Ultrafast to Slow Orientational Dynamics of a Homeotropically Aligned Nematic Liquid Crystal

Dynamics of Acrylamide Hydrogels, Polymers, and Monomers in Water Measured with Optical Heterodyne-Detected Optical Kerr Effect Spectroscopy

The ultrafast dynamics of acrylamide monomers (AAm), polyacrylamide (PAAm), and polyacrylamide hydrogels (PAAm-HG) in water were studied using optical heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy. Previous ultrafast infrared (IR) measurements of the water dynamics showed that at the same concentration of the acrylamide moiety, AAm, PAAm, and PAAm-HG exhibited identical water dynamics and that these dynamics slowed with increasing concentration. In contrast to the IR measurements, OHD-OKE experiments measure the dynamics of both the water and the acrylamide species, which occur on different time scales. In this study, the dynamics of all the acrylamide systems slowed with increasing concentration. We found that AAm exhibits tetraexponential decays, the longest component of which followed Debye-Stokes-Einstein behavior except for the highest concentration, 40% (w/v). Low concentrations of PAAm followed a single power law decay, while high concentrations of PAAm and all concentrations of PAAm-HG decayed with two power laws. The highest concentrations, 25% and 40%, of PAAm and PAAm-HG showed nearly identical dynamics. We interpreted this result as reflecting a similar extent of chain-chain interactions. At low concentrations, PAAm displays non-Markovian, single-chain dynamics (single power law), but PAAm displays entangled chain-chain interactions at high concentrations (two power laws). PAAm-HG has chain-chain interactions at all concentrations that arise from the cross-linking. At high concentrations, the dynamics of the entangled of PAAm become identical within error as those of the cross-linked PAAm-HG.

Long-time relaxation dynamics in nematic and smectic liquid crystals of soft repulsive colloidal rods

Understanding the relaxation dynamics of colloidal suspensions is crucial to identifying the elements that influence the mobility of their constituents, assessing their macroscopic response across the relevant time and length scales, and thus disclosing the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft repulsive rodlike particles, which are able to self-organize into nematic and smectic liquid-crystalline phases. Rods are modeled as soft repulsive spherocylinders with a length-to-diameter ratio L^{★}=5, interacting via the truncated and shifted Kihara potential. By performing dynamic Monte Carlo simulations, we analyze the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess its dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.

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.

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.

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.

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.

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.

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.

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.

Molecular dynamics and interactions of aqueous and dichloromethane solutions of polyvinylpyrrolidone

We have investigated the dynamics of polyvinylpyrrolidone solutions (PVP, M(w)=10 000) on time scales from 20 fs to 42 ps using femtosecond optically heterodyne-detected Raman-induced Kerr effect spectroscopy. To compare the dynamics of polymer solutions with those of the analogous monomer, we also characterized solutions of 1-ethyl-2-pyrrolidone (EP). Dynamics of both PVP and EP solutions have been characterized for sample concentrations of 6.4, 12.7, 24.5, 33.3, and 40.7 wt %. The longest time scale relaxations observed in the Kerr transients for these solutions occur on the picosecond time scale and are best fit to triexponential functions. The intermediate and slow relaxation time constants for PVP and EP solutions are concentration dependent. The time constants for the PVP solutions are not consistent with the predictions of hydrodynamic models, while the analogous time constants for the EP solutions do display hydrodynamic scaling. The predominant relaxation of the polymer is assigned to reorientations of the pyrrolidone side group or torsional motions of the constitutional repeat unit, with additional relaxation pathways including hydrogen bond reorganization in aqueous solution and segmental motion of multiple repeat units. The vibrational dynamics of PVP and EP solutions occur on the femtosecond time scale. These dynamics are analyzed with a focus on the additional degrees of freedom experienced by EP relative to PVP that result from the absence of the tether from the pyrrolidone group on the main chain backbone. The intermolecular Kerr spectra of PVP in H(2)O and CH(2)Cl(2) differ because H(2)O can donate a hydrogen bond to the carbonyl acceptor group on the pyrrolidone ring, while CH(2)Cl(2) cannot.

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.

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.