66 - 4.0 reported in literature for the methyl
53
group.
56,58,82,94,101,104
The observations that (1) azimuthal dependence of the -CH
3
SFG
signal cannot be simulated without signicant alteration of the -CH
3
hyperpolarizabil-
ity tensor and (2) the resonant -CH
3
signal shows the 3-fold azimuthal dependence in
registry with the nonresonant signal of the silicon, strongly suggest that the resonant
molecular hyperpolarizability tensor
(2)
of the surface-bound methyl is signicantly
aected by the Si(111) substrate. Indeed, it is reasonable to assume some degree of
coupling between the -CH
3
molecular vibrations and the electronic degrees of freedom in
the underlying silicon. While the vibrational transition dipole moment
@c
@q
i
in
(2)
, Eq.
(3.22) should not be strongly aected by the Si(111) surface, the polarizability
Si
of
the underlying electronic bath of the silicon substrate likely far exceeds the polarizability
Me
of the methyl group itself, because the polarizability scales with volume. Thus, even
for a small coupling between the C-H vibrations q
i
and the electronic polarizability
Si
of the silicon, the polarizability derivative:
@
@q
i
=
@
Si
@q
i
+
@
Me
@q
i
(3.24)
can be dominated by the bulk silicon response (the rst term in Eq. 3.24).
On the basis of this consideration, the model for the nonresonant (electronic) response
of Si(111) described in the previous section was adopted to describe the azimuthal depen-
dence of the vibrationally resonant CH
3
signal. An assumption made herein is that the
vibrationally resonant SFG signal from the methyl stretch modes of the atop layer of
CH
3
groups has an isotropic component, and has an anisotropic component of the same
symmetry as Si(111) surface. As in the case of the electronic response, both bulk and
surface terms (Eqs. (3.9, 3.11, 3.12) and Eqs. (3.14, 3.15, 3.16), respectively) contribute
to the resonant SFG signal. The bulk contribution to the vibrational signal is dened
by two parameters,
i
and
i
, which describe the coupling of the vibrational mode i
(ss or as) to the bulk electronic responses of silicon
and , Eq. (3.9). As shown in
Figures 3.8, 3.9, and 3.12, the experimental data can be modeled by assuming the ratio
54
of
i
=
i
to be the same as the ratio of
=. To model the surface contribution (Eq. 3.13),
the CH
3
group is assumed to be oriented perpendicular to the Si(111) surface, implying
that the CH
3
transition dipoles for symmetric (r
+
) and asymmetric (r
) stretch modes
are perpendicular and parallel to the surface, respectively. The CH
3
hyperpolarizability
tensor elements
(2)
xxx
and
(2)
zxx
must be zero for the CH
3
symmetric stretch,r
+
, and thus
we assume that the surface contribution parameters @
ss
11
,@
ss
31
are zero, whereas @
ss
15
, @
ss
33
are assumed to be nonzero. Since @
ss
11
= 0 for the symmetric stretch, the anisotropy in
the SFGr
+
signal is therefore solely due to the Raman polarizability of the silicon bulk.
Similarly,
(2)
zzz
and
(2)
xxz
are zero for the CH
3
asymmetric stretch, r
, that sets @
as
15
, @
as
33
to zero and @
as
11
,@
as
31
to nonzero elements
@
ss
11
= 0 , @
ss
31
= 0 , @
ss
15
6= 0 , @
ss
33
6= 0 (3.25)
@
as
11
6= 0 , @
as
31
6= 0 , @
as
15
= 0 , @
as
33
= 0 (3.26)
As shown by the solid blue lines in Figures 3.8, 3.9, and 3.12, the resonant SFG
signals simulated using this model, Eq. (3.17, 3.18), reproduce the modulation depth
and phase of the azimuthal dependences of the symmetric and asymmetric CH
3
stretch
modes for both SSP and PPP polarization combinations (note that the phase of the
azimuthal dependence is not adjustable). In analogy to nonresonant signal modeling, the
ratio R
ppp;ssp
of the anisotropic and isotropic parts for the symmetric and asymmetric
stretches can be evaluated (see Tables 3.4 { 3.6 of the Appendix). Two ratios for the CH
3
symmetric stretchR
ss
PPP
= 1:5 andR
ss
SSP
= 3:3 are deduced. TheR
ss
PPP
value was taken
from the 300 fs delay PPP SFG resonant amplitude t. For the CH
3
asymmetric stretch
(observed only in the PPP spectrum), one experimentally measured ratio,R
as
PPP
= 1:5,
was determined. TheR
ppp;ssp
ratios for the resonant vibrational response are in the same
range as for the nonresonant electronic response that has been determined in this study
and elsewhere,
81
in accord with the assumption that the electronic polarizability of the
55
Si, modulated by the molecular vibrations of CH
3
, contributes to the response, per Eq.
(3.24). As in the case of the nonresonant response, the t does not provide a unique
set of parameters, but produces values for four parameters for every vibrational mode:
two surface tensor elements and two bulk parameters
i
and
i
,. Table 3.6 in Addendum
presents one possible solution.
3.4.3 Rotational Dynamics of the Surface-bound Methyl Groups
The azimuthal anisotropy of the CH
3
resonant amplitude suggests that the methyl groups
are not randomly oriented and also that they do not undergo free in-plane rotation.
Instead, the 3-fold symmetry of the resonant signal suggests that the methyl hydrogens
are pointing into three preferred directions, in registry with the crystal lattice of the
Si(111) substrate. The data, however, do not preclude the possibility of hindered rotation
proceeding via discrete 120
jumps between the 3 preferred orientations.
The contribution of the orientational dynamics to the SFG spectroscopic line shapes
is considered in detail elsewhere.
29
Brie
y, when orientational relaxation occurs on a time
scale comparable to vibrational dephasing, the reorientation dynamics can be extracted
from polarization-selected SFG line shape measurements. In particular, the in-plane
rotation of the vertically oriented CH
3
group should manifest itself as line broadening
of the asymmetric stretch, whose transition dipole moment is parallel to the Si(111)
surface, in the SPS spectrum relative to the PPP spectrum.
29
Previously, the eect of
reorientation dynamics on SFG amplitudes in the fast motion limit was considered by
Wei and Shen
61
and by Fourkas et al.,
60,105
who showed that fast rotational relaxation
suppresses the SFG signal for the SPS polarization combination. The eective nonlinear
susceptibility contributing to the SPS polarization SFG signal contains only one tensor
element,
(2)
yzy
, which is selective to molecules with transition dipoles in the plane of the
surface. Consistently, we observed the asymmetric CH
3
stretch (2976 cm
1
) in the SPS
spectrum as well as in the PPP spectrum. Figure 3.13 superimposes the SPS and PPP
spectra, showing that the CH
3
asymmetric stretch r
linewidth is broader in the SPS
56
spectrum (
SPS
= 15:9 1:0 cm
1
) than in the PPP spectrum (
PPP
= 12:4 0:5
cm
1
).
Methyl-terminated Si(111) is a single-crystal surface that is likely to be nearly free of
inhomogeneous broadening, corroborated by the spectral line shapes for both the PPP
and SPS spectra being well t by a Lorenztian prole, Eq. (3.6). In this situation, the
deconvolution of the instrument spectral resolution due to the time-delayed visible pulse
is simplied,
47
and the Lorentzian half width at half maximum can be approximated as
a sum of the visible pulse width,
vis
, the vibrational dephasing
vib
, and the rotational
dephasing
rot
47,106
=
vis
+
vib
+
rot
(3.27)
The narrow-band visible pulse, produced by an etalon in our measurement, decays expo-
nentially in the time domain (see Fig. 3.3), and thus is a Lorentzian in the frequency
domain. We also assume an exponential decay for the vibrational and rotational dephas-
ing. The PPP spectrum has negligible contribution from the rotational relaxation, and
provides information mainly on the vibrational dephasing.
29
Thus, when
vis
= 8:6 cm
1
is subtracted from
PPP
= 12:4 cm
1
, we obtained a value for the vibrational dephasing
of 3.8 cm
1
, or
vib
= 1=
vib
1:4 ps, for the CH
3
asymmetric stretch. The dierence
between the SPS and PPP line width provides the rotational dephasing of the methyl
groups on the silicon surface as
rot
= 3:5 1:5 cm
1
, which corresponds to a rotational
relaxation time scale of
rot
1 2 ps.
It is interesting to compare the rotational dephasing of the methyl groups on CH
3
-
Si(111) to the gas-phase rotational dephasing of a free methyl moiety. Assuming a quasi-
classical Maxwellian distribution of free rotors, the rotational dephasing is described by
the following correlation function C
1
(t):
107
C
1
(t) =hP
1
(cos
t
)i =
I
z
k
B
T
1
Z
0
P
1
[cos(
t)]
exp
I
z
2
2k
B
T
d
(3.28)
57
whereP
1
is the rst Legendre polynomial, andI
z
is moment of inertia for rotation about
the molecular symmetry axis (C
3
symmetry axis for methyl). From Eq. (3.28) the rota-
tional dephasing for a free methyl rotor is calculated to be100 fs at room temperature.
On CH
3
-Si(111) surfaces, the rotation of methyl groups on the Si(111) is thus slowed
by an order of magnitude, suggesting a hindered potential for rotation. The rotational
relaxation of methyl groups may proceed as 120
jumps between the three equal minima
of the rotational potential. Because the CH
3
groups form a well-ordered, densely packed
adlayer covalently bonded on Si(111), the rotation of CH
3
groups about the C-Si bonds
might be interlocked,
78
consistent with the observation of rotational anisotropy in the
SFG signals reported herein. We note that while the resonant vibrational energy transfer
between neighboring methyl groups is also a possible mechanism for orientational dephas-
ing the weak transition dipole of the methyl group makes this mechanism unlikely. The
Forster radius for methyl asymmetric stretch, i.e., the separation at which the rate of
energy transfer through dipole-dipole coupling is comparable with the vibrational life-
time, is likely less than 1
A(for example, it is 2.1
A) in liquid water with its much higher
OH-stretch transition dipole
108
), i.e., much smaller than the distance between methyls
on the Si(111) surface,3.8
A.
3.5 Conclusion
Sum frequency generation has provided detailed information on the molecular structure
and dynamics of CH
3
-terminated Si(111) surfaces. The vibrational C-H stretch reso-
nances in SFG spectra probe the orientation of the surface-bound methyl groups relative
to the surface normal as well as relative to the crystalline axes of the silicon substrate,
which is probed by the vibrationally nonresonant (electronic) response. The hyperpo-
larizability of the surface-bound methyl group was observed to be drastically dierent
from that of free methyl groups, likely due to the coupling of the molecular vibration to
the above-band-gap Raman polarizability of the Si substrate. The propeller-like rotation
58
of the methyl about the Si-C bond was hindered, as evidenced by a pronounced 3-fold
azimuthal anisotropy of the resonant SFG response. The data indicate that the methyl
groups are primarily locked in one of three minima in registry with the 3-fold symmetry
of the Si(111) surface. Rotational motion occured on a 12 ps time scale, i.e., hindered by
an order of magnitude compared to a free methyl rotor at room temperature (100 fs
rotational dephasing). The ndings are consistent with a mechanism in which the methyl
groups undergo 120
jumps between the 3 equal rotational minima on the CH
3
-Si(111)
surface.
59
3.6 Appendix
Figure 3.14. Geometry of SFG, surface coordinate system, orientation
of the methyl group on Si(111) surface, and the wave vectors and com-
ponents for the propagating visible eld. For the model we assume
that is approximately the same for !
1
and !
2
. The refractive index
of Si is n and N at !
1
and (!
1
+!
2
), respectively.
We have approximated for simplicity that all optical parameters for the IR and visible
beams are roughly equal, since both incidence angles of the beams are roughly the same
and their refractive indices in silicon are relatively similar (3.43 and 3.68 respectively).
The component of the visible eld wave vector ^
0
parallel to the surface is given by
=j
0
j sin (
0
) =
!
1
c
sin (
0
). This wave vector is related to the incidence wave vector
normal w
0
by
w
0
=
p
~ !
2
2
60
where ~ ! = !=c. We also introduce w for the medium with dielectric constant " (!
1
):
w =
p
~ !
2
" (!
1
)
2
. The SFG eld wave vectors and components can also be introduced
in a similar fashion for the SFG frequency
= !
1
+!
2
by capitalizing the symbols
(similar to Sipe et al.
80
). The proportionality constants for bulk isotropic and anisotropic
coecients can then be written
80
A
s
=
4
~
W
0
+W
, A
p
=
4
~
N
W
0
"(
)+W
. We additionally
introduced D =
n
~
8(2w+W )
. A
p
=A
s
1.5 and D 0.063 for our system was evaluated
using above equations. Below we list the bulk and surface isotropic and anisotropic
coecients given by Sipe et al.
80
:
a
s
bulk
=
4
3
f
s
f
c
c
s
bulk
=
4
p
2
3
f
2
c
f
2
s
a
p
bulk
=
4
3
F
s
f
c
2
3
f
s
f
2
c
8
3
F
s
f
2
s
f
c
+
4
3
f
3
s
F
c
c
p
bulk
=F
s
f
3
c
2f
2
s
F
c
f
c
+F
s
f
s
f
2
c
a
s
surf
= 2@
15
f
s
c
s
surf
=2@
11
f
c
a
p
surf
=" (!
1
+!
2
)@
31
F
s
f
2
c
2@
15
f
s
F
c
f
c
+" (!
1
+!
2
)@
33
F
s
f
2
s
c
p
surf
=2@
11
F
c
f
2
c
where F
s;c
are the sine and cosine of the angle of the SFG beam in the silicon, f
s;c
are the sine and cosine of the angle of the visible beam in the silicon, and " (
) is the
dielectric constant of the medium at the SFG frequency.
61
Table 3.1. Fitting parameters for PPP spectra recorded with 0 fs delay
between IR and visible pulses.
Rotation angle (deg) A
NR
, (a.u.) !
g
, (cm
1
)
g
, (cm
1
)
NR
, (rad) B(r
+
), (a.u.) B(r
), (a.u.) (r
+
), (cm
1
) (r
), (cm
1
) !(r
+
), (cm
1
) !(r
), (cm
1
)
0 27 2870 181 3.3 246 144 14.9 10.8 2917 2977
20 63 2897 250 3.2 257 156 14 10 2920 2983
40 65 2895 251 3.1 259 156 14 10 2920 2982
60 30.3 2877 197 3 264 132 14.4 10 2918 2979
80 33.4 2902 296 -1.5 -436 -276 20 16.5 2915 2975
100 32.7 2903 308 -1.7 -420 -261 20 16.5 2914 2974
120 21.4 2880 182 -2.9 236 155 13.2 11.9 2917 2978
140 63 2896 251 3.4 250 139 14 10 2918 2979
160 67 2897 251 3.1 262 158 14 10 2919 2982
180 29 2878 194 -3.1 274 134 14.4 10 2916 2976
200 34.7 2916 320 -1.5 -430 -240 20 16.5 2913 2971
220 34.9 2923 333 -1.6 -420 -240 20 16.5 2912 2971
240 23.6 2880 173 3.4 251 132 14.4 10 2916 2976
260 63.5 2903 256 3.3 284.2 160 14 10 2917 2979
280 67 2902 252 3.3 270 144 14 10 2916 2980
300 31.4 2875 195 3.2 290 150 14.4 10 2915 2975
320 33.6 2924 323 -1.3 -450 -270 20 16.5 2912 2971
340 34.6 2919 324 -1.5 -446.9 -268 20 16.5 2913 2972
62
Table 3.2. Fitting parameters for PPP spectra recorded with 300 fs
delay between IR and visible pulses.
Rotation angle (deg) A
NR
, (a.u.) !
g
, (cm
1
)
g
, (cm
1
)
NR
, (rad) B(r
+
), (a.u.) B(r
), (a.u.) (r
+
), (cm
1
) (r
), (cm
1
) !(r
+
), (cm
1
) !(r
), (cm
1
)
1.5 9 - - -2.9 408 -338 12.5 12 2915 2975
20 13.7 2991 500 -6.2 605 -398 13.6 10.6 2914 2977
40 14.9 2940 300 -3.1 657 -406 14.2 10.7 2914 2976
60 9.8 - - -3.1 473 -315 13.1 12.2 2914 2974
80 17.1 2940 300 0.39 -167 120 14.3 14 2907 2979
100 18.4 2920 325 0.3 -133 146 15 14 2907 2983
120 9.3 - - -2.9 431 -363 13.4 12.7 2914 2976
140 16.7 2940 300 -3.3 803 -426 15.5 10.9 2914 2976
160 18 2940 300 -3.2 844 -470 16.1 11.2 2914 2975
180 11.4 - - -3.2 551 -370 13.5 13.1 2913 2972
200 20.1 2946 351 0.17 -174 140 15 14 2908 2983
220 23.1 2970 390 0.42 -120 109 16 10 2907 2975
240 10.7 - - -3.2 507 -386 13.4 13.4 2914 2975
260 20.7 2940 300 -2.8 850 -544 17.1 10.6 2913 2975
280 21.8 2940 300 -3 973 -544 18.2 10.8 2913 2974
300 12.7 - - -3.4 649 -358 14.5 12.4 2914 2973
320 19.8 2940 385 0.42 -180 170 16 15 2911 2980
340 20 2930 410 0.42 -145 175 16 13 2908 2980
360 10.7 - - -3.22 546 -367 14.3 13 2915 2976
63
Table 3.3. Fitting parameters for SSP recorded with 0 fs delay between
IR and visible pulses. AmplitudesA
NR
and B(r
+
) are normalized with
respect to PPP 0 fs delay amplitudes.
', (deg) A
NR
, (a.u.) !
g
, (cm
1
)
g
, (cm
1
)
NR
, (rad) B(r
+
), (a.u.) (r
+
), (cm
1
) !(r
+
), (cm
1
)
0 12.6 2907 234 1.53 109 19.5 2900
20 17.1 2908 282 1.66 84 18.5 2900
40 8.2 2802 188 -0.087 -126 15.3 2907
60 25.3 2845 288 0.32 -231 26 2909
80 25.9 2866 288 0.29 -221 24.8 2910
100 4.9 2875 260 0.29 -55 16.2 2900
120 13.6 2937 229 1.3 107 19.6 2904
140 15.8 2950 225 1 149 22.6 2910
160 6.4 2936 257 -0.01 -104 15.7 2905
180 24.6 2938 330 0.19 -286 33 2912
200 24 2926 345 0.24 -255 30.7 2916
205 20.4 2880 332 0.27 -219 27.2 2917
210 6.2 2896 362 0.46 -168 20.3 2913
220 6.7 2924 289 0.25 -160 20.8 2910
230 15.7 2923 192 1.31 186 26.9 2919
240 15.7 2914 244 1.11 186 26.9 2917
250 18.2 2895 292 1.4 133 20.2 2908
260 15.8 2906 288 1.43 136 20 2903
270 10 2936 200 1.59 209 34.7 2903
280 6.9 2931 220 -0.17 -126 18.5 2910
290 17.5 2938 229 -0.063 -167 23 2917
300 25.3 2877 326 0.17 -322 35.6 2914
310 29.1 2907 317 0.15 -316 34.8 2914
320 26.9 2908 310 0.107 -319 34 2914
340 6.3 2802 269 0.095 -174 21.8 2905
64
Table 3.4. Fitting parameters for the rotational anisotropy in resonant
and nonresonant amplitudes for PPP and SSP spectra.
a, (a.u.) c, (a.u.) '
0
, (deg.) k, (a.u.)
PPP
B(r
+
)/(r
+
) 24 36 -91 {
B(r
)/(r
) -20.4 -31.1 -89 {
A
NR
17.3 50.8 -94 -21
SSP
B(r
+
)/(r
+
) -3.3 -14.3 159 {
A
NR
6.9 35.3 153 8.3
Table 3.5. Nonresonant nonlinear susceptibilities of methyl-terminated
Si(111) surface obtained by tting the nonresonat SFG signal for PPP
and SSP polarization combinations to equations (3.19-3.21)
@
11
@
33
@
31
@
15
180 60 -10 -23.5 -4.4 -7.6
Table 3.6. Vibrationally resonant nonlinear susceptibilities of CH
3
-
Si(111) surface for symmetric and asymmetric C-H stretch modes
obtained by tting the resonat SFG signal for PPP and SSP polar-
ization combinations to equations (3.19-3.21).
@
as
11
@
ss
33
@
as
31
@
ss
15
150 6.7 13 -55 -5 -6.5
65
Chapter 4
Relative Phase Flip of Nearby
Resonances in Temporally
Delayed SFG Spectra
Surface-selective sum frequency generation (SFG) spectroscopy has been previously
shown to benet from a nite time delay between two input laser pulses, which sup-
presses the nonresonant background and improves spectral resolution. In this chapter,
we demonstrate another consequence of the time delay in SFG: depending on the mag-
nitude of the delay, nearby resonances (e.g., vibrational modes) can
ip their relative
phase, i.e. appear either in-phase or out-of-phase with one another, resulting in either
constructive or destructive interference in SFG spectra. This is signicant for interpreta-
tion of the SFG spectra, in particular because the sign of the resonant amplitude provides
the absolute molecular orientation (up vs. down) of the vibrational chromophore. We
present results and model calculations for symmetric and asymmetric CH-stretch modes
of the methyl-terminated Si(111) surface (which was discussed in Chapter 3), showing
that the phase
ip occurs when the delay matches half-cycle of the dierence frequency
between the two modes.
4.1 Background on Time Delay SFG Techniques
Sum frequency generation (SFG) is rapidly becoming a standard tool used in chemistry,
physics, and biology for characterizing structure, orientation, and dynamics of molecules
at surfaces and interfaces.
83{85,87,109,110
The surface-selectivity of SFG, which results
66
from the second-order susceptibility
(2)
vanishing in centrosymmetric media under the
electric dipole approximation, readily allows vibrational spectroscopy and orientational
analysis to be performed with monolayer and sub-monolayer sensitivity. The detection
limits can be further lowered to percent monolayer levels by using optical heterodyne
detection.
52
Although SFG from interfaces between two isotropic media is generally free from
bulk-phase contribution to the signal, in practice it is rarely a completely background-free
measurement. Because of the relatively small number of surface molecules, their resonant
signatures in SFG spectra are always contaminated by the nonresonant (NR) background
signal arising, for example, from electronic response of the substrate material. The
resonant
(2)
R
(!) and nonresonant
(2)
NR
signals interfere because SFG is a coherent optical
technique,
I
SFG
(!)/
(2)
2
=
(2)
NR
+
(2)
R
(!)
2
(4.1)
which complicates the spectroscopic analysis. The NR signal varies depending on the
sample, but its amplitude is often comparable or stronger than the molecular vibrational
resonances and the interference makes it dicult to subtract the NR contribution. On
the other hand, this interference can also be useful, for example in allowing one to
determine the phase (e.g., positive or negative sign) of the resonant features. The sign
of the resonant signal carries useful molecular information such as absolute orientation
of the vibrational chromophore moiety (e.g., CH
3
group orientation with hydrogens up
vs. down).
27,85,111{114
While optical heterodyne detection can provide both amplitude and phase of the
SFG signal
52,85,114{116
and thus allows one to separate the resonant and nonresonant
signals,
27,112,114
in many cases it is desirable to suppress the NR background. As
rst demonstrated by Lagutchev et al.,
91
this can be achieved for broad-band
117,118
IR+visible vibrational SFG (BB-SFG) by realizing that the NR signal is instantaneous
67
in the time-domain while the resonant response has a nite (vibrational) dephasing time
and thus can be up-converted with a delayed time-asymmetric picosecond visible pulse
following a broad-band (femtosecond) IR pulse. Stiopkin et al. showed how the time
delay between the IR and visible pulses and the spectral width and temporal shape of the
visible pulse aect the spectroscopic line shapes, resolution, and the signal level of SFG.
47
Although suppression of the NR background has proven to be a major improvement in
the analysis of the vibrationally relevant information,
27,47,91
Curtis et al. demonstrated
that suppression of the NR signal can lead to other distortions in the SFG signal, which
can complicate the analysis of the SFG spectra.
119
In this chapter we present both experimental measurements and theoretical analysis
of the eect of the time delay on the broad-band SFG spectra of a surface with two
nearby vibrational resonances (frequency oset by ! 70 cm
1
). We show that the
relative phase between the two coherently excited vibrational modes
ips for certain val-
ues of the time delay: the two modes can appear with the same sign (e.g., as two dips
against the NR background) for zero delay, but with opposite signs (one dip and one
peak) at certain nite values of the delay. Clearly, such behavior can aect the molec-
ular interpretation of the SFG spectra and thus needs to be understood quantitatively.
This frequency-dependent phase shift has been previously described for other coherent
spectroscopies such as 2D IR
120
and noted in the time-domain theoretical calculations
of SFG spectra.
115
4.2 Experimental Results
The model system chosen for this study is the methyl-terminated Si(111) surface, CH
3
-
Si(111), described in detail in the previous chapter. The BB-SFG spectra of the sym-
metric and asymmetric stretch vibrational modes of the methyl recorded with time delay
= 0 fs and = 300 fs between the broad-band IR and narrow-band visible pulses are
shown in Figure 4.1. The polarization combination is PPP (parallel to the plane of inci-
68
Figure 4.1. Experimental SFG spectra of CH
3
-Si(111) for IR-vis delay
= 0 fs (a) and = 300 fs delay (b). Solid black lines show ts to Eq.
(4.3), and dashed lines show decomposition of the t into a Gaussian
(nonresonant) envelope and two resonant Lorentzian terms, per Eq.
(4.3), with resonant amplitudes B
0
r
+ =1:0 and B
0
r
=0:63 (a.u.)
for = 0 fs spectrum (a) and B
0
r
+ = +0.38 and B
0
r
=0:28 (a.u.)
for = 300 fs delay spectrum (b).
dence for IR, visible, and SFG beams), although the polarization combination should
not aect the observed phase
ipping. We note that CH
3
-Si(111) exhibits three-fold
azimuthal rotational anisotropy, described in detail elsewhere in Chapter 3.
121
The non-
resonant signal due to the Si response changes signicantly with the azimuthal angle.
Here we show the BB-SFG spectra for the azimuthal angle 50
with respect to one of the
mirror planes of the C
3v
symmetry of Si(111) surface where the nonresonant amplitude
is near its maximum,
121
for which the relative phase
ip behavior is most pronounced.
69
The BB-SFG spectra in Fig. 4.1 are t by assuming Lorentzian proles for the
two vibrational resonances contributing to
(2)
R
(!), which interfere with the frequency-
independent NR background contribution
(2)
NR
:
I
SFG
(!) =
(2)
NR
+
(2)
R
(!)
E
IR
(!)
E
vis
(!)
2
(4.2)
=
A
NR
e
i
NR
+
X
i
B
0
i
!!
i
+i
i
2
exp
(!!
g
)
2
2
g
!
(4.3)
whereA
NR
is the nonresonant amplitude,'
NR
is the relative phase between the NR and
the resonant signal, and !
i
,
i
, and B
0
i
are the central frequency, line width, and the
apparent amplitude of i-th resonant band, respectively. Although a truly nonresonant
signal would be purely real, in practice electronic resonances of the substrate (in the
visible or UV region) impart a phase
NR
on this part of the response, as re
ected in
Eq. (4.3). The last term in Eq. (4.3) is the spectral shape of the IR pulseE
IR
(!), which
is approximated by a Gaussian with central frequency!
g
, and width
g
. The Lorentzian
spectral shape of the visible pulse E
vis
(!) (produced by an etalon), is assumed to be
convoluted into the Lorentzian line shapes of the resonances (i.e.,
i
, are not the true
Lorentzian line widths of the transitions).
CH
3
-Si(111) surface features two vibrational modes in the C-H stretch region a CH
3
symmetric stretch (r
+
) at2907 cm
1
and a CH
3
asymmetric stretch (r
) at2979
cm
1
. The BB-SFG spectrum with no IR-visible delay ( = 0 fs) (Figure 4.1a) shows
a large NR background, with both resonant bands clearly appearing as dips against the
NR background, with negative Lorentzian amplitudes B
0
r
+ =1:0 and B
0
r
=0:63
(a.u.).
The BB-SFG spectrum for = 300 fs delay, Figure 4.1b, has little NR background
because there is almost no time-domain overlap between the IR and the time-asymmetric
visible pulse produced by an etalon. We note that (1) our visible pulse, shown in Figure
4.2b, is not ideally
at at early times; there is a small (1%) intensity bump before
70
Figure 4.2. (A) Frequency-resolved cross-correlation of the femtosecond
IR and picosecond visible pulses. (B) Temporal prole of the narrow-
band visible pulse. (C) Frequency-domain spectrum (red line) of the
narrow-band visible pulse produced by passing the compressed pulse
through the etalon. Blue line shows a Lorenztian t.
the sharp rise and (2) the IR pulse may also have similar magnitude wings at 300 fs.
This contributes a non-zero NR background contribution to the signal. The BB-SFG
spectrum at = 300 fs delay can only be t with the amplitudes of the two resonant
bands having opposite signs, B
0
r
+ = +0:38 and B
0
r
=0:28 (a.u.). The complete set
of tting parameters is provided in the Appendix at the end of this chapter.
4.3 Time-Domain Description of SFG
The theory of BB-SFG spectroscopic line shapes was presented in detail else-
where.
47,55,115,122
Here we only brie
y describe the main equations used to calculate
71
Figure 4.3. Temporally-delayed asymmetric visible pulse E
vis
(t) used
to suppress nonresonant signal produced by IR pulse E
IR
(t) at t = 0.
the signals. In the SFG process, two laser pulses combine on the surface to induce the
second order polarization P
(2)
(t)
P
(2)
(t) =
1
Z
1
dt
1
1
Z
1
dt
2
S
(2)
(t
1
;t
2
)E (tt
1
)E (tt
2
t
1
) (4.4)
The laser pulses interact with the surface at times tt
1
and tt
2
t
1
and S
(2)
(t
1
;t
2
)
is the second-order response function. In the case of IR+visible vibrational SFG, a mid-
infrared pulseE
IR
(t) resonantly excites molecular vibrations at the surface, creating the
rst order polarization P
(1)
(t)
P
(1)
(t) =
1
Z
1
dt
1
S (t
1
)E
IR
(tt
1
) (4.5)
where S (t
1
) is the rst-order response function. The IR pulse is followed, after a time-
delay , by the visible pulse E
vis
(t), as pictured in Figure 4.3
72
The second interaction is nonresonant (i.e., instantaneous) and thus the molecular
response is a-function with respect to the visible eld, S
(2)
(t
1
;t
2
) =S (t
1
)(t
2
), which
removes second integration step in Eq. (4.4),
P
(2)
(t;) =P
(1)
(t)E
vis
(t) (4.6)
The SFG signal eld is emitted by the second order polarization in the phase-matched
direction, such that the signal intensity (in the time domain description) is
I
SFG
(t;)/
P
(2)
(t;)
2
(4.7)
In the frequency-domain measurement, the BB-SFG signal is Fourier transformed by
a monochromator (i.e., a monochromator separates the discrete frequency components
(a spectrum) of a signal)
I
SFG
(!;)/
1
Z
1
P
(2)
(t;)e
i!t
dt
2
=
1
Z
1
P
(1)
(t)E
vis
(t)e
i!t
dt
2
(4.8)
The rst-order time-domain molecular response function that characterizes evolution
of the system after a single interaction with the vibrationally resonant IR eld can be
written as
47,48,122
S (t
1
) =A
NR
exp (i'
NR
) (t
1
)i (t
1
)
X
i
B
i
i
exp (i!
i
t
1
i
t
1
) (4.9)
where (t
1
)is a Heaviside step function, A
NR
is the amplitude of the nonresonant sig-
nal with the phase '
NR
. The second term represents the resonant molecular response
that andB
i
,
i
, and !
i
are amplitude, line width and central frequency of the resonant
response for i-th vibrational molecular mode. The Fourier transform of the response
function (Eq. 4.9) and substitution into Eqs. (4.5)-(4.8) yields the BB-SFG spectral
73
shape as a set of coherently added Lorentzians interfering with the NR background, as
per Eq. (4.3). Note, however, that, unlike the frequency-domain expression Eq. (4.3),
the response function Eq. (4.9) explicitly accounts for the time evolution of the optical
phase of the vibrational coherences, which then translates into the interference in the
frequency-domain BB-SFG spectra recorded with a delayed visible pulse Eq. (4.8).
4.4 Simulation of SFG Spectra
In order to qualitatively simulate the BB-SFG spectra obtained in the experiment, the
time-domain electric eld of the narrow-band visible pulse E
vis
(t) transmitted through
the etalon is represented as a sum of a train of replicas of the input broad-band Gaussian
visible pulse spaced in time by round-trip time
RT
= 2d=c = 32fs where d is the air
gap between mirrors,
47,91,123
E
etalon
vis
(t) =E
0
vis
(1R)
100
X
n=0
R
n
exp
(tn
RT
)
2
2
vis
!
exp (i!
vis
(tn
RT
)) (4.10)
Here R = 0:953 is re
ectivity of etalon mirrors,
vis
= 50 fs and !
vis
= 12563 cm
1
are the duration and central frequency of the input broad-band Gaussain visible pulse.
When
vis
>
RT
, the pulses in the output train overlap signicantly in time, producing
smooth envelope that has a sharp leading edge and decays exponentially in time. In
the frequency domain, pulses interfere resulting in a narrowed, nearly Lorentzian line
shape (the exact line shape is given by the Airy formula.
123
The IR pulse shape was
approximated by a single Gaussian-type pulse with zero-chirp
E
IR
(t) =E
0
IR
exp
t
2
2
IR
exp (i!
IR
t) (4.11)
with the IR frequency !
IR
= 2907 cm
1
and pulse duration
IR
= 80 fs.
74
Figure 4.4. Simulated SFG spectra for IR-visible delay = 0 fs (a)
and = 300 fs (b). Solid black lines show ts to Eq. (4.3), and dashed
lines show t decompositions.
The BB-SFG spectra simulated using Eqs. (4.8) - (4.11) are shown in Figure 4.4.
While the exact t would require the accurate knowledge of the IR and visible laser eld
pulse shapes, our goal here is to illustrate the relative phase
ip phenomenon observed
in the experimental spectra.
The convolution was performed by numerical integration over the time interval from
-3 ps to +3 ps with 0.2 fs step. The values for the duration and bandwidth of the
IR and visible pulses were chosen to match their measured spectra and cross-correlation
measurements (Fig. 4.2) and were not adjusted during the simulation of the SFG spectra.
The resonant amplitudesB
i
for the asymmetric and symmetric stretch modes were set to
have a ratioB
r
=B
r
+ = 0:7. The other molecular response parameters for the symmetric
75
(r
+
) and asymmetric (r
) CH
3
stretch modes (the full list provided in Appendix at
the end of this chapter) were adjusted to obtain the best qualitative agreement with
the experimental spectra in Figure 4.1. In particular, in our simulation we could not
accurately simulate the low intensity tail of the narrow-band visible eld at early times
(Figure 4.2b, from -1.0 ps to -0.3 ps). To compensate for this, A
NR
and '
NR
were
adjusted independently for both delays.
The simulated BB-SFG spectra for both = 0 fs and = 300 fs delays faithfully
reproduce the phase
ip as the function of the IR-visible delay. At zero delay, both
symmetric and asymmetric methyl stretches appear as dips against the NR background.
When the delay time between IR and visible pulses increased to = 300 fs, the non-
resonant contribution decreases and the lower-frequency symmetric stretch resonance
becomes a peak. However, the higher frequency asymmetric stretch still appears as a
dip.
The simulated spectra were also tted with Eq.(4.3), with the ts shown as solid black
lines in Figure 4.4 and the full set of tting parameters provided in the Appendix section
of this chapter. As with the experimental spectra, tting of the = 0 fs spectrum shows
the same (negative) sign for the amplitudes of the symmetric and asymmetric stretch
modes, B
r
+ =1:0 and B
r
=0:63 (a.u.). Fitting the = 300 fs simulated spectrum
requires that the two Lorentzians have opposite signs, B
r
+ = +0:39 and B
r
=0:50
(a.u.). The value and sign for the symmetric and asymmetric stretch amplitude were not
adjusted during the simulation. Thus, change in the sign for the tted Lorentzian can
be attributed to the phase shift of the symmetric versus asymmetric modes accumulated
during the = 300 fs delay time due to their dierent carrier frequencies. Indeed,
the frequency oset between the two modes, ! 70 cm
1
, corresponds to the phase
dierence of ' = (!
r
!
r
+) 1:1 accumulated during the = 300 fs delay. Thus,
the symmetric and asymmetric modes are almost exactly out-of-phase at = 300 fs,
assuming they were in-phase at 0 fs delay.
76
Other time-delaying approaches
47
used to minimize the NR background and improve
spectral resolution and signal level should also capture this phase-
ipping eect. For
instance, a time-delayed Gaussian visible pulse would also result in a phase-
ip between
two resonances if the time delay coincides with the half-cycle of the dierence frequency.
However, for time-symmetric pulses with durations longer than the period of the phase
oscillation between the nearby resonances, the phase would be averaged over many oscil-
lations and thus diminish the eect.
4.5 Phase of Vibrational Coherences
The phase
ip of nearby resonances recorded with a time-delayed visible pulse is the
frequency-domain manifestation of the quantum beats observed in the time-domain SFG
free induction decay (SFG-FID) measurements on two or more vibrational modes.
48,124
Figure 4.5. Picture depicting two vibrational coherences, who oscil-
late at slightly dierent frequencies, are in-phase at t = 0, and almost
exactly out-of-phase at300 fs delay.
77
All modes coherently excited by a short IR pulse initially oscillate in-phase, and
undergo the free induction decay. However, if the vibrational dephasing time
v
is com-
parable or longer than the frequency osets between the modes,
v
>
1=!, the modes
go in- and out-of-phase before the vibrational dephasing is complete, beating against
one another at the dierences between their central carrier frequencies !, as illus-
trated in Figure 4.5. The phase-
ip in the SFG spectra recorded using a time-delayed
up-conversion visible pulse captures this behavior in the frequency domain.
4.6 Conclusion
In this chapter, we demonstrated the importance of the time-domain description of the
coherent spectroscopic processes such as SFG. The phase-
ip phenomenon described in
this chapter would be entirely missed by a purely frequency-domain description such
as Eq. (4.3). Our experimental and simulated spectra show that in the case when the
nonresonant signal is not fully suppressed by o-setting the IR-visible delay, the two
resonant modes may appear in- or out-of-phase, depending on the time delay used for
the measurement. Without taking these time-domain eects into account, Eq. (4.3),
which is normally used for tting SFG spectra, could give the wrong sign of the resonant
amplitude. The phase of the SFG signal carries molecular information, e.g., on the abso-
lute orientation of the vibrational chromophore. In this case, the standard orientation
analysis model
56,95,96
that is commonly used in SFG spectroscopy for experimental ts
would not give true amplitude ratios, which is important to determine the molecular
orientation. Thus, without proper time-domain analysis, the time delay eects can lead
to wrong chemical interpretation of the SFG spectra.
78
4.7 Appendix
Table 4.1. List of parameters obtained by tting experimental PPP
spectra at 0 fs and 300 fs IR-visible delay (shown in Figure 4.1 in the
main text) with Eq. (4.3). Units for A
NR
, B(r
+
), and B(r
) are in
arb. units,
NR
is in rad., and !
g
,
g
, (r
+
), (r
), !(r
+
), !(r
) are
in cm
1
0 fs 300 fs
A
NR
0.07 0.04
!
g
2902 2940
g
296 300
NR
-1.5 0.39
B(r
+
) -1 0.38
B(r
) -0.63 -0.28
(r
+
) 20 14.3
(r
) 16.5 14
!(r
+
) 2915 2907
!(r
) 2975 2979
79
Table 4.2. List of parameters obtained by tting simulated PPP spectra
at 0 fs and 300 fs IR-visible delay (shown in Figure 4.1 in the main text)
with Eq. (4.3). Units for A
NR
, B(r
+
), and B(r
) are in arb. units,
NR
is in rad., and !
g
,
g
, (r
+
), (r
), !(r
+
), !(r
) are in cm
1
0 fs 300 fs
A
NR
0.09 0.05
!
g
2904 2917
g
206 237
NR
-1.7 -2.6
B(r
+
) -1 0.39
B(r
) -0.63 -0.5
(r
+
) 18.6 16.7
(r
) 16.3 13.6
!(r
+
) 2917 2922
!(r
) 2974 2979
Table 4.3. Wavelength and pulse duration parameters used in Eqs.
(4.10) and (4.11) to simulate the electric elds of the visible and IR
pulses.
(nm) (fs)
IR 3440 80
Visible 796 50
80
Table 4.4. The amplitudes B, line widths and central frequencies !
of the resonant response for the symmetric (r
+
) and asymmetric (r
)
CH
3
-stretch vibrational modes, as well as the amplitude and phase of
the nonresonant background used in the simulations (Eq. (4.9) of the
main text). Units for A
NR
, B(r
+
), and B(r
) are in arb. units,
NR
is in rad., and (r
+
), (r
), !(r
+
), !(r
) are in cm
1
0 fs 300 fs
A
NR
130 1:5 10
8
NR
245 190
B(r
+
) -0.1 0.1
B(r
) -0.07 0.07
(r
+
) 12 12
(r
) 10 8
!(r
+
) 2915 2915
!(r
) 2964 2975
Note: the nonresonant background amplitude A
NR
for the 300 fs delayed case is large
because it represents interaction with the (very weak) leading edge of the visible pulse
(see Figure 4.2 of the main text). The amplitude of the visible pulse at -300 fs could
not be quantied as it was below our detection limit, and thus the spectra for the 300 fs
delay are t using A
NR
as an independent adjustable parameter.
81
Chapter 5
Reaction Intermediates on
Plasmonic Photocatalysts
5.1 CO
2
Reduction on Au/TiO
2
Surfaces
5.1.1 Introduction
Photocatalytic processes on semiconductor surfaces have received great interest in the
last few decades due to their importance in a number of industrial and environmental
problems, including carbon remediation, fuel production, and chemical synthesis. The
search for ecient renewable energy sources is of signicant importance especially when
facing the realities of diminishing fossil fuels and their associated negative environmental
eects. Honda and Fujishima rst demonstrated the photo-initiated splitting of water
into hydrogen and oxygen using an n-type TiO
2
electrochemical cell in 1972.
125
Since
then, semiconductor photocatalysts have been used in several other applications such
as oxidation of pollutants,
126,127
conversion of CO
2
into hydrocarbon fuels,
128{131
and
self-cleaning surfaces.
132
Photocatalytic devices address the three main challenges facing solar energy usage,
which include solar energy harvesting, conversion, and storage. Photovoltaic devices,
in which solar energy is directly converted into electricity, tackle all but one of these
challenges: energy storage. This is where photocatalytic solar fuel production oers
an alternative path to harness solar energy. Photocatalytic solar fuel production takes
naturally abundant materials such as water and CO
2
, and directly converts them into
hydrogen, oxygen, or energetic hydrocarbon species by means of a photochemical process.
82
A semiconductor photocatalyst converts incoming photon energy into chemical
energy in three basic stages: (1) photoexcitation, where absorption of above-bandgap
energy photons excite electrons from the valence band to the conduction band to create
positively-charged holes to form electron-hole (e
{h
+
) pairs; (2) charge separation and
migration, where e
{h
+
pairs are separated and subsequently transferred to the surface
active sites (although charge recombination can also occur); and (3) reduction-oxidation
reactions, where the generated electrons and holes at the surface drive chemical redox
reactions.
Although titania (TiO
2
) is the most widely used photocatalytic material, mainly
because it is cheap and chemically stable, it cannot be used for eective solar energy
harvesting and conversions. TiO
2
is a poor absorber of solar photons since it has a large
bandgap (E
g
> 3 eV) and therefore the vast majority of e
{h
+
pairs created (96%)
are from photons in the UV region (<400 nm) (Fig. 5.1).
Figure 5.1. Spectral distribution of solar photons (air mass = 1.5)
(shown in red) and absorption spectrum of TiO
2
(blue). Figure based
on Seinfeld and Pandis, 1998.
133
83
Various approaches have been explored on improving the solar absorption of photo-
catalysts such as chemical doping or deposition of visible light sensitizers (e.g., organic
dyes, metal nanopartcles). It has been demonstrated that combining photocatalytic
semiconductors with plasmonic metallic nanostructures signicantly enhances catalytic
activity, as well as extending coverage of the solar spectrum.
128,134{136
Hou et al recently
observed the plasmonic enhancement of photocatalytic methane formation by the reduc-
tion of CO
2
with water.
128
A 24-fold enhancement in the photoconversion eciency with
respect to bare TiO
2
was observed for Au nano-islands deposited on the TiO
2
surface.
Plasmons are the collective oscillations of the free electron gas density in metals. The
frequency of the oscillation (or resonance) highly depends on the shape and size of the
metal nanostructure.
137,138
Linear infrared (FTIR) spectroscopic studies of photo-initiated activation of CO
2
on
neat TiO
2
powders revealed surface-bound intermediates such as bent and partially neg-
atively charged CO
2
(bands at 1640 cm
1
and 1219 cm
1
) and CO.
139
The catalytically
active site on titania has been proposed to be photoinduced (Ti
3+
-O
)
species, where
reduction of CO
2
by Ti
3+
electron center and oxidation of H
2
O by the O
hole center
proceed competitively.
130,139
Whether the same active site contributes to the plasmon-
assisted catalysis mechanism is not known at present. CO adsorption on various metal
and metal-oxide surfaces has been actively studied.
127,140{143
CO adsorbs readily to a
number of surfaces, and due to its strong interaction with the substrate, the CO stretch
frequency shifts, and this can be a sensitive indicator of the nature of the adsorption
site.
Vibrational spectroscopy is one of the most information-rich techniques in terms
of identifying the structure of the adsorbed intermediate species. However, because of
the relatively small magnitude of the vibrational transition dipoles, FTIR is generally
unable to characterize plasmon-enhanced photocatalyst surfaces due to the small number
of the hot-spot active sites. Additionally, when the plasmonic structures are optimized
84
to have plasmon resonance in the visible part of the spectrum (e.g., solar light), mid-
infrared elds are far from resonance and only weakly enhanced. On the other hand,
plasmon-enhanced spectroscopies, such as surface-enhanced Raman and surface-selective
nonlinear optics techniques such as sum frequency generation (SFG), provide both the
required sub-monolayer sensitivity and the vibrational frequencies.
44,46,144,145
In this
study, we investigate CO
2
reduction with water and identify adsorption sites of TiO
2
-
supported Au nano-islands using SFG.
5.1.2 Experimental
Au/TiO
2
samples were provided by our collaborators Prof. Stephen Cronin and his group
in the Electrical Engineering Department at USC. A description of sample fabrication is
given in detail elsewhere.
128
Brie
y, 400 nm of TiO
2
sol-gel was spin-coated on a silicon
wafer substrate, allowed to dry in air for 24 h, and then annealed at 400
C in air for 4
h to obtain the anatase form of TiO
2
. A 5 nm lm of Au was then deposited in vacuum
using electron beam evaporation to form an island-like morphology (Fig. 5.2). Annealing
at 400
C in air for 1 h produces nearly spherical Au nanoparticles.
Details of the SFG spectrometer are given in Chapter 2. The power of the visible
beam at the sample was attenuated to < 5 J/pulse and 6 J/pulse for the IR beam.
All measurements were performed { unless otherwise noted { in a sealed, home-built
temperature-controlled gas cell at room temperature (20
C), and SFG spectra were
recorded with PPP polarization combination for 300 fs IR-visible delay. Ar, CO
2
, CO,
O
2
gases were purchased from Gilmore and were greater than 99% pure. Dosing times
of 10 min were used.
Samples were placed inside the gas cell, which was then purged with Ar for approxi-
mately 10 min to remove CO
2
and water from the chamber. A SFG spectrum (\initial")
was recorded. The choice adsorbate (either CO
2
, CO, or O
2
) was then mixed with Ar
in a 3:1 ratio at1 atm and passed over the sample for 10 min. The sample cham-
ber was
ushed with pure Ar for 2-5 min and a second SFG spectrum was recorded.
85
Measurements that involved water vapor were obtained by passing the choice adsorbate
gas/Ar carrier gas mixture through a water bubbler before reaching the sample chamber.
Measurements that involved the sample being annealed were accomplished by heating
the sample in pure Ar and then allowing the system to equilibrate to room temperature
before recording an SFG spectrum. These experiments were carried out in a similar
fashion to the ones described in 5.2.2.
5.1.3 Results and Discussion
Preliminary results were obtained by VSFG spectroscopy of surface CO on Au/TiO
2
plasmonic photocatalysts depicted in Fig. 5.2. First, no CO adsorption or photopro-
duction was observed at room temperature on bare TiO
2
(Fig. 5.3), as expected (CO
desorbs from titania above 200 K).
139
However, when TiO
2
is covered with Au nano-
islands, a strong peak at2120 cm
1
emerges in the VSFG spectra (Fig. 5.3) acquired
in open air conditions. Interestingly, this peak is stable at room temperature and is only
partially reduced by annealing above 100
C, indicating that CO at this surface site is
extremely strongly bound (Fig. 5.4). After annealing, the peak regenerates itself upon
exposure to air and ambient room light (Fig. 5.4), while no regeneration occurs if the
surface is kept in the dark.
86
Figure 5.2. SEM image of 5 nm of Au nano-island lm on TiO
2
. Image
courtesy of Prof. Stephen Cronin group, USC.
Figure 5.3. VSFG spectra of neat TiO
2
(blue) and TiO
2
covered with
Au nano-islands (red).
87
Figure 5.4. VSFG spectra showing CO stretch on Au/TiO
2
. Red:
initial spectrum; blue: annealed at 140
C; black: next day (left in air
and light). PPP polarization, 300 fs delay.
While the frequency of this peak is within 20-30 cm
1
of that reported for the atop
site CO on Au,
127,140,141
its desorption temperature is drastically dierent (the reported
CO adsorbs onto gold surfaces only below 200 K).
140
This may be an indication of the
CO poisoning
146
an active plasmon catalytic site, likely on the perimeter of the Au
nano-islands.
Following the revelation that CO adsorbs to the Au/TiO
2
surface when left in the air
and in light conditions, we tried to reproduce these results in a controlled environment.
Figure 5.5 shows a VSFG spectrum of the Au/TiO
2
in argon atmosphere (red) after
the sample had been initially annealed to remove as much CO as possible. The idea
was to try to regenerate the CO peak intensity in a controlled atmosphere, with the
presumption that during the reduction of CO
2
with water, CO is an intermediate that
adsorbs to the surface.
128
After 1 h of bubbling CO
2
through water with the room light
on, a spectrum was acquired (blue). The sample was then directly illuminated with a
88
UV lamp for 2 min and another spectrum was obtained (green). When compared with
the red spectrum, the intensity of the CO peak from the blue and green spectra did not
change signicantly. However, when the sample was exposed to air for <5 min, the CO
peak signicantly increased, by a factor of3 (black).
Figure 5.5. VSFG of controlled dosing experiments mimicking atmo-
spheric conditions. PPP polarization, 300 fs delay.
The controlled atmosphere experiments discussed above seemed to suggest the CO
observed on the surface was not the result of CO
2
reduction with water. An alternate
hypothesis was then proposed that the origin of the CO on the surface may have been
the result of oxidation of organic molecules (e.g., from dust particulates) on the surface.
Figure 5.6 shows the results of exposing Au/TiO
2
to O
2
and room light for 30 min (green)
and a mixture of CO
2
, O
2
, and room light for 30 min (black). The CO peak intensity for
both spectra do not change signicantly relative to the annealed spectrum (blue), which
may indicate oxidation of the surface species did not occur to completion or conditions did
not promote oxidation. However, subsequent experiments on a dierent sample showed
an increase in the CO peak after exposing the surface with O
2
and light (Appendix I,
89
Fig. 5.16). From these results, we could not make a denitive conclusion with regard
to surface oxidation, and how the CO peak only regenerates when the Au/TiO
2
surface
is exposed to the air and light conditions remains an unanswered question until further
tests can be conducted. However, volatile hydrocarbons in the air may be oxidized to
CO, which may explain the increased CO peak after the sample is exposed to air.
Figure 5.6. VSFG spectra of Au/TiO
2
before annealing (red), after
annealing (blue), after O
2
and light dosing (green), and after CO
2
and
light dosing (green).
We also studied 5 nm Au lm deposited on SiO
2
. First, unannealed Au/SiO
2
, which
has a similar nano-island morphology as Au/TiO
2
, showed a CO frequency close to that
reported for adsorbed CO in TiO
2
and ZnO powders loaded with Au nanoparticles (2110
cm
1
).
147,148
On the contrary, CO adsorbed at Ti
4+
sites of TiO
2
shows as a peak at
2185 cm
1
.
127,149
When the sample was exposed to only the visible beam (796 nm, 3
mW) for 40 min while in an Ar atmosphere, the CO peak intensity only increased by a
factor of3 (Fig. 5.7b). However, when the sample was exposed to the laser beam while
in air, the CO peak intensity increased by almost an order of magnitude after 10 min
90
(Fig. 5.7a). It seems that irradiating the sample changes the morphology of the Au lm,
producing more spherical Au nanoparticles,
128
similar to the eect of annealing (Fig.
5.7c, d). There are two possible explanations for the observed morphology change: (1)
the visible beam (1.55 eV) is electronically `resonant' with the silicon substrate (band
gap1.1 eV) thereby annealing the Au lm, and/or (2) the visible beam is resonant with
the plasmon bands of the non-uniform Au nano-islands, where the plasmon frequency is
well-known to depend on the shape and size of the metal nanoparticle.
137,138
91
Figure 5.7. VSFG spectra of unannealed 5 nm Au deposited on SiO
2
exposed to visible laser beam in air (A) and an argon atmosphere (B).
SEM images of non-irradiated spot (C) and laser irradiated spot (D).
On the other hand, annealed (during sample preparation, 400
C) Au/SiO
2
samples,
where the Au nano-islands become more like spherical nanoparticles,
128
exhibited dif-
ferent behavior than from the unannealed sample. While the sample was irradiated in
argon, the CO peak did not increase (within experimental error) even after 40 min of
92
exposure (Fig. 5.8, bottom). When irradiated in the air, however, the CO peak intensity
increased by a factor of4 after 30 min of laser exposure (Fig. 5.8, top).
Figure 5.8. VSFG spectra of annealed 5 nm Au deposited on SiO
2
exposed to visible laser beam of varying times in air (top) and argon
atmosphere (bottom).
93
Figure 5.9. VSFG spectra of annealed 5 nm Au deposited on SiO
2
initially in argon (red), after dosing with CO without (blue) and with
(green) laser irradiation, after dosing with CO and water with (pink)
and without (black) laser irradiation, and after
ash annealing sample
to 100
C (spot 2 orange, and spot 1 teal). Spectra were oset for
clarity.
Next, we tried to see if dosing CO gas molecules over the Au/SiO
2
sample would
increase the CO adsorption peak at 2110 cm
1
. Interestingly, no detectable increase in
the CO peak is observed when CO gas is passed over the sample, likely because most
of those adsorption sites were already occupied. However, when water vapor was mixed
with CO gas, a new peak at1950 cm
1
is generated (indicating cooperativity at this
adsorption site), regardless of irradiating the sample during dosing (Fig. 5.9, pink and
94
black lines). The peak at 1950 cm
1
is annealed away at 100
C, while the peak at
2110 cm
1
remains, as expected (Fig. 5.9, orange and teal lines). The peak at 1950
cm
1
corresponds to bridge-like metastable adsorption sites (most likely, defects), and
is further investigated on continuous vapor-deposited Au lms in section 5.2.
5.1.4 Conclusions
The CO
2
reduction with water on the photocatalyst Au/TiO
2
was qualitatively investi-
gated with VSFG spectroscopy. A CO peak at 2120 cm
1
, which was attributed to an
atop adsorption site on Au (and likely on the perimeter of the Au nano-islands), was
found to be strongly-bound, even at temperatures above 100
C. After annealing, the
peak regenerates itself upon exposure to air and ambient room light, while no regen-
eration occurs if the surface was kept in the dark. However, the peak could not be
regenerated in controlled conditions.
Moreover, Au/SiO
2
of similar morphology to Au/TiO
2
showed a new peak at 1950
cm
1
(bridge-site) upon co-dosing CO and water vapor, indicating cooperativity at the
site. The CO adsorption at the 1950 cm
1
bridging-site is weakly-bound compared to the
one at 2120 cm
1
. These VSFG experiments showed that photocatalyst active sites can
be identied, an important step to obtaining a fundamental understanding of reaction
mechanisms involved in photocatalytic conversion of CO
2
and water into hydrocarbon
fuels.
95
5.2 Water-enhanced CO Adsorption on Roughened Gold
Surfaces at Ambient Conditions
Following the results from the Au/TiO
2
studies in the previous section, we wanted to test
our hypothesis that the CO peak at2110 cm
1
was CO adsorbed to the perimeter of the
gold nano-islands, and not the top of the gold nano-islands. Interestingly, we found that
continuous vapor-deposited gold lms produces a peak at1955 cm
1
, unlike anything
we have observed previously for Au/TiO
2
or Au/SiO
2
samples. Serendipitously, we
found that by co-dosing CO gas with water vapor, the CO peak increases signicantly,
indicating cooperativity at the CO adsorption site.
5.2.1 Introduction
Heterogeneous catalysis is the foundation of the chemical industry and the study of the
surfaces where the reactions take place is of signicant importance. Investigation of
the adsorption of molecules on metal (e.g., Au, Pt, Pd, Rh, Cu) and metal-oxide (e.g.,
TiO
2
, Al
2
O
3
, SiO
2
) surfaces has been of great technological interest. Reactions that have
gained considerable focus over the last few decades have been the reduction of CO
2
into
useful hydrocarbon fuels, such as methane or methanol,
128,129,131,150
and the oxidation of
CO,
126,127,149,151
which is important for many industrial processes. CO adsorbs readily
to a number of surfaces, and the eect for heterogeneous catalysis is that CO tends to
block active sites by obstructing adsorption of reactants, and thus is well-known as a
catalyst poison.
146,152,153
On the other hand, CO is a common reaction intermediate in
the conversions between CO
2
and hydrocarbons.
130
Spectroscopically, CO adsorption on metal surfaces is a simple model for catalytic
reactions. Due to its strong interactions with the substrate, the frequency of the CO
stretch vibrations is a sensitive indicator of the nature of the adsorption site. For exam-
ple, FTIR studies of CO adsorption on solution-deposited Au on TiO
2
powder showed
several spectral features: 2184 cm
1
CO on TiO
2
powder, 2112 cm
1
CO on metallic
96
Au, and 2151 cm
1
CO on oxidized Au.
127
Ultrahigh vacuum (UHV) infrared re
ection
absorption spectroscopy (IRAS) studies of CO adsorption on the Au(110)-(1 2) sur-
face performed as a function of CO pressure and sample temperature showed a single
CO peak whose frequency varied from 2108 cm
1
to 2118 cm
1
depending on coverage
and temperature.
140
UHV SFG studies of the interaction of CO with Au(111) revealed
a single peak at 2100 cm
1
for CO atop a Au atom for surface modied by ion bom-
bardment.
141
More dramatic frequency shifts are observed for CO adsorbed on Pd and
Pt. On Pd(111), two spectral signatures are observed at 190 K, at 1890 cm
1
(bridg-
ing site) and 2109 cm
1
(atop site).
142
On Pt(111), the bridging site was measured at
1855 cm
1
, while the atop site peak was reported between 2083-2100 cm
1
depending
on temperature and surface coverage.
50,154
Dissolved CO adsorbed on Pt electrodes was
observed to have similar bridge (1850 cm
1
) and atop (2100 cm
1
) site frequencies.
143
In this study, SFG spectroscopy was used to identify two quasi-stable CO adsorp-
tion sites (most likely, defects) on roughened continuous vapor-deposited Au surfaces at
room temperature (293 K) and ambient pressures (1 atm). CO adsorption was signif-
icantly enhanced in the presence of water vapor, indicating cooperativity in CO + H
2
O
adsorption at these defect sites.
5.2.2 Experimental
SFG Setup
A full description of the SFG laser setup is described in Chapter 2. The laser power at
the sample was10 J/pulse and5-6 J/pulse for the visible and IR pulses, respec-
tively. The SFG spectra were measured for PPP polarization (SFG-visible-IR). The
data were collected with 1 s or 1 min acquisition times for 0 and 300 fs IR-visible time-
delayed spectra, respectively. All measurements were performed in a sealed, home-built
temperature-controlled gas cell at room temperature (20
C), and 0 fs or 300 fs IR-visible
delay.
97
Gas Dosing
CO Stretch Region: A SFG spectrum (in the CO stretch region) (with a 300 fs delay)
of the gold sample was rst taken in an argon (99.9% pure, Gilmore) atmosphere, which
we called the initial spectrum (before CO or water exposure). A 3:1 mixture of argon
to carbon monoxide (99.5% pure, Gilmore) with total pressure1 atm was then passed
over the sample at a
ow rate of100 mL/min for 10 min to ensure complete purging of
the gas line with Ar/CO mixture. The sample cell was then purged with argon to remove
any CO gas before acquiring another SFG spectrum (called CO dose). This ensured that
the SFG spectrum is free of gas-phase CO, which strongly absorbs between 2000-2250
cm
1
. To introduce water vapor into the cell, the Ar/CO mixture was continuously
bubbled through ltered 15 M
water (Millipore) and passed over the sample for 10
min at100 mL/min. The water partial pressure at 20
C is0.025 atm. The cell
was purged again with argon, and an SFG spectrum was acquired (called \CO + H
2
O
dose").
Thermal annealing, which entailed heating of a sample to 120
C for<10 s in an argon
atmosphere and then allowed to equilibrate back to room temperature, was performed
for some samples (see Results). A heating rate of1-2
C/s was used. The temperature
was monitored by a thermocouple (K-type, Omega) embedded directly underneath the
sample platform with estimated accuracy of2
C. Once the sample equilibrated to
room temperature, a SFG spectrum was acquired and the dosing sequence from above
was repeated.
OH Stretch Region: A 0 fs IR-visible delay was used to acquire spectra in this region.
A SFG spectrum (in the OH stretch region) of the gold sample was rst taken in an
argon atmosphere, which we called the \initial" spectrum (before CO or water exposure).
Argon was then continuously bubbled through the ltered water while passing over the
sample for 10 min at100 mL/min. A SFG spectrum (called \H
2
O dose") was then
recorded. A 3:1 mixture of argon to carbon monoxide with total pressure1 atm was
then bubbled through the ltered water and passed over the sample at a
ow rate of
98
100 mL/min for 10 min. The sample cell was purged with argon and another SFG
spectrum (called \CO + H
2
O dose") was then recorded.
Sample Preparation
Gold Deposition: Gold samples were prepared by starting with a 10 cm Si(100) wafer
(0.5 mm thick) and depositing a 5 nm titanium binding inter-layer and then 100 nm of
gold from an electron-beam evaporator. The wafer was then cut into2 cm
2
pieces.
Piranha-cleaned Au: Samples were cleaned by placing them in a piranha solution (3:1
mixture of concentrated sulfuric acid to 30% hydrogen peroxide) for20 min, rinsed with
distilled water, acetone, and methanol, and then dried by
owing nitrogen gas across the
sample.
Electrochemically Roughened Au. The electrochemical oxidation-reduction cycle
(ORC) procedure was used to roughen samples.
155,156
Au samples were rst cleaned
in piranha solution. The voltage was varied from -1.0 V to +20.0 V and cycled 15-20
times in a 0.1 M KCl solution with another gold sample used as the counter electrode.
Both the counter and working electrodes were roughened in the process.
Hydrogen
ame annealed Au. A piranha-cleaned Au sample was hydrogen
ame
annealed by sweeping a4 cm hydrogen
ame back and forth across the sample for1
min.
Non-treated Au. Non-treated Au samples were taken as is (without piranha-cleaning,
electrochemical etching, or
ame annealing) after vapor deposition.
5.2.3 Results and Discussion
Figure 5.10 shows VSFG spectra for hydrogen
ame annealed 100 nm-thick continuous
vapor-deposited Au. Hydrogen
ame annealing has been shown to produce contaminant-
free reconstructed Au(111),
157
and after dosing CO (blue line) or CO + H
2
O vapor
(green line) over the surface at room temperature (293 K), no CO adsorption peaks were
observed, which agrees with previous temperature-programmed desorption and IRAS
99
studies on crystalline Au that showed CO desorbs at temperatures <185 K.
140,158
Simi-
larly, no detectable CO adsorption was observed on non-treated Au samples (Fig. 5.10).
The VSFG spectra are t by assuming Lorentzian proles for vibrational resonances
contributing to
(2)
R
(!), which interfere with the frequency-independent nonresonant
(NR) background contribution
(2)
NR
:
I
SFG
(!) =
(2)
NR
+
(2)
R
(!)
E
IR
(!)
E
vis
(!)
2
(5.1)
=
A
NR
e
i
+
X
i
B
i
!!
i
+i
i
2
exp
(!!
g
)
2
2
g
!
(5.2)
where A
NR
is the nonresonant amplitude, '
NR
is the relative phase between the NR
and the resonant signal, and !
i
,
i
, and B
i
are the central frequency, line width, and
the amplitude of i-th resonant band, respectively. The last term in Eq. (5.2) is the
spectral shape of the IR pulseE
IR
(!), which is approximated by a Gaussian with central
frequency!
g
, and width
g
. The narrow-band visible pulse is assumed to be convoluted
into the Lorentzian line shapes of the vibrational resonances.
100
Figure 5.10. VSFG spectra of hydrogen
ame annealed (A), and non-
treated (B) continuous vapor-deposited Au. Spectrum before dosing
adsorbates (red line), after dosing CO only (blue), and after co-dosing
CO and H
2
O (green).
As shown in Figure 5.11, for one particular piranha-cleaned Au surface (sample 1), no
detectable CO adsorption peak (B
initial
= 0 a.u.) was observed initially (red spectrum)
before gas dosing on. However, an intense CO adsorption peak with B
CO
= 2610 a.u.
at 1960 cm
1
is observed after CO gas was passed over the surface for 10 min (blue
spectrum). Piranha removes organic impurities from the surface, freeing adsorption sites
where CO can bind. However, piranha may also be etching the surface by creating defect
sites, but there is no evidence to suggest this from our SEM images. Upon dosing the
sample with a mixture of CO and water vapor for another 10 min, a third VSFG spectrum
(green spectrum) was acquired from the same region on the sample, and this time the CO
peak amplitude (B
CO+H
2O
= 3990 a.u.) increased signicantly, by approximately 50%.
101
We should note that even dosing CO with higher water partial pressures (created by
heating the water), no additional enhancement was observed, indicating we were already
dosing at the saturated water vapor pressure at 20
C.
In VSFG, the intensityI/N
2
, where N is the surface concentration of chromophores,
and thus N/ B. In other words, a 50% increase in the CO amplitude corresponds to
50% more CO adsorbed to the Au surface when CO was co-dosed with water vapor.
On average, for all roughened samples, we observed an increase in the amplitude from
10-55%. We provide spectra of other piranha-treated Au samples (samples 4-7) as well
as tting parameters for all the samples (1-7) in Table 5.1 in the Appendix.
Figure 5.11. VSFG spectra piranha-cleaned continuous vapor-
deposited gold (sample 1). Spectrum before dosing adsorbates (red
line), after dosing CO only (blue), and after co-dosing CO and H
2
O
(green). Black lines are ts to Eq. (5.2).
102
Figure 5.12 shows VSFG spectra for an electrochemically roughened Au sample (sam-
ple 2). Initially (before dosing adsorbates) there were two CO adsorption peaks: a strong
peak at 1960 cm
1
with amplitudeB
a
initial
= 2050 a.u., and a weaker peak at 2020 cm
1
with B
b
initial
= 40 a.u., where B
a
and B
b
denote the amplitudes of the lower and higher
frequency CO adsorption peaks, respectively. We observe CO adsorption in the initial
spectrum because CO gas was likely not entirely purged from the lines from previous
experiments. Upon dosing the sample with CO, B
1
CO
increased by33%, while B
2
CO
increased by a factor of 3. After dosing the surface with both CO and water vapor,
B
1
CO+H
2
O
= 3121 a.u., an increase in15%, and B
2
CO+H
2
O
= 295 a.u., an order of
magnitude increase compared to if only CO was dosed. The higher frequency mode may
be due to low-coordinated Au adsorption sites, such as step-edges or kinks.
158,159
Figure 5.12. VSFG spectra of electrochemically roughened continuous
vapor-deposited gold (sample 2). Spectrum before dosing adsorbates
(red line), after dosing CO only (blue), and after co-dosing CO and
H
2
O (green). Black lines are ts to Eq. (5.2).
103
Shown in Figure 5.13 are the VSFG spectra after CO + H
2
O dosing for dierent Au
samples along with their respective scanning electron microscopy (SEM) images (Figs.
5.13b-e). The SEM for the non-treated Au sample is given in the Appendix. The SEM
image for the hydrogen
ame annealed sample (Figure 5.13b) shows a relatively smooth
surface, as expected, since
ame annealing has been shown to yield high-quality recon-
structed Au(111) surfaces,
157
and no detectable CO adsorption peak is observed (black
spectrum). Figures 5.13c-e show relatively similar surface roughness for the piranha-
cleaned, electrochemically roughened, and electrochemically then piranha-cleaned Au
surfaces, and thus similar CO peak amplitudes at 1960 cm
1
.
Figure 5.13. (A) VSFG spectra after co-dosing CO and H
2
O
vapor on non-treated (green line), hydrogen
ame-annealed (black),
piranha-cleaned (pink), electrochemically roughened (blue), and elec-
trochemically roughened then piranha-cleaned (red) continuous vapor-
deposited gold surfaces. SEM images of hydrogen
ame-annealed gold
(B), piranha-cleaned gold (C), electrochemically roughened (D), and
electrochemically/piranha-cleaned gold (E).
Shown in Fig. 5.14 is the eect that thermal annealing of the Au surface under
argon (for sample 3) had on subsequent CO + H
2
O adsorption. In the top panel, the
104
CO peak at1950 cm
1
can be easily annealed away at 120
C, as the black spectrum
shows almost no CO peak remaining. We note that CO can be removed from the surface
at temperatures as low as 50
C, however the desorption process is much slower at
temperatures below 120
C. Upon a second dosing of CO + H
2
O, the CO peak reappears
(blue spectrum, center panel), albeit a weaker amplitude (decreased by factor2). A
second thermal annealing at 120
C once again desorbs CO from the Au surface (orange
spectrum). Upon the third and nal dosing of CO + H
2
O, the CO peak regenerates
(purple spectrum, right panel), although a much weaker amplitude than before (decrease
by factor8). Subsequent annealing removes the adsorption site for CO.
Previous density functional theory (DFT) calculations performed for CO on a p(1
2) Au(332) surface showed a bridge CO adsorption site with frequency of 1950 cm
1
and binding energy of -0.51 eV (-11.7 kcal/mol),
158
while DFT calculations performed
on CO adsorbed to Au/TiO
2
surface showed a bridging CO between two Au atoms
with frequency 1927 cm
1
and binding energy of -18 kcal/mol.
160
The CO desorption
energy has to be larger than 20 kcal/mol in order to stay on the surface at tempera-
tures higher than 300 K. Indeed, using the Redhead model for temperature-programmed
desorption,
161
given in Eq. (5.3), the CO activation energy for rst-order desorption
can be approximated. The peak temperature T
peak
at which the rate of desorption is a
maximum, and in our case T
peak
300-400 K, gives E
des
20-30 kcal/mol (assuming
heating rates 1-10 K/s), which is in agreement with theoretical calculations. DFT
indicates that bridged CO is less stable than atop CO, which has a binding energy of
-27 kcal/mol.
E
des
=RT
peak
ln
AT
peak
3:46
(5.3)
105
Figure 5.14. VSFG spectra of piranha-cleaned Au (sample 3) acquired
before dosing adsorbates (red spectrum), after rst co-dosing of CO
and H
2
O vapor (green), after rst
ash annealing (black), after second
co-dosing of CO and H
2
O vapor (blue), after second
ash annealing
(orange), and after third co-dosing of CO and H
2
O vapor (purple).
106
By denition of cooperativity, since CO adsorption on Au was enhanced in the pres-
ence water vapor, H
2
O adsorption should also be enhanced in the presence of CO. To test
this hypothesis, we measured the VSFG spectrum in the OH stretch region (3100-3700
cm
1
). Since the spectra were acquired without an IR-visible delay, the nonresonant
signal was enhanced, and the resonant features were not as pronounced.
47,91
Moreover,
the vibrational dephasing time of the OH stretch is on the order of100 fs, so using a
delay would not have been practical in our case. Subtracting the background in the OH
stretch region is dicult and the following results are tentative.
Shown in Figure 5.15a are the spectra before dosing adsorbates (red line), after
dosing H
2
O vapor (blue), and after co-dosing CO and H
2
O vapor (green). Here, the
VSFG intensity after dosing with water (blue) decreases relative to the initial spectrum
(red). Likewise, the intensity decreases after co-dosing with CO and H
2
O relative to
the blue spectrum. This eect is the opposite of the VSFG intensities acquired in the
CO stretch region (1950 cm
1
). The corresponding dierence spectra are shown in
Figure 5.15b. The blue spectrum in (b) is the dierence in VSFG intensity between the
initial (red) and H
2
O dose (blue) from (a). The green spectrum in (b) is the dierence
in VSFG intensity between the initial (red) and the CO + H
2
O dose (green) from (a).
The dierence spectra in Fig. 5.15b clearly show an enhanced intensity upon dosing CO
+ H
2
O.
Shown in Figure 5.15c are the spectra after annealing the Au sample at 120
C and
thereafter carrying out the dosing experiments. The overall VSFG intensity is lower than
from the spectra in Figure 5.15a, possibly due to restructuring of the Au surface caused
by annealing, thus changing the nonresonant signal. The spectra in Figure 5.15d are the
corresponding dierence spectra. Similarly, an enhancement was observed with dosing
CO + H
2
O.
107
Figure 5.15. VSFG spectra of piranha-cleaned continuous vapor-
deposited gold. The spectra in (a) are direct measurements of the
SFG intensity upon dosing H
2
O (blue) and co-dosing CO and H
2
O
vapor (green), and (b) shows the dierence in the intensity relative to
the initial (red) spectrum from (a) of dosing H
2
O (blue) and co-dosing
CO and H
2
O vapor (green). The same description follows for (c) and
(d) except the gold sample was
ash annealed at 120
C.
5.2.4 Conclusion
Using VSFG, we observed CO adsorption on roughened Au surfaces at room temperature
and identied two quasi-stable adsorption sites: an intense bridge CO at 1955 cm
1
and a weaker CO at2023 cm
1
(at a low-coordinated Au site). CO adsorption on
roughened Au surfaces is signicantly enhanced when CO is dosed with water vapor: an
increase in the VSFG resonant amplitude from as low as10% to as high as55% for the
bridge CO adsorption site at1955 cm
1
. More experiments are needed to determine
water-enhancement statistics for the CO adsorption site at2023 cm
1
. Successive
108
annealings of the Au surfaces at 120
C decreases CO adsorption until no detectable
CO can be observed, possibly due to restructuring of the Au and the removal of the CO
adsorption site.
5.3 Appendix
Figure 5.16. VSFG spectra of Au/TiO
2
initially in argon (red), after
annealing (blue), and after dosing oxygen in the dark (green), in the
light for 30 min (pink) and 60 min (black).
109
Figure 5.17. VSFG spectra of unannealed Au/SiO
2
while dosing with
oxygen (top) at increasing times, and while oxygen is being purged
from the sample at increasing times (bottom). PPP polarization and
0 fs delay.
110
Figure 5.18. VSFG spectra of piranha-cleaned Au samples 4-7 (A-D).
Sample 7 was also electrochemically etched.
111
Figure 5.19. Scanning electron microscopy image of non-treated Au
sample.
112
Table 5.1. Fitting parameters using Eq. (5.2) from main text.
Sample Spectrum A
NR
NR
B
1
B
2
1
2
!
1
!
2
!
g
g
Initial 77 1.4 0 0 - - - - 1918 195
1 CO 80 1.35 2610 0 17 - 1960 - 1923 187
CO+water 80 0.96 3990 0 20 - 1954 - 1909 137
Initial 23.9 1.31 2050 40 25 10 1956 2018 2108 300
2 CO 16.6 0.77 2725 133 27 12 1960 2021 2145 300
CO+water 18.2 0.78 3121 295 27 17 1962 2028 2080 300
Initial 46.8 21 10 0 35 - 1950 - 2013 345
1st CO+water 46 -0.7 905 0 21 - 1949 - 1981 390
3 1st annealing 46 -0.19 26 0 21 - 1951 - 2002 350
2nd CO+water 46 -1.2 510 0 27 - 1953 - 2100 344
2nd annealing 37 0.7 5 0 23 - 1950 - 1995 345
3rd CO+water 46 -0.3 65 0 23 - 1946 - 1954 365
Initial 30.6 1.77 0 0 - - - - 2100 300
4 CO 31 1.33 2378 0 30 - 1960 - 2136 300
CO+water 31 1.22 2611 0 30 - 1956 - 2131 300
Initial 67 0.1 0 0 - - - - 1965 239
5 CO 70 0.3 585 0 20 - 1939 - 1953 209
CO+water 68 0.07 910 0 20 - 1945 - 1934 205
Initial 86 1 0 0 - - - - 1957 245
6 CO 85 1.38 3626 0 21 - 1943 - 1936 243
CO+water 84 1.27 3900 0 21 - 1947 - 1931 210
Initial 31.2 -13.3 0 0 - - - - 1995 162
7 CO 23.6 1.1 1337 125 23 16 1963 2019 1958 211
CO+water 18.2 0.78 1627 107 25 16 1968 2028 1945 264
113
Chapter 6
Vibrational Coupling and
Hydrogen Bonding at the
Air-Water Interface
In this chapter heterodyne-detected sum frequency generation (HD-SFG) was imple-
mented to investigate hydrogen bonding at the air-water interface. Igor Stiopkin and
Champika Weeraman contributed to this study.
27
Igor optimized the design of the HD-
SFG system and the tting procedure. The molecular dynamics simulations were per-
formed by our collaborators, Piotr Pieniazek and James Skinner, at the University of
Wisonsin-Madison. After Champika graduated, I assumed his role in the project. My
contribution to this study was analyzing and processing the HD-SFG data. Using stan-
dard spectral interferometry (SI) methods that include inverse and forward Fourier trans-
forms as well as ltering in the time domain to recover phase and amplitude of the SFG
spectrum and to subtract the nonresonant background revealing spectral line shapes.
6.1 The Water Surface
Water is omnipresent. It comprises more than 70% of the Earth's surface as oceans or
lakes in the form of a liquid, as icebergs in solid form, or in the atmosphere as a vapor.
It is the main constituent of the human body and the essential ingredient to sustain life.
It is the rst thing we interact with in the morning, whether when taking a shower or
when brushing our teeth. It is part of everyone's daily routine, yet water is considered to
be a peculiar molecule. When compared to its molecular analogs such as methane (CH
4
)
114
or ammonia (NH
3
), water (H
2
O) is the only one that is a liquid at room temperature.
Liquid water expands when it freezes, which is the reason why icebergs
oat and oceans
do not freeze over (from top to bottom), otherwise life as we know it would not exist.
Liquid water possesses other anomalous properties that make it unique among liquids:
it becomes less viscous when compressed at room temperature, and it has a very high
melting and boiling point, considering the fact that it only has three atoms.
The reason that liquid water exhibits such unique properties arises from its ability to
accept and donate two hydrogen bonds. A hydrogen bond (H-bond) is a weak electro-
static interaction formed between an electropositive H atom and an electronegative atom
such as O, N, or F. The average energy per OHO bond in liquid water, 3-7 kcal/mol, is
only a few times larger than thermal energy at room temperature (k
B
T = 0:6 kcal/mol).
Consequently, since the molecules are in constant motion, H-bonds are being made and
broken at all times (< 1 ps time scale), and the number of H-bonds per molecule varies
at any given time. In the formation of ice, water molecules in the liquid phase separate
from one another to accommodate the formation of four H-bonds, hence making ice less
dense and able to
oat. Water's H-bonding network plays an important role in many
biological, chemical, and physical processes, and many of these processes take place at
the water surface. For example, the transport and exchange of ions and solutes across
the interface between an aqueous phase and hydrophobic biological membranes consti-
tute what is, perhaps, the most important process in plants and animals. Processes such
as membrane and micelle formation, and protein folding all involve hydrogen bonding
interactions with water molecules at their surfaces.
One approach for understanding the interfacial properties of liquid water, such as its
structure and dynamics, is to probe the OH stretch frequency using IR spectroscopy. The
frequency of the OH vibrational stretch is highly dependent on its molecular environment,
and thus is a good indicator of local structure and dynamics. Vibrational spectroscopy
of the aqueous interface has progressed signicantly in recent years with the development
of the surface-selective sum frequency generation (SFG) spectroscopy,
52,83,116,162{164
and
115
with the ability to model the dynamic H-bond network of bulk-phase and interfacial
water using computer simulations and improved methods of calculating spectroscopic
signals.
165{169
Vibrational spectroscopy has been used to correlate the frequency of the OH stretch
mode
OH
and the strength of the H-bond, which can be qualitatively characterized in
terms of the OHO bond distance.
122
SFG spectra of aqueous interfaces show more
structure than bulk-phase spectra, indicating that the H-bonding network at the surface
is dierent from that found in bulk water.
24,170
A well-isolated sharp peak appears
at3700 cm
1
at the air-water interface, corresponding to the `free' (not hydrogen
bonded) OH. The H-bonded
OH
band of the water surface is typically narrower and
more structured than in the bulk-phase, with two prominent subbands often appearing at
3200 cm
1
and3450 cm
1
. Originally, the red-shifted 3200 cm
1
band was assigned
as `ice-like' tetrahedrally-coordinated H-bonded structures, and the 3450 cm
1
feature as
`water-like' structures
24
while others have attributed the features to OH stretch modes
of primarily symmetric versus asymmetric character.
83,164
However, both assignments
are incorrect. Skinner et al recently addressed the assignment of this part of the water
spectrum satisfactorily.
171
Adding to the diculty in assigning spectral features is the fact that intra- and
intermolecular vibrational coupling between OH oscillators often broadens lineshapes
and further complicates assignments. One way to minimize these complications is by
using dilute solutions of isotopically substituted water, since the OH and OD stretch
frequencies are spectrally far apart. Isotopic dilution studies have been an invaluable
tool for spectroscopists. SFG spectra of isotopically dilute solutions are much simpler
and the nonresonant background signal can be deconvoluted from the resonant signal
with spectral-tting procedures. However, these are extremely challenging due to the
SFG signal level decreasing with isotopic dilution.
116
The main goal of this study was to not only investigate the H-bonded network at the
water surface, but to answer one fundamental question being just how thin it is. Theo-
retical studies have suggested the surface is only about 3
A thick, with the bulk-phase
properties of water recovered within the top few monolayers.
165,172,173
Direct experimen-
tal evidence of this hypothesis has been elusive owing to the perplexity of depth-proling
the liquid surface on the angstrom scale. Here, we used isotopically diluted solutions of
D
2
O in H
2
O to study the free OD at the water surface with heterodyne-detected (HD-
SFG) spectroscopy, which is selective to only the OD stretches at the topmost layer of
the water surface.
6.2 Theory of Heterodyne-Detected SFG
The intramolecular and intermolecular vibrational coupling betweeen the OH transition
dipoles of the same molecule or neighboring molecules aect the spectral line shapes of
the water OH-stretch band.
108,174
To disentangle these vibrational coupling contributions
to the line shape, we measure the free OD spectra at the air/water interface while using
isotopic dilution in D
2
O:HOD:H
2
O mixtures to gradually `turn o' the intermolecular
vibrational coupling.
175,176
This, however, challenges spectroscopic detection limits. The
free OD (or free OH) spectral feature can only be observed using the surface-selective
SFG technique.
24,170
Because SFG is a coherent optical process, the homodyne signal
intensity decreases quadratically with dilution (surface coverage, N):
I
homo
SFG
(!) =jE
SFG
(!)j
2
/N
2
D
(2)
E
2
(6.1)
where
(2)
is the ensemble averaged second-order molecular hyperpolarizability. For
example, if the surface coverage is reduced by a factor of 10, the signal-to-noise ratio
would be reduced by a factor of 100, while the experimental acquisition time would need
117
to be increased by 10
4
to keep the same signal-to-noise ratio. Moreover, at low con-
centration, SFG spectra are overwhelmed by the nonresonant (NR) background, which
interferes with the resonant OD-stretch signal.
To overcome these challenges we used HD-SFG technique,
52
which uses interference
of the SFG signal with a reference beam to (1) amplify the SFG signal, (2) make it linear
with N, and (3) allow separation of the resonant part of the signal from the NR back-
ground by providing both the amplitude and the phase (or, alternatively, real and imagi-
nary parts) of the signal.
52,116,162,176
This approach allowed us to record background-free
SFG spectra with a suciently high signal-to-noise to reveal the structure of the free
OD-stretch line shapes at the air-water interface of isotopic mixtures.
In heterodyne detection, two collinear beams, a local oscialltor (LO) reference beam
and the SFG signal, are allowed to interfere at the detector (Fig. 6.1). The heterodyne
signal intensity is
I
HD
SFG
(!)/jE
SFG
(!) +E
LO
(!)j
2
(6.2)
=jE
SFG
(!)j
2
+jE
LO
(!)j
2
+I
crossterm
SFG
(!) (6.3)
wherejE
SFG
(!)j
2
andjE
LO
(!)j
2
are the spectral intensities of the SFG and LO, respec-
tively. The cross term I
crossterm
SFG
in Eq. 6.3 is dened as
I
crossterm
SFG
(!) = 2jE
SFG
E
LO
j cos(
SFG
LO
!) (6.4)
/ N (6.5)
The cross-term contains the product of the two electric elds (signal and reference) and
depends on the phase dierence betweeen the LO and SFG, and the temporal delay
between the LO and signal. It scales linearly with surface coverage N. Therefore if N is
reduced by a factor of 10, the intensity only drops by 10 and the acquisition time would
118
have to be increased by only 100 times to keep the same signal-to-noise ratio, i.e., 100
times shorter than in the case of homodyne detection. Because the signal and LO pulses
interfere with each other in the time domain, an interferogram in the frequency domain is
what is actually measured by the detector. By applying standard spectral interferometry
analysis
177
(which is discussed in detail in section 6.3.3), both the signal spectral phase
and its amplitude can be recovered, while the temporal prole of the signal is recovered
through the Fourier transform.
6.3 Experimental Details
6.3.1 Heterodyne-detected SFG Setup
Here, we describe the HD-SFG system built at Wayne State University (Detroit, MI),
which is where this study was conducted. The SFG system
48,52,122
at Wayne State is
similar, in principle, to the one described in Chapter 2 (although the main dierence
is the method of generating broad-band IR pulses). Moreover, the system described in
Chapter 2 was not equipped to perform heterodyne detection.
The reference LO beam is generated by spatially and temporally overlapping small
portions of the visible and IR beams (1% of the visible and5% of the IR) in a thin
quartz crystal (100 m). The intensity of the LO beam is adjusted using a variable
density lter to optimize detection of the cross-term. The LO beam is recombined with
the visible beam before the sample using a dichroic beam splitter. IR, visible, and LO
beams are spatially overlapped and focused at the sample surface by a 25 cm focal length
silver-coated concave mirror. The LO beam is aligned such that after re
ection o the
sample surface it propagates collinearly with the SFG signal generated at the sample
surface. The intensity of the LO was adjusted to produce15% modulation depth in
the interference fringes.
The IR beam power was 2 mW at the sample and its diameter was 80-100 m. The
visible beam was produced by spectral ltering of the unused portion (50%) of the
119
Figure 6.1. Schematic representation of heterodyne-detected SFG.
amplied 800 nm beam. The visible beam power at the sample was10 mW and its
diameter was50 m.
Using another recent technical development, a 350 fs time delay was introduced
between the IR and visible pulses in order to maximize the SFG signal while improving
spectral resolution and reduce the NR background.
47
A 2.5 ps time delay between the
SFG signal and LO pulses was used to produce a fringe pattern in the frequency domain
that is recorded by the CCD detector; a fringe spacing of 14 cm
1
corresponds to 2.5
ps delay.
HD-SFG interferograms were recorded using 1 min acquisition time for SSP and
PPP polarization combinations. The phase drift between the signal and LO pulses was
measured to be less than =10 over a 10 min period, so that phase
uctuations did not
aect the contrast of the interference fringes. Standard SI analysis including inverse and
forward Fourier transforms as well as ltering in the time domain was implemented to
recover phase and amplitude of the SFG spectrum.
52,177
120
All recorded spectra were phased (phasing procedure described in Section 6.3.3)
with respect to single selected reference, the 100% H
2
O spectrum, using the fringes
in the o-resonance part of the interferogram above 2800 cm
1
. After phasing, 20-50
interferograms were averaged for each isotopic dilution. The spectral phase of all SFG
signals was then set such that the imaginary part of the SFG spectrum is zero in the
o-resonance part of the spectrum, around 2820 cm
1
.
6.3.2 Sample Preparation
D
2
O:HOD:H
2
O isotopic mixtures were prepared by using doubly-distilled water and
deuterium oxide (D
2
O, 99.9%, Cambridge Isotope Laboratories). D
2
O concentrations
(v/v) of 100%, 75%, 50%, and 25% were used. 100% H
2
O was used as the reference
(nonresonant) spectrum. A mixture was placed in a glass dish and covered with a plastic
lid to prevent evaporation and surface contamination (a hole was cut large enough to
allow the IR, vis, and LO beams to pass through, and another hole to allow the passage
of the re
ected LO and SFG signals).
6.3.3 Data Processing
Heterodyne detection requires the interpretation of the spectral interferograms obtained
from the CCD. The raw HD-SFG interferogram (Figure 6.2a) is obtained by the interfer-
ence between the SFG signal and LO pulses. The LO spectrum (Figure 6.2b) is recorded
by blocking the IR pulse (in the SFG channel), thereby 'turning o' the SFG signal.
121
Figure 6.2. The local oscillator (B) is subtracted from the HD-SFG
interferogram (A) to obtain the cross-term (C), assumingjE
LO
j
2
jE
SFG
j
2
.
The cross-term contains all of the information about the system and is obtained by
subtracting the LO spectrum from HD-SFG spectrum. (Note, however, that the cross-
term can be obtained even without recording the LO spectrum, by simply ltering out
the LO signal in the time domain after inverse Fourier transforming the raw HD-SFG
interferogram.) Due to subtraction error, a square window is applied to remove any
122
remaining LO signal in the time domain (Figure 6.3b). Once the LO signal has been
completely removed, the cleaned-up cross-term spectrum is obtained, as shown in Figure
6.3c.
Figure 6.3. The cross-term (A) is inverse Fourier transformed (IFFT)
to obtain the time domain amplitude (B). A square window is applied
to lter out the LO at t = 0, and then the spectrum is forward Fourier
transformed (FFT) to give the cleaned-up cross-term (C).
Once the above procedure is done for all interferograms, they must be phased before
averaging. Phasing is a procedure that ensures all interferograms have the same phase
within a given spectral region. Phasing is accomplished by simply multiplying the cross-
term by a phase factor, e
i
, which, eectively shifs the spectrum (Figure 6.4). If one
were to bypass the phasing procedure and go straight to averaging all the cross-terms,
one would quickly realize that they will destructively interfere (assuming the phase drifts
123
within the experimental time window), resulting in cancellation of the signal. Figure 6.4
shows the basic principle of the phasing procedure. After all interferograms have been
phased, they then can be averaged to increase the signal-to-noise ratio.
Figure 6.4. Principle of the phasing procedure. Phasing of spectra
comprises of multiplying a spectrum by a phase factor e
i
.
One of qualities of HD-SFG is that it allows the subtraction of the NR background,
given the phase and amplitude. Unlike NR background suppression,
47,91
NR background
subtraction in HD-SFG removes the NR signal almost entirely, without sacricing signal-
to-noise ratio, thus allowing for easier interpretation of the resonant response. To sub-
tract the NR background, the HD-SFG signal of a NR sample must rst be recorded. In
our case, pure H
2
O was the NR sample, but in principle, any sample that is not resonant
with either the IR (vibrationally resonant) or visible (electronically resonant) pulse, can
be used (such as e.g., a gold surface). Figure 6.5 illustrates the basic principles of NR
124
background subtraction in HD-SFG. Before subtraction of the NR background (Figure
6.5b), it must be phased with the cross-term of the HD-SFG signal (Figure 6.5a), per
procedure described above.
Figure 6.5. Nonresonant (NR) background subtraction in HD-SFG.
The NR background (100% H
2
O) (B) is subtracted from the 100%
D
2
O spectrum (A) to obtain the purely resonant spectrum (C).
125
6.4 Results and Discussion
6.4.1 HD-SFG
HD-SFG spectra for isotopically diluted D
2
O:HOD:H
2
O mixtures (for 100%, 75%, 50%,
and 25% D/H mole fraction) at room temperature (20
C) were recorded for PPP and
SSP polarization combinations (`S' and `P' indicate the electric eld polariation per-
pendicular and parallel to the plane of incidence, respectively, for the SFG, visible, and
infrared beams). The spectra covered the free O-D vibrational stretch region2650-2800
cm
1
. We performed curve tting (per Eq. 6.6) of both the real and imaginary parts
of the SFG signals to extract the peak positions (
j
), amplitudes (B
j
), and line widths
(
j
). Two distinct peaks are observed in the free OD-stretch spectrum of the air-water
interface; one at 2728 cm
1
corresponding to the free OD of the D
2
O molecule, and the
other at 2745 cm
1
corresponding to the free OD of the HOD molecule.
(2)
(!
IR
)/A
NR
e
i'
NR
+
X
j
B
j
j
(!
IR
j
) +i
j
(6.6)
The resonant part of the nonlinear susceptibility
(2)
is described as a sum of Lorentzian
terms, whereas the nonresonant background (A
NR
) is represented as a constant term
in the real part of the signal. HD-SFG enables us to separate the NR background in
the SFG spectra, which is crucial to revealing the true resonant lineshapes of the peak
structure shown in Fig. 6.6.
126
Figure 6.6. Real (solid blue lines) and imaginary parts (solid red lines)
of the vibrational HD-SFG spectra of the free OD-stretch at the air-
water interface of H
2
O:HOD:D
2
O isotopic mixtures, for SSP and PPP
polarizations. Dashed lines represent the ts to Eq. 6.6
The tting results are summarized in Fig. 6.7. The observed peak amplitudes track
the expected HOD:D
2
O isotopic scrambling ratio (Fig 6.7a, b), taking into account that
D
2
O molecules have two OD stretches that can be exhibited at the surface as free OD,
whereas HOD molecules have one (Appendix 6.6.1). We therefore assign the 2745 2
127
cm
1
peak observed in pure D
2
O to the free OD stretch of the D
2
O molecule, and the
2728 2 cm
1
peak to the free OD stretch of the HOD molecule. The amplitude of the
HOD peak rst increases and then decreases with dilution, as expected (Table 6.1).
Figure 6.7. A, B: Peak areas (LorentzianB
j
j
) of the free OD of DOD
peak (blue squares), and free OD of HOD peak (red squares), as a
function of isotopic dilution. The scaling expected based on isotopic
scrambling, taking into account that D
2
O has two potential free ODs
while HOD has one, is shown in solid lines (right axis). C, D: Peaks
frequencies of the free OD of DOD peak (blue circles), and free OD
of HOD peak (red circles), as a function of isotopic dilution. E, F:
Lorentzian line widths of the free OD of DOD peak (blue), and free
OD of HOD peak (red).
128
The free OD frequency of HOD molecules,
HOD
= 2728 cm
1
, coincides within
experimental uncertainty with the OD-stretch local mode of 2727 cm
1
of HOD molecules
in the gas phase.
178
This suggests that the free OD mode of the HOD at the air-water
interface is essentially decoupled from all other vibrational modes in the system. Indeed,
in a dilute HOD:D
2
O mixture, the free OD is far o-resonance with the neighboring
OH-stretch vibrational modes (1000 cm
1
higher in frequency).
The free OD frequency of D
2
O molecules
DOD
= 2745 cm
1
, is blueshifted by
= 17 1.5 cm
1
from that of HOD. The sign of the shift can be understood in terms
of a simple model of two coupled oscillators (Fig. 6.8). Because the free OD mode
OD
occurs on the extreme blue side of the OD-stretch band, the majority of possible coupling
partners { that is, the nearby OD-stretch modes with the frequency !
OD
{ are likely to
be of lower frequency. In the absence of coupling (free OD of HOD diluted in H
2
O), the
two modes are described by a (2 2) Hamiltonian matrix:
H
0
=
0
@
0
0 !
1
A
;
>! (6.7)
Switching on the coupling
H
0
=
0
@
0
0
1
A
(6.8)
leads to the blueshift of the higher-frequency mode and an equal red-shift of the lower-
frequency mode, so that
0
=
+ and !
0
=! , with
=
s
2
2
+
2
2
2
(6.9)
when
, and where =
! is the frequency mismatch between the two coupled
modes. We note that is positive regardless of the sign of the coupling strength
,
consistent with the blueshift of the free OD of D
2
O (the coupled case) with respect to
the completely decoupled free OD of HOD.
129
Figure 6.8. The vibrational coupling scheme of the free OD stretch
at the air-water interface.
is the free OD frequency, ! is the fre-
quency of the coupling partner mode (the other OD stretch), and is
the frequency shift;
is the coupling strength. D/H are indicated as
blue/white spheres, O as red spheres. Dotted lines pictorially represent
H-bonds.
The free OD frequency of DOD can be coupled either to OD stretches on other water
molecules owing to intermolecular (predominantly dipole-dipole) interactions or to the
other OD stretch on the same D
2
O molecule. Although their amplitudes change, the
peak frequencies
HOD
and
DOD
do not exhibit appreciable shifts on isotopic dilution,
within the experimental uncertainty (Fig. 6.7c and d). This immediately rules out
intermolecular vibrational coupling as the source of the = 17 cm
1
shift. Indeed,
in that case, the coupling strength
and the amount of the shift would depend on
the average distance between the OD chromophores and would change by nearly an
130
order of magnitude as concentration decreases from 100% D
2
O to 25% D
2
O:75% H
2
O
(corresponding to D
2
O: HOD:H
2
O 1:6:9).
We therefore conclude that the = 17 cm
1
shift between the free OD stretch of
HOD and of D
2
O at the airwater interface is caused by the intramolecular coupling of
the free OD stretch to the other OD stretch on the same D
2
O molecule. Through this
intramolecular coupling, the free OD stretch re
ects the frequency !
0
of the other OD
stretch (Eq. 6.9) and hence the strength of the donor hydrogen bond of the D
2
O molecule
straddling the interface (Fig. 6.8).
6.4.2 Molecular Dynamics Simulations and Spectral Calculations
Molecular dynamics (MD) simulations and theoretical modeling of the SFG spectra
were performed by J. Skinner and P. Pieniazek (U. Wisconsin-Madison) to analyze the
experimental results further and to provide a molecular view of the vibrational excitations
and H-bonds at the interface. Spectral simulations used the mixed quantum/classical
approach and local electric eld maps for spectroscopic parameters such as frequency,
transition dipole and coupling, as previously described.
166,179
The MD simulations were performed on slabs of 512 extended simple point charge
model (SPC/E) H
2
O and D
2
O molecules for 20 ns. SPC/E water is a slight reparam-
eterization of the SPC model of water, which models the molecule as a rigid isosceles
triangle, having partial charges placed on each atom. The box dimensions were 25
A
25
A 80
A and the temperature was kept at 300 K.
Spectral simulations were performed using the mixed quantum/classical approach,
i.e., the O-H(D) oscillators were treated quantum mechanically, while the rest of the
system was treated classically. The intensity I(!) of the SFG signal is
I (!)
R
ijk
(!) +
NR
ijk
2
; (6.10)
131
where
R
ijk
(!) and
NR
ijk
are the resonant and nonresonant contribution to the second-
order nonlinear susceptibility, respectively. In order to simulate the spectrum, only the
resonant part must be calculated (assuming the NR susceptibility can be treated as an
adjustable constant).
The resonant part can be rewritten in terms of the polarizability and dipole operators
for the ground electronic state and the eigenstates of the nuclear Hamiltonian. It is useful
to rewrite the
R
ijk
(!) in terms of a quantum time-correlation function (TCF)
166,179
:
R
ijk
(!) =i
Z
1
0
dte
i!t
Tr [
ij
(t)
k
(0)]; (6.11)
where the trace is over all nuclear quantum states, is the the equilibrium density
operator for the nuclear Hamiltonian,
ij
(t) is the tensor element of the polarizability
operator for the ground state electronic state, and
k
(0) is the vector component of the
dipole operator for the ground state electronic state.
To simplify the calculation, additional approximations are made by replacing the
quantum TCF with its classical counterpart. Thus
ij
and
k
become classical vari-
ables of the nuclear coordinates. Since the IR frequencies ~!
IR
k
B
T , this classical
approximation leads to great errors, therefore it is important to multiply this result by
a quantum correction factor
166,179
:
R
ijk
(!)iQ
H
(!)
Z
1
0
dte
i!t
h
ij
(t)
k
(0)i; (6.12)
whereQ
H
(!) is the harmonic quantum correction factor
180{183
and the brackets denote
a classical canonical statistical mechanical average.
However, since the OH(D) stretch frequencies ~!
OH
k
B
T , and SFG spectroscopy
involves one quantum of vibrational excitation of a very anharmonic potential, the har-
monic frequencies calculated from a classical simulation would be poor approximations to
the experimental transition frequncies. Thus, the mixed quantum/classical approach is
commonly used to overcome this problem. The OH(D) chromophore is therefore treated
132
quantum mechanically, and the bath (all other degrees of freedom) are either kept rigid
or treated classically. Using this approach, the resonant susceptibility is given by
166,179
R
ijk
(!) i
Z
1
0
dte
i!t
a
ij
(t)m
k
(0) exp
i
Z
t
0
d! ()
e
t=2T
1
; (6.13)
where a
ij
(t) is the tensor element of the transition polarizability for the OH(D) vibra-
tional chromophore, m
k
(t) is the vector component of the transition dipole, !() is the
chromophore's
uctuating transition frequency, and T
1
is the excited vibrational state
lifetime.
The following criteria were used to identify the molecules containing the free OD
oscillator: (1) the OD-stretch frequency is above 2680 cm
1
; (2) the molecule is posi-
tioned within 6
A of the Gibbs dividing surface; (3) the angle between the free OD vector
and the vector from D atom to the nearest O atom of another water molecule is larger
than 90
. Analysis of the MD trajectories shows that 23% of water molecules at the air-
water interface have free OD (Fig. 6.9a), in agreement with earlier MD simulations
165
and experimental estimates.
24
The calculated spectra reproduce the experimentally observed trends in a nearly
quantitative fashion, as illustrated by the comparison between the calculated SSP spectra
for pure D
2
O and dilute HOD in H
2
O and the experimental spectra of 100% D
2
O and
25% D
2
O: 75% H
2
O mixture (Fig. 6.9b, c). The simulated spectra show a blueshift of
about 12 cm
1
and additional broadening (3 cm
1
) of the free OD stretch line of D
2
O
versus the uncoupled case of HOD in H
2
O. The experimental Lorentzian linewidth of
the free OD of HOD is
HOD
= 11 1.5 cm
1
, whereas for D
2
O it is
DOD
= 14 1
cm
1
(Fig. 6.7e, f). The theoretical linewidths are broader than the experimental ones,
probably because the map of frequency versus local electric eld used to calculate the
spectra is imperfect.
133
Figure 6.9. A. Snapshot of the MD trajectory showing molecules iden-
tied as having free OD (blue, green). B. Experimental Im[
(2)
] SSP
spectra of the air-water interface of pure D
2
O (blue) and 25%:75%
D
2
O:H
2
O mixture (red). C. Theoretical Im[
(2)
] SSP spectra for free
OD of isolated surface HOD molecule in H
2
O (red) and D
2
O molecule
in pure D
2
O (blue). D. Spectral density of the free OD stretch cal-
culated for the uncoupled case of HOD in H
2
O (red); fully coupled
case of DOD in D
2
O (blue line); including only intermolecular cou-
pling (brown), and including only intermolecular coupling (green). E.
Distribution of the coupling strengths
s
for dierent OD environments.
134
The mixed quantum/classical methodology allows one to turn on/o selectively
the intermolecular and intramolecular vibrational coupling and observe their respec-
tive eects on the calculated lineshapes. The spectral densities shown in Fig. 6.9d
(lifetime eects and motional narrowing not included) identify the intramolecular cou-
pling between the free OD bond and the other OD bonds of the same molecule as
mainly responsible for the frequency shift and broadening of the free OD stretch of pure
D
2
O versus HOD in H
2
O. Most of the shift (about 9 cm
1
of the total calculated 12
cm
1
shift) is reproduced by including intramolecular coupling only, whereas the shift
of 2 cm
1
when retaining only intermolecular coupling is insucient to account for the
experimental observation.
The distribution of the strengths of vibrational couplings involving OD in Fig. 6.9e
shows that the intermolecular (predominantly dipole-dipole) coupling for the free OD
oscillators peaks at around 5 cm
1
(in contrast, bulk-phase water molecules average
about 18 cm
1
). That the free OD stretch is not eectively coupled to the OD stretches
on other water molecules can be understood in terms of its frequency mismatch with
most of the hydrogen-bonded (redshifted) OD partners and its having fewer immediate
neighbours at the interface compared to bulk-phase water. Also, the free OD transition
dipole is about three times weaker than the average OD stretch in bulk-phase water
owing to non-Condon eects
167,184,185
. The orientation of the free OD (orthogonal to
the interface, on average) relative to potential coupling partners (OD stretches in the
underlying layer of water molecules tend to be oriented in-plane
165
) probably also dimin-
ishes the intermolecular coupling. Free OD-free OD coupling is negligible because of the
small transition dipole of such vibrations (which appears squared in the expression of
the coupling in this case) and because of the large average distance between the free
ODs: even in pure D
2
O, the 23% surface coverage translates into an average separation
of about 7
A.
The simulations also reproduce the broad shoulder with positive imaginary part at
about 2680 cm
1
in the SSP spectrum of pure D
2
O (Fig. 6.9b, c). This feature is
135
suppressed in the uncoupled case of dilute HOD in H
2
O, and is not observed in the
PPP spectra (Fig. 6.6). This feature is tentatively assigned to D
2
O molecules with
two donor hydrogen bonds and one acceptor hydrogen bond. While such molecules are
oriented with both hydrogens down (on average), the intramolecular coupling switches
on an antisymmetric linear combination of the two local modes; this combination has a
higher frequency and a transition dipole pointing up, giving a positive contribution to
the imaginary part of
(2)
.
Using an electrostatic map of the intramolecular coupling in D
2
O obtained from
ab initio calculations on water clusters
167
and the molecular dynamics simulations, we
determine the intramolecular coupling between the free OD and the other OD stretch
on the same D
2
O molecule at the interface to be about
S
-48 cm
1
(Fig. 6.9e); this
coupling is weaker than the gas-phase value
178,186
of
-60 cm
1
owing to the local
interfacial environment. Using the surface value for
S
and eq. 6.9, we estimate that the
other OD stretch frequency is !
0
2580 cm
1
{ putting it well within the OD stretch
band of bulk-phase water, which is centred at 2480 cm
1
and broadened by hydrogen
bonding to the fwhm of about 300 cm
1
.
187
This nding implies that one of the rst
hydrogen bonds encountered in the topmost layer at the water surface is only slightly
weaker than the bulk-phase average. We note that although the other OD stretch is
probably broadened by hydrogen bonding, this does not lead to signicant broadening
of the free OD: for example, according to eq. 6.9, a width of about 50 cm
1
of the other
OD band would result in only about 5 cm
1
broadening of the free OD bond. This is
the probable mechanism for the additional width of the free OD of D
2
O versus that of
HOD (Fig. 6.7e, f).
We also note that for the stretching mode of free OH around 3700 cm
1
, the vibra-
tional coupling model presented here would predict a smaller shift ( 10 cm
1
)
between this mode in HOD and in H
2
O, compared to 17 cm
1
for the free OD,
owing to (1) weaker intramolecular coupling
in H
2
O versus D
2
O (about -50 cm
1
ver-
sus -60 cm
1
in the gas phase)
178,186
, and (2) a larger frequency mismatch =
!
136
between the free OH and the hydrogen-bonded region of the OH-stretch band (about
300 cm
1
in H
2
O) versus about 250 cm
1
in D
2
O. Taking into account the width of
the free OH feature, this prediction would make it more dicult to observe two distinct
peaks for the free OH of HOD and H
2
O, consistent with previous reports.
175,176
6.5 Conclusion
Surface-selective HD-SFG was used to study the free OD stretch found only in the
topmost layer of water. By using deuterated water and isotopic dilution to reveal the
vibrational coupling mechanism, the free OD stretch was found to be aected only by
intramolecular coupling to the stretching of the other OD group on the same molecule
(i.e., the one pointing down into the bulk-phase). The other OD stretch frequency
indicates the strength of one of the rst hydrogen bonds encountered at the surface;
this is the donor hydrogen bond of the water molecule straddling the interface, which
was found to be only slightly weaker than bulk-phase water hydrogen bonds. From this
observation, a remarkably fast onset of bulk-phase behavior on crossing from the air into
the water phase was inferred.
6.6 Appendix
6.6.1 H/D Isotopic Scrambling
Given the volume-volume percent concentration N of D
2
O in H
2
O, the H/D isotopic
scrambling can be found using the chemical equation
D
2
O +H
2
O
2HOD (6.14)
Thus, the hydrogen deuterium exchange equilibrium constant K
HD
is
K
HD
=
[HOD]
2
[D
2
O] [H
2
O]
(6.15)
137
At room temperature K
HD
ranges from 3.76{3.85
188{192
. Table 6.1 lists the possible
scrambling ratios for each N used in the experiment.
Table 6.1. H/D isotopic scrambling ratios for a given concentration, N.
N, % D
2
O, % HOD, % H
2
O, % HOD:D
2
O
HOD
(OD):
DOD
(OD)
100 100 0 0 0 0
75 56.25 37.5 6.25 2:3 1:3
50 25 50 25 2:1 1:1
25 6.25 37.5 56.25 6:1 3:1
6.6.2 Normalization: Apparatus Function, f(!)
As in any other spectroscopic measurement, the HD-SFG signal must be normalized by
the so-called apparatus function f(!), which re
ects the LO spectrum and the inter-
ference quality (imaging, chromatic abberations, etc.) across the CCD. This apparatus
function can be obtained from the heterodyne SFG signal from gold, quartz, gallium
selenide, etc., however, it must be dierent than the sample.
f (!) =
E
0
SFG
2
/jE
IR
j
2
(6.16)
I
Norm
HDSFG
(!) =I
HDSFG
1
f (!)
/
jE
SFG
+E
LO
j
2
jE
IR
j
2
(6.17)
6.6.3 Amplitude and Phase
The intensity (power spectrum) is proportional to magnitude squared of the electric eld
E(!):
I (!)/jE (!)j
2
(6.18)
In the time domain, the electric eld can be expressed as
E (t) = cos (!t +') +i sin (!t +') (6.19)
138
where the real and imaginary terms are expressed as
Re [E (t)] = cos (!t +') (6.20)
Im [E (t)] =i sin (!t +') (6.21)
Thus, the amplitude of the electric eld is
p
Re
2
+ Im
2
, and has a spectral phase
S (!) = arctan
0
@
Im
h
~
E (!)
i
Re
h
~
E (!)
i
1
A
(6.22)
139
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156
Autobiographical Statement
Fadel Y. Shalhout
University of Southern California
Department of Chemistry
Los Angeles, CA 90089
shalhout@usc.edu
Education
Ph.D. Chemistry (Physical), University of Southern California, 2013
Thesis: Vibrational Sum Frequency Spectroscopy of Molecules on Metals,
Semiconductors, and Aqueous Surfaces
Thesis Advisor: Alexander Benderskii
Thesis Committee: Alexander Benderskii, Stephen Bradforth, Moh El-Naggar
B.S. Chemistry Honors, cum laude, Wayne State University, 2006
Co-Major: University Honors
Minor: Mathematics
Thesis: Synthesis, Properties, and Characterization of Pentamethylcyclopentadiene
Amine Adducts
Thesis Advisor: Charles H. Winter
157
Abstract (if available)
Abstract
Surface-selective vibrational sum frequency generation spectroscopy (SFG) has been used to investigate the structure, orientation, and dynamics of molecules at metal, semiconductor, and aqueous interfaces. In the first part of the thesis, SFG has been used to elucidate the molecular orientation of methyl groups terminating Si(111). Both the symmetric and asymmetric stretches of the surface-bound methyl group showed a pronounced azimuthal anisotropy of the 3-fold symmetry in registry with the signal from the Si(111) substrate, indicating that the propeller-like rotation of the methyl groups was hindered at room temperature. The difference in the SFG line widths for the CH3 symmetric stretch that was observed for different polarization combinations (SPS and PPP for SFG, visible, and IR) indicated that the rotation proceeded on a 1-2 ps time scale, as compared to the ~100 fs rotational dephasing of a free methyl rotor at room temperature. The second part of this thesis describes a simple but general phenomenon observed in temporally-delayed SFG spectra. Depending on the magnitude of the delay, nearby vibrational resonances can flip their relative phase, i.e., appear either in- or out-of-phase with one another, resulting in either constructive or destructive interference in SFG spectra. This is significant for interpretation of the SFG spectra, in particular because the sign of the resonant amplitude provides the absolute molecular orientation (up versus down) of the vibrational chromophore. The third part of the thesis uses SFG to describe CO adsorption to gold surfaces at room temperature and pressure. In the presence of water, CO adsorption was significantly enhanced compared to if no water was present, indicating cooperativity in the CO adsorption behavior. Two CO adsorption peaks have been observed, indicating two different adsorption sites are present on the gold surface. In the last part of the thesis, heterodyne-detected SFG (HD-SFG) has been used to investigate hydrogen bonding at the air-water interface. Implementation of HD-SFG allowed to extract both the phase and amplitude of the spectroscopic signal, thus allowing to subtract the nonresonant (NR) background signal. In this study, the question of just how thin is the water surface is addressed.
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Shalhout, Fadel Y.
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Vibrational sum frequency spectroscopy of molecules on metal, semiconductor, and aqueous surfaces
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
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Chemistry
Publication Date
06/28/2013
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air-water interface,CO adsorption on metals,heterodyne-detected SFG,hydrogen bonding,OAI-PMH Harvest,photocatalysis,SFG,Si(111),sum frequency generation,surfaces,vibrational spectroscopy
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Benderskii, Alexander V. (
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shalhout@usc.edu
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Tags
air-water interface
CO adsorption on metals
heterodyne-detected SFG
hydrogen bonding
photocatalysis
SFG
Si(111)
sum frequency generation
surfaces
vibrational spectroscopy