Comparison of the ultrafast to slow time scale dynamics of three liquid crystals in the isotropic phase

Ultrafast all-optical response of a nematic liquid crystal

Liquid crystals are superior optical materials for large area displays, but it is considered that their collective and slow-millisecond response makes them useless for ultrafast optical applications. In contrast to that, we here demonstrate an ultrafast optical response of a nematic liquid crystal, which is induced by an intense femtosecond optical impulse. We show that the refractive index of the nematic liquid crystal pentyl-cyanobiphenyl can be modulated at a time scale as fast as 500 fs via a coherently excited optical Kerr effect. The change in the refractive index is in the order of 10^-4 at a fluence of 4 mJ/cm² and is strongly polarization dependent. This unprecedented result opens new ways towards ultrafast all-optical modulation in liquid crystal-based devices.

Phase equilibria, fluid structure, and diffusivity of a discotic liquid crystal

Molecular Dynamics simulations were performed for the Gay-Berne discotic fluid parameterized by GB(0.345, 0.2, 1.0, 2.0). The volumetric phase diagram exhibits isotropic (IL), nematic (ND), and two columnar phases characterized by radial distribution functions: the transversal fluid structure varies between a hexagonal columnar (CD) phase (at higher temperatures and pressures) and a rectangular columnar (CO) phase (at lower temperatures and pressures). The slab-wise analysis of fluid dynamics suggests the formation of grain-boundary defects in the CO phase. Longitudinal fluid structure is highly periodic with narrow peaks for the CO phase, suggestive of a near-crystalline (yet diffusive) system, but is only short-ranged for the CD phase. The IL phase does not exhibit anisotropic diffusion. Transversal diffusion is more favorable in the ND phase at all times, but only favorable at short times for the columnar phases. In the columnar phases, a crossover occurs where longitudinal diffusion is favored over transversal diffusion at intermediate-to-long timescales. The anomalous diffusivity is pronounced in both columnar phases, with three identifiable contributions: (a) the rattling of discogens within a transient "interdigitation" cage, (b) the hopping of discogens across columns, and (c) the drifting motion of discogens along the orientation of the director.

Dynamics in the isotropic phase of nematogens using 2D IR vibrational echo measurements on natural-abundance 13CN and extended lifetime probes

The long time scale orientational relaxation of nematogens in the isotropic phase is associated with the randomization of pseudonematic domains, which have a correlation length that grows as the isotropic-to-nematic phase transition temperature is approached from above. Here we begin to address the fast dynamics of the nematogen molecules within the domains using two-dimensional infrared (2D IR) vibrational echo experiments. The problems of performing ultrafast IR experiments in pure liquids are discussed, and solutions are presented. In addition, the issue of short vibrational lifetimes, which limit the ability of 2D IR experiments to examine dynamics over a wide range of times, is addressed. The experiments were performed on the nematogen 4-cyano-4'-pentylbiphenyl (5CB), with the CN stretch initially used as the vibrational probe. Although the CN stretch has a small transition dipole, because the sample is a pure liquid it is necessary to use an exceedingly thin sample to perform the experiments. The small sample volume leads to massive heating effects that distort the results. In addition, the high concentration in the pure liquid can result in vibrational excitation transfer that interferes with the measurements of structural dynamics, and the CN vibrational lifetime is very short (3.6 ps). These problems were overcome by performing the experiments on the natural-abundance (13)CN stretch (5(13)CB), which greatly reduced the absorbance, eliminating the heating problems; also, this stretch has a longer lifetime (7.9 ps). Experiments were also performed on benzonitrile, which showed that the heating problems associated with pure liquids are not unique to 5CB. Again, the problems were eliminated by conducting measurements on the (13)CN stretch, which has an even longer lifetime (20.2 ps) compared with the (12)CN stretch (5.6 ps). Finally, to extend the range of the dynamical measurements, 4-pentyl-4'-thiocyanobiphenyl (5SCB) was synthesized and studied as a dilute solute in 5CB. The CN stretch of 5SCB has a vibrational lifetime of 103 ps, which permits dynamical measurements to 200 ps, revealing the full range of fast structural dynamics in the isotropic phase of 5CB. It is shown that the 5SCB probe reports essentially the same dynamics as 5(13)CB on the short time scale that is observable with the 5(13)CB vibrational probe.

Universal pattern for the distribution of relaxation times in the isotropic phase of liquid crystalline n-cyanobiphenyls

A universal pattern emerging from the analysis of the distribution of relaxation times in the isotropic phase of liquid crystalline n-alkylcyanobiphenyls (nCB) from 4CB to 14CB is presented. The increase of the length of nCB molecules causes the high-frequency (short-time) branch of the primary relaxation loss curve to approach the form epsilon(f>fpeak) approximately omega(-n), with n-->1/2 in frequency (omega=2pif) or approximately sqrt[t] in time on cooling toward the isotropic-mesophase "clearing" phase-transition temperature (TC). Recently, such behavior was suggested as a hypothetical universal pattern for diverse glass forming organic liquids on approaching the glass temperature [A. I. Nielsen, T. Christensen, B. Jakobsen, K. Niss, N. B. Olsen, R. Richert, and J. C. Dyre, J. Chem. Phys. 130, 154508 (2009)]. The isotropic phase of rodlike liquid crystalline compounds is considered to be an important experimental model system for studying glassy dynamics since it constitutes a link with the model fluid of hard ellipsoids of revolution.

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.

Inter- and intramolecular hydrogen bonding in phenol derivatives: a model system for poly-L-tyrosine

The ultrafast dynamics of solutions of phenol and two phenol derivatives--hydroquinone (1,4-benzenediol) and pyrocatechol (1,2-benzenediol)--have been studied with Optically Heterodyne-Detected Optical Kerr-Effect (OHD-OKE) spectroscopy. The solvents, methanol and acetonitrile, were selected to provide strong and weak solvent-solute hydrogen-bonding interactions, respectively, while pyrocatechol features an intramolecular hydrogen bond. Together these provide a series of model systems for polypeptides such as polytyrosine, which facilitate the direct study of inter- and intramolecular hydrogen bonding. A broad contribution to the Raman spectral density of the methanol solutions at frequencies between 150 and 300 cm(-1) has been observed that is absent in acetonitrile. This contribution has been assigned to solvent-solute hydrogen-bond stretching vibrations. The OHD-OKE response of poly-L-tyrosine has been measured and was found to contain a similar contribution. Density functional theory geometry optimizations and normal mode calculations have been performed using the B3LYP hybrid functional and 6-311++G** basis set. These have yielded a complete assignment of the low-frequency Raman and far-infrared spectra of pyrocatechol for the first time, which has provided information on the nature of the intramolecular hydrogen bond of pyrocatechol.

The Ultrafast Dynamics of Hydrogen-Bonded Liquids: Molecular Structure-Dependent Occurrence of Normal Arrhenius or Fractional Stokes−Einstein−Debye Rotational Diffusive Relaxation

The ultrafast rotational-diffusive dynamics of the peptide linkage model compounds N-methylacetamide (NMA), acetamide (Ac), and N,N-dimethylacetamide (DMA) have been studied as a function of temperature using optically heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy. Both NMA and Ac exhibit a non-Arrhenius temperature dependence of the rotational diffusive relaxation time. By contrast, the non-hydrogen-bonding DMA exhibits normal hydrodynamic behavior. The unusual dynamics of NMA and Ac are attributed to the decoupling of single-molecule rotational diffusive relaxation from the shear viscosity via a transition between stick and slip boundary conditions, which arises from local heterogeneity in the liquid due to the formation of hydrogen-bonded chains or clusters. This provides new insight into the structure and dynamics of an important peptide model compound and the first instance of such a phenomenon in a room-temperature liquid. The OHD-OKE responses of carboxylic acids acetic acid (AcOH) and dichloroacetic acid (DCA) are also reported. These, along with the terahertz Raman spectra, show no evidence of the effects observed in amide systems, but display trends consistent with the presence of an equilibrium between the linear and cyclic dimer structures at all temperatures and moderate-to-high mole fractions in aqueous solution. This equilibrium manifests itself as hydrodynamic behavior in the liquid phase.

Glassy orientational dynamics of rodlike molecules near the isotropic-nematic transition

We investigate the single-particle orientational dynamics of rodlike molecules across the isotropic-nematic transition in computer simulations of a family of model systems of thermotropic liquid crystals. Several remarkable features of glassy dynamics are on display including nonexponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. In order to obtain a quantitative measure of glassy dynamics in line with the established methods in supercooled liquids, we construct a relaxation time versus scaled inverse temperature plot and demonstrate that one can indeed define a "fragility index" for thermotropic liquid crystals that depends on density and aspect ratio. The values of the fragility parameter are surprisingly in the range observed for glass-forming liquids. A plausible correlation between the energy landscape features and the observed fragility is discussed.

Orientational relaxation in a discotic liquid crystal

We investigate orientational relaxation of a model discotic liquid crystal, consisting of disclike molecules, by molecular dynamics simulations along two isobars starting from the high temperature isotropic phase. The two isobars have been so chosen that (a) the phase sequence isotropic- (I-) nematic- (N-) columnar (C) appears upon cooling along one of them and (b) the sequence isotropic- (I-) columnar- (C) along the other. While the orientational relaxation in the isotropic phase near the I-N phase transition in system (a) shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I-C phase boundary in system (b). In order to understand this difference (the existence or the absence of the power law decay), we calculated the growth of the orientational pair distribution functions (OPDFs) near the I-N phase boundary and also near the I-C phase boundary. We find that the OPDF shows a marked growth in long range correlation as the I-N phase boundary is approached in the I-N-C system (a), but such a growth is absent in the I-C system, which appears to be consistent with the result that I-N phase transition in the former is weakly first order while the I-C phase transition in the latter is not weak. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational time correlation function follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.

Origin of glassy dynamics in a liquid crystal studied by broadband dielectric and specific heat spectroscopy

A combination of broadband dielectric (10{-2}Hz-10{9}Hz) and specific heat (10{-3}Hz-2 x 10{3}Hz) spectroscopy is employed to study the molecular dynamics of the glass-forming nematic liquid crystal E7 in a wide temperature range. In the region of the nematic phase the dielectric spectra show two relaxation processes which are expected theoretically: the delta relaxation which corresponds to rotational fluctuations of the molecules around its short axis and the tumbling mode at higher frequencies than the former one. For both processes the temperature dependence of the relaxation rates follows the Vogel-Fulcher-Tammann formula which is characteristic for glassy dynamics. By applying a detailed data analysis, it is shown that close to the glass transition the tumbling mode has a much steeper temperature dependence than the delta process. The former has a Vogel temperature which is by 30K higher than that of the delta relaxation. Specific heat spectroscopy gives one relaxation process in its temperature and frequency dependence which has to be assigned to the alpha relaxation (dynamic glass transition). The unique and detailed comparison of the temperature dependence of the dielectric and the thermal relaxation rates delivers unambiguously that the dielectric tumbling mode has to be related to the dynamic glass transition.

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.

Ultrafast dynamics in complex fluids observed through the ultrafast optically-heterodyne-detected optical-Kerr-effect (OHD-OKE)

The ultrafast molecular dynamics of complex fluids have been recorded using the optically-heterodyne-detected optical-Kerr-effect (OHD-OKE). The OHD-OKE method is reviewed and some recent refinements to the method are described. Applications to a range of complex fluids, including microemulsions, polymer melts and solutions, liquid crystal and ionic liquids are surveyed. The level of detail attainable with the OHD-OKE method in these complex fluids is discussed. The prospects for future experiments are discussed.

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 <P2>(2), where <P2> 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.

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.

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

The time correlation function C(t) identical with <x(0)x(t)> 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.

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.

Power law relaxation and glassy dynamics in Lebwohl-Lasher model near the isotropic-nematic phase transition

Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase transition is studied using molecular dynamics simulations of the well-known Lebwohl-Lasher model. As the IN transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate time scales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a subdiffusive regime which is followed by a superdiffusive regime before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in orientational motion particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of the transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective, and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.

Energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals

Thermotropic liquid crystals are known to display rich phase behavior on temperature variation. Although the nematic phase is orientationally ordered but translationally disordered, a smectic phase is characterized by the appearance of a partial translational order in addition to a further increase in orientational order. In an attempt to understand the interplay between orientational and translational order in the mesophases that thermotropic liquid crystals typically exhibit upon cooling from the high-temperature isotropic phase, we investigate the potential energy landscapes of a family of model liquid crystalline systems. The configurations of the system corresponding to the local potential energy minima, known as the inherent structures, are determined from computer simulations across the mesophases. We find that the depth of the potential energy minima explored by the system along an isochor grows through the nematic phase as temperature drops in contrast to its insensitivity to temperature in the isotropic and smectic phases. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures; the inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the isotropic-nematic transition. We find that this breakdown occurs at a temperature below which the system explores increasingly deeper potential energy minima.

Complete breakdown of the Debye model of rotational relaxation near the isotropic-nematic phase boundary: effects of intermolecular correlations in orientational dynamics

The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the orientational correlation times tau l vary as [l(l+1)]-1, where l is the rank of the orientational time correlation function (given in terms of the Legendre polynomial of rank l). One often finds significant deviation from this prediction, in either direction. In supercooled molecular liquids where the ratio tau 1/tau 2 falls considerably below 3 (the Debye limit), one usually invokes a jump diffusion model to explain the approach of the ratio tau 1/tau 2 to unity. Here we show in a computer simulation study of a standard model system for thermotropic liquid crystals that this ratio becomes much less than unity as the isotropic-nematic phase boundary is approached from the isotropic side. Simultaneously, the ratio tau 2/eta, eta, being the shear viscosity of the liquid, becomes much larger than the hydrodynamic value near the I-N transition. We also analyze the breakdown of the Debye model of rotational diffusion in ratios of higher order orientational correlation times. We show that the breakdown of the DSE model is due to the growth of orientational pair correlation and provide a mode coupling theory analysis to explain the results.

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.

Modeling a Liquid Crystal Dynamics by Atomistic Simulation with an Ab Initio Derived Force Field

Atomistic molecular dynamics (MD) simulations of 4-n-pentyl 4'-cyano-biphenyl (5CB) have been performed, adopting a specific ab initio derived force field. Two state points in the nematic phase and three in the isotropic phase, as determined in a previous work, have been considered. At each state point, at least 10 ns have been produced, allowing us to accurately calculate single-molecule properties. In the isotropic phase, the values of the translational diffusion coefficient, and even more so the activation energy for the process, agree well with experimental data. Qualitatively, also the dynamic anisotropy of the nematic phase is correctly accounted for. Rotational diffusion coefficients, which describe spinning and tumbling motions, fall well within the range of experimental values. The reorientational dynamics of our model 5CB covers diverse time regimes. The longest one is strongly temperature dependent and characterized by a relaxation time in accord with experimental dielectric relaxation data. Shear viscosity and Landau-de Gennes relaxation times, typically collective variables, reproduce the experimental results very well in the isotropic phase. In the nematic phase, despite a large statistical uncertainty due to the extremely slow relaxation of the correlation functions involved, our simulation yields the correct relative order of the three experimental Miesowicz viscosities.

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.

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.

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.

Universal power law in the orientational relaxation in thermotropic liquid crystals

We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of model systems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.

Relaxation Processes in Semidilute Solutions of Polymers in Liquid Crystal Solvents

We investigate the relaxation phenomena in a polymer (polystyrene)/liquid crystal (4-cyano-4'-n-octyl-biphenyl) system, in its homogeneous isotropic phase near the isotropic-isotropic, isotropic-nematic, and isotropic-smectic coexistence curve, using both polarized and depolarized photon correlation spectroscopy (PCS). We study this system for different polystyrene molecular weights (4750, 12 500, and 65 000 g/mol), different compositions (50, 40, 30, and 10% polystyrene (PS) by weight), and different temperatures close to phase boundaries. First of all, we determine the phase diagrams of this system for the different molecular weights. The shape of the phase diagrams strongly depends on the molecular weight. However, in all cases, at low temperatures, these systems separate into an almost pure liquid crystalline (LC) phase and polystyrene-rich phase. PCS measurements show that the relaxation processes in the homogeneous phase are not affected by the proximity of the nematic, or smectic, boundaries (even at a temperature of 0.1 degrees C above the phase separation in two phases). In polarized PCS experiments, we always see three relaxation processes well separated in time: one, very fast, with a relaxation time of the order of 10(-5) s; a second one with a relaxation time within the range 10(-2)-10(-3) s; and a last one, very slow, with a relaxation time of the order of 1 s. Both the fast and slow modes are independent of the wave vector magnitude, while the intermediate relaxation process is diffusive. In depolarized PCS experiments, the intermediate mode disappears and only the fast and slow relaxation processes remain, and they are independent of the magnitude of the wave vector. The diffusive mode is the classical diffusive mode, which is associated with the diffusion of polymer chains in all polymer solutions. The fast mode is due to the rotational diffusion of 4-cyano-4'-n-octyl-biphenyl (8CB) molecules close to polystyrene chains (transient network). Finally, we assign the slowest mode to reorientational processes of small aggregates of PS chains that are not dissolved in 8CB.

Ultrafast Dynamics of Liquid Poly(ethylene glycol)s and Crown Ethers Studied by Femtosecond Raman-Induced Kerr Effect Spectroscopy

Ultrafast molecular dynamics of liquid poly(ethylene glycol)s, tetra(ethylene glycol), penta(ethylene glycol), and poly(ethylene glycol) with the molecular weight of 600, and crown ethers, 12-crown-4 and 15-crown-5, have been investigated by means of femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy. Picosecond Kerr transients of poly(ethylene glycol)s and crown ethers are characterized by a biexponential function with the time constants of about 2 and 20 ps. Both the faster and slower time constants do not vary much among the five oligo(ethylene oxide)s. Femtosecond dynamics is discussed based on the Kerr (depolarized Raman) spectra obtained by Fourier transform deconvolution analysis of the high time resolution Kerr transients. The broad low-frequency band (0-200 cm(-1)) in the Kerr spectrum is analyzed by two Brownian oscillators. The spectral shapes of linear poly(ethylene glycol) and cyclic crown ether are very different. Both the low- and high-frequency Brownian oscillators for crown ethers show lower frequency and broader spectral features than those for poly(ethylene glycol)s. The comparison of the low-frequency spectra of poly(ethylene glycol)s and crown ethers shows that the low-frequency spectrum of 15-crown-5 is closer to that of poly(ethylene glycol)s than that of 12-crown-4 is. The difference of the low-frequency spectra between poly(ethylene glycol) and crown ether is discussed with the concepts of molecular conformation and liquid density. The features of the observed intramolecular vibrational bands are also correlated with the molecular conformations.

Anomalous glassy relaxation near the isotropic-nematic phase transition

Dynamical heterogeneity in a system of Gay-Berne ellipsoids near its isotropic-nematic (I-N) transition, and also in an equimolar mixture of Lennard-Jones spheres and Gay-Berne ellipsoids in deeply supercooled regime, is probed by the time evolution of non-Gaussian parameters (NGP). The appearance of a dominant second peak in the rotational NGP near the I-N transition signals the growth of pseudonematic domains. Surprisingly, such a second peak is instead observed in the translational NGP for the glassy binary mixture. Localization of orientational motion near the I-N transition is found to be responsible for the observed anomalous orientational relaxation.

Optical Kerr Effect Spectroscopy Using Time-Delayed Pairs of Pump Pulses with Orthogonal Polarizations

We characterize in detail a recently introduced technique in which perpendicularly polarized pulses with controllable intensities and timing are used for the excitation step in optical Kerr effect spectroscopy. We examine the ratio of pump pulse intensities required to cancel the contribution of reorientational diffusion or of a Raman-active intramolecular vibration to the signal as a function of the delay time between excitation pulses. These results indicate that the signal can be described well as arising from the sum of independent third-order responses initiated by each pump pulse. This conclusion is further supported by using data obtained with a single pump pulse to model decays obtained with two pump pulses.

Ultrafast molecular dynamics of liquid aromatic molecules and the mixtures with CCl4

The ultrafast molecular dynamics of liquid aromatic molecules, benzene, toluene, ethylbenzene, cumene, and 1,3-diphenylpropane, and the mixtures with CCl(4) have been investigated by means of femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy. The picosecond Kerr transients of benzene, toluene, ethylbenzene, and cumene and the mixtures with CCl(4) show a biexponential feature. 1,3-Diphenylpropane and the mixtures with CCl(4) show triexponential picosecond Kerr transients. The slow relaxation time constants of the aromatic molecules and the mixtures with CCl(4) are qualitatively described by the Stoke-Einstein-Debye hydrodynamic model. The ultrafast dynamics have been discussed based on the Kerr spectra in the frequency range of 0-800 cm(-1) obtained by the Fourier transform analysis of the Kerr transients. The line shapes of the low-frequency intermolecular spectra located at 0-180 cm(-1) frequency range have been analyzed by two Brownian oscillators ( approximately 11 cm(-1) and approximately 45 cm(-1) peaks) and an antisymmetric Gaussian function ( approximately 65 cm(-1) peak). The spectrum shape of 1,3-diphenylpropane is quite different from the spectrum shapes of the other aromatic molecules for the low magnitude of the low-frequency mode of 1,3-diphenylpropane and/or an intramolecular vibration. Although the concentration dependences of the low- and intermediate-frequency intermolecular modes (Brownian oscillators) do not show a significant trend, the width of high-frequency intermolecular mode (antisymmetric Gaussian) becomes narrower with the higher CCl(4) concentration for all the aromatics mixtures with CCl(4). The result indicates that the inhomogeneity of the intermolecular vibrational mode in aromatics/CCl(4) mixtures is decreasing with the lower concentration of aromatics. The intramolecular vibrational modes of the aromatic molecules observed in the Kerr spectra are also shown with the calculation results based on the density functional theory.

Unusual Dynamic Behavior in the Isotropic Phase of Banana Mesogens Detected by 2H NMR Line Width and T2 Measurements

In this work the first experimental observation of a peculiar behavior in the isotropic phase of liquid crystals by means of 2H NMR is reported. In particular, two five-ring banana-shaped mesogens, the 1,3-phenylenebis{4,4'-(11-undecenyloxy)benzoyloxy}benzoate (Pbis11BB) and its 4-chloro homologue (ClPbis11BB), selectively deuterium labeled on their central rings, are the subject of our investigation. The dynamic behavior of the two liquid crystals was studied in their isotropic phases and in the nematic phase of ClPbis11BB by means of 2H NMR line width and spin-spin relaxation time (T2) analysis. The results obtained reveal that the unusual line broadening observed in the 2H NMR spectra in the isotropic phase, even far above the isotropic phase-mesophase transition, has a homogeneous nature, thus indicating the presence of reorientational motions much slower than in conventional isotropic liquid-crystalline phases.

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.

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.

In search of temporal power laws in the orientational relaxation near isotropic–nematic phase transition in model nematogens

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

Orientational and interaction induced dynamics in the isotropic phase of a liquid crystal: Polarization resolved ultrafast optical Kerr effect spectroscopy

The ultrafast dynamics of the isotropic phase of a liquid crystal 4'-pentyl-4-p-biphenylcarbonitrile (5CB) have been investigated using polarization resolved optical Kerr effect spectroscopy. Measurements were made as a function of both temperature and dilution in nonpolar solvents. To separate single molecule and interaction induced components to the relaxation of the induced birefringence, measurements of both the anisotropic and isotropic response were made. The isotropic response was found to be dominated by a damped low-frequency mode of intramolecular origin. There is a minor additional component assigned to an interaction induced contribution. There is at most an extremely weak isotropic signal beyond 1 ps, showing that the picosecond time scale dynamics of 5CB are dominated by orientational relaxation. The isotropic response is independent of temperature in the range studied (0.2-50 K above the nematic to isotropic phase-transition temperature). The anisotropic response exhibits relaxation dynamics on time scales spanning subpicosecond to several hundred picoseconds and beyond. The fastest components are dominated by a librational response, but there are smaller contributions from three low-frequency intramolecular modes, and a contribution from interaction induced effects. The low-frequency spectral density extracted from these data are independent of temperature in the range studied, 0.2-30 K above the phase-transition temperature, but shift to lower frequency on dilution in alkane solvents. In neat 5CB the picosecond time scale orientational dynamics are dominated by temperature-independent reorientation within the pseudonematic domains, while in solution these are disrupted, and the orientational response becomes faster and temperature dependent.