Multiple short time power laws in the orientational relaxation of nematic liquid crystals

Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.     

Comparative study of temperature dependent orientational relaxation in a model thermotropic liquid crystal and in a model supercooled liquid

Recent optical Kerr effect experiments have revealed a power law decay of the measured signal with a temperature independent exponent at short-to-intermediate times for a number of liquid crystals in the isotropic phase near the isotropic-nematic transition and supercooled molecular liquids above the mode coupling theory critical temperature. In this work, the authors investigate the temperature dependence of short-to-intermediate time orientational relaxation in a model thermotropic liquid crystal across the isotropic-nematic transition and in a binary mixture across the supercooled liquid regime in molecular dynamics simulations. The measure of the experimentally observable optical Kerr effect signal is found to follow a power law decay at short-to-intermediate times for both systems in agreement with recent experiments. In addition, the temperature dependence of the power law exponent is found to be rather weak. As the model liquid crystalline system settles into the nematic phase upon cooling, the decay of the single-particle second-rank orientational time correlation function exhibits a pattern that is similar to what has been observed for supercooled liquids.     

Anomalous viscoelasticity near the isotropic-nematic phase transition in liquid crystals

Recent optical Kerr effect experiments have shown that orientational relaxation of nematogens shows a pronounced slow down of the response function at intermediate times and also a power law decay near the isotropic-nematic (I-N) transition. In many aspects, this behavior appears to be rather similar to the ones observed in the supercooled liquid near-glass transition. We have performed molecular dynamics simulations of model nematogens (Gay-Berne with aspect ratio 3) to explore the viscoelasticity near the I-N transition and also investigated the correlation of viscoelasticity (if any) with orientational relaxation. It is found that although the viscosity indeed undergoes a somewhat sharper than normal change near the I-N transition, it is not characterized by any divergence-like behavior (like the ones observed in the supercooled liquid). The rotational friction, on the other hand, shows a much sharper rise as the I-N transition is approached. Interestingly, the probability distribution of the amplitude of the three components of the stress tensor shows anisotropy near the I-N transition-similar anisotropy has also been seen in the deeply supercooled liquid. Frequency dependence of viscosity shows several unusual behaviors: (a) There is a weak, power law dependence on frequency [eta(')(omega) approximately omega(-alpha)] at low frequencies and (b) there is a rapid increase in the sharp peak observed in eta(')(omega) in the intermediate frequency on approach to the I-N transition density. These features can be explained from the stress-stress time correlation function. The angular velocity correlation function also exhibits a power law decay in time. The reason for this is discussed.     

Structural relaxation in complex liquids: non-Markovian dynamics in a bistable potential

The time correlation function C(t) identical with of the distance fluctuations of a particle moving in a bistable potential under the action of fractional Gaussian noise (fGn) is calculated from a Smoluchowski-type equation derived from a generalized Langevin equation (GLE). The time derivative of this function, dC(t)dt, is compared with data from optical Kerr effect measurements of liquid crystal dynamics in the vicinity of the isotropic-to-nematic transition, which are related to the time derivative of an orientational correlation function. A number of characteristic features of the experimental decay curves, including short and intermediate time power law behavior and long time exponential relaxation, are qualitatively reproduced by the analytical calculations, even though the latter do not explicitly treat orientational degrees of freedom. The GLE formalism with fGn was, in fact, originally proposed as a model of protein conformational fluctuations, so the present results suggest that it may also serve more generally as a model of structural relaxation in complex condensed phase media.     

Orientational dynamics in the isotropic phase of a calamitic liquid-crystal model

We report a molecular dynamics simulation study on the isotropic phase of an idealized calamitic liquid crystal model with a length-to-width ratio of approximately 5-6. The study focuses on the characterization of single-particle and collective orientational dynamics on approaching the phase transition to the nematic phase. Recent experimental and simulation works have suggested that a power law behavior exists at relatively short times in the decay of the time derivative of the orientational correlation functions. Qualitatively, our simulation data are consistent with these findings. Both single-particle and collective time correlation function derivatives possess, in their respective log-log plots, a linear region at very short times, whose slope is essentially independent from the thermodynamic state. Nevertheless, the single-particle orientational correlation functions are better described by a function which is the sum of a fast exponential, an intermediate stretched-exponential and a slow exponential, while the collective orientational correlation functions are satisfactorily described by a sum of two exponentials, at higher density, or by just one exponential, at lower density.     

Short time dynamics in the isotropic phase of liquid crystals: the aspect ratio and the power law decay

Optical heterodyne detected optical Kerr effect (OHD-OKE) experiments are used to study the orientational dynamics of the liquid crystal 4^′-octyl-4-biphenylcarbonitrile (8CB) in the isotropic phase near the isotropic to nematic phase transition. The results are compared to those for three other liquid crystals. The 8CB data display a short time scale temperature independent power law decay and a long time scale exponential decay with a temperature dependence described by Landau–de Gennes theory. The power law exponent is −0.56. Combining this result with previous results for three other liquid crystals [J. Chem. Phys. 116 (2002) 6339; J. Chem. Phys. 116 (2002) 360], it is found that the power law exponent depends linearly on the aspect ratio of the liquid crystal.     

Orientational dynamics and energy landscape features of thermotropic liquid crystals: An analogy with supercooled liquids

Recent optical kerr effect (OKE) studies have revealed that orientational relaxation of rodlike nematogens near the isotropic-nematic (I-N) phase boundary and also in the nematic phase exhibit temporal power law decay at intermediate times. Such behaviour has drawn an intriguing analogy with supercooled liquids. Here, we have investigated the single-particle and collective orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I-N phase boundary, the system behaves like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system.     

Dynamics in supercooled ionic organic liquids and mode coupling theory analysis

Optically heterodyne-detected optical Kerr effect experiments are applied to study the orientational dynamics of the supercooled ionic organic liquids N-propyl-3-methylpyridinium bis(trifluoromethylsulfonyl)imide (PMPIm) and 1-ethyl-3-methylimidazolium tosylate (EMImTOS). The orientational dynamics are complex with relaxation involving several power law decays followed by a final exponential decay. A mode coupling theory (MCT) schematic model, the Sj?gren model, was able to reproduce the PMPIm data very successfully over a wide range of times from 1 ps to hundreds of ns for all temperatures studied. Over the temperature range from room temperature down to the critical temperature Tc of 231 K, the OHD-OKE signal of PMPIm is characterized by the intermediate power law t(-1.00+/-0.04) at short times, a von Schweidler power law t(-0.51+/-0.03) at intermediate times, and a highly temperature-dependent exponential (alpha relaxation) at long times. This form of the decay is identical to the form observed previously for a large number of organic van der Waals liquids. MCT analysis indicates that the theory can explain the experimental data very well for a range of temperatures above Tc, but as might be expected, there are some deviations from the theoretical modeling at temperatures close to Tc. For EMImTOS, the orientational dynamics were studied on the ps time scale in the deeply supercooled region near its glass transition temperature. The orientational relaxation of EMImTOS clearly displays the feature associated with the boson peak at approximately 2 ps, which is the first time domain evidence of the boson peak in ionic organic liquids. Overall, all the dynamical features observed earlier for organic van der Waals liquids using the same experimental technique are also observed for organic ionic liquids.     

Glassiness of thermotropic liquid crystals across the isotropic-nematic transition

The orientational dynamics of thermotropic liquid crystals across the isotropic-nematic phase transition have traditionally been investigated at long times or low frequencies using frequency domain measurements. The situation has now changed significantly with the recent report of a series of interesting transient optical Kerr effect (OKE) experiments that probed orientational relaxation of a number of calamitic liquid crystals (which consist of rod-like molecules) directly in the time domain, over a wide time window ranging from subpicoseconds to tens of microseconds. The most intriguing revelation is that the decay of the OKE signal at short to intermediate times (from a few tens of picoseconds to several hundred nanoseconds) follows multiple temporal power laws. Another remarkable feature that has emerged from these OKE measurements is the similarity in the orientational relaxation behavior between the isotropic phase of calamitic liquid crystals near the isotropic-nematic transition and supercooled molecular liquids, notwithstanding their largely different macroscopic states. In this article, we present an overview of the understanding that has emerged from recent computational and theoretical studies of calamitic liquid crystals across the isotropic-nematic transition. Topics discussed include (a) single-particle as well as collective orientational dynamics at a short-to-intermediate time window, (b) heterogeneous dynamics in orientational degrees of freedom diagnosed by a non-Gaussian parameter, (c) fragility, and (d) temperature-dependent exploration of underlying energy landscapes as calamitic liquid crystals settle into increasingly ordered mesophases upon cooling from the high-temperature isotropic phase. A comparison of our results with those of supercooled molecular liquids reveals an array of analogous features in these two important classes of soft matter systems. We further find that the onset of growth of the orientational order in the parent nematic phase induces translational order, resulting in smectic-like layers in the potential energy minima of calamitic systems if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. We discuss implications of this startling observation. We also discuss recent results on the orientational dynamics of discotic liquid crystals that are found to be rather similar to those of calamitic liquid crystals.     

Temperature- and solvation-dependent dynamics of liquid sulfur dioxide studied through the ultrafast optical Kerr effect

The ultrafast dynamics of liquid sulphur dioxide have been studied over a wide temperature range and in solution. The optically heterodyne-detected and spatially masked optical Kerr effect (OKE) has been used to record the anisotropic and isotropic third-order responses, respectively. Analysis of the anisotropic response reveals two components, an ultrafast nonexponential relaxation and a slower exponential relaxation. The slower component is well described by the Stokes-Einstein-Debye equation for diffusive orientational relaxation. The simple form of the temperature dependence and the agreement between collective (OKE) and single molecule (e.g., NMR) measurements of the orientational relaxation time suggests that orientational pair correlation is not significant in this liquid. The relative contributions of intermolecular interaction-induced and single-molecule orientational dynamics to the ultrafast part of the spectral density are discussed. Single-molecule librational-orientational dynamics appear to dominate the ultrafast OKE response of liquid SO2. The temperature-dependent OKE data are transformed to the frequency domain to yield the Raman spectral density for the low-frequency intermolecular modes. These are bimodal with the lowest-frequency component arising from diffusive orientational relaxation and a higher-frequency component connected with the ultrafast time-domain response. This component is characterized by a shift to higher frequency at lower temperature. This result is analyzed in terms of a harmonic librational oscillator model, which describes the data accurately. The observed spectral shifts with temperature are ascribed to increasing intermolecular interactions with increasing liquid density. Overall, the dynamics of liquid SO2 are found to be well described in terms of molecular orientational relaxation which is controlled over every relevant time range by intermolecular interactions.     

Three homeotropically aligned nematic liquid crystals: comparison of ultrafast to slow time-scale dynamics

The dynamics of two nematic liquid crystals, 4-(trans-4(')-n-octylcyclohexyl)isothiocyanatobenzene and 4-(4-pentyl-cyclohexyl)-benzonitrile, are investigated as a function of temperature both in the homeotropically aligned nematic phase and in the isotropic phase using optical heterodyne-detected optical Kerr effect experiments, which measures the time derivative of the polarizability-polarizability-correlation function (orientational relaxation). Data are presented over a time range of 500 fs-70 micros for the nematic phase and 500 fs to a few hundred nanoseconds for the isotropic phase. The nematic dynamics are compared with a previously studied liquid crystal in the nematic phase. All three liquid crystals have very similar dynamics in the nematic phase that are very different from the isotropic phase. On the slowest time scale (20 ns-70 micros), a temperature-independent power law, the final power law, t(-f) with f approximately 0.5, is observed. On short time scales (approximately 3 ps to approximately 1 ns), a temperature-dependent intermediate power law is observed with an exponent that displays a linear dependence on the nematic order parameter. Between the intermediate power law and the final power law, there is a crossover region that has an inflection point. For times that are short compared to the intermediate power law (approximately <2 ps), the data decay much faster, and can be described as a third power law, although this functional form is not definitive. The isotopic phase data have the same features as found in previous studies of nematogens in the isotropic phase, i.e., the temperature-independent intermediate power law and von Schweidler power law at short to intermediate times, and a highly temperature-dependent long time exponential decay that is well described by the Landau-de Gennes theory. The results show that liquid-crystal dynamics in the nematic phase exhibit universal behavior.     

A mode coupling theory description of the short- and long-time dynamics of nematogens in the isotropic phase

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experimental data are pre-sented on nematogens 4-(trans-4-n-octylcyclohexyl)isothiocyanatobenzene (8-CHBT), and 4-(4-pentyl-cyclohexyl)-benzonitrile (5-PCH) in the isotropic phase. The 8-CHBT and 5-PCH data and previously published data on 4-pentyl-4-biphenylcarbonitrile (5-CB) are analyzed using a modification of a schematic mode coupling theory (MCT) that has been successful in describing the dynamics of supercooled liquids. At long time, the OHD-OKE data (orientational relaxation) are well described with the standard Landau-de Gennes (LdG) theory. The data decay as a single exponential. The decay time diverges as the isotropic to nematic phase transition is approached from above. Previously there has been no theory that can describe the complex dynamics that occur at times short compared to the LdG exponential decay. Earlier, it has been noted that the short-time nematogen dynamics, which consist of several power laws, have a functional form identical to that observed for the short time behavior of the orientational relaxation of supercooled liquids. The temperature-dependent orientational dynamics of supercooled liquids have recently been successfully described using a schematic mode coupling theory. The schematic MCT theory that fits the supercooled liquid data does not reproduce the nematogen data within experimental error. The similarities of the nematogen data to the supercooled liquid data are the motivation for applying a modification of the successful MCT theory to nematogen dynamics in the isotropic phase. The results presented below show that the new schematic MCT theory does an excellent job of reproducing the nematogen isotropic phase OHD-OKE data on all time scales and at all temperatures.     

Dynamics of a discotic liquid crystal in the isotropic phase

Optically heterodyne-detected optical Kerr effect (OHD-OKE) experiments are conducted to study the orientational dynamics of a discotic liquid crystal 2,3,6,7,10,11-hexakis(pentyloxy)triphenylene (HPT) in the isotropic phase near the columnar-isotropic (C-I) phase transition. The OHD-OKE signal of HPT is characterized by an intermediate power law t(-0.76+/-0.02) at short times (a few picoseconds), a von Schweidler power law t(-0.26+/-0.01) at intermediate times (hundreds of picoseconds), and an exponential decay at long times (tens of nanoseconds). The exponential decay has Arrhenius temperature dependence. The functional form of the total time dependent decay is identical to the one observed previously for a large number of molecular supercooled liquids. The mode coupling theory schematic model based on the Sjogren [Phys. Rev. A 33, 1254 (1986)] model is able to reproduce the HPT data over a wide range of times from <1 ps to tens of nanoseconds. The studies indicate that the HPT C-I phase transition is a strong first order transition, and the dynamics in the isotropic phase display a complex time dependent profile that is common to other molecular liquids that lack mesoscopic structure.     

Ultrafast to slow orientational dynamics of a homeotropically aligned nematic liquid crystal

The orientational dynamics of a homeotropically aligned nematic liquid crystal, 4'-pentyl-4-biphenylcarbonitrile (5-CB), is studied over more than six decades of time (500 fs to 2 mus) using optical heterodyne detected optical Kerr effect experiments. In contrast to the dynamics of nematogens in the isotropic phase, the data do not decay as a highly temperature-dependent exponential on the longest time scale, but rather, a temperature-independent power law spanning more than two decades of time, the final power law, is observed. On short time scales (approximately 3 ps to approximately 1 ns) another power law, the intermediate power law, is observed that is temperature dependent. The power law exponent of the correlation function associated with the intermediate power law displays a linear dependence on the change in the nematic order parameter with temperature. Between the intermediate power law and the final power law, there is a crossover region that displays an inflection point. The temperature-dependent orientational dynamics in the nematic phase are shown to be very different than those observed in the isotropic phase.     

Polar solvation dynamics in water and methanol: search for molecularity

Time-dependent Stokes shifts (TDSS) were measured for diverse polarity probes in water, heavy water, methanol, and benzonitrile, by broadband fluorescence up-conversion with 85 fs time resolution. In water the spectral dynamics is solute-independent and quantitatively described by simple dielectric continuum theory of solvation. In methanol the slower part of the TDSS is solute-dependent. A correlation with anisotropy decay suggests that methanol solvation dynamics is modulated by orientational solute diffusion. An empirical power law which links the solvation relaxation function of a mobile solute to that of an immobile solute is experimentally verified. Activation energies for the average relaxation rate are also given. Solvation dynamics in H(2)O and D(2)O are identical at and above 20 °C but diverge below.     

Characteristic behavior of short-term dynamics in reorientation for Gay-Berne particles near the nematic-isotropic phase transition temperature

A specific transition behavior was found in the tumbling motion near the nematic-isotropic phase boundary using molecular dynamics simulations of the Gay-Berne mesogenic model under isobaric conditions at a reduced pressure P* of 2.0. The relaxation time for the motion obtained from the second-rank orientational time correlation function and the rotational diffusion coefficient showed a clear jump at the nematic-isotropic phase transition temperature. Regardless of the temperature dependence of the relaxation time, the change in the rotational diffusion coefficient evaluated from the orientational order parameters and the relaxation time agreed qualitatively with that of real mesogens. The rotational viscosity coefficients gamma(1) and gamma(2) were obtained from the simulation data for the relaxation time for the short-term dynamics and for the rotational diffusion coefficients. gamma(1) was proportional to (2), where is the second-rank orientational parameter. Furthermore, the rotational behavior of the model was compared with that of the Debye approximation in the isotropic phase.     

Local hydrogen bonding dynamics and collective reorganization in water: ultrafast infrared spectroscopy of HOD/D(2)O

We present an investigation into hydrogen bonding dynamics and kinetics in water using femtosecond infrared spectroscopy of the OH stretching vibration of HOD in D(2)O. Infrared vibrational echo peak shift and polarization-selective pump-probe experiments were performed with mid-IR pulses short enough to capture all relevant dynamical processes. The experiments are self-consistently analyzed with a nonlinear response function expressed in terms of three dynamical parameters for the OH stretching vibration: the frequency correlation function, the lifetime, and the second Legendre polynomial dipole reorientation correlation function. It also accounts for vibrational-relaxation-induced excitation of intermolecular motion that appears as heating. The long time, picosecond behavior is consistent with previous work, but new dynamics are revealed on the sub-200 fs time scale. The frequency correlation function is characterized by a 50 fs decay and 180 fs beat associated with underdamped intermolecular vibrations of hydrogen bonding partners prior to 1.4 ps exponential relaxation. The reorientational correlation function observes a 50 fs librational decay prior to 3 ps diffusive reorientation. Both of these correlation functions compare favorably with the predictions from classical molecular dynamics simulations. The time-dependent behavior can be separated into short and long time scales by the 340 fs correlation time for OH frequency shifts. The fast time scales arise from dynamics that are mainly local: fluctuations in hydrogen bond distances and angles within relatively fixed intermolecular configurations. On time scales longer than the correlation time, dephasing and reorientations reflect collective reorganization of the liquid structure. Since the OH transition frequency and dipole are only weakly sensitive to these collective coordinates, this is a kinetic regime which gives an effective rate for exchange of intermolecular structures.     

Molecular dynamics study of the temperature-dependent Optical Kerr effect spectra and intermolecular dynamics of room temperature ionic liquid 1-methoxyethylpyridinium dicyanoamide

We have performed classical molecular dynamics simulations to calculate the Optical Kerr effect (OKE) spectra of 1-methoxyethylpyridinium dicyanoamide, a room-temperature ionic liquid (IL) which has been recently studied by Shirota and Castner (Shirota, H. ; Castner, E. J. Phys. Chem. A 2005, 109, 9388-9392) in comparison to its neutral isoelectronic solvent mixture. Our theoretical and computational studies show that the decay of the collective polarizability anisotropy correlation exhibits several different time scales originating from inter- and intramolecular dynamics, in good agreement with experiments. What's more, we find that the portion of the collective anisotropic polarizability relaxation due to "interaction-induced" phenomena is important at times much longer than those observed in normal solvents when these are far from their glass transition temperature. From our long (60 ns) molecular dynamics simulations, we are able to determine the appropriate time scales for orientational relaxation and interaction-induced processes occurring in the liquid. We find that the cationic contribution to the OKE signal is predominant. Because of the slow nature of relaxation processes in ILs, these calculations are very time, memory, and storage intensive. In the context of this research, we have developed a polarizable force field for this system and also theoretical methodology to generate molecular polarizabilities for arbitrarily shaped molecules and ions from corresponding atomic polarizabilities. We expect this methodology to have an important impact on the speed of molecular dynamics simulations of polarizable systems in the future.     

Effects of molecular association on polarizability relaxation in liquid mixtures of benzene and hexafluorobenzene

In this work we have studied the relaxation dynamics of the many-body polarizability anisotropy in liquid mixtures of benzene (Bz) and hexafluorobenzene (Hf) at room temperature by femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) experiments and molecular dynamics (MD) simulations. The computed polarizability response arising from intermolecular interactions was included using the first-order dipole-induced-dipole model with the molecular polarizability distributed over the carbon sites of each molecule. We found good qualitative agreement between experiments and simulations in the features exhibited by the nuclear response function R(t) for pure liquids and mixtures. The long-time diffusive decay of R(t) was observed to vary substantially with composition, slowing down noticeably with dilution of each of the species as compared with that in the corresponding pure liquids. MD simulation shows that the effect on R(t) is due to the formation of strong and localized intermolecular association between Bz and Hf species that hinder the rotational diffusive dynamics. The formation of these Bz-Hf complexes in the liquid mixtures also modifies the rotational diffusive dynamics of the component species in such a way that cannot be explained solely in terms of a viscosity effect. Even though the computed orientational diffusive relaxation times associated with Bz and Hf are larger by a factor of approximately 2 than those from experiments, we found similar trends in experiments and simulations for these characteristic times as a function of composition. Namely, the collective and single-molecule orientational correlation times associated with Bz are observed to grow monotonically with the dilution of Bz, while those corresponding to Hf species exhibit a maximum at the equimolar composition. We attribute the quantitative discrepancy between experiments and simulations to the use of the Williams potential, which seems to overestimate the intermolecular interactions and thus predicts not only a slower translational dynamics but also a slower rotational diffusion dynamics than in real fluids.