Optical Kerr Effect Spectroscopy of Simple Liquids - The Journal of

J. Phys. Chem. B 2008, 112, 15529–15539

15529

CENTENNIAL FEATURE ARTICLE Optical Kerr Effect Spectroscopy of Simple Liquids† Qin Zhong‡ and John T. Fourkas*,‡,§,|,⊥ Department of Chemistry and Biochemistry, UniVersity of Maryland, College Park, Maryland 20742, Institute for Physical Science and Technology, UniVersity of Maryland, College Park, Maryland 20742, Maryland NanoCenter, UniVersity of Maryland, College Park, Maryland 20742, and Center for Nanophysics and AdVanced Materials, UniVersity of Maryland, College Park, Maryland 20742 ReceiVed: August 30, 2008

In this paper, we review the state of the field of optical Kerr effect (OKE) spectroscopy of simple liquids, with a focus on results from our laboratory. We discuss the history and the theoretical underpinnings of this technique. We consider contemporary issues in the interpretation of OKE spectra, including the origin of the “intermediate” response and the factors affecting the shape of the reduced spectral density. We highlight some applications of the OKE spectroscopy of simple liquids, including the study of liquid mixtures and the behavior of liquids in nanoconfinement. We also discuss future prospects for OKE spectroscopy and related techniques. I. Introduction 1969,1

Since its first demonstration in optical Kerr effect (OKE) spectroscopy2-5 has become a widely used technique for studying ultrafast dynamics in transparent fluids. 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. 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,6-8 supercooled liquids,9-12 ionic liquids,13-18 confined liquids,19-21 and liquids inside polymer networks.22-26 In this article, we will discuss work on the OKE spectroscopy of simple liquids by our group and by others; for a discussion of OKE work on complex systems, we refer the reader to a recent review by Hunt, Jaye, and Meech.5 We will begin with a brief review of the history of OKE spectroscopy. We will then discuss the basic theory of this technique and of its implementation, after which we will recount some of the important results in the OKE spectroscopy of simple liquids over the past 20 years. We will finish with a brief discussion of future prospects for this technique. II. History In 1875, John Kerr discovered the effect that now bears his name. In the Kerr effect, a DC electric field applied to a † This year marks the Centennial of the American Chemical Society’s Division of Physical Chemistry. To celebrate and to highlight the field of physical chemistry from both historical and future perspectives, The Journal of Physical Chemistry is publishing a special series of Centennial Feature Articles. These articles are invited contributions from current and former officers and members of the Physical Chemistry Division Executive Committee and from J. Phys. Chem. Senior Editors. * To whom correspondence should be addressed. E-mail: fourkas@ umd.edu. ‡ Department of Chemistry and Biochemistry. § Institute for Physical Science and Technology. | Maryland NanoCenter. ⊥ Center for Nanophysics and Advanced Materials.

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 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 Gires27 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 oscillating light field of a laser pulse creates induced dipoles in the liquid molecules. These induced dipoles interact with the laser field, creating a slight preference for molecules to align with their axis of maximum polarizability parallel to the laser polarization. This alignment creates a transient birefringence in the liquid that can be read out with a second pulse of light. The time dependence of the birefringence reveals information about microscopic dynamics. 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.1 In 1975, Ippen and Shank28 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.29 In Fouriertransform 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.

10.1021/jp807730u CCC: $40.75  2008 American Chemical Society Published on Web 10/10/2008

15530 J. Phys. Chem. B, Vol. 112, No. 49, 2008

Zhong and Fourkas

Qin Zhong received his B.S. degree from University of Science and Technology of China, in 2004. He is currently a graduate student with John Fourkas at the University of Maryland, College Park. His research is focused on studying the dynamics of simple liquids using ultrafast optical Kerr effect (OKE) spectroscopy and on the development of optical Kerr effect microscopy. John T. Fourkas received his B.S. and M.S. degrees in chemistry from the California Institute of Technology in 1986. He did his graduate work with Michael Fayer at Stanford University, where he received his Ph.D. in 1991. He was an NSF Postdoctoral Fellow with Mark Berg at the University of Texas at Austin and Keith Nelson at the Massachusetts Institute of Technology before joining the Chemistry faculty of Boston College in 1994. He has been the Millard Alexander Professor of Chemistry at the University of Maryland, College Park, since 2005. He is a Fellow of the American Physical Society, the Optical Society of America, and the American Association for the Advancement of Science.

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,30-36 revealing important microscopic details of the liquid dynamics and allowing specific contributions to the signal to be isolated. Multiple-beam techniques involving diffractive optics have proven to be powerful and robust methods for collecting data for different elements of the response tensor.33,36 III. Theory III.A. Experimental Geometry and Signal. The most common implementation of the optical Kerr effect is in a polarization spectroscopy geometry (Figure 1). 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. 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. The polarization spectroscopy configuration is sensitive to the difference between two elements of the third(3) order response, R(3) xxxx(t) and Rxxyy(t). In an isotropic medium, this 37 which is known as the difference is proportional to R(3) xyxy(t), 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.

Figure 1. Schematic layout for a polarization spectroscopy implementation of the optical Kerr effect. The pump pulse is polarized at 45°, and the probe pulse is polarized vertically. The analyzer polarizer is set to pass horizontally polarized light, and the leakage is measured as a function of delay between the pump and probe pulses. To implement optical heterodyne detection, a quarter-wave plate (QWP) is placed after the first polarizer in the probe beam.

Figure 2. 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.

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. The total electric field that passes through the analyzer is then ELO + EOKE(t). The intensity detected is the magnitude squared of this field, ILO + 2ELOEOKE(t) + IOKE(t). 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, IOKE(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, 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 heterodynedetected OKE decay, in this case for 2,4,6-trifluoropyridine at 306 K, are shown in Figure 2. This decay shows all of the features seen in typical time-domain OKE data. Around zero delay time there is a sharp feature that tracks the laser pulses. This feature is often called the electronic response, and arises from the electronic hyperpolarizability of the sample. The remainder of the decay is known collectively as the nuclear response. At times up to a few picoseconds, there is a gently decaying portion of the nuclear response that arises from the decay of Raman-active, collective intermolecular motions that are excited coherently by the pump pulse. We will discuss the microscopic origin of this portion of the response below. The long-time, monotonically decaying portion of the nuclear response arises from collective orientational diffusion of the liquid molecules. The oscillations in the nuclear response arise from low-frequency intramolecular modes that are excited coherently by the pump pulse. For an intramolecular Raman mode to appear in the OKE decay, it must be Raman active and have some degree of polarizability anisotropy. The OKE response is proportional to the negative time derivative of the collective orientational correlation function,

Centennial Feature Article

J. Phys. Chem. B, Vol. 112, No. 49, 2008 15531

S ∝ [Ipump X Iprobe] X R(3) xyxy

(2)

where X denotes a convolution. The quantity in square brackets is the instrument response, which can be written as

G(2)(t) )

Figure 3. Comparison of the OKE decay (black) and Ccoll(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.

Ccoll(t).38 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.39,40 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,41 and so integration is a straightforward process. A semilogarithmic plot of the OKE decay from Figure 2 and the corresponding Ccoll(t) are shown in Figure 3. 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. 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, τcoll, is related to the single-molecule orientational correlation time, τsm, via42

τcoll )

g2 τ j2 sm

(1)

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 yield microscopic structural information about a liquid. III.B. 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.29 The heterodyne-detected OKE signal S(t) is given by

∫-∞∞ Ipump(t′) Iprobe(t - t′) dt′

(3)

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,43 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) F [G(2)(t) X R(3) xyxy(t)] ) F [G (t)] × F [Rsysy (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 R(3) xyxy(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 4, we show the spectral density that corresponds to the OKE decay from Figure 2 as well as the deconvolved nuclear response function obtained by inverse Fourier transformation of the spectral density. 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(-t/τOKE)[1 - exp(-t/τrise)]

(4)

is subtracted from the nuclear response function, which is then Fourier transformed to obtain the RSD. The rise time τrise 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 2 is shown in Figure 5, along with the nuclear response function from which the contribution of orientational diffusion has been removed. This is an example of a “triangular” RSD (Vide infra). 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. III.C. 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 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.44 Although librations may involve complex motions of multiple molecules, librational scattering can be described in


Figure 4. 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.

Figure 5. 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.

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.45 The mechanism for this phenomenon is called interaction-induced (II) scattering, which arises from dipole/induced dipole (DID) effects.44 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. 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.46,47 Using CS2 as a model system, we have performed detailed molecular dynamics simulations and used instantaneous normal

Zhong and Fourkas mode theory to analyze the contributions to the OKE signal.48,49 We employed a point atomic polarizability model 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. Our studies indicated that, in both normal48 and supercooled49 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).48 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, we further found that even the isotropic spectrum, which arises solely from II effects, has a large component due to orientational motions.49 IV. Results IV.A. Intermediate Response. As discussed above, when the contribution of orientational relaxation to the nuclear response is removed, there generally remains another component of the decay that also has exponential or near-exponential behavior. This relaxation component is known as the “intermediate response”, and is a near universal feature of OKE decays in simple liquids. Although the intermediate response was first reported more than two decades ago,50 its origin is still poorly understood. McMorrow and Lotshaw modeled the intermolecular portion of the OKE decay by treating the intermolecular modes as a set of coherently excited oscillators that, depending on frequency, could be underdamped, critically damped, or overdamped.51 They suggested that the intermediate response arises from the latter two types of oscillators, which could explain the universality of this component of the OKE decay in simple liquids. We later proposed an extended version of this model that introduced frequency-dependent damping based on the thermal populations of the quantum levels of these intermolecular oscillators.52 This model successfully reproduced the essential features of the temperature-dependent OKE data for CS2 and acetonitrile but did not offer any sort of physical picture of the motions or damping mechanisms contributing to the intermediate response. The introduction of commercial Ti:sapphire lasers in the early 1990s made it feasible to obtain OKE data of considerably higher quality than had been achievable previously. The ability to measure orientational decays out to significantly longer time scales made it possible to determine the intermediate response time considerably more accurately than before. To help understand the origin of the intermediate response, we performed a detailed OKE study of six simple liquids: acetonitrile, acetonitrile-d3, benzene, CS2, chloroform, and methyl iodide.41 For each liquid, we determined the collective orientational correlation time and the intermediate response time (τi) over a broad range of temperatures. Where available, we also compared with single-molecule orientational correlation times derived from Raman and NMR spectroscopy. We will summarize a number of interesting results that stemmed from this work. According to the Debye-Stokes-Einstein (DSE) relation, the orientational correlation time of a molecule in a liquid should be proportional to viscosity over temperature (η/T).42,53 This relation is intended to apply to solute molecules in a solvent


Figure 6. Plot of the intermediate response time as a function of the collective orientational correlation time for a range of simple liquids. The red and dark red symbols are for nitriles,40 the blue and dark blue symbols are for dinitriles,56 the green and dark green symbols are for aromatics,54,55 and the black symbols are for CS2, methyl iodide, and chloroform.41

composed of molecules that are considerably smaller. However, the DSE relation generally works well for neat liquids as well. We found for the liquids studied that not only did τcoll and τsm scale with η/T, but so did τi.41 This result suggests that the intermediate response is connected to hydrodynamic processes. Since τcoll and τi both exhibit DSE behavior, it is natural to ask whether the intermediate response and orientational diffusion are related in some way. To test this hypothesis, we plotted τcoll as a function of τi for the six liquids studied. We found for these liquids that the two time constants are related by a factor that ranges between 3 and 5.41 Remarkably, this relationship has held true for every non-networked, simple liquid that we have studied since. In Figure 6, we show such a plot for a broad range of substances that include aromatics,54,55 nitriles,40 dinitriles,56 and other small-molecule liquids.41 We have proposed a model for the origin of the intermediate response based on its strong connection to orientational diffusion.41 The spectral density for the low-frequency modes of a liquid spans a broad range of frequencies, from roughly 200 cm-1 down to less than 1 cm-1. The time scale for one period of the intermolecular modes of the lowest intrinsic frequencies is comparable to or longer than the time scale for structural rearrangement of the liquid. Thus, the frequencies of the slowest modes in a liquid change on a time scale that can be shorter than their periods, and as a result, these modes are subject to motional narrowing. We proposed, on the basis of ideas from Kubo line shape theory,57 that such motional narrowing is responsible for the intermediate response. Faster orientational diffusion implies faster structural dynamics and therefore a greater degree of motional narrowing. Importantly, motional narrowing tends to smear details of the intrinsic form of the instantaneous, low-frequency spectral density, which can lead to the observed exponential intermediate response. Beyond the demonstration that τcoll and τi are closely related in an extensive range of simple liquids, experimental and simulation work on the temperature-dependent OKE spectroscopy of benzene by Righini and co-workers has provided additional support for this model.58,59 Although the intermediate response originally referred to relaxation on a time scale that was generally subpicosecond, it is clear from the data in Figure 6 that τi can extend out to considerably longer time scales in liquids with slow orientational diffusion. Within the framework of motional narrowing, a liquid that has slower structural evolution can have modes with clear identities down to lower frequencies than does a liquid with faster structural evolution.


Figure 7. Normalized amplitude of the contribution of orientational diffusion to Ccoll(t) as a function of temperature for a range of simple liquids. The symbols are the same as those in Figure 6.

Beyond the connection between the time scales of collective orientational diffusion and the intermediate response, we can also examine the relative magnitudes of each process. In Figure 7, we examine the relative contribution of orientational diffusion to Ccoll(t) as a function of temperature for the same liquids for which data are plotted in Figure 6. For these liquids, orientational diffusion typically accounts for between 60% and 90% of the decay due to these two processes. While there is no clear trend apparent in the comparison of the results for the different liquids, it is evident that the contribution of orientational diffusion tends to grow as the temperature of the liquid is decreased. The slope of this temperature dependence is similar for the different liquids that we have studied. One possible source of this behavior is the densification of liquids with decreasing temperature. The loss of free volume that accompanies densification will tend to reduce the amplitude of librations and other oscillatory intermolecular modes, which may in turn reduce the intensity of the portion of the OKE decay that arises from these motions. On the other hand, to first approximation, the amplitude of the contribution of orientational diffusion to Ccoll(t) should not depend upon density. To investigate these issues further, it would be of great interest to measure OKE spectra of liquids such as these over a broad range of pressures. IV.B. What Determines the Shape of RSDs? Assigning a microscopic interpretation of the OKE RSDs of simple, nonnetworked liquids has proven challenging. The RSDs of these liquids tend not to have distinct features. RSDs generally rise quickly at low frequency and then take on an appearance that is flat (“rectangular”), rounded, or sloped downward (“triangular”) as the frequency increases. No specific physical meaning has been associated conclusively with these shapes to date, although there are a number of different empirical functions that can do a good job of fitting typical RSDs. In studying depolarized scattering in noble-gas fluids, Bucaro and Litovitz found that the spectra could often be fit to a modified exponential function of the form60

I(ω) ∝ ωb exp(-ω/ωBL)

(5)

Since isolated atoms do not have a polarizability anisotropy, scattering in these systems necessarily arises from II effects. OKE RSDs can often be fit well to a combination of this Bucaro-Litovitz (BL) line shape and an antisymmetrized Gaussian (AG) line shape given by

I(ω) ∝ exp[-(ω - ω0)2 /(∆ω)2] exp[-(ω + ω0)2 /(∆ω)2] (6)


Figure 8. Temperature-dependent, height-normalized RSDs for benzene.54 The low-temperature spectra have a shape typical of “rectangular” RSDs. The data have been offset for clarity.

Although fits of RSDs to the sum of a BL function and an AG function are empirical, the reasoning behind the use of this combination is that the former function describes the II scattering and the latter represents the molecular scattering. Simulations of the OKE spectroscopy of simple liquids48,49 render this physical interpretation of fits based on the BL and AG functions doubtful for a number of reasons. First, there is generally a significant, negative cross-term between II and molecular scattering that distorts the shape of the RSD. Second, simulations performed with realistic distributed polarizability models indicate that II scattering tends to be considerably weaker than molecular scattering in depolarized spectra. Indeed, the cross-term between the two types of scattering is often of greater magnitude than the II scattering itself. Finally, while II scattering stems from translational motions in atomic fluids, in molecular liquids, it is usually generated predominantly by orientational rather than translational motions.49 As a result, there is no reason to believe that a BL function should describe the overall II scattering. The librational component of II scattering may resemble that of molecular scattering, but there is also a crossterm between the II scattering from translational and orientational motions that further complicates interpretation of RSDs. This viewpoint is bolstered by a comparison of the far-infrared spectrum of benzene with its OKE RSD.61 Because benzene has no dipole moment, its far-infrared spectrum stems entirely from II effects. However, over a broad range of temperatures, the far-infrared spectrum of this liquid is as broad as the corresponding OKE RSD, and the two types of spectra match well on the high-frequency side.61 We can gain some insight into OKE RSDs by examining how they depend on temperature. As an example, the RSDs of benzene are shown as a function of temperature in Figure 8. Benzene exhibits a typical temperature dependence for a liquid composed of molecules with a substantial polarizability and polarizability anisotropy. At high temperature, the spectrum has no distinct features but is skewed somewhat toward lower frequencies. As the temperature is decreased, the spectrum broadens at both the low-frequency and high-frequency sides to become “rectangular”. The behavior of the high-frequency portion of the benzene 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

Zhong and Fourkas

Figure 9. Temperature-dependent, height-normalized RSDs for tetrahydrofuran.64 These spectra are typical “rounded” RSDs. The data have been offset for clarity.

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 some liquids do not follow this typical behavior. For instance, aromatic liquids with fluorine substituents often have “triangular” RSDs.54,55,62 While the low-frequency portion of the RSD for such liquids does broaden somewhat with decreasing temperature, the influence of decreasing temperature on the high-frequency side of the RSD is subtle. SO2 is another anomalous liquid, as its entire RSD moves to higher frequency with decreasing temperature.63 For liquids with relatively low polarizabilities, such as saturated alkanes, the RSDs may change relatively little with temperature, and in particular do not generally appear rectangular at low temperatures.64 As an example, in Figure 9, we show temperature-dependent RSDs for tetrahydrofuran. The underlying causes of the differences in the temperature-dependent behavior of the RSDs of this last class of liquids are not known with any certainty, but based on the above observations, we can speculate that the magnitude of the polarizability and the manner in which it is spread about a molecule may play an important role. On the basis of simulations of the OKE spectrum of benzene, Ryu and Stratt47 suggested that molecular shape plays an important role in determining the form of the RSD. Inspired by experiments by Rajian, Hyun, and Quitevis showing that the RSDs of biphenyl are similar to those of benzene,65 Tao and Stratt extended this idea further.66 They showed that, to a good first approximation, the librational frequencies of planar molecules should be independent of the specific molecular geometry, and in particular of the moments of inertia. This theory can explain the similarity of the RSDs for the nonfluorinated aromatic liquids that have been studied by our group54,55,61 and others,58,67,68 although the shape of the RSDs of fluorinated aromatics remains more mysterious. OKE data from numerous liquids, from our group and others, support many aspects of this model. For instance, we have found many instances in which molecules of the same shape have RSDs that are also of the same shape, regardless of differences in electrostatics. A good example of a pair of liquids that exhibits this phenomenon is benzene and pyridine,55,68 for which RSDs are compared at two different temperatures in Figure 10. The frequency axis of the benzene RSDs has been scaled in these data to emphasize the overlap between the shapes of the spectra. The similarity between the RSDs of these two liquids is striking. Pyridine has a substantial dipole moment, while benzene has none. As a result, the liquid structure of benzene69 differs markedly from that of pyridine.70 The similarity of the RSDs of the two liquids suggests that molecular shape, rather than


Figure 10. Comparison of the height-normalized RSDs for benzene (black) and pyridine (red) at two different temperatures.55 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.

Figure 11. Comparison of the RSD for benzene at 300 K (black) with that of benzene-d6 at the same temperature (red) with the frequencies scaled by a factor of 1.1.54

local environment or electrostatics, is playing a leading role in determining the shape of the spectrum. Other examples of pairs of liquids for which similar results are seen include 1,3,5trifluorobenzene and 2,4,6-trifluoropyridine,55 tetrahydrofuran and cyclopentane,64 diethyl ether and n-pentane,64 and benzonitrile and nitrobenzene.67 The RSDs of the liquids in these examples span the breadth of different basic RSD shapes that are observed, suggesting that the importance of molecular shape is nearly universal in the OKE spectroscopy of simple, nonnetworked liquids. Comparative studies of the RSDs of aromatic liquids also allow us to examine the prediction by Tao and Stratt66 that moment of inertia should not play a strong role in determining librational frequencies. Isotopologues (molecules that differ only in isotopic composition) give us an ideal means of assessing this issue. Isotopologues have shapes that are virtually identical, and differ primarily in their moments of inertia and masses. In this situation, Tao and Stratt’s model predicts that the librational frequency should scale inversely with the square root of the mass of the molecule (rather than inversely with the square root of moment of inertia).66 Shown in Figure 11 are RSDs for benzene and benzene-d6 at the same temperature. The frequency axis of the RSD for benzene-d6 has been scaled by the inverse of the square root of the ratio of moments of inertia of these molecules. The ratio of the masses of the molecules (1.077) differs enough from the ratio of the moments of inertia (1.224) that we can clearly distinguish between the two possible scalings in our data. We should also note that the molar volume in benzene-d6 is slightly smaller than that in benzene, which may serve to make the apparent scaling factor somewhat smaller still. We have found


Figure 12. OKE decays (red) and biexponential fits (black) for various mole fractions of CS2 in 2-methylhexane.71 The data have been offset for clarity.

similar results in a comparison of the OKE RSDs for pyridine and pyridine-d5, but more isotopologues should be examined. 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 factor, 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, nonnetworked liquids. This is a somewhat discouraging conclusion from the standpoint of using OKE spectroscopy to learn about the microscopic properties of liquids, but the issue is worthy of further scrutiny before this conclusion can be considered definitive. IV.C. OKE Spectroscopy of Mixtures of Simple Liquids. The behavior of mixtures of simple liquids in OKE spectroscopy is another topic that has received a significant amount of attention. The systems studied in these experiments can be divided roughly into weakly interacting liquids and strongly interacting liquids. In a typical experiment in a weakly interacting system, a liquid with a strong optical Kerr response (such as CS2 or benzene) is mixed with a liquid with a weak optical Kerr response (such as a saturated alkane or CCl4). One application of such an experiment is the measurement of g2. As the concentration of the species of interest is decreased, g2 also decreases, reaching unity in the limit of infinite dilution.42 If the host liquid has the same viscosity as the liquid of interest, then g2 (or, more accurately, g2/j2) can be determined by comparing the collective orientational correlation time in the neat and infinitely dilute limits. One catch in this strategy is that saturated alkanes (and even CCl4) do exhibit orientational responses in their OKE decays, making data fitting more difficult at high dilutions. For instance, in Figure 12, we show OKE decays for mixtures of CS2 and 2-methylhexane at a temperature at which these liquids are isoviscous.71 Even at relatively high mole fractions of CS2, the contribution of the alkane to the decay is quite evident. Another complication is that, if the orientational dynamics of the two components are correlated, the two decay times will be modulated by these cross-correlations.72 This effect does not seem to be a problem for CS2 in alkanes71 but may well arise in other systems. In the case of CS2, τsm is known over a broad range of temperatures from NMR measurements.73 Thus, we were able to make a direct test of the effectiveness of the dilution method in determining g2/j2.71 In isoviscous mixtures of CS2 in


Zhong and Fourkas

Figure 13. Height-normalized RSDs for various mole fractions of CS2 in 2-methylhexane.71 The dashed plot is the RSD for the pure alkane. The data have been offset for clarity.

Figure 14. Integrated OKE decays for mixtures of benzene and HFB at various benzene mole fractions.85 The data have been offset for clarity.

2-methylhexane, the value of g2/j2 at infinite dilution is about 1.2 times greater than that determined using τsm from NMR. Similarly, in isoviscous solutions of CS2 in n-hexane, the value of g2/j2 at infinite dilution is about 1.05 times greater than the value determined using τsm from NMR. These results highlight another complication that can arise in experiments with mixtures: when the “solvent” molecules are larger than the “solute” molecules, the microscopic viscosity is not necessarily the same as the macroscopic viscosity. Another effect that is commonly observed in the OKE spectroscopy of weakly interacting liquids is that the RSD depends strongly upon composition.71,74-76 As an example, RSDs for mixtures of CS2 and 2-methylhexane are shown in Figure 13. The RSD shifts to significantly lower frequencies as the fraction of CS2 is decreased, and for no mixture can the RSD be described in terms of a linear combination of the RSDs for the neat liquids.71 There has been some controversy as to the origin of this type of shift in RSD upon dilution, although the suggestion of McMorrow et al.76 that this effect stems from a softening of the intermolecular potential upon dilution now appears to have strong support. We have shown that data such as those in Figure 13 can be fit with a model77 in which there is an inhomogeneous distribution of damped harmonic oscillators. Describing this distribution using an antisymmetrized Gaussian, we found that the effective broadening is constant with composition, with only the characteristic frequency ω0 varying. The apparent narrowing of the spectra with increasing dilution can thus be interpreted as arising solely from a spectral shift that is roughly linear in the CS2 volume fraction. Within the framework of this model, we have compared the behavior of CS2 in mixtures with 2-methylhexane and with n-hexane, in each case at the temperature at which the mixtures are isoviscous at all compositions. We found that the RSDs in 2-methylhexane are consistently red-shifted compared to those in n-hexane.71 To give an idea of the size of this effect, the limiting value of ω0 at infinite dilution in n-hexane is approximately 20% greater than the corresponding value in 2-methylhexane. We have proposed that this difference arises from the fact that n-hexane has a higher degree of microscopic order,78-80 effectively stiffening the local potential about an isolated CS2 molecule. In strongly interacting systems, there is significant molecular association that adds new complexity to the OKE decays. A prime example is mixtures of benzene and hexafluorobenzene (HFB). In benzene the π clouds are electron rich and the edges of the molecule are electron poor, whereas in HFB the opposite is the case. These molecules thus end up having quadrupole moments that are nearly equal in magnitude but are opposite in

sign. As a result, in mixtures of these two liquids, there is a strong tendency for benzene and HFB to make face-to-face heterodimers.81,82 Due to this effect, equimolar mixtures of the two liquids freeze at a significantly higher temperature than do the neat liquids.83 The benzene/HFB system was first studied with OKE spectroscopy by Neelakandan, Pant, and Quitevis, who observed large deviations from additivity in the RSDs.84 This system was later studied in greater detail with a combination of experimental data from our group and theory and simulations by Elola and Ladanyi.85 This study underscores the importance of using such a multipronged approach in strongly interacting liquid mixtures. The collective orientational decay time of HFB is more than 5 times greater than that of benzene. One immediately striking feature of the OKE decays for mixtures of these liquids is that the orientational decay times are longer than that of HFB, even when the mole fraction of HFB is less than 0.1 (Figure 14). The orientational portion of the decays can be fit well to a biexponential function. Understanding the microscopic origin of these two exponentials is a challenge, as the collective orientational correlation function formally includes contributions from benzene-benzene correlations, HFB-HFB correlations, and benzene-HFB correlations. Previous theoretical work has suggested that this situation should lead to biexponential decays in which the slowest decay time becomes slower and the fastest decay time becomes faster.72 However, simulations of this system indicate that the minority component in the benzene/ HFB mixtures has the slower relaxation rate for self-correlations.85 The surprising implication of this result is that the slower relaxation in mixtures that are rich in HFB is connected to benzene-benzene correlations rather than to HFB-HFB correlations. These simulations additionally showed that the relaxation rate for cross-correlations is the same as that for the slower self-correlations.85 Given this guidance from simulation, we were able to make a clear interpretation of the experimental OKE decays for benzene/HFB mixtures.85 As shown in Figure 15, the collective orientational correlation time for the benzene component increases linearly with decreasing benzene mole fraction. The collective orientational correlation time for HFB, on the other hand, is nearly equal for the neat liquid and in the limit of infinite dilution, and reaches a maximum value that is roughly 25% larger near a mole fraction of 0.5. This example illustrates that the OKE spectroscopy of mixtures of strongly interacting, simple liquids can be far from simple. However, it is also clear that theory and simulation can be powerful tools that facilitate the interpretation of experimental data. It will be interesting to see if the behavior of this system is mirrored in other mixtures of strongly interacting liquids.



Figure 16. OKE decays for 2-butyne in the bulk and confined in pores of different diameters.91 Dotted lines are triexponential fits to the data. The data have been offset for clarity. Figure 15. Collective orientational correlation times for benzene and HFB in mixtures at various benzene mole fractions.85

IV.D. OKE Spectroscopy of Simple Liquids in Complex Environments. As is clear from the above discussion of strongly interacting systems, the behavior of a simple liquid can be highly dependent upon the environment in which it is placed. OKE spectroscopy has proven to be a powerful means of studying the influence of different media on liquid dynamics. For example, Heisler et al. have used OKE spectroscopy to study the dynamics of CS2 in polystyrene,26 and Meech and coworkers have used OKE spectroscopy to probe the dynamics of a number of different simple liquids in microemulsions.24,86,87 Our group has used OKE spectroscopy to study the structure and dynamics of a range of simple liquids confined in nanoporous, sol-gel glass samples.19,20 These materials have pores that are roughly cylindrical and whose average diameter can be controlled synthetically down to less than 20 Å.88 Monolithic samples with relatively narrow pore-size distributions can be fabricated. The pores of a monolith can be filled completely with the liquid of interest by immersion. Our work on OKE spectroscopy of liquids confined in these media has been reviewed in detail elsewhere,19,20 so here we will only give two illustrative examples. As was the case for mixtures, it is useful to categorize liquids confined in these sol-gel glasses based upon the strength of their interactions with the silica surfaces relative to the strength of the interactions among the liquid molecules themselves. We begin by considering weakly interacting liquids, examples of which include CS2,89,90 2-butyne,91 chloroform,92 and methyl iodide.93 A recurring theme in the OKE spectroscopy of these liquids in confinement is that the decays have one exponential component that matches the decay of the bulk liquid as well as an additional component or components that decay considerably more slowly. As an example, OKE decays of 2-butyne in the bulk and in pores of different diameters are shown in Figure 16. Our interpretation of the behavior of weakly interacting liquids in confinement is that molecules at the pore surfaces have inhibited dynamics, whereas molecules in the pore centers are relatively unaffected by confinement. The amplitudes of the exponentials in the decay can be used to show that the surface layer of molecules with inhibited dynamics is generally less than a monolayer thick in such systems. This observation suggests that the dynamics at the pore surfaces depend upon molecular orientation. We have proposed a model in which molecules that are perpendicular to the pore surfaces are essentially unaffected by proximity to the surfaces, whereas molecules that are parallel to the surfaces experience two types of dynamic inhibition.91 First, reorientation of a molecule off of the pore surface requires that a greater volume of liquid be

Figure 17. OKE decays for acetonitrile in the bulk and confined in pores of different diameters.94 The data have been offset for clarity.

displaced than for the same motion to occur in the bulk. This effect should be independent of pore diameter, and for a cylindrical molecule should double the orientational correlation time. Second, reorientation along a curved surface will be inhibited due to geometrical effects that will grow stronger as the pore curvature increases but that will disappear at a flat surface. Our data for 2-butyne are in excellent agreement with this model.91 A prototypical strongly interacting system is acetonitrile.94,95 Acetonitrile molecules can accept hydrogen bonds from surface silanol groups, providing a stronger interaction with the pore surfaces than with other liquid molecules. As can be seen in Figure 17, these strong interactions with the pore surfaces can lead to extremely slow orientational dynamics. All of the OKE decays for this liquid in confinement can be fit to a sum of three exponentials, the time constants for which do not depend on pore diameter at a given temperature. As was the case for weakly interacting liquids, the time scale of the fastest exponential matches that for orientational relaxation in the bulk liquid. We have developed a model to account for the behavior seen in the OKE spectra of confined acetonitrile.94,95 Due to the significant dipole moment of this molecule, it has a strong tendency to form antiparallel dimers in the bulk liquid. Similar behavior would be expected at the pore surfaces. Thus, roughly half of the molecules would have a chance to hydrogen bond to the surface silanol groups, whereas the other half would be interdigitated and facing in the opposite direction. The slow dynamics of the hydrogen-bonded molecules constrain the dynamics of the interdigitated molecules, accounting for the slowest decay observed. However, the interdigitated molecules can also exchange into the bulk-like fraction of the liquid, providing a new channel for relaxation that we believe accounts for the exponential decay with the relaxation time that is slower

15538 J. Phys. Chem. B, Vol. 112, No. 49, 2008 than that of the bulk but faster than that of the hydrogen-bonded molecules. In support of this model, our data indicate that about half of the surface molecules are exchangeable. In addition, comparison with NMR experiments96 indicates that there is a greater degree of parallel ordering at the pore surfaces than in the bulk. Results from other techniques, such as infrared spectroscopy97 and vibrational sum frequency generation,98 also support this picture. These examples give a flavor for how OKE spectroscopy can be used to obtain dynamic information about simple liquids in complex environments, in turn yielding structural insights. This approach is all the more powerful when OKE spectroscopy is combined with other techniques that give complementary information. V. Future Prospects and Conclusions As the above examples illustrate, OKE spectroscopy has developed into a powerful method for probing microscopic dynamics in simple liquids. It has become a well-established, sensitive tool for studying orientational diffusion in transparent liquids. We are also beginning to gain a solid understanding of the information available from RSDs, although additional work such as pressure-dependent studies would be quite helpful in this regard. OKE spectroscopy has also proven to be an effective means of learning about the microscopic properties of liquids in mixtures and in complex environments, and interest in using it to study these types of systems is continuing to grow. 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.99 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.100 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-workers101 and PORS (polarizability response spectroscopy) developed by Scherer and co-workers102 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. Acknowledgment. This work was supported by the National Science Foundation, grants CHE-9501598, CHE-0073228, CHE0314020, CHE-0608045, and CHE-0628178. We are grateful to former group members who have taken part in some of the work described here, including Brian Loughnane, Rick Farrer, Bob Murry, Alessandra Scodinu, and Xiang Zhu. We also gratefully acknowledge collaborators on this work, including

Zhong and Fourkas Tom Keyes, Udayan Mohanty, Branka Ladanyi, Dolores Elola, Cecilie Rønne, and Søren Keiding. References and Notes (1) Duguay, M. A.; Hansen, J. W. Appl. Phys. Lett. 1969, 15, 192. (2) Righini, R. Science 1993, 262, 1386. (3) Kinoshita, S.; Kai, Y.; Ariyoshi, T.; Shimada, Y. Int. J. Mod. Phys. B 1996, 10, 1229. (4) 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. (5) Hunt, N. T.; Jaye, A. A.; Meech, S. R. Phys. Chem. Chem. Phys. 2007, 9, 2167. (6) Deeg, F. W.; Fayer, M. D. J. Mol. Liq. 1990, 45, 19. (7) Gottke, S. D.; Cang, H.; Bagchi, B.; Fayer, M. D. J. Chem. Phys. 2002, 116, 6339. (8) Hunt, N. T.; Meech, S. R. J. Chem. Phys. 2004, 120, 10828. (9) Torre, R.; Bartolini, P.; Pick, R. M. Phys. ReV. E 1998, 57, 1912. (10) Torre, R.; Bartolini, P.; Ricci, M.; Pick, R. M. Europhys. Lett. 2000, 52, 324. (11) Hinze, G.; Brace, D. D.; Gottke, S. D.; Fayer, M. D. J. Chem. Phys. 2000, 113, 3723. (12) Glorieux, C.; Nelson, K. A.; Hinze, G.; Fayer, M. D. J. Chem. Phys. 2002, 116, 3384. (13) Cang, H.; Li, J.; Fayer, M. D. J. Chem. Phys. 2003, 119, 13017. (14) Rajian, J. R.; Li, S. F.; Bartsch, R. A.; Quitevis, E. L. Chem. Phys. Lett. 2004, 393, 372. (15) Shirota, H.; Castner, E. W. J. Phys. Chem. A 2005, 109, 9388. (16) Li, J.; Wang, I.; Fruchey, K.; Fayer, M. D. J. Phys. Chem. A 2006, 110, 10384. (17) Xiao, D.; Rajian, J. R.; Li, S. F.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. B 2006, 110, 16174. (18) Shirota, H.; Wishart, J. F.; Castner, E. W. J. Phys. Chem. B 2007, 111, 4819. (19) Loughnane, B. J.; Farrer, R. A.; Scodinu, A.; Reilly, T.; Fourkas, J. T. J. Phys. Chem. B 2000, 104, 5421. (20) Farrer, R. A.; Fourkas, J. T. Acc. Chem. Res. 2003, 36, 605. (21) Portuondo-Campa, E.; Tortschanoff, A.; van Mourik, F.; Chergui, M. Chem. Phys. 2007, 341, 11. (22) Shirota, H.; Castner, E. W. J. Chem. Phys. 2006, 125, 034904. (23) Shirota, H. J. Phys. Chem. B 2005, 109, 7053. (24) Hunt, N. T.; Jaye, A. A.; Hellman, A.; Meech, S. R. J. Phys. Chem. B 2004, 108, 100. (25) Hunt, N. T.; Meech, S. R. Chem. Phys. Lett. 2004, 400, 368. (26) Heisler, I. A.; Correia, R. R. B.; Buckup, T.; Cunha, S. L. S.; da Silveira, N. P. J. Chem. Phys. 2005, 123, 6. (27) Mayer, G.; Gires, F. Compt. Rend. 1964, 258, 2039. (28) Ippen, E. P.; Shank, C. V. Appl. Phys. Lett. 1975, 26, 92. (29) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. (30) Cong, P. J.; Chang, Y. J.; Simon, J. D. J. Phys. Chem. 1996, 100, 8613. (31) Chang, Y. J.; Cong, P. J.; Simon, J. D. J. Chem. Phys. 1997, 106, 8639. (32) Zhong, Q.; Zhu, X.; Fourkas, J. T. Opt. Express 2007, 15, 6561. (33) Hunt, N. T.; Jaye, A. A.; Meech, S. R. Chem. Phys. Lett. 2003, 371, 304. (34) Fecko, C. J.; Eaves, J. D.; Tokmakoff, A. J. Chem. Phys. 2002, 117, 1139. (35) Constantine, S.; Gardecki, J. A.; Zhou, Y.; Ziegler, L. D.; Ji, X. D.; Space, B. J. Phys. Chem. A 2001, 105, 9851. (36) Khalil, M.; Demirdoven, N.; Golonzka, O.; Fecko, C. J.; Tokmakoff, A. J. Phys. Chem. A 2000, 104, 5711. (37) Butcher, P. N.; Cotter, D. The Elements of Nonlinear Optics; Cambridge University Press: Cambridge, U.K., 1990. (38) Dhar, L.; Rogers, J. A.; Nelson, K. A. Chem. ReV. 1994, 94, 157. (39) Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2002, 106, 10292. (40) Zhu, X.; Farrer, R. A.; Zhong, Q.; Fourkas, J. T. J. Phys.: Condens. Matter 2005, 17, S4105. (41) Loughnane, B. J.; Scodinu, A.; Farrer, R. A.; Fourkas, J. T.; Mohanty, U. J. Chem. Phys. 1999, 111, 2686. (42) Kivelson, D.; Madden, P. A. Annu. ReV. Phys. Chem. 1980, 31, 523. (43) Gradshteyn, I. S.; Ryzhik, I. M. Tables of Integrals, Series, and Products; Academic Press: San Diego, CA, 1980. (44) Murry, R. L.; Fourkas, J. T. J. Chem. Phys. 1997, 107, 9726. (45) Castner, E. W., Jr.; Chang, Y. J.; Melinger, J. S.; McMorrow, D. J. Lumin. 1994, 60/61, 723. (46) Ladanyi, B. M.; Klein, S. J. Chem. Phys. 1996, 105, 1552. (47) Ryu, S.; Stratt, R. M. J. Phys. Chem. B 2004, 108, 6782. (48) Murry, R. L.; Fourkas, J. T.; Keyes, T. J. Chem. Phys. 1998, 109, 2814.

Centennial Feature Article (49) Murry, R. L.; Fourkas, J. T.; Li, W.-X.; Keyes, T. Phys. ReV. Lett. 1999, 83, 3550. (50) Kalpouzos, C.; Lotshaw, W. T.; McMorrow, D.; Kenney-Wallace, G. A. J. Phys. Chem. 1987, 91, 2028. (51) McMorrow, D.; Lotshaw, W. T. Chem. Phys. Lett. 1991, 178, 69. (52) Farrer, R. A.; Loughnane, B. J.; Deschenes, L. A.; Fourkas, J. T. J. Chem. Phys. 1997, 106, 6901. (53) Debye, P. Polar Molecules; Dover: New York, 1929. (54) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2006, 110, 5708. (55) Zhong, Q.; Fourkas, J. T. J. Phys. Chem. B, in press. (56) Zhong, Q.; Zhu, X.; Fourkas, J. T. J. Phys. Chem. B 2008, 112, 3115. (57) Kubo, R. A Stochastic Theory of Line-Shape and Relaxation. In Fluctutation, Relaxation and Resonance in Magnetic Systems; Haar, D. T., Ed.; Oliver and Boyd: Edinburgh, Scotland, 1961; p 23. (58) Ricci, M.; Bartolini, P.; Chelli, R.; Cardini, G.; Califano, S.; Righini, R. Phys. Chem. Chem. Phys. 2001, 3, 2795. (59) Chelli, R.; Cardini, G.; Ricci, M.; Bartolini, P.; Righini, R.; Califano, S. Phys. Chem. Chem. Phys. 2001, 3, 2803. (60) Bucaro, J. A.; Litovitz, T. A. J. Chem. Phys. 1971, 54, 3846. (61) Rønne, C.; Jensby, K.; Loughnane, B. J.; Fourkas, J.; Nielsen, O. F.; Keiding, S. R. J. Chem. Phys. 2000, 113, 3749. (62) Neelakandan, M.; Pant, D.; Quitevis, E. L. J. Phys. Chem. A 1997, 101, 2936. (63) Jaye, A. A.; Hunt, N. T.; Meech, S. R. J. Chem. Phys. 2006, 124, 024506. (64) Zhong, Q.; Fourkas, J. T. J. Phys. Chem. B 2008, 112, 8656. (65) Rajian, J. R.; Hyun, B. R.; Quitevis, E. L. J. Phys. Chem. A 2004, 108, 10107. (66) Tao, G. H.; Stratt, R. M. J. Phys. Chem. B 2006, 110, 976. (67) Smith, N. A.; Meech, S. R. J. Phys. Chem. A 2000, 104, 4223. (68) McMorrow, D.; Lotshaw, W. T. Chem. Phys. Lett. 1993, 201, 369. (69) Bartsch, E.; Bertagnolli, H.; Schulz, G.; Chieux, P. Ber. BunsenGes. Phys. Chem. 1985, 89, 147. (70) Bertagnolli, H.; Engelhardt, T.; Chieux, P. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 512. (71) Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 2003, 107, 44. (72) Bauer, D. R.; Braumann, J. I.; Pecora, R. J. Chem. Phys. 1975, 63, 53. (73) Korb, J.-P.; Xu, S.; Cros, F.; Malier, L.; Jonas, J. J. Chem. Phys. 1997, 107, 4044. (74) Kalpouzos, C.; McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. Chem. Phys. Lett. 1988, 150, 138. (75) Kalpouzos, C.; McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. Chem. Phys. Lett. 1989, 155, 240.

J. Phys. Chem. B, Vol. 112, No. 49, 2008 15539 (76) McMorrow, D.; Thantu, N.; Melinger, J. S.; Kim, S. K.; Lotshaw, W. T. J. Phys. Chem. 1996, 100, 10389. (77) McMorrow, D.; Thantu, N.; Kleiman, V.; Melinger, J. S.; Lotshaw, W. T. J. Phys. Chem. A 2001, 105, 7960. (78) Brady, G. W.; Fein, D. B. J. Appl. Crystallogr. 1975, 8, 261. (79) Rigby, D.; Roe, R. J. J. Chem. Phys. 1988, 89, 5280. (80) Small, D. M. The Physical Chemistry of Lipids; Plenum: New York, 1986. (81) Bartsch, E.; Bertagnolli, H.; Chieux, P. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 34. (82) Cabac¸o, M. I.; Danten, Y.; Besnard, M.; Guissani, Y.; Guillot, B. J. Phys. Chem. B 1998, 102, 10712. (83) Patrick, C. R.; Prosser, G. S. Nature 1960, 187, 1021. (84) Neelakandan, M.; Pant, D.; Quitevis, E. L. Chem. Phys. Lett. 1997, 265, 283. (85) Elola, M. D.; Landanyi, B. M.; Scodinu, A.; Loughnane, B. J.; Fourkas, J. T. J. Phys. Chem. B 2005, 109, 24085. (86) Hunt, N. T.; Jaye, A. A.; Meech, S. R. J. Phys. Chem. B 2003, 107, 3405. (87) Jaye, A. A.; Hunt, N. T.; Meech, S. R. Langmuir 2005, 21, 1238. (88) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing; Academic Press: San Diego, CA, 1990. (89) Farrer, R. A.; Loughnane, B. J.; Fourkas, J. T. J. Phys. Chem. A 1997, 101, 4005. (90) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 1999, 103, 6061. (91) Scodinu, A.; Farrer, R. A.; Fourkas, J. T. J. Phys. Chem. B 2002, 106, 12863. (92) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. Chem. Phys. 2000, 253, 323. (93) Loughnane, B. J.; Fourkas, J. T. J. Phys. Chem. B 1998, 102, 10288. (94) Loughnane, B. J.; Farrer, R. A.; Fourkas, J. T. J. Phys. Chem. B 1998, 102, 5409. (95) Loughnane, B. J.; Farrer, R. A.; Scodinu, A.; Fourkas, J. T. J. Chem. Phys. 1999, 111, 5116. (96) Zhang, J.; Jonas, J. J. Phys. Chem. 1993, 97, 8812. (97) Kittaka, S.; Iwashita, T.; Serizawa, A.; Kranishi, M.; Takahara, S.; Kuroda, Y.; Mori, T.; Yamaguchi, T. J. Phys. Chem. B 2005, 109, 23162. (98) Henry, M. C.; Wolf, L. K.; Messmer, M. C. J. Phys. Chem. B 2003, 107, 2765. (99) Tanimura, Y.; Mukamel, S. J. Chem. Phys. 1993, 99, 9496. (100) Kaufman, L. J.; Heo, J. Y.; Ziegler, L. D.; Fleming, G. R. Phys. ReV. Lett. 2002, 88, 207402. (101) Schmidtke, S. J.; Underwood, D. F.; Blank, D. A. J. Phys. Chem. A 2005, 109, 7033. (102) Moran, A. M.; Nome, R. A.; Scherer, N. F. J. Chem. Phys. 2007, 127, 13.

JP807730U

Optical Kerr Effect Spectroscopy of Simple Liquids - The Journal of

Recommend Documents