ABSTRACT 
 
 
 
 
Title of Document: OPTICAL KERR EFFECT SPECTROSCOPY 
OF SIMPLE LIQUIDS 
  
 Qin Zhong, Doctor of Philosophy, 2009 
  
Directed By: Professor John T. Fourkas, Department of 
Chemistry and Biochemistry 
 
 
Optical Kerr effect (OKE) spectroscopy has become a prominent nonlinear optical 
technique for studying liquids, which allows for the direct, time-resolved probing of 
collective orientational diffusion as well as Raman-active intermolecular and 
intramolecular modes.  
The temperature-dependent orientational dynamics of 1, n-dicyano n-alkane liquids 
ranging from dicyanomethane to 1,8-dicyanooctane has been investigated by ultrafast 
OKE spectroscopy. The dependence of the reorientational times on temperature and 
viscosity is consistent with the molecules adopting a largely extended structure in the 
liquid state, with a preference for gauche conformations at the methylenes bonded to 
the cyanide groups. The data are also suggestive of temperature-dependent, collective 
structural rearrangements in these liquids. 
Ultrafast OKE spectroscopy has also been used to study the intermolecular 
dynamics of aromatic liquids. A model that links the differences in the OKE spectra 
to corresponding differences in the local ordering of the liquids has been proposed 
  
previously based on the temperature-dependent OKE study of five aromatic liquids. 
The spectra of some other aromatic liquids such as pyridine, pyridine-d5, 2,4,6-
trifluoropyridine and 1,3,5-tris(trifluoromethyl) benzene has been obtained to test this 
model, and the relative importance of molecular shape and electrostatic forces in 
determining the form of the OKE reduced spectral density for such liquids has been 
realized. It has recently been shown that liquid tetrahydrofuran (THF) has an unusual 
structure that features voids of significant dimension. Such voids should affect other 
observable properties of this liquid. Temperature-dependent, optical Kerr effect 
spectra for THF and a number of related liquids (furan, cyclopentane, tetrahydropyran, 
cyclohexane, diethyl ether, hexamethylphosphoramide and n-pentane) has been 
obtained to test whether the shape of the spectra can be used to reveal the presence of 
sizeable voids in liquids. Liquid under tension is another interesting system to study: 
A method based on Berthelot tube technique has been developed to hold benzene and 
acetonitrile under tension successfully. 
A new scheme for measuring different tensor elements of the OKE response is 
developed. A dual-ring, polarization dependent Sagnac interferometer is used to 
create two co-propagating probe pulses that arrive at the sample at different times but 
that reach the detector simultaneously and collinearly. The tensor element of the 
response that is measured is determined by the polarization of the pump pulse. By 
controlling the relative timing of the probe pulses it is also possible to perform optical 
subtraction of two different tensor elements of the response at two different times, a 
strategy that can be used to enhance or suppress particular contributions to the OKE 
response.  
  
 
 
 
 
 
 
 
 
 
 
 
 
OPTICAL KERR EFFECT SPECTROSCOPY OF SIMPLE LIQUIDS 
 
 
 
By 
 
 
Qin Zhong 
 
 
 
 
 
Thesis submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2009 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor John T. Fourkas, Chair 
Professor Amy S. Mullin 
Professor Thomas E. Murphy 
Professor John D. Weeks 
Professor Robert A. Walker 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Qin Zhong 
2009 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ii 
 
Acknowledgements 
It is a pleasure to thank the many people who made this thesis possible. 
It is difficult to overstate my gratitude to my Ph.D. supervisor - Dr. John T. 
Fourkas, who was the main creator of the great ideas and techniques of this thesis.  
Throughout my whole graduate period, he provided tons of great ideas, advanced 
device, sufficient funding, and even nice colleagues.  He was always patient and 
encouraging when I was in trouble during experiments.  He tought me how to work 
independently, but at any time, his useful advice was always available to me.  I 
should say I have lived a very happy life during my five years in Fourkas group and I 
feel so lucky to work for such a nice and polite person. 
I am grateful to my committee members ? Dr. Amy S. Mullin, Dr. Thomas E. 
Murphy, Dr. John D. Weeks and Dr. Robert A. Walker.  For their kind assistance 
with helpful discussions, giving wise advice, refining my thesis and helping with 
postdoc applications, and so on.   
I would like to express my warmest thanks to all my presnt and former colleagues 
in Fourkas group: 
Dr. Xiang Zhu, former colleague of our OKE project.  He taught me everything 
about OKE experiment and also gave me a lot of helps in everyday life such as taught 
me how to drive; Dr. Feng (Terry) Ding, current colleague of SFG project, we 
experienced together all the ups and downs when setting up the SFG spectrometer, 
her good knowledge, huge work experience and patience were necessary for finishing 
this project, and it?s a great experience to work with her; Dr Christopher N. LaFratta, 
he has been very kind to me and especially very patient in teaching me.  I learned a 
 
 iii 
 
lot of knowledge from him not only about science but also about American culture.  
He was also the leader of our BBQ group and coach of our Wiffle ball team; Dr. Erez 
Gershgoren, he passed his great passion in science to everyone in the group and he 
gave me a lot of supports in OKE project including helpful disccusions and writing 
powerful Labview programs for data analysis; Dr. George Kumi, he worked together 
with me on holding liquids under tension and his cautious attitude on research sets 
good example for me; Dr. Rafael R. Gattass, he taught me how to repair laser, helped 
us write Labview programs, and also brought a lot of laugh and fun to tour lab; Linjie 
Li, current colleague, my best friend and also my five-year long roommate, we get 
through many difficulties together from Boston to College Park, thank him for all the 
support, comraderie, entertainment? Thanks also go to Xiaoxiao He and Katherine 
Manfred for their diligent work, making our project advancing faster; all other present 
and former colleagues of Fourkas group, for their assistance and providing an 
excellent working atmosphere: Mike Stocker, Kathleen Monaco, Hana Hwang, 
Sanghee Nah, Pearl Horng, Yunbo Shi, Soner Erduran, Meghan Driscoll, Sijia Qin, 
Floyd Bates, Juliet Znovena, Daniel Lim and Amity Ziegler. 
I would like to thank the many other people in the department: Dr. Liwei Yuan and 
Dr. Qingnan Liu for helpful disccusion about research; Dr. Yuanhua Wang, Dr. Jing 
Zhang, Huan Wang and Yang Zhao for their helps on organic chemistry knowledge; 
Dr. Wei Zhang for help on sealing glass cell; Dr. Suleyman Can and Michael Brindza 
for collaborations on SFG experiment; Dr. Wendy Heiserman for teaching me how to 
use the contact angle goniometer; Dr. Yiu-Fai Lam for NMR training; people at 
Physics and IPST machine shop and Robert Letiecq at Coherent.   
 
 iv 
 
Lastly, I sincerely thank my family ? my parents and my sister for their 
encouragements and supports through all these years.  Special thanks to my wife Jiao 
for her great support, understanding and love.  
Most of the work presented in this thesis was supported by funds from the National 
Science Foundation.  
   
 
 v 
 
Table of Contents 
 
 
Acknowledgements...................................................................................................ii 
Table of Contents......................................................................................................v 
List of Table............................................................................................................vii 
List of Figures..........................................................................................................ix 
Abbreviations.........................................................................................................xiii 
Chapter 1: Introduction..............................................................................................1 
1.1 Introduction and Motivation.............................................................................1 
1.2 History.............................................................................................................7 
1.3 Theory of the Optical Kerr Effect.....................................................................9 
1.3.1 Origin of the Optical Kerr Effect (OKE)....................................................9 
1.3.2 Experimental Geometry and Heterodyne Detected Signal........................10 
1.3.3 Fourier-Transform Deconvolution...........................................................17 
1.3.4 Microscopic Origin of  the Intermolecular Portion of the OKE Signal.....20 
1.4 Outline of the Thesis......................................................................................23 
1.5 References.....................................................................................................25 
Chapter 2: Experimental Methods............................................................................32 
2.1 Introduction...................................................................................................32 
2.2 Experimental Setup........................................................................................33 
2.3 Data Acquisition ...........................................................................................35 
2.4 Method of Analysis........................................................................................40 
2.5 References.....................................................................................................42 
Chapter 3: Temperature-dependent Orientational Dynamics of 1,n-Dicyano n-Alkanes
................................................................................................................................43 
3.1 Introduction...................................................................................................43 
3.2 Experimental Section.....................................................................................44 
3.3 Results...........................................................................................................47 
3.4 Discussion.....................................................................................................55 
3.5 Conclusions...................................................................................................64 
3.6 References.....................................................................................................64 
Chapter 4: Shape and Electrostatic Effects in Optical Kerr Effect Spectroscopy of 
Aromatic Liquids.....................................................................................................67 
4.1 Introduction...................................................................................................67 
4.2 Experimental Section.....................................................................................70 
4.3 Results...........................................................................................................73 
4.4 Discussion.....................................................................................................78 
4.5 Conclusions...................................................................................................89 
4.6 References.....................................................................................................89 
Chapter 5:  Searching for Voids in Liquids with Optical Kerr Effect Spectroscopy..93 
5.1 Introduction...................................................................................................93 
5.2 Experimental Section.....................................................................................95 
5.3 Results...........................................................................................................97 
5.4 Discussion...................................................................................................115 
 
 vi 
 
5.5 Conclusions.................................................................................................119 
5.6 References...................................................................................................120 
Chapter 6:  Preliminary Study of Liquids Under Tension.......................................123 
6.1 Introduction.................................................................................................123 
6.2 Experimental Section...................................................................................126 
6.3 Preliminary Results and Discussion..............................................................131 
6.4 Conclusions.................................................................................................137 
6.5 References...................................................................................................138 
Chapter 7:  Antiresonant-ring Kerr Spectroscopy...................................................140 
7.1 Introduction.................................................................................................140 
7.2 Experimental Section...................................................................................142 
7.3 Results and Discussion.................................................................................147 
7.4 Conclusions and Future Work......................................................................153 
7.5 References...................................................................................................154 
Chapter 8: Conclusions and Future Prospects.........................................................157 
8.1 Conclusions and Future Prospects................................................................157 
8.2 References...................................................................................................160 
Appendix A: OKE Data Analysis Procedure Using Labview Program...................161 
Appendix B: Temperature-dependent Viscosity, Parameters from Biexponential Fits 
to the Integrated OKE Data, and Fitting Ranges for 1,n-Dicyano n-Alkanes Studied in 
Chapter 3...............................................................................................................168 
Appendix C: Fit Parameters of Integrated OKE Data for All Five Aromatic Liquids 
studied in Chapter 4...............................................................................................175 
Appendix D: Viscosity and Fit Parameters of Integrated OKE Data for All Liquids 
studied in Chapter 5...............................................................................................180 
Glossary................................................................................................................183 
Bibliography..........................................................................................................184 
All References.......................................................................................................185 
 
 
 
 
 
 
 
 
 
 
 
 vii 
 
List of Tables 
 
Table 3.1 Formula Weight, Density at Room Temperature, Minimum and 
Maximum Temperatures Studied, and Activation Energy for 
Collective Reorientation for the Dicyanoalkanes Examined 
 
Table 3.2 DSE Slopes in Regions A, B, and C and Transition Temperatures 
between Regions A and B and Regions B and C for the 
Dicyanoalkanes Studied  
 
Table 4.1 Formula weight, density at 298 K, molar volume and dipole 
moment for the liquids studied here and related liquids. 
 
Table 5.1 Formula Weight, Density at 298 K, and Viscosity at 298 K for the 
Liquids Studied 
 
Table 6.1 Physical parameters of Benzene and Acetonitrile  
Table 6.2 Time period (minutes) Acetonitrile can maintain under tension at 
293.8 K 
 
Table 7.1 Expected performance of ARKS  
Table B.1 Fit parameters, single-molecule orientational correlation times 
and viscosities for integrated dicyanomethane OKE decays. 
 
Table B.2 Fit parameters, single-molecule orientational correlation times 
and viscosities for integrated 1,2-dicyanoethane OKE decays. 
 
Table B.3 Fit parameters, single-molecule orientational correlation times 
and viscosities for integrated 1,3-dicyanopropane OKE decays. 
 
Table B.4 Fit parameters, single-molecule orientational correlation times 
and viscosities for integrated 1,4-dicyanobutane OKE decays. 
 
Table B.5 Fit parameters, single-molecule orientational correlation times 
and viscosities for integrated 1,5-dicyanopentane OKE decays. 
 
Table B.6 Fit parameters, single-molecule orientational correlation times 
and viscosities for integrated 1,6-dicyanohexane OKE decays. 
 
Table B.7 Fit parameters, single-molecule orientational correlation times 
and viscosities for integrated 1,7-dicyanoheptane OKE decays. 
 
Table B.8 Fit parameters, single-molecule orientational correlation times  
 
 viii 
 
and viscosities for integrated 1,8-dicyanooctane OKE decays. 
Table C.1 Viscosity and fit parameters for integrated pyridine OKE decays.  
Table C.2 Viscosity and fit parameters for integrated pyridine-d5 OKE 
decays. 
 
Table C.3 Fit parameters for integrated 2,4,6-trifluoropyridine OKE decays.  
Table C.4 Fit parameters for integrated 2,4,6-trimethylpyridine OKE decays.  
Table C.5 Fit parameters for integrated 1,3,5-tris(trifluoromethyl)benzene 
OKE decays. 
 
Table D.1 Viscosity and fit parameters for integrated furan OKE decays.  
Table D.2 Viscosity and fit parameters for integrated THF OKE decays.  
Table D.3 Viscosities and fit parameters for integrated cyclopentane OKE 
decays. 
 
Table D.4 Viscosities and fit parameters for integrated diethyl ether OKE 
decays. 
 
Table D.5 Viscosities and fit parameters for integrated n-pentane OKE 
decays. 
 
Table D.6 Viscosities and fit parameters for integrated tetrahydropyran OKE 
decays. 
 
Table D.7 Viscosities and fit parameters for integrated cyclohexane OKE 
decays. 
 
Table D.8 Viscosities and fit parameters for integrated HMPA OKE decays.  
 
 ix 
 
List of Figures 
Figure 1.1 The Berthelot method schematically illustrated.  
Figure 1.2 Schematic layout for a polarization spectroscopy implementation 
of the optical Kerr effect. 
 
Figure 1.3 A typical OKE decay, in this case for 2,4,6-trifluoropyridine at 
306 K. 
 
Figure 1.4 Comparison of the OKE decay (black) and Ccoll(t) derived by 
integrating the OKE decay  for 2,4,6-trifluoropyridine at 306 K. 
 
Figure 1.5 Spectral density for 2,4,6-trifluoropyridine at 306 K.  
Figure 1.6 Reduced spectral density for 2,4,6-trifluoropyridine at 306 K.  
Figure 2.1 Heterodyne-detected OKE setup.  
Figure 2.2 Data acquisition window ?: Getting GPIB addresses.  
Figure 2.3 Data acquisition window ?: Run settings.  
Figure 2.4 Data acquisition window ?: More run settings.  
Figure 2.5 Data acquisition window ?: Total run program.  
Figure 3.1 Logarithm of the collective orientational correlation function of 
1,5-dicyanopentane at 288 K (red) and a biexponential fit to the 
data (black). 
 
Figure 3.2 Plot of fast versus slow relaxation times for OKE decays of the 
dicyanoalkanes. 
 
Figure 3.3 Debye-Stokes-Einstein plot for 1,4-dicyanobutane.  
Figure 3.4 Values of ?/T for the transition between regions A and B (circles) 
and between regions B and C (triangles) as a function of the 
number of methylene groups in each liquid. 
 
Figure 3.5 Arrhenius plot of the relaxation times of the dinitriles.  
Figure 3.6 Slopes of the Debye-Stokes-Einstein plots for the liquids studied 
here as a function of the hydrodynamic volume for reorientation 
assuming that the molecules adopt a completely extended 
conformation. 
 
 
 x 
 
Figure 3.7 Slopes of the Debye-Stokes-Einstein plots for the liquids studied 
here as a function of the volume per molecule. 
 
Figure 3.8 Views of the gauche-gauche structure of 1,4-dicyanobutane along 
the x-axis (a) and the y-axis (b) and of 1,5-dicyanopentane along 
the x-axis (c) and the y-axis (d). In all cases the z-axis is vertical. 
 
Figure 3.9 Slopes of the Debye-Stokes-Einstein plots for the liquids studied 
here as a function of the hydrodynamic volume for reorientation 
assuming that the molecules adopt an extended conformation but 
have gauche defects at each terminal methylene group. 
 
Figure 4.1 Representative integrated OKE decay for pyridine at 297 K 
(black) and biexponential fit (red). 
 
Figure 4.2 Plot of the intermediate relaxation time as a function of the 
collective orientational correlation time for the liquids studied. 
 
Figure 4.3 Height-normalized RSDs for pyridine at temperatures ranging 
from 240 to 349 K. The data have been offset for clarity. 
 
Figure 4.4 Height-normalized RSDs for pyridine-d5 at temperatures ranging 
from 240 to 349 K. The data have been offset for clarity. 
 
Figure 4.5 Height-normalized RSDs for TFP at temperatures ranging from 
230 to 332 K. The data have been offset for clarity. 
 
Figure 4.6 Height-normalized RSDs for TMP at temperatures ranging from 
243 to 351 K. The data have been offset for clarity. 
 
Figure 4.7 Height-normalized RSDs for NFM at temperatures ranging from 
285 to 348 K. The data have been offset for clarity. 
 
Figure 4.8 Comparison of the height-normalized RSDs for pyridine (black) 
and pyridine-d5 (red) at 297 K. 
 
Figure 4.9 Comparison of the height-normalized RSDs for benzene (black) 
and pyridine (red) at two different temperatures. 
 
Figure 4.10 DSE plot for pyridine (black) and pyridine-d5 (red), along with a 
fit to the data (solid line). Data for benzene (green) and benzened6 
(blue) have also been included, but were not used in the fit.  
 
Figure 4.11 Temperature dependence of g2/j2 for pyridine.  
 
 xi 
 
Figure 4.12 Comparison of the height-normalized RSDs for TFP (black) and 
TFB (red) at two different temperatures. 
 
Figure 4.13 Comparison of the height-normalized RSDs for TMP (black) and 
mesitylene (red) at two different temperatures. 
 
Figure 5.1 Logarithm of the collective orientational correlation function for 
THF at 285 K (black line, upper panel) as well as a biexponential 
fit to the data (red line). 
 
Figure 5.2 Representative Bose-Einstein-corrected spectral density (black) 
and reduced spectral density (red) for THF at 286 K. 
 
Figure 5.3 Height-normalized RSDs for furan at various temperatures. The 
plots have been offset vertically for clarity. 
 
Figure 5.4 Height-normalized RSDs for THF at various temperatures.  
Figure 5.5 Height-normalized RSDs for cyclopentane at various 
temperatures. 
 
Figure 5.6 Comparison of the room-temperature RSDs for THF (black) and 
cyclopentane (red). 
 
Figure 5.7 Height-normalized RSDs for diethyl ether at various 
temperatures. 
 
Figure 5.8 Height-normalized RSDs for n-pentane at various temperatures.  
Figure 5.9 Comparison of the room-temperature RSDs for n-pentane (black) 
and diethyl ether (red). 
 
Figure 5.10 Height-normalized RSDs for tetrahydropyran at 242 and 297 K.  
Figure 5.11 Height-normalized RSDs for cyclohexane at 297 and 325 K.  
Figure 5.12 Comparison of the room-temperature RSDs for tetrahydropyran 
(black) and cyclohexane (red). 
 
Figure 5.13 Height-normalized RSDs for hexamethylphosphoramide at 285 
and 337 K. 
 
Figure 5.14 DSE plots for THF, cyclopentane, tetrahydropyran, cyclohexane, 
and HMPA. 
 
Figure 5.15 DSE plots for THF, furan, diethyl ether, and n-pentane.  
Figure 6.1 Experimental setup for preparing liquid samples under tension.  
 
 xii 
 
Figure 6.2 Experimental setup for sealing the capillary sample tube.  
Figure 6.3 Design of the sample holder.  
Figure 6.4 Phase diagram of benzene  
Figure 7.1 Experimental setup for ARKS.  
Figure 7.2 Pathways through which horizontally-polarized light that enters 
the ARKS apparatus can exit in the direction in which the signal 
is detected. 
 
Figure 7.3 Normalized ARKS data for CS2 under difference polarization 
conditions. 
 
Figure 7.4 Normalized ARKS data for S2Cl2 under difference polarization 
conditions. 
 
Figure 7.5 Depolarized and isotropic OKE power spectra for S2Cl2.  
Figure 7.6 Normalized S2Cl2 ARKS data for the xxxx and yyxx tensor 
elements, as well as scans in which these tesnor elements are 
optically subtracted with different time shifts to enhance or 
suppress the contribution of the ?3 mode. 
 
 
 
 xiii 
 
List of Abbreviations 
a.u. Arbitrary Unit 
ARKS Antiresonant Ring Kerr Spectrometer 
cm-1 Wavenumber 
cP Centipoise 
DC Direct Current 
DID Dipole/Induced Dipole 
DSE Debye-Stokes-Einstein 
EA Activation Energy 
fs Femtosecond 
FW Formula Weight 
HFB Hexafluorobenzene 
HMPA Hexamethylphosphoramide 
HWP Half-wave Plate 
II Interaction-Induced 
kB Boltzmann Constant 
K Kelvin 
KDP Potassium Dihydrogen Phosphate 
LO Local Oscillator 
NFM Nonafluoromesitylene 
OHD Optical Heterodyne Detected 
OKE Optical Kerr Effect 
p Dipole Moment 
ps Picosecond 
PBC Polarizing Beam Cube 
QWP Qarter-wave Plate 
RSD Reduced Spectral Density 
TFB 1,3,5-trifluorobenzene 
TFP 2,4,6-trifluoropyridine 
 
 xiv 
 
THF Tetrahydrofuran 
THP Tetrahydropyran 
TMP 2,4,6-trimethylpyridine 
Vm Molar Volume 
? Viscosity 
?  Decay Time Constant 
?  Density 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                                                                     1  
Chapter 1: Introduction  
 
1.1 Introduction and Motivation 
Being able to understand complex systems, ranging from liquids to biological 
tissues, on a microscopic level is increasingly important to research in chemistry, 
physics, biology, and other physical and natural sciences. Many experimental 
methods have been developed for studying complex systems, among which one 
powerful category is ultrafast spectroscopy. Popular ultrafast spectroscopy techniques 
include time-resolved fluorescence spectroscopy1,2, pump/probe spectroscopy3,4, 
transient grating spectroscopy5,6, and photon echo spectroscopy7,8. 
Pump/probe spectroscopy is the simplest format of nonlinear ultrafast spectroscopy. 
The basic idea of this technique is that one ultrafast pulse (the pump) is used to affect 
a system of interest and a second pulse (the probe), which arrives at a variable delay 
time, is used to probe how the system has been altered by the pump pulse. The pump-
induced change in the sample can be absorption, stimulated emission, refractive index, 
reflectivity, or some combination of all of four; the probe pulse will record the time 
dependence of these changes. Within the realm of pump/probe spectroscopy, optical 
Kerr effect (OKE) spectroscopy9-12 is one of the longest established methods of 
capturing the ultrafast dynamics of liquids. 
Since its first demonstration in 1969,13 optical Kerr effect (OKE) spectroscopy has 
become a widely used technique for studying ultrafast dynamics in transparent fluids. 
There are several reasons accounting for its popularity. First, the implementation of 
 
                                                                     2  
the experiment is simple. Second, by the implement of optical heterodyne detection 
(OHD) detection14, the experiment provides data of extremely high signal-to-noise 
ratio, permitting detailed analysis. Third, OKE spectroscopy allows for the direct, 
time-resolved probing of collective orientational diffusion as well as of the dynamics 
of Raman-active intramolecular and intermolecular modes. The orientational 
diffusion dynamics can be analyzed in the time domain; Due to the pioneering work 
of McMorrow and Lotshaw,15 we can also transform time-domain OKE data into 
Bose-Einstein-corrected, low-frequency Raman spectra. Upon removal of the 
contribution of orientational diffusion, the low-frequency portion of the ?reduced 
spectral density? (RSD) contains information about intermolecular dynamics.  As 
such, this technique has provided numerous insights into the microscopic behavior of 
fluids such as simple liquids. Examples of more complex systems that have been 
studied include liquid crystals,16-18 supercooled liquids,19-22 ionic liquids,23-28 confined 
liquids,29-31 and liquids inside of polymer networks.32-36  
Our research is focused on simple liquids and we have completed a number of 
OKE studies of orientational dynamics of bulk liquids in the past decades, including 
rod-like molecules such as acetonitrile and 2-butyne37,38 and disk-like molecules such 
as benzene39. Recently OKE studies on temperature-dependent orientational 
dynamics in n-alkyl cyanides (n=1 to 11)40 showed that these molecules adopt 
extended configurations and reorient as rigid rods.  Even more interestingly, the 
liquid molecules with shorter alkyl chains undergo an apparent ordering transition as 
they are cooled. We know of no other liquids in which such a phenomenon has been 
observed above the melting point. This behavior is also reminiscent of transitions that 
 
                                                                     3  
occur in rotator phases of alkanes and n-alkyl alcohols below their melting points. 
Whether or not our observations are indicative of an actual phase transition is an open 
question that merits further investigation. For comparison, we also studied the 
reorientational dynamics of 1, n-dicyano n-alkanes, and similar conclusions have 
been discovered. 
While the orientational dynamics of these simple molecules have been studied in 
detail and the interpretation has been understood well, the same can not be said for 
the intermolecular dynamics, in part due to the featureless reduced spectral density 
(RSD). We have recently shown41, for a series of aromatic liquids for which local 
structural information is available, that there is a direct correlation between local 
structure and the shape of the RSD. Ryu and Stratt42 have suggested that the form of 
the OKE RSD can, in part, be a manifestation of molecular shape, especially insofar 
as the structure of liquids is dominated by effective repulsive interactions. Here we 
have finished further OKE experiments on more aromatic liquids, and the relative 
importance of molecular shape and electrostatic forces in determining the form of the 
OKE reduced spectral density (RSD) for such liquids has been realized43.  
OKE spectroscopy has also proven to be a powerful means of studying the 
influence of different media on liquid dynamics. Nanoscopic confinement (i.e., 
confinement on distance scales up to a few times larger than the dimensions of a 
single molecule) can have a profound influence on the structure and dynamics of 
liquids.44-48 The orientational dynamics of liquids confined in nanoporous sol-gel 
glasses have been studied in detail over the past few years using OKE 
spectroscopy.29,30,37,38,49-55 OKE spectroscopy allows us to measure the collective 
 
                                                                     4  
orientational correlation function of confined liquids on time scales ranging from 
femtoseconds to hundreds of picoseconds, thus providing a powerful means of 
obtaining quantitative microscopic information on the dynamics and dynamic 
populations of nanoconfined liquids. 
We also have great interests in studying liquids under extreme conditions. 
Stretched liquids (i.e. liquids under tension) are one of such interesting systems. The 
density of a liquid under tension will be smaller than under normal conditions, which 
will decrease intermolecular interactions; thus attractive, rather than repulsive forces 
will be the dominant intermolecular interactions. We therefore expect that the 
microscopic structure and dynamics of liquids will be changed under tension, and 
these changes should be measurable by examining the intermolecular dynamics with 
OKE spectroscopy. 
The Berthelot tube technique56 has been the most popular method to stretch water 
to negative pressures. In this method (Figure 1.1), a vessel is filled with liquid water 
at high temperature and positive pressure, then is sealed and cooled down at constant 
volume. The liquid sample follows an isochore and is brought to negative pressure.  
T1 Tfill T2 > Tfill T3 < Tfill Tbreak < T3
 
 
                                                                     5  
Figure 1.1 The Berthelot method schematically illustrated. 
(First, one fills a capillary tube with pure and degassed liquid, cools the sample and 
holds it under modest vacuum, then flame-seal the cell under vacuum, after the 
sample melts, the tube contains the liquid plus a bubble (tube 1); Heating the tube to 
Tfill (filling temperature) until the liquid just occupy the whole volume (tube 2); Keep 
heating the tube to T2, the liquid will keep expanding and therefore will be under 
positive pressure (tube 3); Then cool the liquid to T3 (supposed to be lower than Tfill), 
the liquid would contract, but it would be hold to the wall by surface adhesive forces 
(tube 4), then liquid would be under negative pressure at T3; Keep cooling the liquid 
to Tbreak, nucleation of vapor phase will happen, some bubbles come out, liquid is not 
under negative pressure any more (tube 5).) 
 
Water was the first liquid to have been studied to any significant extent under 
extreme tension.57-64  Water is in many ways an ideal liquid for such studies, in that it 
has an extremely high tensile strength for a liquid due to the high degree of hydrogen 
bonding. However, heterogeneous nucleation generally prevents water from being 
stretched to its intrinsic tensile strength. Furthermore, water is not readily amenable to 
study with OKE spectroscopy due to its extremely low polarizability anisotropy. The 
same holds true for other hydrogen-bonded liquids that would have high tensile 
strengths. As a result, little spectroscopic work has been done on liquids under 
negative pressure. 
The results of our recent experiments suggest that aromatic liquids are excellent 
candidates for initial experiments on liquids under tension. Simple aromatic liquids 
 
                                                                     6  
such as benzene have medium to high surface tensions for organic liquids,65 and yet 
they also have small contact angles on silica. The small contact angles indicate a large 
enough affinity for glass that it should be possible to achieve large tensions in silica 
cells. The fact that the contact angle on silica is so small despite these liquids having 
healthy surface tensions is also an indication that these liquids are likely to have 
relatively large tensile strengths even though they are nondipolar. We believe that 
OKE experiments on aromatic liquids should yield clear signatures of the effects of 
negative pressure, due both to the strength of the OKE signal and the high sensitivity 
of the OKE spectrum to local structures in these liquids. 
The synthesis of nonlinear optical techniques with microscopy over the past decade 
and a half has proven revolutionary for imaging. Nonlinear optical techniques such as 
multiphoton absorption,66,67 second-68,69 and third-70-72 harmonic generation, and 
coherent anti-Stokes Raman scattering73-77 (CARS) are all being used to great 
advantage in microscopy. Due to their nonlinear intensity dependence, all of these 
techniques offer exceptional three-dimensional spatial resolution while generally not 
affecting the sample being studied anywhere except in the focal region. These 
techniques also offer many different options for generating contrast; multiphoton 
absorption is usually used with fluorescent labels, second- and third-harmonic 
generation are sensitive to interfaces, and CARS probes Raman-active vibrations.  
Given the simplicity of the OKE technique,9,11 the nonlinear dependence of the 
signal and its potential to generate different types of contrast,  OKE spectroscopy 
promises to be as powerful a technique for microscopy as any of the other techniques 
discussed above, especially for monitoring some important biological process taking 
 
                                                                     7  
place on ultrafast time scale less than 100 ps.  There has been one report about the use 
of OKE spectroscopy in microscopy78 in which the mobility of water molecules in 
cellular domains was investigated. 
A new scheme for measuring different tensor elements of the optical Kerr effect 
response was developed in our lab79. A dual-ring, polarization dependent Sagnac 
interferometer is used to create two copropagating probe pulses that arrived at the 
sample at different times but that reached the detector simultaneously and collinearly. 
The tensor element of the response that is measured is determined by the polarization 
of the pump pulse. By controlling the relative timing of the probe pulses it is also 
possible to perform optical subtraction of two different tensor elements of the 
response at two different times, a strategy that can be used to enhance or suppress 
particular contributions to the OKE response. We call this technique antiresonant ring 
Kerr spectroscopy (ARKS). Next we need to incorporate microscope objectives rather 
than lenses into this ARKS setup to use spectroscopy for microscopy. We can also 
incorporate a sample-scanning nanostage into the setup for performing imaging 
experiments in the future. 
 
1.2 History 
In 1875, John Kerr discovered the effect that now bears his name. In the Kerr effect, 
a DC electric field applied to a transparent, isotropic medium induces birefringence. 
From a molecular standpoint, the electric field interacts with molecular dipole 
moments, leading to a degree of net alignment in the liquid. So long as the molecules 
 
                                                                     8  
are optically anisotropic, this alignment will lead to the medium having different 
indices of refraction parallel to and perpendicular to the electric field.  
In 1964, Mayer and Gires80 showed theoretically that a laser field could be strong 
enough to induce birefringence in a liquid, in what has become known as the optical 
Kerr effect. The OKE was first demonstrated experimentally in 1969 by Duguay and 
Hansen, who used pulses of a few picoseconds in duration to study the orientational 
dynamics of CS2 and nitrobenzene.13 In 1975, Ippen and Shank81 demonstrated how 
to incorporate optical heterodyne detection in OKE spectroscopy, allowing for the 
direct probing of the nonlinear response of the liquid, rather than its magnitude 
squared. Heterodyne detection also amplifies the OKE signal considerably. 
Another major milestone in the evolution of OKE spectroscopy was the 
development of the Fourier-transform deconvolution technique by McMorrow and 
Lotshaw.15 In Fourier-transform deconvolution, heterodyne-detected OKE data are 
combined with a second-harmonic-generation autocorrelation to calculate the OKE 
spectral density, which is formally equivalent to the Bose-Einstein corrected Raman 
spectral density. This procedure compensates for the effects of the finite bandwidth of 
the laser pulses used, producing spectral densities that should not depend upon the 
instrument used to obtain the data. 
The past two decades have seen many other important advances in OKE 
spectroscopy. For instance, a number of different techniques have been developed 
that allow multiple elements of the OKE response tensor to be investigated,79,82-87 
revealing important microscopic details of the liquid dynamics and allowing specific 
contributions to the signal to be isolated. Multiple-beam techniques involving 
 
                                                                     9  
diffractive optics have proven to be powerful and robust methods for collecting data 
for different elements of the response tensor.84,87 
 
1.3 Theory of the Optical Kerr Effect 
1.3.1 Origin of the Optical Kerr Effect (OKE) 
When a transparent liquid composed of anisotropically polarizable molecules is 
exposed to an intense ultrafast laser pulse (the ?pump?), a dipole moment is induced 
along the axis of maximum polarizability of each molecule. The induced dipole 
moment interacts with the instantaneous electric field of the laser pulse, providing an 
impulsive torque that drives the axis of maximum polarizability of the molecules 
toward alignment with the polarization of the pump pulse. Since it is the polarizability 
of the molecules in a liquid that determines its index of refraction, the pump pulse 
creates a slight birefringence in the liquid. The induced birefringence can be 
monitored by a low-intensity ?probe? pulse. The time dependence of the 
birefringence reveals information about microscopic dynamics. 
There are two obvious effects caused by the intense pump pulse.9 First, it will lead 
to the distortion of the electron cloud of the atoms and molecules and induce a strong 
and instantaneous electronic contribution to the OKE signal. It will also modify the 
random orientational distribution of the molecules, causing a partial alignment of the 
molecules in the direction of the electric field. This slightly uneven distribution is one 
important source for the transient birefringence. The spontaneous rotational diffusion 
of the molecules brings the system back to an isotropic equilibrium situation in a time 
 
                                                                     10  
that is characteristic of rotational diffusion. We can measure this relaxation time 
directly by measuring the intensity change of the transmitted probe as a function of 
the delay time between the pump and probe pulses. We call this time the orientational 
correlation time. These two effects can just give us a simple physical picture of the 
transient OKE. If we focus on a short time range (typically 1-2 ps), some other 
processes have to be taken into account. Processes originating from intermolecular 
interactions may also produce a transient anisotropy, resulting in additional 
contributions to OKE signal. These motions include frustrated oscillatory motions 
(librations), density fluctuations and the collisions between molecules. In addition, if 
ultrafast pulses( with fs pulse width) are used, some intramolecular Raman-active 
low-frequency modes will also be coherently excited and this will also contribute to 
the OKE signal. The pump pulse serves as a ?starting gun? for molecular dynamics, 
and plenty of information can be contained in the OKE signal. By analyzing the OKE 
signal, it is possible for us to extract useful information about the dynamics of many 
liquids we are interested in at a microscopic level.  
 
1.3.2 Experimental Geometry and Heterodyne Detected Signal 
The most common implementation of the optical Kerr effect is in a polarization 
spectroscopy geometry (Figure 1.2). Excitation is accomplished with a pump pulse 
polarized at 45?. The probe pulse, which has a variable time delay t relative to the 
pump pulse, is polarized vertically. After the sample, the probe pulse enters an 
?analyzer? polarizer that is set to pass horizontally polarized light. If the refractive 
index of the sample is isotropic, no light is transmitted by the analyzer polarizer. 
 
                                                                     11  
However, any birefringence induced by the pump pulse leads to depolarization of the 
probe pulse, allowing a signal to pass through the analyzer. This leakage is related 
linearly to the degree of birefringence in the sample, and so by scanning the delay 
between the two pulses the time-dependent birefringence can be measured.  
 
Figure 1.2 Schematic layout for a polarization spectroscopy implementation of the 
optical Kerr effect. 
 
The polarization spectroscopy configuration is sensitive to the difference between 
two elements of the third order response, (3) ( )xxxxR t  and (3) ( )xxyyR t . (In frequency domain, 
these response functions correspond to the third order susceptibility tensor elements: 
(3) ( ; , , )
xxxx signal pump pump probe? ? ? ? ?? ?  and 
(3) ( ; , , )
xxyy signal pump pump probe? ? ? ? ?? ? ; The 
subscripts correspond to the polarizations of signal, probe, pump and pump 
respectively.)  In an isotropic medium, this difference is proportional to (3) ( )xyxyR t  (or 
(3) ( ; , , )
xyxy signal pump pump probe? ? ? ? ?? ? ),
88 which is known as the depolarized response. 
Because it is the intensity that is detected in this experimental configuration, the 
signal is proportional to the magnitude squared of the depolarized response; this 
situation is known as homodyne detection of the signal. By scanning t, the time 
dependence of the depolarized Kerr signal can be determined. 
 
                                                                     12  
The phase of the third-order polarization of the OKE signal is determined purely by 
the phase of the probe field. Referenced to the phase of the probe field, the signal 
field generated by the polarization can be written as?  
(Re Im ) i ts s sE E i E e ??? ?                                 (Eq. 1.1)  
where Re sE  and Im sE  correspond respectively to the absorption and index of 
refraction portions of the response and ? is the carrier frequency. 
By placing a quarter-wave plate (QWP) after the first polarizer in the probe path 
but before the sample, optical heterodyne detection can be implemented. The QWP is 
aligned such that one of its axes is along the polarization of the probe beam. The 
input polarizer is then rotated by a slight amount (a few degrees at most), allowing 
some light to pass through the analyzer polarizer. This leakage is 90? out of phase 
with the rest of the probe beam, and acts as a local oscillator that mixes in phase with 
the OKE signal field.  
/2i t i
LO probeE E e e
? ???                                             (Eq. 1.2) 
The total electric field that passes through the analyzer is then ELO + EOKE(t): 
                              /2(Re Im ) i t i t is s probeE i E e E e e? ? ?? ?? ?                                 (Eq. 1.3) 
The intensity detected is the magnitude squared of this field, ILO + 2ELOEOKE(t) + 
IOKE(t). 
22 /2
2 2 2 2 2
(Re Im )
Re (Im ) (Re ) (Im ) 2 Im
2 Im
i t i t i
s LO s s probe
i t
s s probe probe s s probe s
LO s probe s
I E E E i E e E e e
e E i E E E E E E E
I I E E
? ? ?
?
? ?
?
? ? ? ? ?
? ?? ? ? ? ? ? ?? ?
? ? ?
               
(Eq. 1.4) 
 
                                                                     13  
 The intensity of the local oscillator is the largest term in this equation but does not 
depend on the delay time t and so is a constant; it can also be removed by lock-in 
detection if the pump beam is chopped. The homodyne OKE intensity, IS(t), is the 
smallest term in the equation, and is generally dwarfed by the cross-term. Thus, via 
this crossterm, the local oscillator both amplifies the signal and makes it linear in the 
signal field, and thereby linear in the depolarized response. If the input polarizer is 
rotated by the same amount but in the opposite direction, then the local oscillator field 
is given by: 
                                               /2i t iLO probeE E e e? ?? ??                                         (Eq. 1.5) 
which results in a detected intensity of  ILO - 2ELOEOKE(t) + IOKE(t). 
                                        2 ImLO s probe sI I I E E? ? ?                                       (Eq. 1.6) 
and the sign of the cross-term in the intensity changes sign. By subtracting data 
collected at opposite heterodyne angles, any homodyne contribution to the signal can 
therefore be removed completely. 
The first few picoseconds of a representative heterodyne detected OKE decay, in 
this case for 2, 4, 6-trifluoropyridine at 306 K, are shown in Figure 1.3. This decay 
shows all of the features seen in typical time-domain OKE data.  
 
 
                                                                     14  
 
 
Figure 1.3 A typical OKE decay, in this case for 2,4,6-trifluoropyridine at 306 K. The 
sharp feature at zero delay time is the electronic response. The oscillations arise from 
Raman-active intramolecular vibrational modes. Coherently excited intermolecular 
modes contribute significantly to the decay for more than a picosecond, and 
orientational diffusion dominates at longer times. 
 
For a typical time-resolved OKE signal, five contributions can be distinguished:  
(1) A fast purely electronic contribution, due to the molecular hyperpolarizability, 
gives an instantaneous response; 
(2) An intermolecular contribution is from the librational motion of the molecules in 
the cages of the first neighbor molecules. The librational decay is fast (typically up to 
a few picoseconds) due to the inhomogeneous dephasing in the liquid environment; 
(3) An intramolecular vibrational ?Raman? contribution decays with the dephasing 
time of the molecular vibrations (typically up to a few picoseconds); 
 
                                                                     15  
(4) A term originating from the intermolecular interactions is correlated to the density 
fluctuations and hence to the collision-induced anisotropy of the molecular 
polarizability. Its relaxation is governed by the lifetime of the local structure in the 
liquids, again a few picoseconds; 
(5) There is also a reorientational contribution, whose time scale can span a wide 
range of values, from a few picoseconds to several nanoseconds, depending on the 
molecular size and the viscosity, we call this contribution orientational diffusion. 
The OKE response is proportional to the negative time derivative of the collective 
orientational correlation function, Ccoll(t).89 The derivative nature of the response  
implies that slower processes necessarily give weaker signals. However, in many 
cases, the OKE response can be integrated to determine Ccoll(t) directly.40,54 Proper 
integration requires the accurate determination of the constant of integration, which is 
possible so long as the long-time form of Ccoll(t) is known. For simple liquids, the 
long-time form of Ccoll(t) is generally exponential,90 and so integration is a 
straightforward process. A semilogarithmic plot of the OKE decay from Figure 1.3 
and the corresponding Ccoll(t) are shown in Figure 1.4. Integration not only increases 
the contribution of the slowly decaying portion of the dynamics but also helps to 
remove high-frequency noise. In addition, the delay time at which low-frequency 
noise begins to affect the reliability of the OKE data is readily apparent from 
integrated decays, and the data can be truncated before this point for fitting purposes. 
From the fitting procedure above, the collective orientational correlation time can 
be obtained quite accurately. The orientational correlation time of a solute in a simple 
solvent is given by Debye-Stokes-Einstein (DSE) Equation91: 
 
                                                                     16  
                                                           
34
3
h
B
r
k T
? ?? ?                                                 (Eq. 1.7) 
where ? is the solvent viscosity, hr  is the solute hydrodynamic radius, T is the 
temperature, Bk  is Boltzmann?s constant. The reorientational correlation time can be 
measured at different temperatures for the liquid sample. After measurement of the 
viscosity, information on hydrodynamic volume can be obtained by plotting  ?  vs. 
/T? . By analyzing the the orientational correlation time and the hydrodynamic 
volume, information about dynamics of orientational diffusion will be gained. 
 
 
Figure 1.4 Comparison of the OKE decay (black) and Ccoll(t) 
(0.86exp( /8.1) 0.14exp( /1.8)t t? ? ? ) derived by integrating the OKE decay (red) for 
2,4,6-trifluoropyridine at 306 K. From the magnified portion of Ccoll(t) shown in the 
inset, it is apparent that the integrated data begin to exhibit low-frequency noise and 
deviation from linearity at a time of about 35 ps. This is the cutoff time that was 
chosen in fitting the correlation function. 
 
 
                                                                     17  
Because OKE spectroscopy is sensitive to the collective orientational correlation 
function, orientational decay times measured with this technique may differ from 
those measured by techniques that are sensitive to the single-molecule orientational 
correlation function, such as Raman spectroscopy and NMR. The collective 
orientational correlation time, ?coll, is related to the single-molecule orientational 
correlation time, ?sm, via92 
2
2
coll sm
g
j? ??                                             (Eq. 1.8) 
here, g2 is the static pair orientational correlation parameter and j2 is the dynamic pair 
orientational correlation parameter. The value of g2 depends upon the degree of 
parallel ordering in a liquid, and takes on a value of unity when there is no net 
ordering. It is generally assumed that j2 is unity in simple liquids. Thus, comparison 
of OKE orientational relaxation times with single-molecule relaxation times can give 
us estimation for g2 value and yield microscopic structural information about a liquid. 
 
1.3.3 Fourier-Transform Deconvolution 
Fourier-transform deconvolution makes it possible to remove the effects of a laser 
pulse of finite duration from the OKE data, allowing for the accurate determination of 
Bose-Einstein corrected spectral densities.15 The heterodyne-detected OKE signal S(t) 
is given by  
                                             (3)pump probe xyxyS I I R? ?? ? ?? ?                                      (Eq. 1.9) 
where ? denotes a convolution. The quantity in square brackets is the instrument 
response, which can be written as 
 
                                                                     18  
(2)( ) ( ') ( ') '
pump probeG t I t I t t dt
??
??
? ??                              (Eq. 1.10) 
So long as the pulses used are transform limited, G(2)(t) is exactly the quantity 
measured by taking a second-harmonic-generation cross-correlation between the 
pump and the probe. Thus, G(2)(t) can be determined readily with a simple 
measurement. 
According to the convolution theorem,93 the Fourier transform of the convolution 
of two functions is equal to the product of the Fourier transforms of each function. 
Thus, we can write (2) (3) (2) (3)( ) ( ) ( ) ( )xyxy xyxyG t R t G t R t? ? ? ? ? ?? ? ?? ? ? ? ? ?? ? ? , which implies that 
by dividing the Fourier transform of S(t) by the Fourier transform of G(2)(t) we can 
determine the Fourier transform of (3) ( )xyxyR t . The electronic response is a delta 
function centered at zero time, and therefore, its Fourier transform is a real constant. 
The nuclear response is zero before zero delay time, and therefore its Fourier 
transform is imaginary. This imaginary portion of the Fourier transform is called the 
spectral density. In Figure 1.5, we show the spectral density that corresponds to the 
OKE decay from Figure 1.3 as well as the deconvolved nuclear response function 
obtained by inverse Fourier transformation of the spectral density. 
 
 
                                                                     19  
 
 
Figure 1.5 Spectral density for 2,4,6-trifluoropyridine at 306 K. The peaks near 230 
and 270 cm-1 arise from intramolecular vibrations. Shown in the inset is the 
deconvolved nuclear response function for this liquid. Note that the electronic 
response is no longer present after deconvolution. 
 
It is common practice to remove the diffusive orientational portion of the spectral 
density to obtain what is known as the reduced spectral density (RSD). A function of 
the form 
                                          ? ?exp( / ) 1 exp( /OKE riset t? ?? ? ?                                (Eq. 1.11) 
is subtracted from the nuclear response function, which is then Fourier transformed to 
obtain the RSD. The rise time rise?  is generally assumed to be 200 fs or less, and its 
value does not have a substantial effect on the shape of the RSD. The RSD 
corresponding to the OKE decay in Figure 1.3 is shown in Figure 1.6, along with the 
nuclear response function from which the contribution of orientational diffusion has 
 
                                                                     20  
been removed. This is an example of a ?triangular? RSD. Note that, if we neglect the 
oscillatory contributions from intramolecular vibrations, the response function with 
orientational diffusion removed still appears to decay exponentially. We will discuss 
the origin of this additional exponential decay below. 
 
 
Figure 1.6 Reduced spectral density for 2,4,6-trifluoropyridine at 306 K. This is an 
example of a ?triangular? RSD typical of fluorinated aromatics. Shown in the inset is 
the nuclear response function without the contribution from orientational diffusion. 
Once the contribution from intermolecular modes has decayed completely, any 
remaining contributions from intramolecular modes oscillate about zero. 
 
1.3.4 Microscopic Origin of the Intermolecular Portion of the OKE Signal 
The long-time portion of a typical OKE decay arises from orientational diffusion, 
and any high-frequency oscillations arise from intramolecular Raman modes. The 
source of the remainder of the signal, which is related to intermolecular motions, is 
 
                                                                     21  
somewhat more complicated. As is the case for the intramolecular modes, any 
intermolecular mode that contributes to the OKE signal must be Raman active and 
must have a depolarized component. 
The simplest mechanism through which intermolecular modes can contribute to the 
OKE signal is through librations. A libration is a rocking motion of a molecule that 
arises from the hindrance of rotational motion imposed by the surrounding cage of 
nearest neighbors. So long as the molecule has a polarizability anisotropy, such 
motion can lead to depolarized Raman scattering. 94 Although librations may involve 
complex motions of multiple molecules, librational scattering can be described in 
terms of motions of the polarizability tensors of individual molecules, and so is 
considered to be a molecular effect. 
Liquids whose molecules have isotropic polarizabilities, such as CCl4, can still 
exhibit substantial OKE signals.95 The mechanism for this phenomenon is called 
interaction-induced (II) scattering, which arises from dipole/induced dipole (DID) 
effects.94 A molecule in a liquid experiences not only an applied optical field but also 
the dipoles that the field induces in neighboring molecules. The strength of this DID 
effect on a given molecule depends strongly on the distance of its nearest neighbor or 
neighbors and their positioning relative to the molecule of interest and on the 
direction of the applied electric field. As the molecules move in their local potentials, 
the strength and directionality of the DID interactions is modulated, leading to II 
scattering. Both hindered translations and hindered rotations can contribute to II 
scattering. There can also be a cross-term between the contributions of librational 
scattering and II scattering. 
 
                                                                     22  
To interpret RSDs, it is desirable to be able to understand the relative contributions 
of molecular and II scattering in the signal. Simulations are a powerful tool for 
attacking this problem, but a consensus has not been reached on this issue. 
Simulations that use a point anisotropic polarizability model or a point atomic 
polarizability model in which sites on the same molecule do not interact tend to give 
roughly equal importance to molecular and II scattering.42,96 
Using CS2 as a model system, detailed molecular dynamics simulations and 
instantaneous normal mode theory have been used to analyze the contributions to the 
OKE signal.97,98 A point atomic polarizability model was used in which different 
polarizability sites on the same molecule are allowed to interact. While this type of 
model has some difficulties, we believe that it also more accurately represents the 
polarizability of real molecules, for which a close approach at one site can have a 
significant effect on the polarizability of the entire molecule. These studies indicated 
that, in both normal97 and supercooled98 CS2, depolarized scattering is largely 
dominated by molecular effects, with II effects playing a relatively minor role. The 
same holds true in simulations in which the polarizability of CS2 is made 
considerably larger, considerably smaller, or anisotropic (by giving the two sulfur 
atoms different atomic polarizabilities).97 These results suggest that, for the majority 
of liquids in which the molecules have anisotropic polarizabilities, the OKE signal 
will arise predominantly from molecular effects. For supercooled CS2, it was further 
found that even the isotropic spectrum, which arises solely from II effects, has a large 
component due to orientational motions.98 
 
                                                                     23  
1.4 Outline of the Thesis 
This thesis addresses a number of questions regarding the orientational diffusion 
and intermolecular dynamics of simple liquids. Questions addressed include what 
kind of microscopic structural information (conformation, local structure and 
molecular association) can we extract from the orientational diffusion data? How do 
intermolecular interactions affect the microscopic structure of liquids? What is the 
origin for the intermediate response, which appears in the OKE decay for all simple 
liquids? What is the dominant motion in determining the depolarized intermolecular 
dynamics, libration, translation or others? Which is the dominant factor in 
determining the shape of Reduced Spectral Density (RSD): molecular shape, local 
structure or distribution of polarizability? Is the breadth of the Reduced Spectral 
Density (RSD) dependent on moment of inertia of liquid molecules or not? What is 
the temperature dependence of depolarized intermolecular dynamics? Besides the 
depolarized response, how can we measure the other OKE responses such as isotropic 
response? Is it possible to develop an OKE microscopy technique? All these 
questions will be addressed in the following chapters and they are organized as 
follows: 
? Chapter 2. We describe the setup for the optical-heterodyne-detected optical 
Kerr effect (OKE) spectrometer, and also the method to obtain the Reduced 
Spectral Density (RSD) from time-domain OKE data; 
? Chapter 3. The temperature dependent orientational dynamics of 1,n-dicyano n-
alkane liquids ranging from dicyanomethane to 1,8-dicyanooctane are described. 
The dependence of the reorientational times on temperature and viscosity is 
 
                                                                     24  
consistent with the molecules adopting a largely extended structure in the liquid 
state, with a preference for gauche conformations at the methylenes bonded to 
the cyanide groups. The data are also suggestive of temperature-dependent, 
collective structural rearrangements in these liquids. 
? Chapter 4. I describe a detailed, temperature-dependent, OKE study of pyridine, 
pyridine-d5, 2,4,6-trifluoropyridine, 2,4,6-trimethylpyridine, and 1,3,5-
tris(trifluoromethyl)benzene. By combining these data with those for other 
aromatic liquids that we have studied previously (Loughnane, B. J.; Scodinu, A.; 
Fourkas J. T. J. Phys. Chem. B, 2006, 110, 5708), we are able to assess the 
relative importance of molecular shape and electrostatic forces in determining 
the form of the OKE reduced spectral density for such liquids. 
? Chapter 5. It has recently been shown [J. Chem. Phys. 2005, 122, 134506; J. Am. 
Chem. Soc. 2006, 128, 5119] that liquid tetrahydrofuran has an unusual structure 
that features voids of significant dimension. Such voids should affect other 
observable properties of this liquid. I present a temperature-dependent, OKE 
study of tetrahydrofuran and a number of related liquids (furan, cyclopentane, 
tetrahydropyran, cyclohexane, diethyl ether, and n-pentane) as well as 
hexamethylphosphoramide to test whether this technique can be used to reveal 
the presence of sizable voids in liquids. 
? Chapter 6. Liquids under tension are an interesting system to study, in which the 
intermolecular interactions can be dominated by attractive forces, instead of 
repulsive forces. Based on a Berthelot tube technique, we develop a method to 
stretch liquids to negative pressure. We have been able to hold benzene and 
 
                                                                     25  
acetonitrile samples under tension, and we expect OKE experiments should yield 
clear signatures of the effects of negative pressure of these liquids. 
? Chapter 7 A new spectrometer for measuring different tensor elements of the 
OKE response has been developed. A dual-ring, polarization-dependent Sagnac 
interferometer was used to create two copropagating probe pulses that arrive at 
the sample at different times but that reach the detector simultaneously and 
collinearly. The tensor element of the response that is measured is determined by 
the polarization of the pump pulse. By controlling the relative timing of the 
probe pulses it is also possible to perform optical subtraction of two different 
tensor elements of the response at two different times, a strategy that can be used 
to generate contrast for microscopy. 
 
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                                                                     27  
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Chem. Phys. 2005, 123, 6. 
 
                                                                     28  
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Wiley: New York, 1989.  
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Small Confining Systems; Materials Research Society: Pittsburgh, 1993; Vol. 290, pp 
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3550. 
 
 
 
                                                                     32  
Chapter 2: Experimental Methods 
 
2.1  Introduction 
Optical Kerr effect spectroscopy is a pump/probe spectroscopy used to study 
refractive index changes1-4. The pump pulse induces a change in the refractive index; 
the probe pulse, which comes from the same laser as pump does and arrives at a 
variable delay time, is used to probe the change induced by pump.  
There are many possible implementations of OKE spectroscopy, the most common 
of which is a polarization spectroscopy setup. The pump pulse is polarized at 45? and 
the probe at 90?. The probe passes through an analyzer polarizer set at 0? after the 
sample. Thus, unless the pump beam induces birefringence in the sample, no signal 
will be detected. This polarization spectroscopy setup therefore measures the 
anisotropic portion of the change in the refractive index. 
The intensity of the OKE signal is relatively weak. However, the optical-
heterodyne-detected (OHD) OKE method developed by McMorrow and Lotshaw5,6 
will introduce a local oscillator to enhance the OKE signal greatly. This can be 
simply done by using a quarter-wave plate. 
 
 
                                                                     33  
2.2 Experimental setup 
Ti:Saphire
800 nm, ~100 fs Verdi-10
Pre-amp Lock-in
Lock-in
DX
Iris 1Iris 2
Pinhole
Chopper
De
lay
 lin
e
GLP
QWP
HWP
GLP
GTP
PD
PD
PD
Sample
Temperature
Controller
GLP
PDC
SF
pump
probe
SF
 
 
Fig. 2.1 Heterodyne-detected OKE setup. DX = doubling crystal, GLP = Glan laser 
polarizer, GTP = Glan-Thompson polarizer, HWP = half-wave plate, PD = 
photodiode, PDC = prism dispersion compensator, QWP = quarter-wave plate, SF 
=spatial filter. 
 
Our experimental OKE setup (shown in Figure 2.1) is based upon the optical-
heterodyne-detected OKE method developed by McMorrow and Lotshaw.5,6 A 
modified commercial, mode-locked Ti:sapphire laser produces pulses with a center 
frequency near 800 nm at a repetition rate of 76 MHz. A pair of external LaFN28 
prisms is used to compress the pulses and to compensate for dispersion caused by the 
optics in the experimental setup. The pulses that reach the sample are nearly 
 
                                                                     34  
transform limited, and generally have duration of approximately 35 fs. After the 
prism dispersion compensator, the laser output is spatially filtered, and then is split 
into a strong pump beam and a weaker probe beam. The two beams are chopped at 
frequencies with a 7:5 ratio by the two rings of slots in the wheel of a mechanical 
chopper. The pump beam then passes through a half-wave plate and a Glan laser 
polarizer set to pass light polarized at 45? to the vertical, after which it is focused into 
the sample. The probe beam traverses an optical delay line with 0.1 ?m resolution. It 
then passes through a Glan laser polarizer that is set to pass vertically polarized light, 
followed by a quarter-wave plate with its fast axis set to be along the vertical. The 
probe beam is then focused into the same spot in the sample as the pump beam. After 
the sample, the probe beam is recollimated by another lens and then it is incident on a 
Glan-Thompson polarizer that is set to pass horizontally polarized light. The leakage 
through the analyzer polarizer is spatially filtered and then is detected by a low-noise, 
amplified photodiode. 
To implement optical heterodyne detection, the first polarizer in the path of the 
probe beam is rotated off of the vertical by a small amount (generally around 1?). 
This allows a small horizontally polarized component of the probe beam to pass along 
the slow axis of the quarter-wave plate, where its phase is retarded by 90?. This 
horizontal component passes through the analyzer polarizer, and thus can serve as a 
local oscillator that will amplify and linearize the OKE signal (which is also 90? out 
of phase with the probe beam). By collecting data at equivalent positive and negative 
heterodyne angles and subtracting one set from the other, the homodyne contribution 
to the signal can be removed, leaving the pure heterodyne component. 
 
                                                                     35  
We have made several adaptations to the experimental setup to improve the signal-
to-noise ratio. First, the pump beam is picked off after the sample and is frequency-
doubled in a KDP crystal. The doubled light is detected with a photodiode and lock-in 
amplifier. Because second-harmonic generation has the same nonlinearity as the 
heterodyne-detected OKE signal, the doubled light can be used to normalize for any 
long-term intensity variations in the laser. Second, a small portion of the probe beam 
is picked off after the chopper and detected by a photodiode that is matched to the 
signal photodiode. The outputs of the signal and reference photodiodes are connected 
to the differential inputs of a low-noise preamplifier. With the pump beam blocked, 
the intensity of the reference beam is adjusted to zero the output of the preamplifier, 
thus removing the contribution of the local oscillator to the detected intensity. The 
pump beam is then unblocked, and the output of the preamplifier is sent to a lock-in 
amplifier that is referenced to the sum of the two chopping frequencies. 
Autocorrelation scans are collected by replacing the sample with a KDP crystal. 
The doubled light created by the overlap of the pump and probe pulse is detected by a 
low-noise, amplified photodiode that is connected to a lock-in amplifier with its 
frequency set at the sum of the chopping frequencies of the pump and probe beams. 
Glass blanks are placed in front of the crystal to correct for the glass that is introduced 
by the sample cell and cryostat. 
2.3 Data Acquisition 
The data acquisition is completely computer controlled using programs written in 
LabView. The computer moves the delay line, reads and averages the values in the 
data buffers of each lock-in amplifier, and then saves the normalized signal for that 
 
                                                                     36  
data point. No data are acquired unless the temperature of the sample is within 0.5 ?C 
of the desired value. Between consecutive scans, the computer reverses the angle of 
the first polarizer in the probe path to switch the heterodyne angle. Data are generally 
acquired with short-step scans (0.67 fs) out to delays of several picoseconds, and then 
with long-step scans (33.3 fs or 66.7 fs) for longer delays. 
 
Fig. 2.2 Data acquisition window ?: Getting GPIB addresses. 
 
Here is the first window for the LabView program (Figure 2.2). For this step, one 
needs to input  the GPIB addresses for all the instruments controlled by the program, 
the five instruments that are controlled are the delay line, the rotational stage for 
probe polarizer, the cryostat controller, and the two lock-in amplifiers. One lock-in 
collects OKE signal data from the preamplifier, while the other lock-in collects the 
doubled pump data from the photodiode. Each instrument has a unique address and 
 
                                                                     37  
the LabView program uses the GPIB addresses to recognize and control the motions 
of individual instruments. The correct GPIB addresses of each instrument can be seen 
from the figure 2.2: 
 
Fig. 2.3 Data acquisition window ?: Run settings. 
 
After the user sets all the GPIB addresses correctly and presses the continue button, 
the next window (Figure 2.3) containing new parameters appears. This menu will let 
us set all options necessary for the experiment. The first setting asks if the user wish 
the temperature of sample to be monitored during the experiment, ?Yes? or ?No? 
depends on if you want to run the temperature dependent experiment or not.  If you 
answer ?Yes?, and define the range for the temperature, for example ?0.5 K?, then if 
the real temperature of the sample falls out of the range, the program will suspend 
 
                                                                     38  
operation until the temperature returns to the approved range. The ?Change Angle of 
Rotation?? and ?By What Angle?? queries concern the angle of the automatic rotation 
stage used to introduce the heterodyne portion of the probe beam. ?Use Lock-in #2 
for Reference? asks if the user want the collected OKE signal to be normalized by the 
intensity of double pump. The last three settings of the menu define the number and 
names of the scans to be collected. The first one is ?Total Number of Scans?? in 
which the user enters the number of scans for this run and usually some even number 
between 10 and 20 is favored. The ?Name of Files? are usually defined using the 
current date as the base name and plus a sequence number, for example, if the scan is 
the second run of March 15, 2009, then the name is defined as ?2009Mar1501?. For 
?Starting Index for Files?, zero is usually used as the starting index, so if we use 10 as 
?Total Numbers of Scans?, then the names of  data files collected by this run would 
be from ?2009Mar15010? to ?2009Mar15019?. Once all the parameters on this screen 
are satisfactory, the ?continue? button is pressed. 
 
Fig. 2.4 Data acquisition window ??: More run settings. 
 
                                                                     39  
 
The next, also the last set of parameters is titled ?More Run Settings? (Figure 2.4). 
This menu will define the components of each individual scan. The ?starting? and 
?Ending Point? values will define the beginning and ending point on the delay line for 
each scan. The values are entered in tenths of a micron (the smallest step possible for 
the delay line). The ?Step Size? value defines the distance the delay line travels 
between each successive point collected, ?1? is used for short step size scans and 
?50? or ?100? are often sued for long step size scans. The last two entries, ?Time 
Constant? and ?Time Constants to Read? are concerned with the signal-to-noise ratio 
of the data. As a lock-in amplifier collects data, it continuously computes an average 
of the data in the time range of the value of ?Time Constant?, so the larger this value, 
the better the signal-to-noise ratio, but the longer time the total run takes. ?100 ms? is 
usually used, which can give us not only a good signal-to-noise ratio for the data, but 
also a comfortable length of time for each scan. Finally, when user has entered all the 
necessary parameters for each scan, the ?done? button can be pressed and the 
program starts collecting and saving data. At each scan, the program collects two sets 
of data: the OKE signal from lock-in amplifier #1 and the doubled pump signal from 
lock-in #2. Because each scan takes a significant amount of time to finish, the 
doubled pump is collected for the purpose of correcting the long-time fluctuations of 
laser intensity and normalizing the OKE signal. The normalization is simply done by 
dividing the detected OKE signal by the doubled pump. The pump beam is doubled 
so that it has the same nonlinearity to the intensity of laser as the OKE signal. The 
normalized OKE signal is also displayed on computer screen by ?Total run program? 
 
                                                                     40  
when collecting data (see Fig. 2.5). This is the basic procedure for collecting OKE 
data. 
 
Fig. 2.5 Data acquisition window ?: Total run program. 
 
2.4 Data Analysis 
The analysis of the data can also be done by the program written in LabView. The 
basic analysis procedure can be described in this way: 
First, we collect data for the whole decay by long step size. We know, the OKE 
signal is the negative time derivative of the collective orientational correlation 
function, ( )collC ? , where ? is the delay time between the pump and probe pulses, so 
( )collC ? can be computed by appropriate integration of the OKE decays. Then a 
nonlinear least-squares routine is used to fit ( )collC ? to a biexponential decay starting 
 
                                                                     41  
at delay times greater than 2 ps (usually longer for low temperature data). The two 
time constants, for the collective orientational correlation time and the intermediate 
response time, along with the corresponding amplitudes orA and iA  can be determined. 
We thereby get the functional formula for the long-time tail of the OKE decay.  
Second, OKE data are collected for the first 5 ps decay (including the contributions 
from intramolecular and intermolecular modes) with a short pulse width using a short 
step size. The determined long-time decay from ( )collC ? is used to add the tail for the 
short step size data to extend the time range.  
The third step is to apply the Fourier transform deconcolution procedure to the data 
from step 2, which helps to compensate for the effects of the finite duration of the 
laser pulse used. Once this step is finished, we can get the deconvolved response 
function. Then a function of the form  
( / ) ( / )( ) 1or rr Ae e? ? ? ?? ? ?? ?? ?? ?                                  (Eq. 2.1) 
is subtracted from the response function to remove the contribution of orientational 
diffusion.  
The final step is to get the RSD (Reduced Spectral Density). This can be done by 
Fourier transformation of the response function without the contribution from 
orientaional diffusion. 
Following this procedure, we can get the collective orientational correlation time 
constants for orientational diffusion dynamics study, and also the reduced spectral 
density (RSD) for intermolecular dynamics study. This can be simply done with the 
 
                                                                     42  
help of Labview program written for OKE data analysis, and please refer to Appendix 
A for the detail about how to use the program.  
 
 
2.5 References 
(1) Righini, R. Science 1993, 262, 1386. 
(2) Kinoshita, S.; Kai, Y.; Ariyoshi, T.; Shimada, Y. Int. J. Mod. Phys. B 1996, 10, 
1229. 
(3) Fourkas, J. T. Nonresonant Intermolecular Spectroscopy of Liquids. In Ultrafast 
Infrared and Raman Spectroscopy; Fayer, M. D., Ed.; Marcel Dekker: New York, 
2001; Vol. 26; pp 473. 
(4) Hunt, N. T.; Jaye, A. A.; Meech, S. R. Phys. Chem. Chem. Phys. 2007, 9, 2167. 
(5) McMorrow, D., Opt. Comm., 1991, 86, 236. 
(6) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. 
 
 
                                                                     43  
Chapter 3: Temperature-dependent Orientational Dynamics of 
1,n-Dicyano n-Alkanes 
 
 
3.1 Introduction 
The dynamic behavior of a molecule in solution is highly sensitive to the details of 
its local environment. For example, the orientational diffusion rate of a solute 
molecule is sensitive to its conformation. In general, a solute molecule in an extended 
conformation must displace more solvent molecules in order to reorient than would 
the same solute molecule in a more compact conformation, and therefore the 
molecule in its extended conformation would be expected to have a lower rate of 
orientational diffusion. This behavior is embodied by the Debye-Stokes-Einstein 
(DSE) relation,1,2 which in its simplest form is given by  
                                                        , Hor sm
B
V
k T
?? ?                                                 (Eq. 3.1) 
where ,or sm?  is the single-molecule orientational correlation time, ? is the viscosity, 
HV  is the hydrodynamic volume for reorientation, Bk  is Boltzmann?s constant, and T 
is the temperature. A multiplicative term may also be included in this relation to 
account for the boundary conditions for reorientation. 
The DSE relation was originally intended to apply to solute molecules that are 
considerably larger than the solvent molecules. However, experiments using 
techniques such as Raman spectroscopy, NMR spectroscopy, Rayleigh-wing 
spectroscopy, and optical Kerr effect3-6 (OKE) spectroscopy indicate that in most 
 
                                                                     44  
cases the DSE relation works quite well for neat, simple liquids as well.2 We and 
others have previously observed this to be the case for OKE experiments in a wide 
range of small molecule, nonassociated liquids, for example.7-13 
We have recently reported the results of OKE experiments performed on liquids n-
alkyl cyanides, molecules of the form CH3(CH2)nCN.9 While for small enough values 
of n the molecules in these liquids are expected to adopt an extended conformation, 
we found, unexpectedly, that extended conformations persisted in molecules with as 
many as 10 methylene units. In addition, our studies were suggestive of temperature 
dependent changes in the underlying collective structure of some of these liquids.9 
Here we report OKE studies of 1,n-dicyano n-alkanes, i.e., molecules of the form 
NC(CH2)nCN. The highly polar groups at both ends of these molecules could 
potentially lead to significant differences in the dynamic and structural behaviors of 
these liquids compared to n-alkyl cyanides. Our results indicate, however, that the 
dicyanides also feature significantly extended structures in the neat liquid, with a 
preference for gauche conformations at the terminal methylene groups. Our data also 
suggest that these liquids exhibit temperature-dependent, collective structural changes. 
3.2 Experimental Section 
Our optical-heterodyne-detected14,15 OKE spectrometer and data collection 
procedures have been described in detail elsewhere.16,17 Temperature-dependent OKE 
data were collected for eight dicyanides, ranging from dicyanomethane to 1,8- 
dicyanooctane (Table 3.1) with pulses of 60 fs or greater duration. These relatively 
long pulses were employed both to increase the signal from orientational relaxation 
and to help remove the effects of intramolecular vibrational modes. Due to the pulse 
 
                                                                     45  
lengths used, no attempt was made to determine the intermolecular vibrational spectra 
of these liquids from the OKE data. 
 
Table 3.1 Formula Weight, Density at Room Temperature, Minimum and Maximum 
Temperatures Studied, and Activation Energy for Collective Reorientation for the 
Dicyanoalkanes Examined  
liquid 
FW 
(amu) 
? 
(g/mL) 
Tmin 
(K) 
Tmax 
(K) 
EA 
(cm-1/1000) 
dicyanomethane 66.06 1.191 306 360 0.97 
1,2-dicyanoethane 80.09 0.985 336 380 1.3 
1,3-dicyanopropane 94.11 0.981 289 375 1.4 
1,4-dicyanobutane 108.14 0.968 275 375 1.4 
1,5-dicyanopentane 122.17 0.948 272 374 1.7 
1,6-dicyanohexane 136.19 0.940 289 366 1.6 
1,7-dicyanoheptane 150.22 0.929 306 364 1.5 
1,8-dicyanooctane 164.24 0.913 297 366 1.7 
 
All liquids were purchased in the highest purity form available from Aldrich. The 
liquids were colorless and were used as received, with the exception of 
dicyanomethane, which was brown when received. Consequently, dicyanomethane 
was distilled and then used promptly. After distillation, this substance was slightly 
reddish in color, but it did not discolor further over the course of data acquisition. The 
melting points of all the substances agreed well with literature values. 
 
                                                                     46  
OKE data collected at equal but opposite heterodyne angles were subtracted to 
obtain the pure heterodyne signal. The data were then integrated to give the collective 
orientational correlation function, Ccoll(? ),18 where ?  is the experimental delay time. 
In all cases, the data were taken out to delay times well beyond the point at which 
Ccoll(? ) became too noisy to be fit robustly. Ccoll(? ) was truncated at the point at 
which it became noisy and then was fit to a biexponential function with a variable 
baseline using a nonlinear-least-squares routine.19 The early time fitting limit was 
varied to ensure that the fit parameters were robust. It is important to note that, with 
increasing alkyl chain length, the density of polarizable cyanide groups decreases, 
which in turn reduces the many-body polarizability of the liquid. 
In addition, the orientational correlation time increases with increasing chain length. 
Since the OKE signal is the negative time derivative of Ccoll(? ), liquids that relax 
more slowly necessarily give weaker signals. As a result, for the molecules with the 
longest chains it was not possible to observe decays over as many factors of e as for 
the shorter chain liquids, leading to greater uncertainty in the fit relaxation times. 
Temperature-dependent viscosity data were obtained from the literature20 and were 
fit to 
                                                      ln[ ( )] BT A C T? ? ? ?                                     (Eq. 3.2) 
to derive viscosities for the temperatures used here. Equilibrium molecular 
geometries were calculated using a molecular modeling program21 in order to 
determine hydrodynamic volumes under slip boundary conditions. 
 
                                                                     47  
3.3 Results 
The temperature ranges over which data were collected for each liquid are listed in 
Table 3.1. Shown in Figure 3.1 is a typical collective orientational correlation 
function obtained for one of these liquids, in this case 1,5-dicyanopentane at a 
temperature of 288 K. For this particular decay, the data at times ? ?20 ps have been 
fit to a function of the form  
                             1 2( ) exp( / ) [1 ]exp( / )collC A A? ? ? ? ?? ? ? ? ?                          (Eq. 3.3) 
where 1 2? ??  and A is the normalized amplitude of the portion of the decay with the 
slower relaxation time. Based on the residuals plotted at the bottom of the figure, it 
can be seen that the fit is an excellent one. Biexponential functions were found to 
provide excellent fits to all of the data for each liquid. Complete tables of the 
temperature-dependent viscosity, parameters from biexponential fits to the OKE data, 
and fitting ranges are given for each liquid in the Appendix B. 
 
 
 
 
 
                                                                     48  
 
 
Figure 3.1 Logarithm of the collective orientational correlation function of 1,5-
dicyanopentane at 288 K (red) and a biexponential fit to the data (black). The residual 
obtained by subtracting the fit from the data is shown at the bottom on a linear scale. 
 
Biexponential OKE decays are commonly observed in nonnetworked, small-
molecule liquids.8-10,15,22-31 In general, the slower decay component arises from 
collective orientational diffusion whereas the faster component is ascribed to the 
socalled ?intermediate? response, the source of which has not been fully established. 
However, it should be noted that the contribution of orientational diffusion to the 
OKE decay of a liquid can feature up to five exponentials, depending on the shape 
and orientations of the diffusion and polarizability tensors.32 Thus, if 2?  for the 
dinitriles is to be assigned to the intermediate response, it is important to verify that 
the dinitriles studied here exhibit single-exponential orientational diffusion. Whether 
a single-exponential orientational decay should be observed depends upon factors 
 
                                                                     49  
such as the molecular conformation, the principal values of the orientational diffusion 
and polarizability tensors, and the principal axis systems of these tensors.32 In the 
OKE spectroscopy of n-alkyl cyanides we did observe single-exponential 
orientational decays.9 If the conformations of the dinitriles in the liquid phase are 
similar to those of the n-alkyl cyanides, then we would expect to see single-
exponential orientational decays in the dinitriles as well. 
For a broad range of small-molecule, nonassociated liquids, the OKE intermediate 
relaxation time has been observed to scale with the collective orientational correlation 
time.8-10 If 2?  for the dinitriles corresponds to the intermediate response, then it 
would be expected to track 1?  with a similar scaling factor regardless of temperature 
or the identity of the dinitrile. In Figure 3.2 we plot 2?  as a function of 1?  for all of 
the liquids studied here. In all cases there is a linear relationship between the two 
times, and the constant of proportionality between the two times lies within a range of 
approximately 4-5, which is in good agreement with previous observations for the 
relation between the collective orientational correlation time and the intermediate 
response time.8-10 Given the large range of aspect ratios among the molecules studied 
here, if 1?  and 2?  both corresponded to orientational diffusion, we would expect to 
see a much larger range of scaling factors, as reorientation about the long molecular 
axis should not depend significantly on molecular length whereas reorientation about 
the axes perpendicular to this axis should depend on length. We therefore have good 
evidence that 1?  can be assigned to orientational diffusion and that 2?  can be assigned 
to the intermediate response. 
 
 
                                                                     50  
 
Figure 3.2 Plot of fast versus slow relaxation times for OKE decays of the 
dicyanoalkanes. The relationship between the two times supports the assignment of 
the faster time to the intermediate response and the slower time to orientational 
diffusion. 
 
We should note that, in the literature, the intermediate response time originally 
referred to relaxation with a time constant that was generally on the order of a 
picosecond or less.26 However, with improvements in laser technology it has become 
possible to study liquids with considerably longer relaxation times. This capability 
has led to the realization that the intermediate response tracks the orientational 
relaxation, and can therefore have a time constant that is considerably longer than a 
picosecond.8-10 This is the case for most of the data presented here, and is the reason 
that the fit in Figure 3.1 begins only at 20 ps. In such a slowly relaxing liquid, the 
influence of coherently excited intermolecular modes can be observed out to delay 
times of many picoseconds. 
To determine whether the DSE relation holds for the liquids studied here, we can 
 
                                                                     51  
plot or?  as a function of /T?  for each liquid. Shown in Figure 3.3 is a representative 
DSE plot, in this case for 1,4-dicyanobutane. This plot is clearly not linear, but rather 
appears to be divided into linear regions with distinct slopes (although within the 
experimental uncertainty of the values of or?  we cannot entirely rule out describing 
the DSE data for this and the other liquids studied here by smooth, monotonically 
decreasing curves). The plot is linear for the highest values of /T?  down to 
approximately 0.024 cP/K, and then exhibits a transition to a new, higher slope. A 
second transition to an even larger slope occurs at a value of ?/T near 0.005 cP/K. 
Similar behavior is observed for dicyanomethane through 1,6-dicyanohexane. The 
relaxation times for 1,7-dicyanoheptane and 1,8-dicyanooctane are so long that they 
could not be determined with sufficient precision to ascertain whether transitions 
exist for these liquids as well. 
 
 
Figure 3.3 Debye-Stokes-Einstein plot for 1,4-dicyanobutane. The lines are linear-
least-squares fits to the slope in each region. The inset is a blowup of the data up to 
?/T ) 0.015 cP/K. 
 
                                                                     52  
 
The DSE data for the dinitriles can be divided into three distinct regions. Slopes in 
region A are observed in dicyanomethane through 1,5-dicyanopentane at higher 
temperatures. Slopes in region B are observed in dicyanomethane through 1,3-
dicyanopropane at lower temperatures, in 1,4-dicyanobutane and 1,5-dicyanopentane 
at intermediate temperatures, and in 1,6-dicyanohexane at higher temperatures. 
Slopes in region C are observed for 1,4-dicyanebutane through 1,6-dicyanohexane at 
lower temperatures and for 1,7-dicyanohexane and 1,8-dicyanooctane at all 
temperatures studied here. The slopes in each of these regions and the approximate 
transition temperatures between them are listed in Table 3.2 for all of the liquids 
studied here. We note that given our point spacing and the uncertainty in our values 
of or? , the transitions are not necessarily sharp, but may rather take place over a range 
of 5-10 K. 
 
 
 
 
 
 
 
 
 
 
 
                                                                     53  
TABLE 3.2: DSE Slopes in Regions A, B, and C and Transition Temperatures 
between Regions A and B and Regions B and C for the Dicyanoalkanes Studied Here 
 
liquid 
Slope A 
(ns*K/cP) 
Slope B 
(ns*K/cP) 
Slope C 
(ns*K/cP) 
TAB 
(K) 
TBC 
(K) 
dicyanomethane 0.657 0.137  323  
1,2-dicyanoethane 1.24 0.756  358  
1,3-dicyanopropane 1.90 1.27  340  
1,4-dicyanobutane 2.16 1.89 0.844 361 294 
1,5-dicyanopentane 3.88 3.39 2.29 349 302 
1,6-dicyanohexane  5.06 2.90 340  
1,7-dicyanoheptane   4.69   
1,8-dicyanooctane   6.47   
 
 
 
 
 
                                                                     54  
 
Figure 3.4 Values of ?/T for the transition between regions A and B (circles) and 
between regions B and C (triangles) as a function of the number of methylene groups 
in each liquid. 
 
In Figure 3.4 we plot the value of /T?  at which the transitions between regions A 
and B and between regions B and C appear to occur as a function of the number of 
methylene groups in each molecule. The transition between regions A and B occurs at 
an average value of /T?  of approximately 0.0065 cP/K for dicyanomethane through 
1,6-dicyanohexane. The value of /T?  at which the transition between regions B and 
C occurs appears to decrease with the number of methylene groups for 1,5-
dicyanopentane and 1,6-dicyanohexane, although the two points cannot be 
distinguished definitively within the experimental uncertainty. Being able to obtain 
decays for 1,7-dicyanoheptane and 1,8-dicyanooctane out to considerably longer 
times would help to clarify the behavior of this transition with increasing chain length. 
 
 
                                                                     55  
3.4 Discussion 
Higashigaki and Wang20 (HW) have previously studied dicyanomethane through 
1,6-dicyanohexane using Rayleigh wing scattering, a technique that is related directly 
to OKE spectroscopy. While their results bear some similarities to ours, there are also 
significant differences among them. Most importantly, HW reported linear DSE plots 
for the six liquids that they studied, although their plots do reveal signs of slope 
discontinuities for some of the liquids at low values of /T? .20 Our viscosity numbers 
were derived from the work of HW, so it is unlikely that these values are the cause of 
the discrepancies between the two studies. We must therefore focus attention on 
either the orientational diffusion times or the temperatures. HW found that their 
measured relaxation times obeyed Arrhenius behavior,20 so in Figure 3.5 we present 
an Arrhenius plot of our data for the eight liquids studied here.  
 
Figure 3.5 Arrhenius plot of the relaxation times of the dinitriles. The symbols are the 
same as in Figure 3.2. 
 
                                                                     56  
 
As can be seen from this figure, we also observe Arrhenius behavior for each of 
these liquids, and the activation energies derived from these plots are listed in Table 
3.1. However, there is no clear trend in the differences between our data and those of 
HW. Our data and those of HW for dicyanomethane, 1,3-dicyanopropane, and 1,5-
dicyanopentane are similar, whereas those for the remaining liquids differ 
considerably. The similarity of the data for three liquids and the lack of a consistent 
pattern of differences for the remaining liquids suggests that there is not a systematic 
problem with the temperature determination in our experiments. The slopes of the 
Arrhenius plots for our data increase systematically up to 1,5-dicyanopentane and 
then level off, whereas there was no clear trend in the slopes of the data from HW. 
This leads us to conclude that it is likely that we are able to determine the collective 
orientational diffusion time more accurately than was possible using 
frequencydomain, Rayleigh-wing scattering. 
We now consider the conformation of the dinitrile molecules in the liquids studied 
here. The two extreme possibilities are that the molecules are in a completely 
extended state or in a completely collapsed state. To assess which extreme is more 
representative of these liquids, we can plot the DSE slopes as a function of the 
estimated hydrodynamic volume for reorientation in the extended and collapsed states. 
We compute the former by using molecular modeling21 to estimate the length of an 
isolated molecule in the completely extended geometry. As a proxy for hydrodynamic 
volume in the collapsed state, we can use the volume per molecule, as computed from 
the density and molecular weight of each liquid. This approximation is clearly more 
 
                                                                     57  
accurate for larger molecules. 
In Figure 3.6 we plot the DSE slopes in regions A, B, and C as a function of the 
estimated hydrodynamic volume for reorientation in the extended state. In each 
region the slope increases roughly linearly with hydrodynamic volume, although 
there are deviations for 1,4-dicyanobutane and 1,5-dicyanopentane. The slopes of the 
plots of the DSE slopes in each region are similar to one another. For comparison, in 
Figure 3.7 we plot the same data as a function of molecular volume. Although we 
must keep in mind that our estimate of the hydrodynamic volume for reorientation in 
the collapsed state is too low for molecules with short chain lengths, it is nevertheless 
clear that our data point to configurations that are toward the extended end of the 
continuum. This conclusion is consistent with our previous results for n-alkyl 
cyanides. 
 
Figure 3.6 Slopes of the Debye-Stokes-Einstein plots for the liquids studied here as a 
function of the hydrodynamic volume for reorientation assuming that the molecules 
adopt a completely extended conformation. The red circles are for region A, the green 
squares are for region B, and the blue diamonds are for region C. 
 
                                                                     58  
 
Figure 3.7 Slopes of the Debye-Stokes-Einstein plots for the liquids studied here as a 
function of the volume per molecule. The red circles are for region A, the green 
squares are for region B, and the blue diamonds are for region C. 
 
Evidence from vibrational spectroscopic studies indicates that the lowest energy 
conformations for n-alkyl cyanides and 1,n-dicyanoalkanes, whether isolated or in the 
liquid state, are not fully extended.33,34 Instead, the cyanide groups preferentially 
adopt a gauche conformation with respect to the rest of the molecule. This gauche 
form is favored over the trans form by on the order of 90 cm-1,35 and so a significant 
population of the fully extended molecules is also expected to exist and has been 
observed spectroscopically. The gauche preference exists in isolated molecules, and it 
is thus believed that this conformation arises from steric effects rather than from 
interactions among the polar cyanide groups in the liquid.35 A similar gauche 
preference is found n-alkyl acetylenes,35 further supporting its steric origin. 
 
                                                                     59  
 
Figure 3.8 Views of the gauche-gauche structure of 1,4-dicyanobutane along the x-
axis (a) and the y-axis (b) and of 1,5-dicyanopentane along the x-axis (c) and the y-
axis (d). In all cases the z-axis is vertical. 
 
Shown in Figure 3.8 are models of 1,4-dicyanobutane and 1,5-dicyanopentane in 
gauche-gauche conformations viewed from along what we denote as their x- and y-
axes. Due to the angle between the cyanide groups, the polarizability is only slightly 
anisotropic with respect to reorientation about the y- and z-axes. However, 
reorientation around the x-axis will lead to a significant change in the polarizability. 
To assess whether our data are consistent with these gauche-gauche conformations, 
we have therefore calculated the hydrodynamic volume for reorientation about this 
axis for all of the molecules except for dicyanomethane (for which we have averaged 
the hydrodynamic volume for reorientation about each axis). A plot of the DSE slopes 
as a function of this gauche-gauche hydrodynamic volume is shown in Figure 3.9. 
The slopes for regions A, B, and C are more nearly linear in this plot than in those in 
Figures 3.6 and 3.7, and indeed the three slopes are all quite similar as well. We 
conclude that our data are consistent with the molecules preferentially adopting the 
 
                                                                     60  
gauche-gauche conformation. 
 
Figure 3.9 Slopes of the Debye-Stokes-Einstein plots for the liquids studied here as a 
function of the hydrodynamic volume for reorientation assuming that the molecules 
adopt an extended conformation but have gauche defects at each terminal methylene 
group. The red circles are for region A, the green squares are for region B, and the 
blue diamonds are for region C. 
 
As was the case for n-alkyl cyanides,9 we find here that when there is a transition 
in the slope of the DSE plot, the slope is smaller on the low-temperature side of the 
transition than it is on the high-temperature side. We now assess the potential causes 
for this behavior. One possible candidate for a change in slope would be a change in 
the boundary conditions for reorientation. However, if anything the boundary 
conditions are likely to tend more toward stick at lower temperatures and toward slip 
at higher temperatures, which would lead to the opposite of the observed behavior of 
the slope. 
Given that the amount of energy by which a gauche defect is preferred is less than 
 
                                                                     61  
room temperature thermal energy, it is possible that the conformations of the 
molecules become more extended at higher temperatures. More-extended molecules 
would have higher hydrodynamic volumes for reorientation, and therefore the DSE 
slope would be expected to increase at higher temperature. This mechanism would 
apply equally well to the cyanoalkanes that we have studied previously.9 However, it 
should also be noted that dicyanomethane has only one possible conformation, and 
yet it displays two DSE slopes. Furthermore, conformational changes would be 
expected to occur gradually with temperature, rather than suddenly at a particular 
temperature. In addition, the linear Arrhenius behavior of these liquids argues against 
relatively sharp molecular conformational transitions. We therefore conclude that 
molecular conformational changes are unlikely to be responsible for the observed 
changes in DSE slopes. 
Spectroscopically, the majority of the OKE signal arises from the polarizable 
cyanide groups. Indeed, to a good first approximation the two cyanide groups on each 
molecule can be thought of as being spectroscopically independent, especially for the 
molecules with larger numbers of methylene groups. Because OKE spectroscopy is 
sensitive to collective orientational motion, it measures a somewhat different quantity 
than do techniques such as NMR or Raman spectroscopy, which are sensitive to 
single-molecule orientational motion.2 The relaxation time measured with OKE 
spectroscopy, OKE? , is related to the single-molecule orientational correlation time, 
sm? , via
2 
                                                        2
2
OKE sm
g
j? ??                                                (Eq. 3.4) 
 
                                                                     62  
Here 2g  is the static orientational pair correlation parameter and 2j  is the dynamic 
orientational pair correlation parameter. It is believed that 2j generally takes on a 
value near unity in simple liquids.2 On the other hand, 2g  is a measure of the degree 
of parallel ordering in a liquid, and can take on values of unity or greater. The larger 
the value of 2g , the greater the degree of parallel ordering. 
In the case of the OKE spectroscopy of dicyanoalkanes (and of cyanoalkanes9), the 
relevant ordering is that of the cyanide moieties. We have previously suggested for 
cyanoalkanes that the DSE slope changes are indicative of collective structural 
changes in the liquids affecting the degree of parallel ordering, and thereby changing 
the collective orientational correlation time via 2g .9 A similar mechanism may be 
operating in the case of the dicyanoalkanes. The lower DSE slopes at lower 
temperatures would thus be indicative of a lower degree of parallel organization 
among the cyanide groups. The observed changes in the DSE slope can then be 
interpreted in terms of collective structural changes within the liquid, as we also 
suggested for the cyanoalkane liquids.9 Significant changes in the slope can arise 
from relatively subtle changes in ordering as g2 averages over long distances. We 
should also note that we have not seen any clear evidence for phase transitions using 
differential scanning calorimetry, indicating that any change in the liquid structure 
has at most a minor effect on thermodynamic properties (as might be expected for 
relatively subtle collective structural changes). The fact that the transition between 
regions A and B occurs at a value of T? that is essentially independent of the identity 
of the liquid suggests that dynamic effects may be involved in the structural changes. 
 
                                                                     63  
All of the molecules studied here have similar cross-sectional areas perpendicular to 
the y-axis (as defined in Figure 3.8). Based on the DSE equation,1,2 we would 
therefore expect these molecules to have similar orientational diffusion constants 
about their y-axes for a fixed value of T? . This axis should also be the one about 
which diffusion occurs most readily. As can be seen in Figure 3.8, the cross-sectional 
area perpendicular to y is somewhat larger for molecules with odd numbers of 
methylene groups than for those with even numbers of methylene groups. As a result, 
if diffusion about y is involved, we would expect the molecules with an odd number 
of methylene groups to have somewhat higher values of T?  at the transition between 
regions A and B. There is indeed a modest even/odd effect in these transition values, 
as shown in Figure 3.4. We therefore suggest that, at least for this putative structural 
transition, dynamic effects may play a key role. We do not have enough data on the 
other possible structural transition to be able to suggest a mechanism at this time.  
We again reiterate that within the uncertainty of our data it is possible that the true 
form of the DSE plots of these liquids is a smooth curve that appears linear locally. 
The collective orientational correlation times for all of these liquids obey Arrhenius 
behavior. If the collective structure of the liquid changes smoothly with temperature, 
then the most plausible scenario that is consistent with this Arrhenius behavior is that 
both the single-molecule orientational correlation time and g2 also have Arrhenius 
behavior. For data such as those in Figure 3.4, if we assume that g2 increases in an 
Arrhenius manner from 1 at low temperature to 2 at high temperature, we can make 
approximate fits to the data. However, the locally linear fits still describe the data 
significantly more accurately. In either case, our data offer evidence for temperature-
 
                                                                     64  
dependent, collective structural rearrangements in these liquids. 
 
3.5 Conclusions 
We have presented a detailed OKE study of the orientational dynamics of 
dicyanoalkanes over a broad range of temperatures. Our data are consistent with these 
molecules preferentially adopting a gauche-gauche conformation in the liquid phase. 
As was the case for cyanoalkanes, we find that there are changes in the slopes of DSE 
plots for these liquids that are consistent with underlying, temperature-dependent, 
collective structural rearrangements within the liquids. It will be interesting to search 
for other signatures of such transitions with different experimental techniques. 
 
3.6 References 
(1) Debye, P. Polar Molecules; Dover: New York, 1929. 
(2) Kivelson, D.; Madden, P. A. Annu. Rev. Phys. Chem. 1980, 31, 523. 
(3) Righini, R. Science 1993, 262, 1386. 
(4) Kinoshita, S.; Kai, Y.; Ariyoshi, T.; Shimada, Y. Int. J. Mod. Phys. B 1996, 10, 
1229. 
(5) Smith, N. A.; Meech, S. R. Int. Rev. Phys. Chem. 2002, 21, 75. 
(6) Hunt, N. T.; Jaye, A. A.; Meech, S. R. Phys. Chem. Chem. Phys. 2007, 9, 2167. 
(7) Ruhman, S.; Kohler, B.; Joly, A. G.; Nelson, K. A. Chem. Phys. Lett. 1987, 141, 
16. 
(8) Loughnane, B. J.; Scodinu, A.; Farrer, R. A.; Fourkas, J. T.; Mohanty, U. J. Chem. 
Phys. 1999, 111, 2686. 
 
                                                                     65  
(9) Zhu, X.; Farrer, R. A.; Zhong, Q.; Fourkas, J. T. J. Phys.: Condens. Matter 2005, 
17, 4105. 
(10) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2006, 110, 5708. 
(11) Ricci, M.; Wiebel, S.; Bartolini, P.; Taschin, A.; Torre, R. Philos. Mag. 2004, 84, 
1491. 
(12) Lotshaw, W. T.; McMorrow, D.; Thantu, N.; Melinger, J. S.; Kitchenham, R. J. 
Raman Spectrosc. 1995, 26, 571. 
(13) Ricci, M.; Bartolini, P.; Chelli, R.; Cardini, G.; Califano, S.; Righini, R. Phys. 
Chem. Chem. Phys. 2001, 3, 2795. 
(14) McMorrow, D. Opt. Commun. 1991, 86, 236. 
(15) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. 
(16) Farrer, R. A.; Loughnane, B. J.; Deschenes, L. A.; Fourkas, J. T. J. Chem. Phys. 
1997, 106, 6901. 
(17) Loughnane, B. J.; Farrer, R. A.; Scodinu, A.; Reilly, T.; Fourkas, J. T. J. Phys. 
Chem. B 2000, 104, 5421. 
(18) Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2002, 106, 10292. 
(19) SigmaPlot, version 9.0; Systat: Point Richmond, CA, 2004. 
(20) Higashigaki, Y.; Wang, C. H. Mol. Phys. 1982, 45, 493. 
(21) Chem 3D Pro, version 5.0; CambridgeSoft: Cambridge, MA, 1999. 
(22) Quitevis, E. L.; Neelakandan, M. J. Phys. Chem. 1996, 100, 10005. 
(23) Neelakandan, M.; Pant, D.; Quitevis, E. L. J. Phys. Chem. A 1997, 101, 2936. 
(24) Chang, Y. J.; Castner, E. W., Jr. J. Phys. Chem. 1996, 100, 3330. 
(25) Cong, P.; Deuel, H. P.; Simon, J. D. Chem. Phys. Lett. 1995, 240, 72. 
 
                                                                     66  
(26) Lotshaw, W. T.; McMorrow, D.; Kalpouzos, C.; Kenney-Wallace, G. A. Chem. 
Phys. Lett. 1987, 136, 323. 
(27) McMorrow, D.; Lotshaw, W. T. Chem. Phys. Lett. 1993, 201, 369. 
(28) McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. IEEE J. Quantum 
Electron. 1988, 24, 443. 
(29) Kamada, K.; Ueda, M.; Ohta, K.; Wang, Y.; Ushida, K.; Tominaga, Y. J. Chem. 
Phys. 1998, 109, 10948. 
(30) Smith, N. A.; Meech, S. R. J. Phys. Chem. A 2000, 104, 4223. 
(31) Jaye, A. A.; Hunt, N. T.; Meech, S. R. J. Chem. Phys. 2006, 124, 24506. 
(32) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Wiley: New York, 1976. 
(33) Matsubara, I. J. Chem. Phys. 1961, 35, 373. 
(34) Thorbjor, J.; Ellestad, O. H.; Klaeboe, P.; Torgrims. T. Acta Chem. Scand. 1972, 
26, 3799. 
(35) Durig, J. R.; Drew, B. R.; Koomer, A.; Bell, S. Phys. Chem. Chem. Phys. 2001, 3, 
766. 
 
 
 
 
                                                                     67  
Chapter 4: Shape and Electrostatic Effects in Optical Kerr 
Effect Spectroscopy of Aromatic Liquids 
 
4.1 Introduction 
Ultrafast optical Kerr effect (OKE) spectroscopy has become a broadly-used 
technique for probing the intrinsic dynamics of simple,1-4 complex4 and confined 
liquids.5,6  In the most common implementation of OKE spectroscopy, a linearly-
polarized pump pulse traverses a transparent liquid composed of molecules with an 
anisotropic polarizability.  The pump pulse impulsively excites Raman active 
intramolecular and intermolecular modes, and creates a small net alignment of the 
liquid molecules.  A variably-delayed probe pulse polarized at 45? is then used to 
probe the time dependence of collective orientational diffusion and vibrational 
dephasing by monitoring the decay of the birefringence induced by the pump pulse. 
OKE spectroscopy is the formal time-domain equivalent of low-frequency Raman 
scattering.  By using a Fourier-transform deconvolution technique with OKE data,7 it 
is possible to derive the Bose-Einstein-corrected, low-frequency Raman spectrum of a 
liquid.  It has become common in OKE studies to perform an approximate subtraction 
of the collective orientational diffusion contribution from this spectrum, leaving what 
has become known as the reduced spectral density (RSD).7  The RSD contains 
information about the Raman-active intermolecular modes of a liquid, including 
librations and collective modes that appear as a result of interaction-induced 
scattering. 
 
                                                                     68  
The use of OKE RSDs to develop a molecular-level interpretation of structure and 
dynamics in liquids has proven challenging.  The RSDs are generally broad and do 
not have sharp features.  Interpretation is further complicated by the fact that different 
contributions to the RSD may interfere constructively or destructively, making it 
difficult to isolate the influence of a particular mechanism or mode in the RSD. 
Despite the challenges involved in interpreting RSDs, some progress has been made 
in understanding their microscopic origin.  For instance, temperature-dependent OKE 
studies have revealed that for most liquids the RSD broadens to both higher and lower 
frequency as the temperature is decreased.8-10  At the high-frequency end of the RSD, 
this behavior is interpreted as arising from the densification of the liquid with 
decreasing temperature, which leads to an increase in frequencies of librations and 
other intermolecular modes.  At the low-frequency end of the RSD, it has been 
suggested that the broadening with decreased temperature arises from a decrease in 
the degree of motional narrowing in the spectrum.11  However, a number of liquids 
have recently been shown not to exhibit the low-frequency broadening effect with 
decreasing temperature.12,13  The interpretation of the temperature dependence of the 
low-frequency portion of RSDs for liquids thus remains an open question. 
Ryu and Stratt14 have suggested that the form of the OKE RSD can, in part, be a 
manifestation of molecular shape, especially insofar as the structure of liquids is 
dominated by effective repulsive interactions.15 To explore this idea, we have 
previously reported temperature-dependent OKE studies of a series of aromatic 
liquids, including benzene, benzene-d5, hexafluorobenzene (HFB), 1,3,5-
trifluorobenzene (TFB), and mesitylene.10  Despite the fact that these are all disk-like 
 
                                                                     69  
molecules, the RSDs for benzene differ markedly from those of HFB and TFB, while 
the RSDs of mesitylene resemble those of benzene at low temperature and those of 
HFB and TFB at high temperature.  By correlating the shapes of the RSDs with 
known structural details for these liquids,16-22 we proposed that the higher-frequency 
portion of the RSDs arose from molecules with predominantly perpendicular local 
ordering while the lower-frequency portion of the RSDs arose from molecules with 
predominantly parallel ordering.10 
Elola and Ladanyi performed simulations of benzene, HFB and TFB to test our 
structural proposal.23  They found that for benzene, molecules with predominantly 
parallel local ordering have higher librational frequencies than those with 
perpendicular local ordering.  The same effect exists in TFB, although to a lesser 
extent, and is absent in HFB.  Elola and Ladanyi suggested that the differences in the 
RSDs of these three liquids arise from pairwise potentials of different depths, with a 
deeper potential leading to an RSD that appears more triangular.23  Presumably the 
deeper pairwise potentials of HFB and TFB result from electrostatic effects.  How 
this proposal fits in with the observed behavior of the RSDs of mesitylene is unclear, 
however. 
Another study that is directly relevant to importance of molecular shape and 
electrostatics in OKE spectroscopy was performed by Smith and Meech, who looked 
at polar, monosubstituted benzenes including aniline, benzonitrile, and nitrobenzene.9  
All of these molecules have similar shapes, and their RSDs bear strong resemblance 
to one another as well.  The RSDs of aniline are considerably broader than those of 
the other two liquids, which may be attributed to the ability of aniline to form 
 
                                                                     70  
hydrogen bonds.  Nitrobenzene and benzonitrile have both similar shapes and similar 
dipole moments, both of which may play a role in the similarity of their RSDs. 
To investigate the relative importance of shape and electrostatic interactions further, 
here we report the temperature-dependent OKE spectroscopy of four more aromatic 
liquids, pyridine, pyridine-d5, 2,4,6-trifluoropyridine (TFP), 2,4,6-trimethylpyridine 
(TMP) and 1,3,5-tris(trifluoromethyl)benzene (nonafluoromesitylene, NFM).  The 
shapes of these molecules bear strong similarity to those of aromatic liquids that we 
studied previously.10   However, the electrostatics of the molecules studied here differ 
from those of the molecules we studied previously, allowing us to investigate the 
relative importance of shape and electrostatics in OKE spectroscopy. 
 
4.2 Experimental Section 
The liquids studied here were purchased from Aldrich (except for TFP, which was 
purchased from Alfa Aesar) in the purest form available and were used without any 
additional purification.  Relevant physical properties of these liquids are listed in 
Table 4.1.  The densities reported are those given by the supplier except for that of 
TMP.  For this liquid the density was measured with a 2 mL Gay-Lussac pycnometer. 
 
 
 
 
 
 
 
                                                                     71  
TABLE 4.1: Formula weight, density at 298 K, molar volume and dipole moment for 
the liquids studied here and related liquids. 
 
 
Samples were sealed into cuvettes with a 1 mm optical pathlength and were 
mounted on the cold finger of a nitrogen flow cryostat.  To ensure that the samples 
were kept at constant temperature throughout the course of an experiment, a 
temperature sensor was affixed to the cuvette as near as possible to the point at which 
data were obtained.  The samples were allowed to stabilize for at least 30 minutes at a 
given temperature before data were collected. 
We have described our optical-heterodyne-detected OKE spectrometer in detail in 
previous chapters.5,8  The laser employed was a KMLabs Ti:sapphire oscillator 
operating at a center wavelength of approximately 800 nm.  Typical pulse lengths 
Liquid FW (amu) ? (g/mL) Vm (mL/mol) p (Debye) 
Benzene 78.11 0.874 89.4 0 
Pyridine 79.10 0.978 80.9 2.15 
Benzene-d6 84.16 0.950 88.6 0 
Pyridine-d5 84.14 1.05 80.1 2.15 
TFB 132.08 1.277 103.5 0 
TFP 133.07 1.383 96.2 2.34 
Mesitylene 120.19 0.864 139.1 0 
TMP 121.18 0.917 132.1 1.96 
NFM 282.11 1.514 186.3 0 
HFB 186.05 1.612 115.4 0 
 
                                                                     72  
used were 50 fs, and second-harmonic-generation autocorrelations were measured 
often for purposes of Fourier-transform deconvolution of the data.  Data with a large 
time step (typically 0.67 ps) were taken out to long delays to measure the collective 
orientational decays of the liquids, and data with a short time step (33 fs) were taken 
out to delays of a few picoseconds so that RSDs could be obtained through Fourier-
transform deconvolution.  Decays obtained at equal positive and negative heterodyne 
angles were subtracted from one another to remove the homodyne contribution from 
the data. 
To fit the portion of the decay arising from orientational diffusion, the data were 
integrated to obtain the collective orientational correlation function Ccoll(t), as 
described previously.24  The constant of integration was determined by ensuring that 
the decays were exponential at long times.  The integrated decays were fit to a 
function of the form 
                              ? ? ? ? ? ?? ?ior tAtAB ?? /exp1/exp ????                            (Eq. 4.1) 
where B is an overall amplitude, A is a normalized relative amplitude for the two 
exponentials, t is the delay time, ?or is the collective orientational correlation time, 
and ?i is the ?intermediate? relaxation time, which is shorter than ?r.  Once the 
integrated decays had been fit, the parameters were used to strip a tail onto the short-
step data with the same point spacing as the short-step data set.  This concatenated 
decay was used for the Fourier-transform deconvolution procedure.  To derive the 
RSDs, a rise time of 200 fs was assumed for the diffusive portion of the OKE decays. 
 
 
                                                                     73  
4.3 Results 
 
Shown in Figure 4.1 is a typical integrated OKE decay, in this case for pyridine at 
297 K (black).  A biexponential fit to the data using Eq. 4.1 is shown in red, and the 
residuals for the fit are shown in the lower panel on a linear scale.  All of the fits 
reported here were of similar quality, and the decays all had sufficient dynamic range 
to determine the fit parameters with good precision.  A complete list of fit parameters 
at each temperature studied for each liquid can be found in the Appendix C. 
 
Figure 4.1 Representative integrated OKE decay for pyridine at 297 K (black) and 
biexponential fit (red). The residual is shown on a linear scale in the lower panel. 
 
Exponential ?intermediate? relaxation is a phenomenon that is commonly observed 
in the OKE spectroscopy of simple liquids.7-9,11,13,25-34  The origin of this relaxation is 
still not well understood.  We have shown for a broad range of simple liquids that the 
intermediate relaxation time is proportional to the collective orientational relaxation 
 
                                                                     74  
time.10,11,33,34  The constant of proportionality between these times generally falls 
within a relatively narrow window for most simple liquids.  We have suggested that 
the two times are related because motional narrowing plays a major role in 
determining the dephasing time of coherently excited intermolecular modes.11  As 
shown in Figure 4.2, for the liquid studied here ?i is proportional to ?or.  The constant 
of proportionality is between 3 and 4, as we found previously for other aromatic 
liquids.10 
 
Figure 4.2 Plot of the intermediate relaxation time as a function of the collective 
orientational correlation time for the liquids studied here. 
 
Shown in Figures 4.3 and 4.4 are RSDs for pyridine and pyridine-d5, respectively, 
at temperatures ranging from 240 K to 349 K.  The RSD of pyridine at room 
temperature is in good agreement with that reported previously by McMorrow and 
Lotshaw.35  As is the case for other typical simple liquids, the RSDs broaden to both 
higher and lower frequency as the temperature is decreased.  There is a strong 
 
                                                                     75  
similarity between these RSDs and those of benzene and benzene-d6, which are also 
?rectangular? at low temperature and become increasingly asymmetric at higher 
temperatures.  The similarity between the RSDs of benzene and pyridine has been 
noted previously at room temperature.35 
 
Figure 4.3 Height-normalized RSDs for pyridine at temperatures ranging from 240 to 
349 K. The data have been offset for clarity. 
 
 
 
                                                                     76  
Figure 4.4 Height-normalized RSDs for pyridine-d5 at temperatures ranging from 240 
to 349 K. The data have been offset for clarity. 
 
 
Figure 4.5 Height-normalized RSDs for TFP at temperatures ranging from 230 to 332 
K. The data have been offset for clarity. 
 
In Figure 4.5 we show the RSDs for TFP at temperatures ranging from 230 K to 
332 K.  As is the case for HFB and TFB, these RSDs are ?triangular? in shape and 
change little with temperature other than to develop a slight rounded feature at high 
frequency at lower temperatures.  Shown in Figure 4.6 are the RSDs for TMP at 
temperatures from 243 K to 351 K.  As was the case for mesitylene,10 these RSDs 
have a ?rectangular? shape akin to that of the RSDs of benzene at low temperature 
and become ?triangular? at high temperature.  The RSDs for NFM, shown in Figure 
4.7 at temperatures ranging from 285 K to 348 K, are also roughly triangular and 
 
                                                                     77  
have a similar temperature dependence to that of the RSDs for TFP.  However, the 
RSDs for NFM are considerably narrower than those for TFP. 
 
 
Figure 4.6 Height-normalized RSDs for TMP at temperatures ranging from 243 to 
351 K. The data have been offset for clarity. 
 
Figure 4.7 Height-normalized RSDs for NFM at temperatures ranging from 285 to 
348 K. The data have been offset for clarity. 
 
 
                                                                     78  
4.4 Discussion 
Isotopologues such as pyridine and pyridine-d5 have essentially the same shape and 
the same charge distribution.  As a result, their RSDs would be expected to be quite 
similar, and as can be seen in Figures 4.3 and 4.4 this is indeed the case.  We have 
found previously that the RSDs of benzene and benzene-d6 can be overlapped nearly 
perfectly if the frequency axis for the latter liquid is scaled by 
[Ix(benzene)/Ix(benzene-d6)]?, where Ix is the moment of inertia for tumbling.10  The 
probable implication of this result is that librations dominate the RSDs of these 
liquids, as the librational frequency is expected to scale with Ix-?. 
 
Figure 4.8 Comparison of the height-normalized RSDs for pyridine (black) and 
pyridine-d5 (red) at 297 K. The frequency axis for pyridine-d5 has been scaled by a 
factor of 1.086. 
 
 
                                                                     79  
In analogy to our previous findings for benzene and benzene-d6, in Figure 4.8 we 
show RSDs for pyridine and pyridine-d5 at 297 K.  The frequency axis for pyridine-d5 
has been scaled by a factor of 1.860, which is the square root of the average of the 
ratios of the moments of inertia about the two tumbling axes of these molecules.36  As 
was the case for benzene and benzene-d6, the RSDs for pyridine and pyridine-d5 
correspond quite closely once the frequency axes have been scaled appropriately.  
Thus, given molecules of nearly identical shape and charge distribution, a shift based 
on librational frequencies again does an excellent job of mapping the RSDs of 
different isotopologues onto one another. 
To help understand the relative roles played by shape and electrostatics in OKE 
RSDs, it is instructive to compare spectra of molecules that are isoelectronic but that 
are not isotopologues.  This strategy has been pursued previously with furan, 
thiophene and selenophene, but only at a single temperature.37  Here we compare 
benzene and pyridine, which have shapes that are similar but charge distributions that 
differ considerably.  Due to its symmetry, benzene has no dipole moment.  Pyridine, 
on the other hand, has a significant dipole moment of 2.15 Debye.38  This difference 
in charge distribution would be expected to be reflected in different intermolecular 
structures for these liquids, which in turn may influence the OKE RSDs. 
Experimental data confirm the influence that the different charge distributions have 
on the structures of crystalline and liquid benzene17,20,39 and pyridine.40,41 Even the 
crystal structure of pyridine is42 ?unexpectedly complicated and very different from 
the known ones of geometrically similar molecules.?  By the same token, x-ray and 
 
                                                                     80  
neutron diffraction studies have shown that the intermolecular structure in liquid 
pyridine40 differs markedly from that of benzene and HFB.39  
Despite clear differences in liquid structure, as we have already seen the RSDs of 
benzene and pyridine bear a strong resemblance to one another, and also have similar 
temperature dependences.  In Figure 4.9 we show a direct comparison of the RSDs 
for these two liquids at 267 K and 327 K.  The frequency axis of the benzene RSDs 
has been scaled by a factor of 1.075 at the lower temperature and 1.1 at the higher 
temperature in order to maximize the overlap between the spectra.  Unlike in the case 
of isotopologues, we cannot merely scale the frequency axis of the RSDs based on 
moments of inertia for these liquids.  Due to the dipolar nature of pyridine, it has a 
significantly higher density than benzene and, correspondingly, a molar volume that 
at room temperature is on the order of 10% smaller than that of benzene.  Differences 
in the temperature dependence of the densities of the two liquids probably account for 
the change in the scaling factor for matching up the RSDs of these liquids at low and 
high temperatures.  Issues of scaling notwithstanding, the similarities between the 
RSDs of these liquids at all temperatures are quite striking. 
 
 
                                                                     81  
 
Figure 4.9 Comparison of the height-normalized RSDs for benzene (black) and 
pyridine (red) at two different temperatures. The frequency axis for the benzene 
RSDs has been scaled to make the correspondence between the RSDs as close as 
possible. The data at the two temperatures have been offset for clarity. 
 
It is also instructive to compare the orientational dynamics of these liquids.  For 
simple liquids, the orientational correlation time usually follows the Debye-Stokes-
Einstein (DSE) relation43,44: 
 
                                                       0??? ?? TkV
B
H
or                                              (Eq. 4.2) 
Here, VH is the hydrodynamic volume for reorientation, ? is the viscosity, kB is 
Boltzmann?s constant, and ?0 is the limiting orientational correlation time at infinite 
temperature (or zero viscosity).  Although intended to describe the reorientation of 
large solutes, this relation often works well for neat liquids as well.  The 
hydrodynamic volume term is related to the volume swept out by a molecule as it 
 
                                                                     82  
reorients.  Isotopologues generally fall on a single line on a DSE plot, and as can be 
seen in Figure 10 this is indeed the case of pyridine (in black) and pyridine-d5 (in red).  
The solid line in this plot is a linear least-squares fit to the combined data for the 
isotopologues. 
 
Figure 4.10 DSE plot for pyridine (black) and pyridine-d5 (red), along with a fit to 
the data (solid line). Data for benzene (green) and benzened6 (blue) have also been 
included, but were not used in the fit. 
 
Since benzene and pyridine are isoelectronic, we can also investigate whether 
they have matching DSE behavior.  In Figure 4.10 we have also plotted the DSE data 
for benzene (green) and benzene-d6 (blue).  These data fall nearly on the plot for 
pyridine and pyridine-d5, but the benzene data appear to have a slightly higher slope 
than do the pyridine data.  The implication may be that pyridine has a slightly smaller 
hydrodynamic volume than does benzene. 
 
                                                                     83  
OKE spectroscopy measures a collective orientational correlation time, but the 
DSE relation is intended to describe the single-molecule orientational correlation time.  
The relationship between these times is given by 
                                                      smorcollor jg ,
2
2
, ?? ?                                            (Eq. 4.3) 
where g2 is the static orientational pair correlation parameter and j2 is the dynamic 
orientational pair correlation parameter.44  It is generally believed that j2 is near unity 
for simple liquids.44  On the other hand, g2 can vary considerably, and gives direct 
information on the degree of parallel ordering in a liquid. 
Ito and Kato45 (IK) have performed carbon-13 NMR and depolarized Rayleigh 
scattering experiments on pyridine.  NMR is sensitive to the single-molecule 
orientational correlation time, whereas depolarized Rayleigh scattering is a 
frequency-domain equivalent of OKE spectroscopy, and so measures the collective 
orientational correlation time.46  At temperatures of both 0 ?C and 20 ?C, they found 
that times determined by NMR and Rayleigh scattering were virtually identical, 
implying that g2 is close to unity in pyridine near room temperature.  The collective 
orientational correlation times determined by IK are in good agreement with those 
presented here. 
Liu, Li and Jonas47 (LLJ) performed deuterium NMR studies of reorientation in 
pyridine-d5 over a larger range of temperatures than IK.  The single-molecule 
orientational correlation times derived by LLJ are significantly smaller than the 
collective orientational times determined here for pyridine-d5.  It is unlikely that g2 
differs appreciably for pyridine and pyridine-d5, particularly as both liquids fall on the 
 
                                                                     84  
same line in a DSE plot.  Thus, it is unclear whether to use the results of IK or LLJ in 
calculating g2/j2 for these liquids.   
 
Figure 4.11 Temperature dependence of g2/j2 for pyridine. The data in squares are 
calculated directly from the results of Liu, Li, and Jonas for the single-molecule 
orientational correlation time, whereas the data in circles have been scaled to match 
the single-molecule orientational times measured by Itoh and Kato. 
 
Since the data of LLJ cover a broader range of temperatures than those of IK, we 
will use them as a guideline.  If we assume that the values calculated by LLJ are 
accurate, we find that g2/j2 is near 2.0 at low temperature and decreases to near 1.6 at 
high temperature (squares in Figure 4.11).  If we assume that there is a systematic 
error in the numbers of LLJ and that their numbers should match those of IK at high 
temperature, then we find that g2/j2 is approximately 1.3 at low temperature and 
decreases to unity at high temperature (circles in Figure 4.11).  These two models 
imply significantly different degrees of parallel ordering for pyridine, and should 
probably be viewed as the two extreme possible cases. Neutron and x-ray diffraction 
 
                                                                     85  
data appear to point towards a significant degree of parallel ordering in pyridine, 
which tends to favor the model based directly on the data of LLJ. 
Whichever model of g2/j2 is correct, it is clear that this quantity decreases with 
increasing temperature for pyridine.  In contrast, g2/j2 is essentially independent of 
temperature for benzene.  As we have seen, the OKE RSDs of pyridine and benzene 
bear strong resemblance over a broad temperature range.  These results suggest that 
intermolecular structure does not have a large impact in determining the shape of the 
RSD, whereas molecular shape does play a strong role. 
 
Figure 4.12 Comparison of the height-normalized RSDs for TFP (black) and TFB 
(red) at two different temperatures. The data at the two temperatures have been offset 
for clarity. 
 
We next turn to a comparison of the OKE spectra of TFB and TFP.  In Figure 
4.12 we compare RSDs for these two liquids near 280 K and near 332 K.  In this case 
 
                                                                     86  
we have used no scaling of the frequency axis of the data, yet the RSDs are in strong 
agreement over the entire range of temperatures.  This agreement arises despite the 
fact that the significant dipole moment of TFP48 (2.34 Debye) causes TFP to have a 
significantly higher density (1.383 g/mL) than does TFB (1.277 g/mL).  These results 
again suggest a strong role for shape in determining the appearance of the OKE RSD. 
 
Figure 4.13 Comparison of the height-normalized RSDs for TMP (black) and 
mesitylene (red) at two different temperatures. The data at the two temperatures have 
been offset for clarity. 
 
In Figure 4.13 we compare the RSDs for TMP and mesitylene near 243 K and 349 
K.  Once again there is a significant similarity between the RSDs for the two liquids, 
although the correspondence is not as strong as for some of the other liquids 
discussed here.  TMP has a dipole moment of 1.96 D,49 which leads to it having a 
somewhat smaller molar volume than does mesitylene.  Nevertheless, as was the case 
for TFB and TFP, we have not scaled the frequency axis for the TMP and mesitylene 
RSDs.  
 
                                                                     87  
While the shapes of the RSDs of mesitylene and TMP change considerably in 
going from low temperature to high temperature, this is not the case for NFM.  The 
RSDs for NFM do show evidence of a high-frequency feature that builds in at low 
temperature, but this feature is not nearly as prominent as in the case of mesitylene.  
The RSDs of NFM are thus more reminiscent of those of HFB, TFB and TFP than 
they are of the RSDs of mesitylene. 
We now are ready to consider the factors that work to determine the shapes of the 
OKE RSDs for aromatic liquids.  We have suggested previously that the RSDs of 
aromatic liquids are reflective of their local intermolecular structure.10  However, the 
results presented here show that liquids with considerably different local structures 
but comparable molecular shapes have OKE RSDs that are highly similar.  In fact, 
with appropriate scaling of the frequency axes of the RSDs, these spectra can be 
virtually superimposed over a broad range of temperatures. 
Elola and Ladanyi23 simulated the room-temperature OKE spectra of benzene, 
HFB and TFB, and found good agreement with previous experimental results.  Based 
on their simulations, they suggested that the strengths of the pairwise potentials in 
these liquids play a significant role in determining the shapes of the RSDs.  However, 
the results discussed here suggest that the strength of the attraction between 
neighboring molecules is not the major factor driving the shape of the RSD.  For 
instance, benzene and pyridine have intermolecular interactions that differ 
considerably from one another, as is evidenced by the notably smaller molar volume 
of pyridine.  These differences in intermolecular interactions also lead to considerable 
differences in the intermolecular structures of these liquids.  However, the OKE 
 
                                                                     88  
RSDs for these two liquids are highly similar from low temperature up to high 
temperature. 
Our results support the proposal of Ryu and Stratt14 that molecular shape is a 
primary determinant of the shape of the OKE RSDs of non-associated liquids.  We 
have recently found similar results for a series of alkanes and ethers as well.13  These 
results suggest that OKE spectroscopy may not be a sensitive probe of intermolecular 
structure in liquids. 
Still, a number of issues about the shapes of OKE RSDs remain to be answered.  
For instance, the shapes of benzene and pyridine are not vastly different from those of 
HFB, TFB and TFP, and yet the RSDs of the first two liquids differ markedly from 
those of the other three.  Furthermore, the RSDs of benzene and pyridine have a 
relatively strong temperature dependence, whereas those of the other three liquids do 
not.10  One possible explanation for this behavior is that the distribution of the 
polarizability in these molecules also plays a distinct role in shaping the RSDs.  In 
addition, it is possible that only RSDs with significant content at higher frequencies 
are susceptible to shape changes with increasing temperature, perhaps due to motional 
narrowing.  The RSDs of mesitylene and TMP also present an interesting puzzle, in 
that they resemble those of benzene at low temperature and those of HFB, TFB and 
TFP at high temperature.  All of these issues might be examined profitably with 
molecular dynamics simulations. 
 
 
                                                                     89  
4.5 Conclusion 
We have presented a detailed, temperature-dependent OKE study of a number of 
aromatic liquids that complements a study of similar liquids that we have reported 
previously.  Based on comparisons among the RSDs for these liquids, we conclude 
that molecular shape plays a major role in determining the shape of the OKE RSD in 
non-associated liquids.  The effects of local structure and electrostatic forces on the 
spectra appear to be minor, although the manner in which the molecular polarizability 
is distributed may play some role in shaping the RSDs. 
 
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                                                                     93  
Chapter 5:  Searching for Voids in Liquids with Optical Kerr 
Effect Spectroscopy 
 
5.1 Introduction 
A simple liquid is generally viewed as being a dense medium in which there are no 
large void spaces. While there exist numerous examples of nonideal mixtures that 
have a volume that is smaller than that of the component liquids,1 this phenomenon 
can generally be described as arising from a loss of relatively evenly distributed free 
volume due to favorable interactions between the two components. However, for 
some liquids there are indications of the existence of voids of substantial volume. For 
instance, recent studies have offered strong evidence for the existence of such voids 
in room-temperature tetrahydrofuran (THF).2,3 Large voids are believed to be 
responsible for the unusual spectroscopy and photophysics of solvated electrons in 
THF.2,4,5 Neutron diffraction studies3 and simulations2,3 indicate the presence of voids 
with diameters of 2.5 ? or more in this liquid. 
The presence of large voids in a liquid might be expected to be manifested in an 
obvious manner, but the fact that these voids went undetected in THF until recently 
underscores the subtlety of the signatures of such empty spaces. Indeed, at room 
temperature the volume per molecule in THF is smaller than that for closely related 
liquids that are not known to exhibit significant voids, such as cyclopentane, diethyl 
ether, and n-pentane.6 The coefficient of thermal expansion for THF at room 
 
                                                                     94  
temperature is slightly smaller than those for the other three related liquids, as would 
be expected from the smaller molar volume of THF.6 The void spaces in THF must 
therefore arise from an uneven partitioning of the modest free volume in this liquid. 
In optical Kerr effect (OKE) spectroscopy, 7?10 a linearly polarized, nonresonant 
pump pulse is used to put a torque on the molecules of a liquid and to drive 
intramolecular and intermolecular Raman-active modes impulsively. Depolarization 
of a probe pulse polarized at 45? is then used to measure the time dependence of 
collective orientational diffusion and depolarized intramolecular and intermolecular 
Raman modes. By transforming the data into the frequency domain, 11 the depolarized, 
Bose-Einstein-corrected, low-frequency Raman spectrum can be obtained. 
The presence of sizable voids might be expected to manifest itself in OKE spectra 
in at least two different ways. First, the frequencies of intermolecular modes are 
sensitive to the distribution of free volume in a liquid. If the free volume is 
concentrated in substantial voids that are bordered by a only a fraction of the 
molecules in the liquid, then the remaining molecules have less free volume 
surrounding them than those in a more typical liquid. These tightly packed molecules 
would be expected to exhibit higher-frequency intermolecular modes. Second, the 
time scale for diffusive reorientation is also sensitive to the free volume surrounding a 
molecule and so might be expected to reveal the signature of unequally distributed 
free volume. In addition, we might expect that both of these aspects of the OKE data 
might exhibit an unusual temperature dependence in a liquid with substantial voids. 
To test whether OKE spectroscopy can reveal the presence of significant voids in a 
liquid, here we present a detailed, temperature-dependent study of eight liquids: furan, 
 
                                                                     95  
THF, diethyl ether, n-pentane, cyclopentane, cyclohexane, tetrahydropyran, and 
hexamethylphosphoramide (HMPA). 
5.2 Experimental Section 
All liquids (Table 5.1) were purchased in the purest form available from Aldrich 
and were used without any further purification. The liquids were sealed into 1-mm 
path length glass cuvettes and attached to the sample mount of a nitrogen-flow 
cryostat. To ensure an accurate temperature measurement, a temperature probe was 
placed directly against the cell near the position at which data were collected. After 
being changed, the temperature was allowed to stabilize for at least 30 min before 
data collection commenced. 
 
Table 5.1: Formula Weight, Density at 298 K, and Viscosity at 298 K for the Liquids 
Studied 
Liquid FW (amu) ? (g/mL) ? (cP) 
furan 68.07 0.921 0.361 
THF 72.11 0.902 0.472 
cyclopentane 70.14 0.741 0.419 
diethyl ether 74.12 0.708 0.235 
pentane 72.15 0.621 0.229 
tetrahydropyran 86.13 0.879 0.808 
cyclohexane 84.16 0.774 0.880 
HMPA 179.20 0.879 3.147 
 
                                                                     96  
 
Our optical-heterodyne-detected OKE experimental apparatus has been described 
in detail previously.12, 13 For the data reported here, transform-limited Ti:sapphire 
laser pulses with a duration of approximately 50 fs and a center wavelength of 800 
nm were employed. Data collected at equivalent positive and negative heterodyne 
angles were subtracted from each other to obtain the pure heterodyned contribution to 
the signal. Typically, 10 decays were collected at each angle for a liquid at a given 
temperature. Second-harmonic-generation autocorrelation data were used to perform 
Fourier-transform deconvolution of the OKE data in order to derive the Bose-
Einstein-corrected, low frequency Raman spectra.11 
For purposes of determining the orientational relaxation and ?intermediate? 
relaxation14 times, the data were integrated to determine the collective orientational 
correlation function ( )collC ? ,15 where ? is the experimental delay time. Fits were made 
to a function of the form 
                                1 2[ exp( / ) (1 )exp( / )]B A A? ? ? ?? ? ? ?                                 (Eq. 5.1) 
where the amplitude A is less than unity, B is a scaling factor, 1?  is the orientational 
correlation time, and 2?  is the intermediate relaxation time. Based on these fits, the 
contribution of orientational diffusion was removed from the unintegrated data, 
assuming a rise time of 200 fs, in order to calculate the depolarized reduced spectral 
density (RSD) corresponding to each low-frequency Raman spectrum. 
 
 
                                                                     97  
5.3 Results 
Most of the liquids studied here are not highly polarizable and therefore yield 
relatively weak OKE signals. Representative integrated data for THF at 285 K are 
shown in Figure 5.1 (black line). The long-time portion of the decay has been fit to eq. 
5.1. 
Values of the decay times and their corresponding amplitudes are given in the 
Appendix D. The fit to the data is also shown in Figure 5.1 (red line), and the residual 
can be seen to be quite smooth. 
 
 
Figure 5.1 Logarithm of the collective orientational correlation function for THF at 
285 K (black line, upper panel) as well as a biexponential fit to the data (red line). 
The residuals, shown in the lower panel on a linear scale, demonstrate the high 
quality of the fit to this representative data set. 
 
 
                                                                     98  
OKE spectral densities usually have a relatively sharp feature below 10 cm-1that is 
largely reorientational in origin; as such, this feature is generally not present in the 
reduced spectral density. However, the reorientational contribution to the OKE signal 
for the nonconjugated liquids studied here is weak enough that in many cases the 
spectral density does not have a clear low-frequency feature. As an example, we show 
the full spectral density and the reduced spectral density for THF at 286 K in Figure 
5.2. 
 
Figure 5.2 Representative Bose-Einstein-corrected spectral density (black) and 
reduced spectral density (red) for THF at 286 K. 
 
For most simple liquids that have been studied to date with OKE spectroscopy, the 
behavior of the RSD with temperature follows a simple pattern.12,16,17 With 
decreasing temperature, the RSD generally broadens, with the high-frequency portion 
moving to higher frequencies and the low-frequency portion moving to lower 
frequencies. The shift of the high-frequency portion can be attributed to the increase 
in density with decreasing temperature. The shift of the lower frequency portion is 
less well understood, but is related to the fact that the intermediate response time 
 
                                                                     99  
generally tracks the orientational diffusion time in simple liquids.14 The only 
exception to this behavior that has been reported previously is SO2, for which the 
entire RSD shifts to higher frequency with decreasing temperature.18 
Shown in Figure 5.3 are RSDs for furan at temperatures ranging from 245 to 298 K; 
these and all other RSDs reported here have been scaled to have the same peak 
intensity. The room temperature RSD is consistent with a previously reported OKE 
spectral density.19 This liquid exhibits a typical temperature dependence, with the 
RSD becoming considerably broader at low temperature than it is at high temperature. 
In Figure 5.4 we show RSDs for THF at temperatures ranging from 235 to 298 K. It 
is clear from these data that the RSDs for THF differ markedly from those for furan. 
The THF RSDs are substantially narrower than those of furan, and have a first 
moment at a considerably lower frequency. Furthermore, although the THF RSDs do 
become slightly broader at lower temperatures, they do so in an unusual fashion. The 
low-frequency portion of the THF RSDs exhibits a small shift to lower frequency 
with decreasing temperature (see inset of Figure 5.4), whereas the shape of the high-
frequency portion is essentially constant with temperature. 
 
 
                                                                     100  
 
 
Figure 5.3 Height-normalized RSDs for furan at various temperatures. The plots have 
been offset vertically for clarity. 
 
 
Figure 5.4 Height-normalized RSDs for THF at various temperatures. The inset gives 
a closer view of the lowest-frequency portions of the spectral densities. The plots 
have been offset vertically for clarity. 
 
 
                                                                     101  
What factors account for the differences in the RSDs of furan and THF? One 
common proposal for bimodal OKE RSDs is that the lower-frequency feature arises 
from collision-induced scattering whereas the higher-frequency feature is librational 
in origin.19?25 Furan?s refractive index (1.423) is only modestly larger than that of 
THF (1.407),6 so the polarizabilities of these liquids do not differ tremendously. As a 
result, collision-induced scattering may be of relatively similar importance for both 
liquids, yet the RSDs of THF do not appear bimodal. Indeed, given the modest 
refractive indices of these liquids, collision-induced scattering might not be expected 
to be particularly strong for either liquid. However, the relative importance of 
collision-induced scattering also depends on the magnitude of the polarizability 
anisotropy of a liquid, and it remains possible that differences in the polarizability 
anisotropy account for some of the differences between the RSDs of these liquids as 
well. 
The molar volume of THF is on the order of 10% larger than that of furan, a 
difference that can decrease the librational frequencies and may therefore be partially 
responsible for the lower average frequency of the RSDs of THF. However, the 
differences in width and mean frequency of the RSDs of these liquids are large 
enough that they are unlikely to arise from density effects alone. Furan and THF also 
have different geometries and therefore different moments of inertia. However, the 
differences in moments of inertia are only large enough to account for a change in 
librational frequency on the order of 10%. 
The differences between the furan and THF RSDs may also be related to the 
conjugated nature of furan. It is thus useful to compare the THF RSDs to those of 
 
                                                                     102  
other related, nonconjugated liquids as well. We begin by considering temperature 
dependence of the RSDs for cyclopentane, which has a shape that is similar to that of 
THF. Cyclopentane is nondipolar, and therefore has a significantly lower density than 
THF. At room temperature, for instance, the molar volume of cyclopentane is 
approximately 15% greater than that of THF. The refractive index of cyclopentane 
(1.405)6 is virtually identical to that of THF. RSDs for cyclopentane at 297 K and at 
249 K are shown in Figure 5.5. The RSD at 249 K shows a subtle increase at lower 
frequencies as compared to the RSD at 297 K, but overall these spectra are 
remarkably similar to one another.  In Figure 5.6 we compare the RSD of THF at 298 
K (black) with that of cyclopentane at 297 K (red). The spectral densities peak at 
nearly the same frequency, but the RSD for cyclopentane is somewhat narrower than 
that of THF. The narrower RSD of cyclopentane at room temperature may result from 
its greater molar volume. 
 
 
 
 
                                                                     103  
 
 
Figure 5.5 Height-normalized RSDs for cyclopentane at various temperatures. The 
inset gives a closer view of the lowest-frequency portions of the spectral densities. 
The plots have been offset vertically for clarity. 
 
 
Figure 5.6 Comparison of the room-temperature RSDs for THF (black) and 
cyclopentane (red). 
 
 
                                                                     104  
Ryu and Stratt have suggested that liquids composed of molecules with similar 
shapes may have similar OKE spectra, 26 and our data support this general idea for 
these two liquids. While the basic shapes of the RSDs are similar, the difference in 
widths of the RSDs of THF and cyclopentane does become more substantial at lower 
temperatures. The molar volume of THF increases by nearly 5% in going from 297 to 
249 K, while that of cyclopentane increases by roughly 6%. Thus, the ratio of molar 
volumes of the two liquids remains nearly the same over this temperature range. The 
increasing differences in the RSDs of these liquids at lower temperatures may 
therefore be a signature of different distributions of free volume. The voids in THF 
appear to be associated with (but have surfaces that tend not to include) oxygen atoms, 
3 and therefore may not be present in cyclopentane. 
 
 
Figure 5.7 Height-normalized RSDs for diethyl ether at various temperatures. The 
inset gives a closer view of the lowest-frequency portions of the spectral densities. 
The plots have been offset vertically for clarity. 
 
                                                                     105  
 
We next consider the temperature dependence of the RSD of diethyl ether, which is 
chemically similar to THF but is a linear molecule. RSDs for this liquid at 
temperatures ranging from 250 to 298 K are shown in Figure 5.7. At 298 K the 
diethyl ether RSD resembles that of THF, but peaks at a substantially lower frequency. 
This shift in peak frequency is consistent with the larger molar volume of diethyl 
ether, which is nearly 30% greater than that of THF at room temperature. However, it 
is clear from Figure 5.7 that the diethyl ether RSDs exhibit a more conventional 
temperature dependence, broadening to both higher and lower frequency with 
decreasing temperature.  
Given the flexibility of diethyl ether, this liquid might not be expected to exhibit 
sizable voids. Neutron diffraction or other studies are needed to confirm this 
supposition. However, it is well-known that the structures of simple alkane liquids do 
not generally feature large voids.27?29 We therefore also consider the temperature 
dependence of the RSD of n-pentane, which has strong structural similarity to diethyl 
ether on a molecular level. In the liquid, n-pentane tends to adopt an extended 
conformation, although not to the same extent as longer-chain alkanes.29 In analogy, 
simulations suggest that more than 70% of diethyl ether molecules adopt an all-trans 
configuration in the liquid, with the majority of the remaining molecules featuring a 
single gauche defect. In Figure 5.8 we show RSDs for n-pentane at temperatures that 
range from 214 K to room temperature. Due to the weak polarizability of n-pentane, 
these RSDs are noisier than those of diethyl ether. Nevertheless, the RSDs for n-
pentane and diethyl ether bear strong similarity, as is underscored in Figure 5.9. 
 
                                                                     106  
Although the RSDs for n-pentane do not broaden quite as much to lower frequency 
with decreasing temperature as do those of diethyl ether, the RSDs do remain quite 
similar to one another over the temperature range studied here, in contrast to the 
RSDs for THF and cyclopentane. The similar temperature dependence of the RSDs 
for diethyl ether and n-pentane might suggest that the former liquid does not exhibit 
large voids. However, as opposed to n-pentatne, diethyl ether has a significant, 
localized dipole moment, and so similarities in molecular structure need not imply 
equally strong similarities in liquid structure. 
 
 
Figure 5.8 Height-normalized RSDs for n-pentane at various temperatures. The inset 
gives a closer view of the lowest-frequency portions of the spectral densities. The 
plots have been offset vertically for clarity. 
 
                                                                     107  
 
 
Figure 5.9 Comparison of the room-temperature RSDs for n-pentane (black) and 
diethyl ether (red). 
 
It is possible that part of the reason that THF exhibits large voids is its near 5-fold 
symmetry, which prevents it from filling space efficiently. Furan and cylcopentane 
have similar shapes, so the near 5-fold symmetry of THF cannot alone be responsible 
for it unusual liquid structure. Nevertheless, it is instructive to compare THF to 
similar cyclic molecules with a different number of atoms. With this in mind, in 
Figure 5.10 we present RSDs for tetrahydropyran, a six-membered ring with a single 
oxygen atom, at temperatures of 242 and 297 K. This liquid exhibits a relatively 
conventional temperature dependence, with its RSD broadening to higher and lower 
frequencies with decreasing temperature. At room temperature, the RSD for 
tetrahydropyran is broader than that of THF and peaks at a somewhat lower 
frequency. One possible source of these differences might be that the free volume in 
tetrahydropyran is more uniformly distributed than that in THF. Again, neutron 
 
                                                                     108  
diffraction studies will be required to investigate this issue fully. 
 
Figure 5.10 Height-normalized RSDs for tetrahydropyran at 242 and 297 K. The inset 
gives a closer view of the lowest-frequency portions of the spectral densities. The 
plots have been offset vertically for clarity. 
 
Figure 5.11 Height-normalized RSDs for cyclohexane at 297 and 325 K. The inset 
gives a closer view of the lowest-frequency portions of the spectral densities. The 
plots have been offset vertically for clarity. 
 
                                                                     109  
 
 
Figure 5.12 Comparison of the room-temperature RSDs for tetrahydropyran (black) 
and cyclohexane (red). 
 
In Figure 5.11 we show RSDs for cyclohexane at 297 and 325 K. As was the case 
with cyclopentane, the cyclohexane RSD changes only modestly with temperature, 
suggesting that this may be common behavior for saturated cyclic hydrocarbons. In 
analogy with THF and cyclopentane, Figure 5.12 shows that the RSDs of 
tetrahydropyran and cyclohexane are similar at room temperature. 
 
                                                                     110  
 
 
Figure 5.13 Height-normalized RSDs for hexamethylphosphoramide at 285 and 337 
K. The inset gives a closer view of the lowest-frequency portions of the spectral 
densities. The plots have been offset vertically for clarity. 
 
The final liquid that we consider is HMPA, which has also been proposed to 
contain voids of significant dimension.2 RSDs for this liquid at 285 and 337 K are 
shown in Figure 5.13. The RSDs of HMPA exhibit considerable structure, 
presumably due to low-frequency hindered internal rotational modes. The peaks in 
the spectrum do appear to broaden slightly and shift to higher frequency with 
decreasing temperature, with some broadening to lower frequency as well. Thus, we 
believe that the temperature- dependent behavior of the intermolecular portion of the 
RSD of this liquid is somewhat different from that of THF; however, as the shape of 
the high-frequency intramolecular mode depends significantly upon temperature, it is 
difficult to make a clear determination of how the shape of the low frequency, 
 
                                                                     111  
intermolecular portion of the spectrum changes with temperature. 
Void spaces in THF, if they exist, should manifest themselves in observables 
beyond the OKE RSD. For instance, according to the Debye-Stokes-Einstein (DSE) 
equation,30, 31 the orientational correlation time ?or of a solute molecule in a simple 
liquid should satisfy 
                                                   0Hor
B
V
k T
?? ?? ?                                                   (Eq. 5.2) 
where VH is the hydrodynamic volume for reorientation, ?  is the viscosity, T is the 
temperature, kB is Boltzmann?s constant, and ?0 is a constant that depends on the 
solute and the solvent but whose physical meaning is a subject of continuing debate. 
The hydrodynamic volume should be highly sensitive to the distribution of free 
volume in a liquid, and we might therefore expect that the temperature dependence of 
the orientational correlation time will be sensitive to the presence of voids in a liquid. 
Although it is not intended to apply to neat liquids, the DSE equation generally 
does a good job of describing the temperature and viscosity dependences of the 
reorientation times in these systems as well.14 In addition, the DSE equation applies 
to the single-molecule orientational correlation time, whereas OKE spectroscopy 
measures the collective orientational correlation time, ?coll.32 These two times are 
related via31  
                                           2
2
corr sm
g
j? ??                                                         (Eq. 5.3) 
where g2 is the static pair orientational correlation parameter and j2 is the dynamic 
pair orientational correlation parameter. In general, j2 is believed to take on a value 
near unity for simple liquids, whereas g2 varies depending on the degree of parallel 
 
                                                                     112  
ordering of the liquid molecules.31 For liquids with no net parallel ordering, g2 has a 
value of unity, while in the presence of such ordering it takes on a larger value. 
We investigated the DSE behavior of all of the liquids studied here. Temperature-
dependent viscosity data for each liquid were obtained from the literature.6, 33?40 The 
DSE plots for the OKE relaxation times of the saturated cyclic liquids and of HMPA 
are shown in Figure 5.14. 
 
Figure 5.14 DSE plots for THF, cyclopentane, tetrahydropyran, cyclohexane, and 
HMPA. The solid lines are linear least-squares fits to the data. The dashed line is a 
linear least-squared fit to the THF data that has been constrained to pass through the 
origin. 
 
The slopes of the plots for tetrahydropyran and cyclohexane are close to one 
another. This similarity indicates that these liquids have similar products of the 
hydrodynamic volumes for reorientation and g2, as might be expected based on their 
similar structures. At any given value of ?/T, the overall magnitude of the ?coll for 
 
                                                                     113  
tetrahydropyran is on the order of 0.8 ps greater than that of cyclohexane, a difference 
that is reflected in different values of ?0 for these two liquids. The DSE plot for 
cyclopentane has a smaller slope than those for tetrahydropyran and cyclohexane, 
which is in line with the smaller size, and presumably smaller hydrodynamic volume, 
of cyclopentane. The limiting orientational correlation time, ?0, for cyclopentane is 
virtually identical to that of the chemically similar cyclohexane. The DSE plot for 
HMPA has a slope that is similar to those of tetrahydropyran and cyclohexane, and 
has a limiting orientational correlation time that is considerably greater than that for 
any of the other liquids. The DSE plot for THF differs substantially from those for the 
other saturated cyclic liquids. First, the limiting value of the orientational correlation 
time ?0 for this plot is negative (although a fit that is constrained to pass through the 
origin also does a good job of fitting these data; see the dashed line in Figure 5.14). 
More importantly, the slope of the DSE plot for this liquid is considerably steeper 
than those for the other three liquids. The steeper slope of the DSE plot for THF is too 
large to be accounted for by a large value g2 for this liquid, and the structure derived 
from neutron diffraction studies suggests that g2 should be near unity.3 The slope 
must therefore be indicative of an increase in the hydrodynamic volume for 
reorientation. Such an increase may arise from a change in the boundary conditions 
for reorientation from slip in the other three liquids to stick in THF. 
It is tempting to conclude that the reason that the DSE plot for THF differs greatly 
from those for the other liquids is that a transition in boundary conditions for 
reorientation results from an uneven distribution of free volume that causes the 
molecules in THF to have to reorient in a collective manner. However, it is also 
 
                                                                     114  
important to note that the DSE plot for OKE reorientation times for THF is not 
atypical of similar plots obtained for a wide range of simple molecular liquids. For 
example, DSE plots derived from OKE data for acetonitrile, benzene, carbon 
disulfide, chloroform and methyl iodide14 all have small ?0 values and slopes that are 
similar to that of the THF DSE data presented here. To underscore this point, in 
Figure 5.15 we compare the DSE plot of the OKE relaxation times for THF with 
those of furan, diethyl ether, and n-pentane. The slope of the DSE plot for furan is 
similar to that for THF, although furan has a slightly higher value of ?0. The DSE 
plots for diethyl ether and n-pentane are nearly superimposable. These plots have a 
considerably higher slope that that for THF, presumably because diethyl ether41 and 
n-pentane29 adopt relatively straight conformations in the liquid phase and therefore 
have a larger hydrodynamic volume for reorientation, and potentially a larger value of 
g2. As is the case with THF, the values of ?0 for the DSE plots of diethyl ether and n-
pentane are near zero. 
 
Figure 5.15 DSE plots for THF, furan, diethyl ether, and n-pentane. The solid lines 
are linear least-squares fits to the data. 
 
                                                                     115  
 
 
5.4 Discussion 
The RSDs for THF do not differ radically from those of other liquids studied here. 
Furan?s RSDs display a ?conventional? temperature dependence, broadening 
significantly to higher and lower frequencies with decreasing temperature. The 
behavior of the high-frequency portion of the furan RSD can be rationalized in terms 
of the density increase that goes along with decreasing temperature. This 
densification leads to a decrease in free volume, increasing the frequencies of 
librations and hindered translational motions. The low-frequency behavior is another 
manifestation of the temperature-dependent behavior of the intermediate response. As 
the temperature is decreased, the frequency at which motional narrowing dominates 
the spectrum becomes smaller, thereby making the RSD become more intense at 
lower frequencies. The RSDs of the linear molecules diethyl ether and n-pentane do 
show notable broadening at lower temperatures. For the saturated, cyclic liquids, the 
RSDs exhibit a considerably more subtle temperature dependence, and the behavior 
of the THF RSDs does not stand out among them. 
To gain further insight into these data, it is useful to consider what is known about 
the structure of liquid THF based on neutron diffraction studies coupled with 
empirical potential structure refinement.3 THF molecules are twisted but essentially 
planar in the liquid. There is a significant propensity for pairs of neighboring 
molecules to adopt a T-like configuration in the liquid, which leads to the expectation 
that g2 should be near unity. The positions of the oxygen atoms presumably play 
 
                                                                     116  
some role in determining the preferred relative orientations of pairs of molecules in T 
configurations. The surfaces of the largest voids (of 3 ? diameter) in the liquid are 
composed virtually entirely of hydrogen atoms from all four of the methylene groups 
and of the carbon atoms bonded to the oxygen atoms. In somewhat smaller voids with 
a 2.5 ? diameter, the surfaces do have a small representation from the oxygen atoms 
and from the carbon atoms that are opposite the oxygen atoms.3 Thus, the void 
surfaces are enriched in portions of the molecules with a partial positive charge, to the 
relative exclusion of both the oxygen atoms, which have a partial negative charge, 
and the near neutral carbon atoms that are not bonded to the oxygen atoms. 
Given that the RSDs for the saturated, cyclic molecules are relatively insensitive to 
temperature, it is interesting to consider whether it is possible that cyclopentane, 
tetrahydropyran and cyclohexane also exhibit substantial voids, perhaps due to their 
relative lack of conformational freedom as compared to linear molecules. This 
question must ultimately be addressed by neutron diffraction and/or simulation 
studies, but we can gain some useful insights based on what is known currently. 
The extremely low probability of finding oxygen atoms in the voids of THF 
suggests that these atoms do play a role in the formation of the voids. Thus, it is not 
unreasonable to imagine that tetrahydropyran should exhibit similar voids. It is 
important to keep in mind, however, that tetrahydropyran is considerably more 
flexible than THF. In addition, since THF is nearly planar, its roughly 5-fold 
symmetry may contribute to making it difficult to pack these molecules efficiently. 
Such constraints do not exist to the same extent for tetrahydropyran. 
Although the oxygen atoms in liquid THF clearly play a role in the formation of 
 
                                                                     117  
voids, we should not entirely discount the possibility that cyclopentane also contains 
such voids. It is well known that the structures of simple liquids can be described as 
being determined by effective repulsive interactions.42 While the effective repulsive 
shapes of THF and cyclopentane must certainly differ, the similarities may still be 
great enough to lead to voids in cyclopentane as well. 
Another possibility is that RSDs for liquids, and the temperature dependences of 
these RSDs, are relatively insensitive to the presence of voids. While voids make up a 
notable portion of the free volume of the liquid, they do not account for a sizable 
fraction of the total volume of the liquid. As a result, such voids may not have a 
strong influence on the low-frequency Raman spectra of these liquids. Within this 
picture, the similarity in the RSDs of the liquids may arise from the similar molecular 
shapes, and the relative insensitivity of the RSDs to temperature may be a 
manifestation of the low degree of conformational freedom of cyclic molecules. 
Other than furan, the cyclic liquids studied here do not exhibit significant 
broadening of their RSDs as the temperature is decreased. Such broadening has been 
a near-universal feature in previous OKE studies of simple liquids. The source of the 
different temperature behavior of the RSDs of these saturated, cyclic liquids merits 
further investigation. Although based on their refractive indices, furan and THF have 
similar polarizabilities, it is still likely that these liquids differ significantly in their 
polarizability anisotropies. It is therefore possible that the weak temperature 
dependence of the RSDs of THF and other cyclic liquids studied here is a sign of a 
relatively small polarizability anisotropy, although the fact that a significant 
reorientational decay is observed in all of the liquids studied here suggests that the 
 
                                                                     118  
polarizability anisotropy is not negligible in any of these substances. Linear 
molecules such as diethyl ether and n-pentane would be expected to adopt extended 
conformations and therefore have larger polarizability anisotropies that the cyclic 
liquids, and indeed the linear molecules do show a greater temperature dependence in 
their RSDs than do the saturated, cyclic molecules. 
We should also note that the intermolecular modes and orientational diffusion to 
which OKE spectroscopy is sensitive occur on essentially the same time scale as does 
rearrangement of voids.2 Indeed, these motions are probably involved intimately in 
this rearrangement. This similarity in time scales may be responsible for the lack of a 
clear signature of voids in the OKE spectra. A technique that is sensitive to structure 
on a shorter time scale may have greater sensitivity to the presence of voids. 
As is the case with the RSDs, the orientational behavior of THF does not provide a 
clear signature of void spaces. We have found that the DSE plot for THF differs 
substantially from those for cyclopentane, tetrahydropyran, cyclohexane and HMPA. 
However, the behavior of the DSE plot of THF is rather typical of those for 
nonassociated, small-molecule liquids, including furan, diethyl ether, and n-pentane. 
We should note that the orientational dynamics of the liquids studied here have been 
described by single exponentials, whereas in theory up to five exponentials may be 
needed.32 However, for the vast majority of simple liquids a single-exponential 
treatment appears to work well. Furthermore, even if we are only measuring that 
slowest exponential of a multiexponential decay, DSE behavior would still be 
expected to hold. Thus, the substantial limiting values of ?0 observed for some of the 
liquids studied here are rather unexpected. 
 
                                                                     119  
 
5.5 Conclusion 
Based on simulations and techniques such as neutron diffraction, there is strong 
evidence that substantial voids exist in THF at room temperature.2,3 We have studied 
THF and a number of related liquids over a range of temperatures to determine 
whether or not these voids have a clear OKE spectroscopic signature. The 
temperature dependence of the OKE spectra of THF differs significantly from that of 
its close relative furan. However, other related cyclic liquids that lack double bonds 
have RSDs that have a temperature dependence that is not readily distinguishable 
from that of THF. It remains possible that all of these liquids have significant void 
spaces, and this possibility should be investigated with other techniques.  
The dependence of the orientational correlation time of THF on viscosity and 
temperature does not display any sort of anomalous behavior that can be linked to the 
presence of voids. A number of the other liquids studied here do have somewhat 
surprising DSE behavior, and this is another topic that also merits further 
investigation. 
Our studies offer no clear evidence that the voids spaces in THF are manifested in 
any obvious manner in OKE spectra of THF. Although the liquid structure of THF is 
unusual, the influence of the voids on OKE spectra and orientational correlation times 
is subtle enough that that we must conclude that OKE spectroscopy is not likely to be 
a useful means of searching for such voids in other liquids. 
 
 
                                                                     120  
5.6 References 
(1) Marcus, Y. Solvent Mixtures: Properties and Selective Solvation; Marcel Dekker: 
New York, 2002. 
(2) Bedard-Hearn, M. J.; Larsen, R. E.; Schwartz, B. J. J. Chem. Phys. 2005, 122, 
134506. 
(3) Bowron, D. T.; Finney, J. L.; Soper, A. K. J. Am. Chem. Soc. 2006, 128, 5119. 
(4) Martini, I. B.; Barthel, E. R.; Schwartz, B. J. Science 2001, 293, 462. 
(5) Jou, F. Y.; Freeman, G. R. J. Phys. Chem. 1977, 81, 909. 
(6) Weast, R. C. CRC Handbook of Chemistry and Physics, 66th ed.; CRC Press: 
Boca Raton, 1985. 
(7) Righini, R. Science 1993, 262, 1386. 
(8) Kinoshita, S.; Kai, Y.; Ariyoshi, T.; Shimada, Y. Int. J. Mod. Phys. B 1996, 10, 
1229. 
(9) Fourkas, J. T. Nonresonant Intermolecular Spectroscopy of Liquids. In Ultrafast 
Infrared and Raman Spectroscopy; Fayer, M. D., Ed.; Marcel Dekker: New York, 
2001; Vol. 26; p 473. 
(10) Hunt, N. T.; Jaye, A. A.; Meech, S. R. Phys. Chem. Chem. Phys. 2007, 9, 2167. 
(11) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. 
(12) Farrer, R. A.; Loughnane, B. J.; Deschenes, L. A.; Fourkas, J. T. J. Chem. Phys. 
1997, 106, 6901. 
(13) Loughnane, B. J.; Farrer, R. A.; Scodinu, A.; Reilly, T.; Fourkas, J. T. J. Phys. 
Chem. B 2000, 104, 5421. 
 
                                                                     121  
(14) Loughnane, B. J.; Scodinu, A.; Farrer, R. A.; Fourkas, J. T.; Mohanty, U. J. 
Chem. Phys. 1999, 111, 2686. 
(15) Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2002, 106, 10292. 
(16) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2006, 110, 5708. 
(17) Ricci, M.; Bartolini, P.; Chelli, R.; Cardini, G.; Califano, S.; Righini, R. Phys. 
Chem. Chem. Phys. 2001, 3, 2795. 
(18) Jaye, A. A.; Hunt, N. T.; Meech, S. R. J. Chem. Phys. 2006, 124, 024506. 
(19) Kamada, K.; Ueda, M.; Ohta, K.; Wang, Y.; Ushida, K.; Tominaga, Y. J. Chem. 
Phys. 1998, 109, 10948. 
(20) Chang, Y. J.; Castner Jr., E. W. J. Chem. Phys. 1993, 99, 113. 
(21) Chang, Y. J.; Castner Jr., E. W. J. Chem. Phys. 1993, 99, 7289. 
(22) Chang, Y. J.; Castner Jr., E. W. J. Phys. Chem. 1994, 98, 9712. 
(23) Neelakandan, M.; Pant, D.; Quitevis, E. L. J. Phys. Chem. A 1997, 101, 2936. 
(24) Neelakandan, M.; Pant, D.; Quitevis, E. L. Chem. Phys. Lett. 1997, 265, 283. 
(25) Smith, N. A.; Meech, S. R. J. Phys. Chem. A 2000, 104, 4223. 
(26) Ryu, S.; Stratt, R. M. J. Phys. Chem. B 2004, 108, 6782. 
(27) Brady, G. W.; Fein, D. B. J. Appl. Crystallogr. 1975, 8, 261. 
(28) Rigby, D.; Roe, R. J. J. Chem. Phys. 1988, 89, 5280. 
(29) Small, D. M. The Physical Chemistry of Lipids; Plenum: New York, 1986. 
(30) Debye, P. Polar Molecules; Dover: New York, 1929. 
(31) Kivelson, D.; Madden, P. A. Annu. Rev. Phys. Chem. 1980, 31, 523. 
(32) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Wiley: New York, 1976. 
(33) Holland, R. S.; Smyth, C. P. J. Phys. Chem. 1955, 59, 1088. 
 
                                                                     122  
(34) Sinha, A.; Roy, M. N. J. Chem. Eng. Data 2006, 51, 1415. 
(35) Giner, B.; Gascon, I.; Villares, A.; Cea, P.; Lafuente, C. J. Chem. Eng. Data 
2006, 51, 1321. 
(36) Assael, M. J.; Dalaouti, N. K.; Dymond, J. H. Int. J. Thermophys. 2000, 21, 621. 
(37) Froba, A. P.; Pellegrino, L. P.; Leipertz, A. Int. J. Thermophys. 2004, 25, 1323. 
(38) Comelli, F.; Francesconi, R.; Bigi, A.; Rubini, K. J. Chem. Eng. Data 2007, 52, 
639. 
(39) Aminabhavi, T. M.; Patil, V. B.; Aralaguppi, M. I.; Phayde, H. T. S. J. Chem. 
Eng. Data 1996, 41, 521. 
(40) Bhadani, S. N. Indian J. Chem. 1972, 10, 88. 
(41) Briggs, J. M.; Matsui, T.; Jorgensen, W. L. J. Comput. Chem. 1990, 11, 958. 
(42) Andersen, H. C.; Chandler, D.; Weeks, J. D. Adv. Chem. Phys. 1976, 34, 105. 
 
 
                                                                     123  
Chapter 6:  Preliminary Study of Liquids under Tension 
 
6.1 Introduction 
The seminal work of Weeks, Chandler and Andersen1-3 demonstrates that in the 
absence of specific interactions such as hydrogen bonds, the local structure of 
molecular liquids is determined predominantly by the net repulsive pairwise 
interactions between molecules. Yet it is the attractive interactions between molecules 
that hold a liquid together. Is it possible to find a structural signature (ie. an 
experimental signature that depends on structure) of these attractive interactions? The 
local structure of liquids is undeniably dependent on temperature, but this is arguably 
more a matter of which structures are thermally accessible rather than a density effect. 
Liquids can be densified isothermally by applying pressure, but this only increases 
the importance of repulsive interactions. Thus, in order to increase the importance of 
attractive interactions, one must find a way to decrease the density of a liquid at 
constant temperature.  
This problem was solved over 150 years ago by Berthelot.4 In his experiment, 
water was sealed in a cell under vacuum, and the temperature was raised until the 
water occupied the entire cell volume. When the cell was cooled down to its original 
temperature, the water continued to occupy the entire cell volume due to the energy 
barrier that had to be overcome to nucleate a vapor bubble. This inability to reach its 
equilibrium volume caused the water to be in a state of tension. At some point the 
tension eventually led to a vapor bubble nucleating either heterogeneously (on a cell 
 
                                                                     124  
wall) or homogeneously (when the tensile strength of the liquid is reached).  
Heterogeneous nucleation5,6 is typical in stretched liquids and occurs often. It 
generally occurs at nucleation sites located on surfaces contacting the liquid or vapor. 
Suspended particles or minute bubbles also provide nucleation sites. Homogeneous 
nucleation has no preference for nucleation sites, and it generally occurs in the 
interior of a uniform substance, with much more difficulty than heterogeneous 
nucleation. Homogeneous nucleation occurs spontaneously and randomly, and is rare 
compared to heterogeneous nucleation. In order to keep liquids under tension for a 
time long enough to perform spectroscopic experiments, understanding nucleation, 
especially heterogeneous nucleation is necessary. 
Water was the first liquid to be studied to any significant extent under extreme 
tension.7-14 Water is an ideal liquid for such studies in many ways. For instance, it has 
an extremely high tensile strength for a liquid due to the high degree of hydrogen 
bonding. However, heterogeneous nucleation generally prevents water from being 
stretched to its intrinsic tensile strength. Furthermore, water is not readily amenable to 
study using OKE spectroscopy due to its extremely low polarizability anisotropy. The 
same holds true for other hydrogen-bonded liquids that would have high tensile 
strengths. As a result, little spectroscopic work has been done on these types of 
liquids.  
Aromatic liquids could be excellent candidates for initial experiments on liquids 
under tension. Simple aromatic liquids such as benzene have medium to high surface 
tensions for organic liquids,15 yet they also have small contact angles on silica. The 
small contact angles indicate a large enough affinity for glass that should facilitate 
 
                                                                     125  
liquid large tensions in silica cells. The fact that the contact angles on silica are so 
small despite these liquids having healthy surface tensions is also an indication that 
these liquids are likely to have relatively large tensile strengths even though they are 
not dipolar. Indeed, previous measurements on benzene show that it has a tensile 
strength of at least 150 atm,16 although the authors of this study believed that 
heterogeneous nucleation of vapor bubbles prevented the homogeneous nucleation 
limit from being reached in their experiments. While the tensile strength of benzene is 
substantially less than that of water (believed to be greater than 1000 atm10), 150 atm 
still represents a substantial tension. Under such big tension, the density of benzene 
will be reduced and the intermolecular interactions will change dramatically. Thus, 
OKE experiments on aromatic liquids should yield clear signatures due to the effects 
of negative pressure. These signatures should be evident in reduced spectral density 
(RSD) which provides intermolecular dynamics information.  
For initial experiments, we used glass tubes (1 mm inner diameter) with one end 
sealed as the sample cell. Ultra pure, degassed aromatic liquids are employed. The 
cells are filled to some level, and the liquid is frozen using liquid nitrogen. The cell is 
then evacuated prior to being sealed just above the original fill line with a torch. 
Aromatic liquids have a number of advantages over water in the construction of a 
Berthelot cell in this manner: not only do aromatic liquids contract upon 
crystallization, but they also have much higher thermal expansion coefficients than 
water.15 We can therefore employ a considerably larger vapor volume in Berthelot 
cells of aromatic liquids than is the case for water. 
One issue that we need to address is how to measure the tension to which a liquid 
 
                                                                     126  
sample is subjected. The tensions we are exploring are too small to measure reliably 
with Raman scattering from a ruby chip, and we would rather not add such a chip to a 
Berthelot cell for fear that it will provide heterogeneous nucleation sites. It is 
straightforward to obtain a reasonable estimate of the volume of the cell and the 
amount of liquid in it, but we must know the equation of state in order to turn this 
information into a tension at a given temperature. Given that the tensions that the 
liquids we will study can sustain are likely to be on the order of a few hundred atm, 
we might reasonably estimate the tension from pressure-volume-temperature data for 
these liquids at positive pressures, when such data is available. Also, Henderson and 
Speedy8 designed a clever cell that has a spiral arm that changes its degree of winding 
depending on the pressure in the liquid it holds, allowing for accurate measurement of 
the tension in a liquid. In our method, we use a regular capillary tube with 1 mm inner 
diameter as the sample cell. The length of liquid in the cell can be used to represent 
the volume of the liquid. After the cell is sealed, the liquid and the vapor phase will 
be in equilibrium. If we know the temperature, we can determine the pressure. Thus, 
we will have all the data (temperature-volume-pressure) for the initial liquid state. For 
the final state (under tension), we know the temperature and volume, and its pressure 
can be determined (see below). 
6.2 Experimental Section 
To place liquids under negative pressure, we have developed a method based on 
the Bertherlot tube technique. A diagram of our experimental setup is shown in 
Figure 6.1. The pure liquid is placed in a reservoir hooked up to a vacuum line (Ace 
Glass Inc.), and then this liquid is degassed using several (4-6) freeze-pump-thaw 
 
                                                                     127  
cycles. The sample tube is made from a capillary tube (1 mm inner diameter) by 
sealing one side of the tube. After being annealed in an oven at about 500 ?C for 
about 2 hours, the tube is connected to the vacuum line. The final length of the tube is 
usually about 35 cm.  
Vacuum pump
Liquid nitrogen
Liquid reservoir
 
Figure 6.1 Experimental setup for preparing liquid samples under tension 
 
The detailed procedure for producing a liquid sample under tension can be 
described by four steps: 
(1) The liquid must be degassed using the following freeze-pump-thaw 
procedure: 
(a) Fill the liquid container with about 10 ml liquid, and hook it up to the 
vacuum line (see Figure 6.1);  
(b) Freeze the liquid using liquid nitrogen, and then open valve 3 to reduce 
 
                                                                     128  
the pressure in that liquid container;  
(c) Close valve 1, thaw the frozen sample until it melts using a water bath 
(You will see gas bubbles evolve from the liquid). After the frozen 
liquid completely melts, repeat step (b) ? (c) until you no longer see 
bubbles form as the frozen liquid thaws (usually about five cycles). 
(2) The degassed liquid needs to be transferred to the capillary sample tube: 
(a) Close valves 1 and 2 and open valve 3 (see Figure 6.1). Evacuate the 
chamber (shown in gray in Figure 6.1) to ~ 50 torr. Then keep the pump 
on but close valve 3;  
(b) Open valves 1 and 2, at the same time. Put the empty bottom part (few 
centimeters) of the capillary sample tube inside the mixture of water and 
ice (0 ?C) in a dewar. Some liquid will be deposited into the bottom of 
the tube after a few minutes;  
(c) Repeat steps (a) ? (b) several times until 80% of the tube (25-30 cm) is 
filled up. Remove the dewar, and mark the point of the liquid level at 
room temperature. 
 
                                                                     129  
Sealing point
Liquid level:
Marked point
Vacuum pump
Dry ice
 
Figure 6.2 Experimental setup for sealing the capillary sample tube. 
 
(3) Sealing process: The capillary sample tube should be sealed at a point about 
1 cm above the the height of the liquid level at room temperature.  
(a) Place an empty dewar below the sample tube, and adjust the height of the 
dewar such that the top of the dewar at or a little bit lower than the 
marked point (blue line in Figure 6.2);  
(b) Fill the dewar with crushed dry ice. The liquid will freeze and shrink;  
(c) Seal the tube at the sealing point (red line in Figure 6.2) with a torch and 
take the sealed tube away. 
(4) When the sealed tube returns to the room temperature, the liquid level will 
return to the marked point (ie. its original height at room temperature). 
Warm the liquid slowly until it expands and occupies the whole tube. 
 
                                                                     130  
Record the temperature Tfill at which the liquid just occupies the whole tube. 
Wait until the liquid goes back to room temperature, if it still occupies the 
whole tube, then the liquid is under tension and the sample is ready for 
further experiments.  
  The curved surface of the sample tube causes scattering and diffraction of laser 
beam and this presents challenges to performing OKE experiments. This problem 
is solved by placing the tube in a fluorescence cell (see Figure 6.3) filled with 
glycerin (refractive index: 1.473), which has similar refractive index as Pyrex 
glass (1.474). Our optical-heterodyne-detected17,18 OKE spectrometer and data 
collection procedures have been described in detail elsewhere,19,20 and OKE data 
for acetonitrile under tension have been collected at room temperature (297 K). 
 
Figure 6.3 Design of the sample holder 
 
 
                                                                     131  
6.3 Preliminary Results and Discussion 
Benzene is the first liquid that was placed under tension. Benzene has a medium 
surface tension, a small contact angle on the glass, and a large thermal expansion 
coefficient (see Table 6.1). OKE data for benzene under ambient conditions are also 
available for comparison21.  
Table 6.1 Physical parameters of benzene and acetonitrile 
Liquids Surface tension 
? / (mN/m), 298K 
Contact angle on glass 
(degree, 295K)) 
Thermal expansion 
coefficient (? / 10-5 K-1, 
293K) 
Benzene 28.571 12?5 121 
Acetonitrile 28.162 4?4  
1. Nath, S.: J. Coll. Interf. Sci. 209 (1999) 116. 
2. Kinart, C.M., Kinart, W.J., Kolasinski, A., Cwiklinska, A.: Phys. Chem. Liq. 38 
(2000) 583. 
 
Samples of benzene under tension were created successfully. However, these 
samples only tended to remain stretched for a few (1-2) minutes. The sample tube 
was 27 cm long in total, and the benzene inside was 26 cm long under room 
temperature T1 (293.8 K). The benzene inside expanded to just occupy the whole tube 
after being warmed to some well-defined filling temperature Tfill (which depends on 
the initial fluid/vapor ratio and the thermal expansivity of the liquid). Further heating 
of the benzene places the liquid under positive pressure and may lead to breakage of 
the tube; cooling benzene to some temperature lower than Tfill, for example room 
temperature T1, should lead to a contraction to its original volume, but the surface 
adhesive forces between the liquid and the wall will hold the liquid under tension, 
 
                                                                     132  
which accounts for the negative pressure.  
At Tfill, equilibrium will be achieved between benzene and its vapor, so P = Pv. At 
T1, the negative pressure can be calculated22 from the thermal properties of benzene 
using the thermal pressure coefficient, ?. 
( / ) ( / ) /( / ) /V P TP T V T V P ? ??? ? ? ?? ? ? ? ? ?                       (Eq. 6.1) 
here ?  is the isobaric expansivity, ( ln / )PV T? ? ? ?  and ? is the isothermal 
compressibility, ( ln / )TV P? ?? ? ? . Both ?  and ?  are weakly dependent on P and T. 
As an approximation, one can make the assumption that fill? ~ /fill fill? ? . Then the 
negative pressure which results from cooling the liquid from Tfill to T1 (room 
temperature) can be calculated by22 
dP? ~ fillP P? ~ P? ~ filldT?? ~ 1( )fill fillT T? ?                         (Eq. 6.2) 
For benzene, ? ~10-3  K-1, ? ~10-9 Pa-1, T1=293.8 K. If we know Tfill, we can estimate 
the negative pressure for benzene. A rough value for Tfill can be obtained from 
experiment. Usually after the sample was warmed by about 10 ?C, the benzene liquid 
occupied the whole tube, so the tension achieved was on the order of 100 atm.  
A more accurate determination of Tfill is also possible: The benzene liquid and 
vapor phase are always in equilibrium during the expansion process. Therefore on the 
phase diagram, the pressure and temperature should always follow the curve between 
the liquid and vapor phases. At T1, we can determine the corresponding pressure and 
find out the density d1 using NIST Chemistry Webbook. After the liquid just occupies 
the whole tube at Tfill, we can determine the density d2 (d2 = d1*L1/L2, where L is the 
length of the column of liquid benzene). Based on d2, we can ascertain Tfill and the 
corresponding pressure. 
 
                                                                     133  
 
Figure 6.4 Phase diagram of bezene 
 
In order to perform OKE experiments on a liquid sample under tension, we need to 
stop nucleation to hold the liquid under tension for longer time, which is a big 
challenge. Homogeneous nucleation occurs spontaneously, randomly and extremely 
rarely, and generally occurs with much more difficulty in the interior of a uniform 
substance. Heterogeneous nucleation occurs much more often than homogeneous 
nucleation and is the major challenge. The creation of a nucleus implies the formation 
of an interface at the boundaries of a new phase, and this process requires free energy. 
The balance between the free energy available from driving force and the energy 
consumed in creating new interface will decide whether the nucleation can happen. 
The free energy available is mainly released by the transformation process. In our 
case, liquid that was originally under tension returns to its normal condition after a 
bubble is generated due to nucleation. During this process free energy is gained for 
creating new volume, and the amount of the released free energy is proportional to 
 
                                                                     134  
the volume. The free energy cost due to creation of a new interface is proportional to 
the surface area of the bubble and the interfacial energy, ?.  If the nucleating bubble is 
treated as a sphere, the net change in free energy can be written as: 
                                   ?G = -4?/3 r3 ?Gv + 4?r2 ?                                        (Eq. 6.3) 
where ?GV is free energy released for creating unit new volume, and r is the radius of 
the nucleating bubble. When the overall change in free energy, ?G, is negative, 
nucleation is favored.  
Heterogeneous nucleation occurs at preferential sites, such as phase boundaries or 
impurities (e.g. dust). It requires less energy than homogeneous nucleation. At such 
preferential sites, there is a pre-existing interface or the effective surface energy is 
lower, thus diminishing the free energy barrier and facilitating nucleation. Our study 
about nucleation first focuses on how to stop heterogeneous nucleation. 
 As Eq. 6.3 shows, if we want to stop the heterogeneous nucleation, we need to 
make ?G positive or less negative. We anticipated this could be done by increasing 
the second term 4?r2?. To test this hypothesis, we tried another liquid, acetonitrile. 
Acetonitrile has a smaller contact angle on the glass than benzene, which means there 
is a stronger interaction between acetonitrile molecules and glass surface. Acetonitrile 
therefore requires more free energy to create a new interface, making nucleation more 
difficult compared to benzene. This effect should allow acetonitrile to be maintained 
under tension for a longer time than benzene.  
The experimental results are consistent with our prediction. For the acetonitrile 
sample we made, the total length of the sample tube was 27.7 cm, and the liquid 
length under room temperature (293.8 K) was about 27.5 cm. We measured how long 
 
                                                                     135  
acetonitrile could be held under tension on three different days. The results are shown 
in Table 6.2: 
 
Table 6.2 Time period (minutes) Acetonitrile can sustain tension at 293.8 K 
 Time duaration (minutes) 
Day 1 51, 35, 50, 42, 15 
Day 2 67, 65 
Day 3 45, 13, 73 
 
In most cases, the acetonitrile can sustain tension for longer than 50 minutes. Only 
for a few experiments was the time period for sustaining tension less than 15 minutes. 
We pressume that nucleation may be due to thermal fluctuations in the environment, 
which provide extra energy for heterogeneous nucleation to occur. Nevertheless, 50 
minutes is still not a long enough time period to perform an intermolecular dynamics 
study using the OKE method. However, it is enough time for us to measure the 
reorientational diffusion. Under normal conditions, the orientational correlation time 
for acetonitrile is about 1.67 ps at room temperature (297 K). The biexponential 
fitting result for acetonitrile under ambient condition is: 
                                   0.67 Exp(-t/1.67)+0.33 Exp(-t/0.42)                                (Eq. 6.4) 
When acetonitrile is under tension, the reorientatinal diffusion becomes faster and 
the fitting result is: 
                                    0.70 Exp(-t/1.52)+0.30 Exp(-t/0.32)                               (Eq. 6.5) 
This result can be explained reasonably. When a liquid is under tension, the 
 
                                                                     136  
molecules are stretched and less crowded than in the liquid is in a normal state, so 
after the birefringence is induced, it should be easier and faster for molecules to 
return to the random orientation. Unfortunately, 50 minutes is still not long enough to 
study the intermolecular dynamics, which should give us more information. 
More efforts can be made to avoid heterogeneous nucleation of a vapor bubble. 
Since heterogeneous nucleation occurs at preferential sites, such as phase boundaries 
or impurities like dust, we need to reduce concerntration of these sites in the sample: 
Some precautions, such as distillation and Millipore filtration, should be taken for the 
liquid to get rid of the hydrophobic impurities. Treatment of the sample tube with a 
solution of hydrofluoric acid before it is used8 will drive away the gas in any 
hydrophobic crevices. Also, surface modification techniques can be employed to 
achieve even higher adhesion to the cell surfaces.23 For instance, there is a strong 
attraction between benzene and hexafluorobenzene24, so modification of the wall of 
our sample tube with trichloropentafluorophenylsilane may further decrease the 
contact angle of benzene on silica.  
 
Another potential cause of heterogeneous nucleation is cosmic rays.8 If heterogeneous 
nucleation presents difficulties, we can also test whether shielding with lead bricks 
helps to prevent this problem.  
 
                                                                     137  
If any of these precautions permit a sample to be stretched for a suitable amount 
of time, we will perform an intermolecular dynamics study on this sample using OKE 
method. As mentioned in the introduction to this chapter, while a liquid is under 
tension, its density will be decreased and the attractive interactions will become more 
important. All these changes should be reflected in the reduced spectral density (RSD) 
(e.g., in the breadth and the shape of RSD), based on our former intermolecular 
dynamics studies of simple liquids.25-27 This effect will help us to discover and 
distinguish different microscopic information behind the RSD. However, if all these 
precautions are still not enough to make a sample for an intermolecular dynamics 
study, then we may need to focus on how to reduce the homogeneous nucleation. 
  
6.4 Conclusions 
A method based on the Berthelot tube technique4 was developed to make liquid 
samples under tension. Benzene and acetonitrile were successfully stretched with this 
method. The tensile strength of benzene achieved in our experiment was about 100 
atm. Acetonitrile was found to be able to maintain a stretched state for much longer 
time than benzene. This made it possible to perform OKE experiments on acetonitrile. 
The orientational correlation time for acetonitrile at room temperature was shorter 
under tension than it was for unstretched samples, which is consistent with our 
predictions. However, the time interval under tension is still not long enough for an 
intermolecular dynamics study. In order to solve this problem, heterogeneous 
nucleation must be suppressed. Some ways to supress heterogeneous nucleation have 
 
                                                                     138  
been suggested. Hopefully these possible solutions will make an intermolecular 
dynamics study for liquids under tension feasible in future. 
 
6.5 References 
(1) Andersen, H. C.; Weeks, J. D.; Chandler, D. Phys. Rev. A 1971, 4, 1597.  
(2) Weeks, J. D.; Chandler, D.; Andersen, H. C. J. Chem. Phys. 1971, 54, 5237.  
(3) Andersen, H. C.; Chandler, D.; Weeks, J. D. Adv. Chem. Phys. 1976, 34, 105.   
(4) Berthelot, M. Ann. Chim. Phys. 1850, 30, 232.  
(5) Abraham, F. F. 1974, Homogeneous nucleation theory (Academic Press, NY) 
(6) Rollett, A. D. 2002, Microstructure-properties: ? Nucleation rate (lecture notes) 
(7) Trevana, D. H. Contemp. Phys. 1976, 17, 109.  
(8) Henderson, S. J.; Speedy, R. J. J. Phys. E 1980, 13, 778.  
(9) Green, L.; Durben, D. J.; Wokf, G. H.; Angell, C. A. Science 1990, 249, 649.  
(10) Zheng, Q.; Durben, D. J.; Wolf, G. H.; Angell, C. A. Science 1991, 254, 829.  
(11) Alvarenga, A. D.; Grimsditch, M.; Bodnar, R. J. J. Chem. Phys. 1993, 98, 8392.  
(12) Ruocco, G.; Sampoli, M.; Torcini, A.; Vallauri, R. J. Chem. Phys. 1993, 99, 
8095.  
(13) Sciortino, F.; Essmann, U.; Stanley, H. E.; Hemmati, M.; Shao, J.; Wolf, G. H.; 
Angell, C. A. Phys. Rev. E 1995, 52, 6481.  
(14) Parker, M. E.; Heyes, D. M. J. Chem. Phys. 1998, 108, 9039.  
(15) Weast, R. C. "CRC Handbook of Chemistry and Physics'' 66th edition (CRC 
Press, Boca Raton, 1985).  
(16) Donoghue, J. J.; Vollrath, R. E.; Gerjuoy E. J. Chem. Phys. 1951, 19, 55. 
 
                                                                     139  
(17) McMorrow, D. Opt. Commun. 1991, 86, 236. 
(18) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. 
(19) Farrer, R. A.; Loughnane, B. J.; Deschenes, L. A.; Fourkas, J. T. J. Chem. Phys. 
1997, 106, 6901. 
(20) Loughnane, B. J.; Farrer, R. A.; Scodinu, A.; Reilly, T.; Fourkas, J. T. J. Phys. 
Chem. B 2000, 104, 5421. 
(21) Zhu, X.; Farrer, R. A.; Fourkas, J. T. J. Phys. Chem. B 2005, 109, 12724. 
(22) Imre, A.; Van Hook, W. A. Chem. Soc. Rev. 1998, 27,117. 
(23) Majors, R. E.; Hopper, M. J. J. Chromat. Sci. 1974, 12, 767. 
(24) Patrick, C. R.; Prosser, G. S. Nature 1960, 187, 1021. 
(25) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2006, 110, 5708. 
(26) Zhong, Q.; Zhu, X.; Fourkas, J. T. J. Phys. Chem. B 2008, 112, 3115. 
(27) Zhong, Q.; Fourkas, J. T. J. Phys. Chem. B 2008?112?15529. 
 
 
 
 
 
 
 
 
 
                                                                     140  
Chapter 7:  Antiresonant-Ring Kerr Spectroscopy 
 
7.1 Introduction 
Ultrafast optical Kerr effect (OKE) spectroscopy 1-4 has become a broadly-used 
tool for studying dynamics in bulk liquids 5-7, liquid mixtures 8-11, polymer solutions 
12, 13, confined liquids 14, 15, and other fluid systems 13, 16, 17. In this technique, a pump 
laser pulse passes through a transparent sample, inducing a change in refractive index 
that is measured with a time-delayed probe pulse. In its most common 
implementations, OKE spectroscopy is used to monitor the xyxy tensor element of the 
third-order response as a function the delay time between the pump and probe pulses. 
This so-called depolarized response is sensitive to effects that include collective 
molecular reorientation, scattering from depolarized Raman-active intramolecular 
vibrations, and librational and collective scattering from depolarized intermolecular 
modes. The depolarized response corresponds to the transient birefringence induced 
by the pump pulse. 
In many instances it is of interest to measure tensor elements of the OKE response 
other than xyxy. The most important additional tensor element of the OKE response is 
xxmm, where m is the ?magic? angle (54.7?). This tensor element is known as the 
isotropic response 18, and it arises from isotropic changes that the pump pulse induces 
in the refractive index. Any tensor element of the OKE response in an isotropic 
system can be described using a linear combination of the depolarized response and 
the isotropic response 18. 
While the isotropic response is insensitive to reorientation, it is affected by 
 
                                                                     141  
intramolecular and intermolecular modes with the appropriate symmetry. In some 
samples, such as proteins 19, the isotropic response from intramolecular modes is 
considerably more pronounced than the depolarized response. As a result, there is 
great interest in developing spectroscopic techniques that can cleanly separate the 
depolarized and isotropic OKE responses. A number of techniques for measuring the 
isotropic response have been reported previously, based on effects such as lensing 20 
or spatial shifting of the probe pulse 21, 22. 
Here we present a new strategy for determining different OKE tensor elements. 
The inspiration for this approach comes from the work of Trebino and Hayden on 
antiresonant ring transient electronic spectroscopy 23. In their setup, a Sagnac 
interferometer was used to create counterpropagating probe pulses for pump/probe 
spectroscopy. The sample was positioned away from the center of the ring, such that 
the probe pulse that propagated in the opposite direction from the pump pulse arrived 
at the sample considerably earlier than the pump pulse, whereas the other probe pulse 
arrived in proximity to or after the pump pulse. All of the light that enters such an 
interferometer exits in the same direction unless the probe pulses experience different 
absorption. This difference in absorption is the signal of interest in an electronic 
pump/probe experiment. Since the probe beams travel exactly the same path the 
interferometer is highly stable, and each beam experiences identical distortions due to 
any imperfect optics. Any deviation of the input beam splitter from perfect 50% 
reflectivity serves to create a local oscillator for the signal electric field 23. 
Here we present an antiresonant ring scheme for measuring phase changes rather 
than absorption. We call our technique antiresonant-ring Kerr spectroscopy (ARKS). 
 
                                                                     142  
Our setup employs a double Sagnac interferometer, such that both probe beams 
propagate through the sample in the same direction. As a result, ARKS can be used to 
measure different tensor elements of the OKE response, and can even be used to 
combine responses at two different delay times in order to enhance or suppress 
particular contributions to the OKE decay. 
 
7.2 Experimental Section 
 
Figure 7.1 Experimental setup for ARKS. HWP = half-wave plate, Pol = polarizer, 
QWP = quarter-wave plate, PBC = polarizing beam cube, ? = vertical polarization, 
? = horizontal polarization. Blue denotes polarizations before the sample and red 
polarizations after the sample. The mirror in the green block can be removed to 
measure the depolarized OKE response. 
 
 
                                                                     143  
A diagram of our experimental setup is shown in Figure 7.1. A KMLabs 
Ti:sapphire laser generates 50 fs pulses with a center wavelength near 800 nm. After 
a prism dispersion compensator and spatial filtering, the laser output is split into a 
strong pump beam and a weak probe beam. The pump beam traverses a computer-
controlled optical delay line. The probe beam passes through a half-wave plate, a 
polarizer set at 45?, and then a quarter-wave plate (QWP) before entering the dual-
ring interferometer via a polarizing beam cube (PBC). Orthogonal polarizations travel 
down each leg of the interferometer. The lengths of the two legs can be changed to 
adjust the timing of the probe pulses, and are generally set so that one probe pulse 
arrives at the sample several picoseconds or more before the other. The two probe 
beams are recombined in a second PBC, after which they are focused into the sample 
at the same spot as the pump beam. The probe beams are recollimated after the 
sample. 
For collecting the depolarized OKE signal, the input optics for the interferometer 
are set such that there is a single, horizontally-polarized probe beam. The pump 
polarization is set to 45?. An analyzer polarizer is placed immediately after the 
recollimating lens and is set to pass light that is vertically polarized. The input 
polarizer and QWP are then adjusted to implement a local oscillator for optical 
heterodyne detection (OHD) of the OKE signal 6,24. To measure other tensor elements 
of the OKE response, one axis of the QWP is set such that the polarization state of the 
input light is unaffected. After the sample the recollimated probe beams are fed back 
into the second PBC such that they are collinear with the incoming probe beams (see 
Figure 7.1). The horizontally- and vertically-polarized components of the probe beam 
 
                                                                     144  
once again travel separate paths and are recombined at the original PBC. The two 
different polarization components ultimately travel along the exact same path, albeit 
in different directions, regardless of the delay between the probe pulses at the sample. 
Because the beams travel along identical paths, the dual-ring interferometer is 
relatively insensitive to vibration, as no significant motion of optics can occur during 
a single round trip of the interferometer. However, the laser must have good pointing 
stability so that the optical path through the interferometer is similar from pulse to 
pulse. 
In the limit of weak probe beams, the output polarization of the dual-ring 
interferometer in the absence of a pump pulse should be identical to the input 
polarization (barring a 180? flip of the horizontal component of the polarization for 
each reflection). An analyzer polarizer is therefore placed after the output face of the 
first PBC and adjusted to pass light with a polarization that is orthogonal to the input 
polarization. In the presence of the pump beam, the two probe beams can experience 
different phase shifts in the sample, due to their different arrival times and different 
polarizations. Any differential phase shift introduces a polarization component that is 
orthogonal to the input polarization, and therefore leaks through the analyzer 
polarizer. 
To optimize the signal-to-noise ratio of the data, we use a scheme that is similar to 
one we have reported previously 14. The pump and probe beams are chopped at 
different frequencies with different rings of the same chopper wheel (Figure 7.1). A 
small portion of the chopped probe beam is picked off to form a reference beam (not 
shown in Figure 7.1) and is sent to a separate detector. The output of the reference 
 
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detector is subtracted from that of the signal detector using an analog preamplifier. 
The output of the preamplifier is sent to a lock-in amplifier that is referenced to the 
sum of the chopping frequencies. Care is taken to match the shape of the chopped 
signal and reference waveforms as well as possible. 
The extinction ratio of polarizing beam cubes is not as high as that of other 
polarizing optics. Typical cubes we have employed have an extinction ratio for 
horizontal: vertical polarization on the order of 200 in the transmitted direction; in the 
reflected direction the extinction ratio for vertical:horizontal polarization is 
considerably lower. As a result, leakage of vertically-polarized light can be ignored, 
but there are significant reflections of the horizontal polarization component that 
propagate through the interferometer in undesired directions. It is important to 
understand the effects of these reflections in evaluating the performance of the 
spectrometer. 
 
Figure 7.2 Pathways through which horizontally-polarized light that enters the ARKS 
apparatus can exit in the direction in which the signal is detected. Reflections of the 
predominantly transmitted horizontal polarization are indicated with red arrows. 
 
                                                                     146  
 
In Figure 7.2 we consider all pathways that will allow horizontally-polarized light 
that enters the interferometer to exit in the direction in which the signal is detected. 
The desired path is labeled (a) in Figure 7.2. The influence of the other pathways is 
minimized by a number of factors. First, there must be an even number of reflections 
for the beam to exit the dual-ring interferometer in the same direction as the signal, 
which limits the number of potential interfering pathways to seven, paths (b) through 
(h). Second, many of the paths involve reflections also change the path length of the 
probe beam such that it arrives at the detector at a significantly different time from 
the signal; this is the case for paths (b), (c), (e) and (h). These non-time-coincident 
reflections can reduce the dynamic range of the detection to some extent, but they do 
not interfere with the signal optically. Paths (d) and (g) do not contribute significantly 
to the signal because the probe pulse passes through the sample in the wrong direction. 
Path (h) passes through the sample in the proper direction, but involves four 
reflections and so is very weak. 
Based on the above reasoning, we do not expect imperfect extinction of the PBCs 
to interfere with the desired signal. However, we must also consider a second effect 
of such leakage, namely that it can act as a local oscillator. The PBCs are composed 
of dielectric materials, and the leakage of horizontally-polarized light due to its 
reflection from the diagonal interfaces in these optics leads to a phase shift. The laser 
wavelength is far from any absorption in the PBS material, and so the phase of this 
reflection is not expected to have any significant dependence on wavelength over the 
bandwidth of the laser pulses. We have found that this phase shift is consistent for a 
 
                                                                     147  
given PBC, but varies among PBCs. The phase of the local oscillator therefore cannot 
be controlled, but the quadrature component of the nonresonant OKE signal is so 
much greater than the in-phase component that only the quadrature componenent of 
the local oscillator acts to amplify the signal. Introducing a variable wave plate in 
place of the input quarter-wave plate to control the phase of the local oscillator did 
not change the shape of OKE decays, and led only to a modest increase in signal 
intensity. 
 
7.3 Results and Discussion 
To measure the depolarized OKE response we use the procedure described above. 
To measure OKE response functions of the form xxkk, where k refers to any direction 
in the xy plane, the dual-ring interferometer is employed. One probe beam (generally 
the one that is reflected from the first PBC, whose polarization we will call y) is set to 
arrive at the sample before the other (whose polarization we will call x). The time 
between the probe beams is set to be greater than the longest delay of interest. The 
pump beam, which is polarized in the k direction, is scanned from times slightly after 
the later probe beam out to the greatest delay desired, and data are collected as a 
function of delay time. In this scheme, the pump pulse does not affect the earlier 
probe pulse, and so only the later probe pulse experiences a phase change due to the 
pump. The xxkk tensor element of the OKE response is therefore probed. So different 
tensor elements can be measured by simply changing the polarization and timing of 
all three pulses. In Table 7.1, we list some examples of the tensor elements that can 
be measured by the spectrometer. 
 
                                                                     148  
 
Table 7.1 Expected performance of ARKS 
probe 1 probe 2 Pump 
polarization polarization timing polarization timing 
Tensor 
elements 
x y Before 
pump 
x After 
pump 
Rxxxx(?) 
m y Before 
pump 
x After 
pump 
Rxxmm(?) 
y y Before 
pump 
x After 
pump 
Rxxyy(?) 
x y Same 
time 
x Same 
time 
Rxyxy(?) 
x y ?2  
after 
x ?1 
after 
Rxxxx(?1)- Ryyxx(?2) 
 
 
 
Figure 7.3 Normalized ARKS data for CS2 under difference polarization conditions. 
The data have been offset vertically for clarity. 
 
Shown in Figure 7.3 are typical data for carbon disulfide (CS2) at room temperature. 
The intensities of the decays have been normalized. The depolarized response is in 
 
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good agreement with previous OHD-OKE data for this liquid 5,25. The xxxx (polarized) 
and xxyy responses are similar to the depolarized response, although the magnitude 
(and sign) of the electronic signal near zero time changes with respect to that of the 
nuclear signal at positive delay times for the different tensor elements. The fact that 
the electronic response is negative for some tensor elements of the response is 
expected, and indicates that the signal is indeed heterodyned. The isotropic response 
is quite small, in agreement with previous results 20,26. The dominance of the 
depolarized response in this liquid accounts for the strong similarities among the xyxy, 
xxxx and xxyy tensor elements. The lack of any component of the isotropic response 
that decays with the time scale of collective reorientation indicates that we can 
discriminate strongly against any contamination from the depolarized response. 
 
Figure 7.4 Normalized ARKS data for S2Cl2 under difference polarization conditions. 
The data have been offset vertically for clarity. 
 
To further assess the quality of the isotropic response measured with ARKS, in 
Figure 7.4 we present data for sulfur monochloride (S2Cl2). Once again the decays 
 
                                                                     150  
have been normalized to the same maximum intensity. For this liquid, the 
contribution of Raman-active intramolecular vibrational modes to the OKE response 
is considerably stronger than that of collective orientational relaxation or 
intermolecular modes. The depolarized response exhibits oscillations due to a number 
of different vibrational modes 27-29. The polarized response is similar to the 
depolarized response. The yyxx and isotropic responses are also similar to one another, 
but in contrast to the other two responses are dominated largely by the contribution of 
a single vibrational mode that is highly polarized. The fact that the isotropic decay 
oscillates around the baseline of the scan is additional evidence that the signal is 
heterodyned. 
 
Figure 7.5 Depolarized and isotropic OKE power spectra for S2Cl2. The two spectra 
are not to scale. 
 
To examine the spectral content the OKE decays for S2Cl2, we computed the power 
spectra corresponding to the depolarized and isotropic response functions. These 
power spectra, which are shown in Figure 7.5, confirm the presence of a number of 
 
                                                                     151  
vibrational modes. The peaks at 102 cm-1, 205 cm-1, and 446 cm-1 are assigned to the 
?4 (torsion), ?3 (S-S-Cl symmetric angle deformation) and ?2 (S-Cl symmetric stretch) 
modes, respectively, all of which have A symmetry in the C2 point group of this 
molecule 29. These modes are all polarized and, as is clear from Fig. 5, ?2 and ?3 are 
strongly so. The peaks at 238 cm-1 and 434 cm-1 belong to the ?6 (S-S-Cl asymmetric 
angle deformation) and ?5 (S-Cl asymmetric stretch) modes, which have B symmetry 
and therefore should be completely depolarized 29. The power spectra in Figure 7.5 
confirm the depolarized nature of these vibrations. It is important to note that peaks 
do not appear in the power spectrum at the second harmonic of the fundamental 
frequencies, indicating again that our signal is proportional to the response rather than 
to its magnitude squared.  
While the data in Figure 7.5 are power spectra, we should also note that it is 
possible to perform Fourier-transform deconvolution on ARKS data to obtain the 
Bose-Einstein-corrected, low-frequency spectral density 6,24. To do so, however, 
requires that the pump and probe pulses be transform-limited at the sample. Due to 
the dispersion introduced by the PBCs, attaining transorm-limited pulses requires 
separate dispersion compensation of the pump and probe beams. While compensation 
of each beam is readily possible, we have not attempted it here. 
We have previously demonstrated that by having two pump pulses of controllable 
polarization and intensity, it is possible to perform optical addition of two depolarized 
OKE response functions with a time shift between them 27,30. This strategy can be 
employed for enhancing or suppressing particular contributions to the depolarized 
response, which may be useful, for instance, in OKE microscopy. In the technique 
 
                                                                     152  
presented here, we instead have used two probe pulses. While for all of the 
measurements discussed above one probe pulse always arrives before the pump pulse, 
it is also possible to have both probe pulses arrive after the pump. In this manner, we 
can perform optical subtraction of two different tensor elements of the OKE response 
function with a time shift between them. 
ARKS data for S2Cl2 illustrating the implementation of optical subtraction are 
shown in Figure 7.6. For reference we show the xxxx and yyxx response functions 
obtained with one probe pulse arriving significantly before the pump pulse. In the 
lower two traces both probe pulses arrive after the pump pulse. By adjusting the 
relative timing of the two probe pulses, we can either enhance the response from the 
?2 vibration (red trace) or suppress it virtually completely (green trace). By combining 
this technique with the previously demonstrated use of pump pulse pairs 27, 30, it will 
be possible to control the contribution of vibrational modes of any symmetry to the 
OKE signal. 
 
Figure 7.6 Normalized S2Cl2 ARKS data for the xxxx and yyxx tensor elements, as 
well as scans in which these tesnor elements are optically subtracted with different 
 
                                                                     153  
time shifts to enhance or suppress the contribution of the ?3 mode. 
 
7.4 Conclusions and Future Work 
We have presented a new technique for obtaining different tensor elements of the 
OKE response function. Employing a dual-ring Sagnac interferometer makes possible 
the optical subtraction of the response functions from two different probe beams. 
ARKS is a versatile method of collecting OKE data, and also makes possible the 
enhancement or suppression of different contributions to the response when both 
probe pulses arrive after the pump pulse.  
We will work on implementing ARKS in an OKE microscope in future. We have 
developed mode-selective OKE spectroscopy27,30, in which two-pump geometry is 
used: By controlling the timing and polarizations of the two pumps, particular mode 
of liquid molecules can be selectively excited. The combination of ARKS and 
techniques for mode-selective excitation will provide us with the ability to perform 
OKE microscopy with high contrast.   
The first step in conversion from spectroscopy to microscopy will be to incorporate 
microscope objectives rather than lenses into the ARKS setup. For applications in 
microscopy we will need to design an objective mounting system that will allow us to 
control the distance between objectives readily for dealing with samples of different 
thickness or index of refraction. Long working distance, polarization-preserving 
objectives will be employed, although we will need to perform some characterization 
experiments to determine the experimental geometry that minimizes any 
depolarization. Once we have a handle on these issues from experiments in bulk 
 
                                                                     154  
liquids, we will incorporate a sample-scanning nanostage into the setup so that we can 
perform imaging experiments. For samples to characterize the resolution of the 
microscope, we will attach polymer nanobeads to microscope cover slips and make 
sealed cells that can hold solvent. We will then perform a series of experiments to 
determine the resolution and signal to noise in different contrast modes. When our 
microscope has been fully characterized, we will explore our ability to generate 
contrast for different types of biological samples. In terms of intramolecular 
vibrations, we expect OKE microscopy to be complementary to CARS microscopy, 
which tends to be used to observe modes with frequencies of 1000 cm-1 and greater. 
We will perform experiments to determine which types of modes can most readily be 
interrogated in different types of biological materials, including proteins, nucleic 
acids, polysaccharides, and lipids. 
 
7.5 References 
(1) Righini R. Science 1993, 262, 1386. 
(2) Fourkas, J. T. "Nonresonant Intermolecular Spectroscopy of Liquids," in Ultrafast 
Infrared and Raman Spectroscopy, M. D. Fayer, ed. (Marcel Dekker, New York, 
2001), pp. 473-512. 
(3) Smith, N. A.; Meech, S. R. Int. Rev. Phys. Chem. 2002, 21, 75. 
(4) Kinoshita, S.; Kai, Y.; Ariyoshi T.; Shimada, Y. Int. J. Mod. Phys. B 1996, 10, 
1229. 
(5) Loughnane, B. J.; Scodinu, A.; Farrer, R. A.; Fourkas, J. T.; Mohanty U. J. Chem. 
Phys. 1999, 111, 2686. 
 
                                                                     155  
(6) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. 
(7) Castner, Jr. E. W.; Maroncelli, M. J. Mol. Liq. 1998, 77, 1. 
(8) Kalpouzos, C.; McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A., Chem. 
Phys. Lett. 1988, 150, 138. 
(9) Steffen, T.; Meinders, N. A. C. M.; Duppen, K. J. Phys. Chem. A 1998, 102, 4213. 
(10) Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2003, 107, 44. 
(11) Neelakandan, M.; Pant, D.; Quitevis, E. L. Chem. Phys. Lett. 1997, 265, 283. 
(12) Shirota, H.; Castner, Jr. E. W. J. Am. Chem. Soc. 2001, 123, 12877. 
(13) Hunt, N. T.; Jaye, A. A.; Hellman, A.; Meech, S. R., J. Phys. Chem. B 2004, 108, 
100. 
(14) Loughnane, B. J.; Farrer, R. A.; Scodinu, A.; Reilly, T.; Fourkas, J. T. J. Phys. 
Chem. B 2000, 104, 5421. 
(15) Farrer, R. A.; Fourkas, J T. Acc. Chem. Res. 2003, 36, 605. 
(16) Hunt, N. T.; Jaye, A. A.; Meech, S. R. J. Phys. Chem. B 2003, 107, 3405. 
(17) Hunt, N. T.; Meech, S. R. J. Chem. Phys. 2004, 120, 10828. 
(18) Murry; R. L.; Fourkas, J. T. J. Chem. Phys. 1997, 107, 9726. 
(19) Eaves, J. D.; Fecko, C. J.; Stevens, A. L.; Peng, P.; Tokmakoff, A. Chem. Phys. 
Lett. 2003, 376, 20. 
(20) Fecko, C. J.; Eaves, J. D.; Tokmakoff, A. J. Chem. Phys. 2002, 117, 1139. 
(21) Chang, Y. J.; Cong, P.; Simon, J. D. J. Chem. Phys. 1997, 106, 8639. 
(22) Cong, P.; Chang, Y. J.; Simon, J. D. J. Phys. Chem. 1996, 100, 8613. 
(23) Trebino, R.; Hayden, C. C. Opt. Lett. 1991, 16, 493. 
(24) McMorrow, D. Opt. Commun. 1991, 86, 236. 
 
                                                                     156  
(25) Farrer, R. A.; Loughnane, B. J.; Deschenes, L. A.; Fourkas, J. T. J. Chem. Phys. 
1997, 106, 6901. 
(26) Murry, R. L.; Fourkas, J. T.; Keyes, T. J. Chem. Phys. 1998, 109, 2814. 
(27) Zhu, X.; Farrer, R. A.; Gershgoren,E.; Kapteyn, H. C.; Fourkas, J. T. J. Phys. 
Chem. B 2004, 108, 3384. 
(28) Frankiss, S. G. J. Mol. Struct. 1968, 2, 271. 
(29) Bradley, E. B.; Mathur, M. S.; Frenzel, C. A. J. Chem. Phys. 1967, 47, 4325. 
(30) Zhu, X.; Farrer, R. A.; Fourkas, J. T. J. Phys. Chem. B 2005, 109, 8481. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                                                                     157  
Chapter 8:  Conclusion and Future Prospect 
 
8.1 Conclusions and Future Prospects 
As the above studies illustrate, OKE spectroscopy has developed into a powerful 
method for probing microscopic dynamics in simple liquids1. It has become a well-
established, sensitive tool for studying orientational diffusion in transparent liquids. 
The temperature-dependent orientational dynamics of 1, n-dicyano n-alkane liquids 
ranging from dicyanomethane to 1,8-dicyanooctane have been studied2, and the 
results suggest that  a gauche-gauche conformation is adopted by the molecules in the 
liquids phase and a possible underlying, temperature-dependent, collective structural 
rearrangements within the liquids may exist . 
We are also trying to gain a solid understanding of the information available from 
RSDs. Based on the results of former OKE experiments on benzene and its 
derivatives3, we have proposed a model that connects the shape of the OKE reduced 
spectral density to local structure in liquids. The general validity of this model has 
been tested by performing OKE experiments on more aromatic liquids4. Our 
conclusion from these studies is that molecular shape plays a major role in 
determining the shape of the OKE RSD, although moment of inertia may play a role 
in determining its breadth. Some other factors, such as the distribution of the 
polarizability in a molecule, may play an additional role in determining whether the 
RSD will be ?rectangular?, ?triangular?, or somewhere in between. Nevertheless, it 
appears likely that it is molecular properties rather than local structural properties that 
tend to influence the shape of the RSD in simple, non-networked liquids.  
 
                                                                     158  
OKE spectroscopy has also proven to be a powerful means of studying the 
influence of different media on liquid dynamics. One of our interests is how 
nanoconfiement affects the microscopic properties of liquids. We have used OKE 
spectroscopy to study a sizable number of liquids in nanoconfinement, and the 
reorientational dynamics are greatly changed5. We expect some effects should be 
observed for intermolecular dynamics, and a good comparison between the 
intermolecular portion of OKE spectrum in confinement and in bulk will be quite 
suggestive. Another interest is in liquids under tension, in which the attractive forces 
are dominant between molecules instead of repulsive forces, so the intermolecular 
dynamics should be affected. We have developed a method to make liquid samples 
under tension based on a Berthelot tube technique6, reorientational diffusion data 
have been collected for acetonitrile under tension. We need to improve this method to 
maintain the liquid under tension for longer times so that we can perform 
intermolecular dynamics studies with OKE spectroscopy, which should provide 
interesting results. Besides these, additional experiment such as pressure-dependent 
studies would be also quite helpful for learning the microscopic properties of liquids 
in complex environments. 
The second-generation ARKS spectrometer that we have built7 not only offers 
advantages for obtaining different tensor elements of the optical Kerr response of 
liquids, but will also be a major element of the proposed OKE microscope. In 
combination with the multiple-pulse excitation schemes, this instrument should be 
capable of imaging with a high signal to noise ratio in a number of different contrast 
modes. The beam-shaping technique will further enhance the resolution of this 
 
                                                                     159  
instrument.  
We foresee one of the most exciting applications of OKE spectroscopy in the 
coming years to be its use in higher-order nonlinear-optical techniques. For instance, 
there has been great interest in a fifth-order version of OKE spectroscopy first 
proposed by Tanimura and Mukamel.8 This technique employs five laser pulses and 
two time delays, and has the potential to rephrase intermolecular modes in order to 
reveal information about the degree of inhomogeneous broadening in these modes. 
Implementing this technique in a manner that does not produce experimental artifacts 
proved difficult but was eventually accomplished.9 However, the signal in this 
spectroscopy is generally quite weak, and it has only been possible to obtain high-
quality data for highly polarizable molecules such as CS2. Further experimental 
advances may broaden the applicability of this type of spectroscopy. 
Another approach to the use of the optical Kerr effect in higher-order 
spectroscopies is to combine this technique with other optical processes. As an 
example, techniques called RaPTORS (resonant pump third-order Raman 
spectroscopy) developed by Blank and co-workers10 and PORS (polarizability 
response spectroscopy) developed by Scherer and co-workers11 use the optical Kerr 
effect to probe the response of a solvent to the electronic excitation of a solute. 
RaPTORS and PORS are revealing new details of the solvent response to a localized 
change in charge distribution. These techniques demonstrate the power of using the 
optical Kerr effect in one or more steps of a more complex, nonlinear-optical pulse 
sequence, and we look forward to the development of other methods based on this 
general approach to be developed in the near future. 
 
                                                                     160  
 
8.2 References 
(1) Zhong, Q., Fourkas, J. T. J. Phys. Chem. B 2008, 112, 15529. 
(2) Zhong, Q., Zhu, X., Fourkas, J. T. J. Phys. Chem. B 2008, 112, 3115. 
(3) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2006, 110, 5708. 
(4) Zhong, Q., Fourkas, J. T. J. Phys. Chem. B 2008, 112, 15342. 
(5) Zhu X., Farrer, R. A., Fourkas, J. T. J. Phys. Chem. B, 2005, 109, 12724. 
(6) Berthelot M., Ann. Chim. Phys. 1850, 30, 232. 
(7) Zhong, Q., Zhu, X., Fourkas, J. T. Opt. Expr. 2007, 15, 6561 
(8) Tanimura, Y.; Mukamel, S. J. Chem. Phys. 1993, 99, 9496. 
(9) Kaufman, L. J.; Heo, J. Y.; Ziegler, L. D.; Fleming, G. R. Phys. Rev. Lett. 2002, 
88, 207402. 
(10) Schmidtke, S. J.; Underwood, D. F.; Blank, D. A. J. Phys. Chem. A 2005, 109, 
7033. 
(11) Moran, A. M.; Nome, R. A.; Scherer, N. F. J. Chem. Phys. 2007, 127, 184505. 
 
 
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Appendices 
 
Appendix A: OKE Data Analysis Procedure Using LabView 
Program 
A) Process the Raw data 
For each sample at each temperature, we have three sets of data: 
1) Long step-size data for reorientational diffusion analysis: The step size 
is 50, 100, or 150, we usually collect 10-20 of them, sum them together then get the 
average, save the average data as a txt file named as ?long.txt?; 
2) Short step-size data for intermolecular dynamics study: The step size is 
1, and we usually collect 2 or 4 of them, sum them together, get the average, and then 
save as ?short.txt?; 
3) Autocorrelation data for Fourier transform: The step size is 1, usually 
we need to collect autocorrelation data twice, once before and once after we collect 
short step-size data, sum the two data, get the average and save as ?auto.txt?. 
All the three data files are one-column txt file. 
B) Input files 
1) ?Run? 
2) Input ?long?, ?short?, and ?autocorrelation? data for desired data sets. 
3) Choose appropriate time steps (used in experiment) for long and short 
time-step data. (For example, if the step-size for the ?long? data is 50, 
you should input 5 on the corresponding box.) 
4) ?Start?. 
 
                                                                     162  
 
C) Integrate and Fit 
1) Set ?weight? = 1/y 
2) Input you initial guess for the tri-exponential decay; if you plan to use 
bi-exponential decay to fit data, ?amp 3? should be set at 0. 
(In most cases, we use bi-exponential decay to fit data, so for the 
following procedures, bi-exponential decay is the default case.) 
3) Adjust cursors to choose the section of the graph that best corresponds 
to reorientational diffusion (usually 1.5?1 ps to > 4?2 ps, where ?1<?2) 
a. Note: there is often a ?Fitting Error? ? choose larger range on 
the graph and double click the red box to correct. 
4) View as ?log? graph. 
5) Adjust cursors until the fit line matches the data line (there should be 
no deviations and the data should look smooth). 
(2 
(4
))
(3
) 
 
                                                                     163  
a. The time constants should be stable even when varying the 
cursors slightly. 
6) ?next?  
 
D) AddTail 
1) Zoom out to look at entire graph (use x-axis and y-axis buttons next to 
?time? and ?amplitude?); 
2) Move cursor to trailing edge of data graph (white) and zoom in 
horizontally 
3) Adjust ?gain? until the red fit line matches up with the data (may need 
to continue zooming in) 
Note: if gain is too high, can try to decrease range size in Step 2 
4) ?join files?  
[This step of the procedure adjusts the biexponential decay function more precisely to 
match the short step-size data.] 
(1) 
(2) 
(3) 
(4) 
(5) 
   (6)
7
 
                                                                     164  
 
E) Fourier Transform (Time-domain data to frequency-domain spectrum) 
1) Adjust OKE zero value on bottom left graph until the right end of the 
broad low frequency spectrum goes smoothly to zero. Place the cursor 
somewhere between the low frequency spectrum and the Raman-active 
vibrational peaks; this will remove the contributions to OKE signal 
from low-frequency Raman-active modes. [This graph shows the 
frequency-domain Fourier transform of the signal] 
2) Adjust auto zero until the bottom right graph has smallest amplitude 
3) ?Done? 
(1) 
(2) 
(3) 
(4) 
 
                                                                     165  
 
F) Remove Reorientation Contribution (After inverse FT, back to the time domain) 
[The white line on the left of the yellow cursor is the time-domain data after inverse 
Fourier transform, with low frequency Raman-active modes removed; The white line 
on the right of the cursor is the tail of OKE data simulated using the bi-exponential 
decay formula.] 
1) Move the cursor to around 30 ps to cut the tail of the data on the left. Then, 
add a tail modeled by the bi-exponential decay formula by adjusting the 
?gain? until the two white lines are connected continuously and smoothly. 
2) Set ?Amp1? = 0 and ?Rise Time? = 200 fs. [By adjusting Amp1, the red line 
is only the reorientational diffusion part of the bi-exponential decay formula.]  
3) Adjust the ?Gain? until the tail of the red line fits the white curve. 
4) At the bottom left corner, change ?Time domain? to ?RSD? and 
unzoom/zoom as necessary to see RSD plot 
(1) 
(2) (3) 
 
                                                                     166  
5) ?Save?  
 
G) Excel: normalization and finalization of RSD plot 
1) Open text file with Excel [saved from LabView program] 
2) Column A is the x-axis (frequency) and Column B is y-axis (amplitude) 
(2) 
(1) 
(3) 
(4) 
(5) 
 
                                                                     167  
3) We want positive amplitudes, so for Column C input? =-B1? and extend to all 
cells 
4) To normalize, for Column D input ?=C1/max($C$1:$C$200)? 
5) Plot Column A vs. Column D (probably only need the first 500 points) 
 
 
 
 
 
 
 
                                                                     168  
Appendix B: Temperature-dependent viscosity, parameters from 
biexponential fits to the Integrated OKE data, and fitting ranges 
for 1, n-Dicyano n-Alkanes Studied in Chapter 3 
 
Table B.1: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated dicyanomethane OKE decays. 
 
Temperature (K) A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps)?
306 0.74 8.8(2) 3.1(1) 5.83 3.2 28.0 
314 0.75 7.6(2) 2.7(1) 3.32 3.0 25.0 
323 0.74 7.2(3) 2.3(2) 2.33 2.2 18.0 
330 0.77 5.7(2) 1.9(1) 1.86 2.0 15.0 
339 0.76 5.3(2) 1.7(1) 1.56 2.0 15.0 
347 0.71 5.0(2) 1.7(1) 1.37 2.0 14.0 
354 0.70 4.7(2) 1.7(1) 1.26 1.8 14.0 
360 0.69 4.5(2) 1.6(1) 1.19 1.8 12.5 
 
 
 
 
 
 
                                                                     169  
Table B.2: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated 1, 2-dicyanoethane OKE decays. 
 
 
Temperature (K) A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps) 
336 0.82 8.2(3) 2.3(1) 2.79 2.5 22.0 
343 0.82 7.3(3) 1.9(1) 2.36 2.0 20.0 
350 0.83 6.3(2) 1.7(1) 2.07 2.0 17.0 
358 0.82 5.9(2) 1.6(1) 1.86 2.0 17.0 
365 0.83 5.2(2) 1.4(1) 1.70 1.8 16.0 
372 0.84 4.8(1) 1.2(1) 1.57 1.6 15.0 
380 0.80 4.4(2) 1.2(1) 1.47 1.2 10.0 
 
 
 
 
 
 
 
 
 
 
 
                                                                     170  
Table B.3: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated 1, 3-dicyanopropane OKE decays. 
 
Temperature (K) A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps) 
289 0.76 39(4) 11(2) 7.93 10.0 70.0 
297 0.75 30(2) 8.9(8) 6.16 5.0 65.0 
306 0.73 25(3) 7.5(16) 4.87 8.0 45.0 
315 0.72 21(1) 6.1(4) 3.97 4.0 53.0 
332 0.68 14.9(2) 5.0(1) 2.80 3.0 62.0 
341 0.64 13.6(5) 4.7(3) 2.41 3.0 37.5 
350 0.67 11.4(3) 4.0(2) 2.11 2.8 37.0 
358 0.71 9.5(3) 3.2(3) 1.87 2.5 26.0 
367 0.67 8.8(2) 3.3(2) 1.68 2.6 30.0 
375 0.72 7.4(2) 2.4(2) 1.51 2.4 22.6 
 
 
 
 
 
 
 
 
 
                                                                     171  
Table B.4: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated 1, 4-dicyanobutane OKE decays. 
 
Temperature 
(K) 
A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps) 
275 0.83 71(9) 17(3) 14.0 10.0 110.0 
289 0.80 51(3) 14(1) 8.35 10.0 110.0 
293 0.73 50(4) 14(2) 7.28 8.0 90.0 
306 0.72 35(1) 10.4(6) 5.02 5.0 95.0 
319 0.73 24.2(7) 6.9(3) 3.69 4.5 70.0 
327 0.69 20.9(6) 6.6(4) 3.12 3.5 60.0 
341 0.68 16.8(5) 5.4(3) 2.47 3.0 47.0 
349 0.66 14.9(4) 5.0(2) 2.16 3.0 47.0 
358 0.66 12.9(3) 4.4(3) 1.92 3.0 40.0 
366 0.62 12.2(2) 4.1(2) 1.72 2.5 45.0 
375 0.66 10.2(2) 3.4(1) 1.56 2.5 40.0 
 
 
 
 
 
 
 
 
                                                                     172  
Table B.5: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated 1, 5-dicyanopentane OKE decays. 
 
Temperature 
(K) 
A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps) 
272 0.74 173(12) 51(5) 18.3 30.0 350.0 
281 0.75 136(42) 32(14) 12.6 20.0 160.0 
289 0.71 98(11) 25(4) 9.14 20.0 170.0 
297 0.70 76(6) 21(3) 6.93 15.0 145.0 
306 0.66 61(3) 17(2) 5.42 12.0 135.0 
314 0.65 50(2) 14(1) 4.35 10.0 120.0 
323 0.66 39(2) 11(1) 3.56 8.0 90.0 
331 0.62 34(2) 10(1) 2.99 8.0 80.0 
340 0.65 27(1) 7.9(8) 2.55 5.0 70.0 
348 0.62 24.6(7) 7.5(5) 2.22 5.0 72.0 
357 0.67 19.5(8) 5.7(6) 1.95 4.0 50.0 
374 0.64 15.9(7) 4.6(5) 1.56 4.0 40.0 
 
 
 
 
 
 
 
                                                                     173  
Table B.6: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated 1,6-dicyanohexane OKE decays. 
Temperature 
(K) 
A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps) 
289 0.74 102(12) 23(4) 10.1 10.0 160.0 
314 0.70 53(6) 12(2) 4.57 7.0 85.0 
323 0.67 45(9) 11(3) 3.70 5.0 60.0 
332 0.67 37(4) 9(2) 3.06 5.0 60.0 
340 0.65 33(6) 8(3) 2.59 5.0 47.0 
349 0.67 27(8) 6(2) 2.22 5.0 33.0 
366 0.71 18(1) 4.4(5) 1.70 5.0 45.0 
 
Table B.7: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated 1, 7-dicyanoheptane OKE decays. 
Temperature 
(K) 
A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps) 
306 0.70 104(24) 20(6) 6.48 10.0 130.0 
314 0.65 93(15) 17(4) 5.12 10.0 130.0 
331 0.64 64(9) 13(4) 3.42 8.0 95.0 
348 0.63 43(4) 8.0(13) 2.47 6.0 78.0 
357 0.61 41(5) 8.6(24) 2.15 5.0 65.0 
364 0.62 37(7) 7.6(28) 1.91 5.0 40.0 
 
 
                                                                     174  
 
Table B.8: Fit parameters, single-molecule orientational correlation times and 
viscosities for integrated 1,8-dicyanooctane OKE decays. 
 
Temperature 
(K) 
A ?1 (ps) ?2 (ps)? ? (cP) Fit start 
(ps) 
Fit end 
(ps) 
297 0.59 205(60) 43(13) 10.0 30.0 245.0 
306 0.58 173(22) 32(6) 7.49 25.0 270.0 
315 0.59 125(28) 26(8) 5.84 20.0 150.0 
323 0.59 110(10) 21(4) 4.66 15.0 190.0 
332 0.61 83(5) 15(2) 3.79 12.0 175.0 
340 0.60 73(6) 14(2) 3.18 10.0 135.0 
349 0.60 64(5) 11(2) 2.70 8.0 120.0 
358 0.62 47(5) 9(2) 2.32 6.0 80.0 
366 0.60 44(2) 8(1) 2.03 5.0 100.0 
 
 
 
                                                                     175  
Appendix C: Fit Parameters of Integrated OKE Data for All 
Five Aromatic Liquids Studied in Chapter 4 
Table C.1: Viscosity1 and fit parameters for integrated pyridine OKE decays. 
 
Temperature  
(K) 
Viscosity  
(cP) 
A ?or  
(ps) 
?i  
(ps)?
Fit start 
(ps) 
Fit end  
(ps)?
249 2.11 0.75 10.4(6) 2.8(5) 5 35 
258 1.77 0.73 8.7(5) 3.0(5) 5 28 
267 1.50 0.73 7.2(5) 2.6(4) 4.2 28 
275 1.29 0.75 5.8(4) 1.8(3) 3 22 
284 1.12 0.71 4.9(3) 1.4(3) 2.8 20 
297 0.926 0.73 4.1(3) 1.5(3) 2.8 16 
310. 0.778 0.72 3.3(2) 1.1(2) 2.5 15 
328 0.628 0.72 2.6(2) 0.86(8) 2.5 12 
349 0.496 0.71 2.1(2) 0.79(7) 2 10 
1 From Ito, N.; Kato, T. J. Phys. Chem. 1984, 88, 801. 
 
 
 
 
 
 
 
 
                                                                     176  
Table C.2: Viscosity2 and fit parameters for integrated pyridine-d5 OKE decays. 
 
Temperature  
(K) 
Viscosity 
(cP) 
A ?or (ps) ?i (ps)? Fit start 
(ps) 
Fit end  
(ps) 
240 2.76 0.72 14.2(8) 4.1(5) 6 45 
249 2.27 0.73 10.4(7) 2.7(4) 4 35 
257 1.91 0.72 9.6(7) 2.8(5) 4 35 
266 1.62 0.72 7.3(6) 2.0(3) 4 27 
275 1.39 0.73 6.2(4) 1.9(3) 3.5 22 
284 1.20 0.74 5.2(3) 1.5(3) 3.5 21 
298 0.983 0.73 4.2(3) 1.4(2) 3.6 20 
310 0.825 0.73 3.5(3) 1.3(2) 3 16 
328 0.664 0.70 2.7(2) 0.83(8) 2.8 12 
349 0.523 0.69 2.1(2) 0.69(7) 2.2 10 
2 From Holz, M.; Mao, X.-A.; Seiferling, D.; Sacco, A., J. Chem. Phys. 1996, 104, 
669. 
 
 
 
 
 
 
 
 
 
                                                                     177  
Table C.3: Fit parameters for integrated 2,4,6-trifluoropyridine OKE decays. 
 
Temperature (K) A ?or (ps) ?i (ps)? Fit start (ps) Fit end (ps) 
230 0.90 50(5) 12(1) 15 140 
239 0.89 38(4) 8.8(8) 10 90 
249 0.90 27(3) 5.3(6) 10 100 
258 0.88 22(3) 5.1(6) 8 85 
267 0.88 17(2) 4.1(5) 5 70 
280 0.88 13(1) 3.2(4) 5 50 
289 0.88 10.8(8) 3.0(4) 5 42 
298 0.88 9.4(7) 2.7(4) 5 40 
306 0.86 8.1(6) 1.8(3) 4 35 
315 0.85 7.2(5) 1.7(3) 4 35 
323 0.84 6. 2(5) 1.3(2) 3.5 25 
332 0.84 5.6(4) 1.3(2) 3 24 
 
 
 
 
 
 
 
 
 
                                                                     178  
Table C.4: Fit parameters for integrated 2,4,6-trimethylpyridine OKE decays. 
Temperature (K) A ?or (ps) ?i (ps)? Fit start (ps) Fit end (ps) 
243 0.82 58(5) 14(2) 11 125 
262 0.84 29(3) 8.1(9) 10 75 
278 0.76 21.5(9) 6.8(9) 9 60 
295 0.75 15.6(7) 5.3(7) 5.5 44 
312 0.64 12.6(8) 5.3(9) 5.4 48 
329 0.77 8.7(5) 2.9(5) 3.5 30 
351 0.80 6.2(4) 1.8(3) 2 22 
 
Table C.5: Fit parameters for integrated 1,3,5-tris(trifluoromethyl)benzene OKE 
decays. 
Temperature (K) A ?or (ps) ?i (ps)? Fit start (ps) Fit end (ps) 
285 0.64 41(7) 13(3) 8 75 
290 0.79 29(4) 8(2) 8 98 
298 0.70 27(4) 9(2) 8 50 
306 0.80 20(3) 6(1) 8 58 
315 0.81 16(2) 4(1) 5 40 
323 0.80 15(1) 4(1) 5 49 
331 0.73 14(1) 4(1) 4 38 
340 0.74 12.0(6) 3.7(5) 4 37.5 
348 0.75 10.6(5) 3.6(4) 4 32 
 
 
                                                                     179  
 
                                                                     180  
Appendix D: Viscosity and Fit Parameters of Integrated OKE 
Data for All Liquids Studied in Chapter 5 
Table D.1: Viscosity1 and fit parameters for integrated furan OKE decays. 
Temperature 
(K) 
Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start 
(ps) 
Fit end 
(ps)?
246 0.693 0.55 2.2(2) 0.57(8) 0.85 6.5 
254 0.608 0.54 1.9(2) 0.51(8) 0.78 5.5 
263 0.539 0.53 1.7(2) 0.48(8) 0.76 5.5 
272 0.481 0.53 1.5(2) 0.41(8) 0.65 4.5 
285 0.414 0.53 1.3(1) 0.38(7) 0.6 4.0 
298 0.361 0.51 1.1(1) 0.34(7) 0.6 4.0 
1 From Holland, R. S.; Smyth, C. P. J. Phys. Chem. 1955, 59, 1088. 
 
Table D.2: Viscosity2 and fit parameters for integrated THF OKE decays. 
 
2 From Sinha, A.; Roy, M. N. J. Chem. Eng. Data 2006, 51, 1415 and Giner, B.; 
Gascon, I.; Villares, A.; Cea, P.; Lafuente, C. J. Chem. Eng. Data 2006, 51, 1321. 
Temperature 
(K) 
Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start  
(ps) 
Fit end  
(ps) 
235 0.809 0.54 2.6(3) 0.67(8) 1.00 8.0 
253 0.689 0.50 2.1(3) 0.59(8) 0.86 6.4 
271 0.588 0.47 1.6(2) 0.48(7) 0.77 4.8 
285 0.517 0.47 1.3(2) 0.41(7) 0.70 4.2 
298 0.466 0.49 1.1(1) 0.33(6) 0.65 3.25 
 
                                                                     181  
Table D.3: Viscosities3 and fit parameters for integrated cyclopentane OKE decays. 
Temperature  
(K) 
Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start 
(ps) 
Fit end  
(ps) 
249 0.763 0.82 0.80(5) 0.23(4) 0.6 2.2 
297 0.423 0.74 0.61(5) 0.15(3) 0.56 2 
3 From Assael, M. J.; Dalaouti, N. K.; Dymond, J. H. Int. J. Thermophys. 2000, 21, 
621. 
 
Table D.4: Viscosities4 and fit parameters for integrated diethyl ether OKE decays. 
Temperature  
(K) 
Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start 
(ps) 
Fit end  
(ps) 
250 0.384 0.81 4.4(4) 1.0(1) 1.5 11 
258 0.345 0.76 3.7(3) 0.61(8) 0.8 7.5 
276 0.277 0.73 2.8(2) 0.51(7) 0.8 5.2 
298 0.220 0.67 2.1(2) 0.45(6) 0.8 5 
4 From Weast, R. C. CRC Handbook of Chemistry and Physics, 66th ed.; CRC Press: 
Boca Raton, 1985. 
 
Table D.5: Viscosities5 and fit parameters for integrated n-pentane OKE decays. 
Temperature 
(K) 
Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start 
(ps) 
Fit end  
(ps) 
215 0.571 0.78 7.9(8) 0.85(5) 1.5 12 
236 0.426 0.75 5.3(6) 0.69(5) 1.2 9 
297 0.230 0.57 2.2(4) 0.47(4) 1 5 
5 From Froba, A. P.; Pellegrino, L. P.; Leipertz, A. Int. J. Thermophys. 2004, 25, 1323. 
 
 
                                                                     182  
Table D.6: Viscosities6 and fit parameters for integrated tetrahydropyran OKE decays. 
 
Temperature 
(K) 
Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start 
(ps) 
Fit end  
(ps) 
242 2.17 0.63 2.55(7) 0.58(6) 0.75 5 
297 0.819 0.46 1.65(5) 0.43(5) 0.7 4.8 
6 From Comelli, F.; Francesconi, R.; Bigi, A.; Rubini, K. J. Chem. Eng. Data 2007, 
52, 639. 
 
Table D.7: Viscosities7 and fit parameters for integrated cyclohexane OKE decays. 
Temperature (K) Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start 
(ps) 
Fit end  
(ps) 
297 0.893 0.44 0.90(5) 0.27(5) 0.5 2.5 
324 0.638 0.48 0.75(4) 0.27(4) 0.5 2.25 
7 From Aminabhavi, T. M.; Patil, V. B.; Aralaguppi, M. I.; Phayde, H. T. S. J. Chem. 
Eng. Data 1996, 41, 521. 
 
Table D.8: Viscosities8 and fit parameters for integrated HMPA OKE decays. 
Temperature (K) Viscosity 
(cP) 
A ?1 (ps) ?2 (ps)? Fit start 
(ps) 
Fit end  
(ps) 
285 4.16 0.72 4.7(5) 0.66(9) 1 8 
337 1.59 0.63 3.3(4) 0.59(8) 1 7 
8 From Bhadani, S. N. Indian J. Chem. 1972, 10, 88. 
 
 
 
                                                                     183  
Glossary 
Four-wave Mixing 
Heterodyne 
Libration 
Nonlinear Optics  
Nonlinear Spectroscopy 
Optical Kerr Effect (OKE) 
Reorientational Diffusion 
Reduced Spectral Density (RSD) 
Spectrometer 
Tension 
 
                                                                     184  
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