Rotational Brownian motion and nonlinear dielectric relaxation of asymmetric top molecules in strong electric fields

Hidden scale invariance in the Gay-Berne model

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.

Nonlinear response theory for Markov processes. II. Fifth-order response functions

The nonlinear response of stochastic models obeying a master equation is calculated up to fifth order in the external field, thus extending the third-order results obtained earlier [G. Diezemann, Phys. Rev. E 85, 051502 (2012)PLEEE81539-375510.1103/PhysRevE.85.051502]. For sinusoidal fields the 5ω component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurrence of such a hump as compared to a single characteristic regime in the case of the third-order response. In the case of the trap model the results strongly depend on the variable coupled to the field. As for the third-order response, the low-frequency limit of the susceptibility plays a crucial role with respect to the occurrence of a hump. The findings are discussed in light of recent experimental results obtained for supercooled liquids. The differences found for the third-order and the fifth-order response indicate that nonlinear response functions might serve as a powerful tool to discriminate among the large number of existing models for glassy relaxation.

Photoinduced reordering in thin azo-dye films and light-induced reorientation dynamics of the nematic liquid-crystal easy axis

We theoretically study the kinetics of photoinduced reordering triggered by linearly polarized (LP) reorienting light in thin azo-dye films that were initially illuminated with LP ultraviolet pumping beam. The process of reordering is treated as a rotational diffusion of molecules in the light intensity-dependent mean-field potential. The two-dimensional diffusion model which is based on the free energy rotational Fokker-Planck equation and describes the regime of in-plane reorientation is generalized to analyze the dynamics of the azo-dye order parameter tensor at varying polarization azimuth of the reorienting light. It is found that, in the photosteady state, the intensity of LP reorienting light determines the scalar order parameter (the largest eigenvalue of the order parameter tensor), whereas the steady state orientation of the corresponding eigenvector (the in-plane principal axis) depends solely on the polarization azimuth. We show that, under certain conditions, reorientation takes place only if the reorienting light intensity exceeds its critical value. Such threshold behavior is predicted to occur in the bistability region provided that the initial principal axis lies in the polarization plane of reorienting light. The model is used to interpret the experimental data on the light-induced azimuthal gliding of the liquid-crystal easy axis on photoaligned azo-dye substrates.

Nonlinear response theory for Markov processes: simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature T_{0} determined by the value of the asymmetry. In a narrow temperature range around T_{0}, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than T_{0}), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.

Matrix method calculation of the Kerr effect transient and ac stationary responses of arbitrary shaped macromolecules

A new and simple matrix method of evaluating the Kerr effect transient and ac stationary responses of rigid polar and polarizable particles (macromolecules) of arbitrary shape undergoing the noninertial anisotropic rotational diffusion in the presence of an external electric field is presented. The matrix calculations are accomplished by solving the corresponding coupled differential-recurrence equations for the statistical moments (ensemble averages of the Wigner D functions). The results so obtained are in agreement with previously available solutions for various particular cases and are amenable to comparison with experiment.

Kinetics of photoinduced ordering in azo-dye films: two-state and diffusion models

We theoretically study the kinetics of photoinduced ordering in azo-dye photoaligning layers and present the results of modeling performed using two different phenomenological approaches. A phenomenological two-state model is deduced from the master equation for the one-particle distribution functions of an ensemble of two-level molecular systems by specifying the angular redistribution probabilities and by expressing the order parameter correlation functions in terms of the order parameter tensor. Using an alternative approach that describes light-induced reorientation of azo-dye molecules in terms of a rotational Brownian motion, we formulate the two-dimensional diffusion model as the free energy Fokker-Planck equation simplified for the limiting regime of purely in-plane reorientation. The models are employed to interpret the irradiation time dependence of the absorption order parameters defined in terms of the principal extinction (absorption) coefficients. Using the exact solution to the light transmission problem for a biaxially anisotropic absorbing layer, these coefficients are extracted from the absorbance-vs-incidence angle curves measured at different irradiation doses for the probe light linearly polarized parallel and perpendicular to the plane of incidence. It is found that, in the azo-dye films, the transient photoinduced structures are biaxially anisotropic whereas the photosteady and the initial states are uniaxial.

Anisotropic rotational diffusion and dielectric relaxation of rigid dipolar particles in a strong external dc field

Dielectric response functions of polar particles (macromolecules) diluted in a nonpolar solvent subjected to a strong external dc electric field are evaluated using the anisotropic noninertial rotational diffusion model. Simple analytic formulas for the longitudinal and transverse components of the dielectric susceptibility and relaxation times are given using the effective relaxation time method. These formulas are tested against numerical solutions of the underlying infinite hierarchy of differential-recurrence equations for statistical moments (ensemble averages of the Wigner D functions) which are obtained by averaging the governing Langevin equation for noninertial rotational Brownian motion over its realizations. The calculations, involving matrix continued fractions, ultimately yield the exact solution of the infinite hierarchy of differential-recurrence relations for the dielectric response functions. In the isotropic rotational diffusion limit, the solution reduces to the known results.

Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.

Anisotropic rotational diffusion and transient nonlinear responses of rigid macromolecules in a strong external electric field

Nonlinear transient responses of polar polarizable particles (macromolecules) diluted in a nonpolar solvent to a sudden change in magnitude of a strong external dc field are evaluated using the anisotropic noninertial rotational diffusion model. The relaxation functions and relaxation times appropriate to the transient dynamic Kerr effect and nonlinear dielectric relaxation are calculated by solving the infinite hierarchy of differential-recurrence equations for statistical moments (ensemble averages of the Wigner D functions). The calculations involve matrix continued fractions, which ultimately yield the exact solution of the infinite hierarchy of differential-recurrence relations for the first- and second-order transient responses.

Birefringence and dielectric relaxation decay transients and anisotropic rotational diffusion of macromolecules in a strong external electric field

The decay transient response of polar and polarizable rigid bodies (macromolecules) diluted in a nonpolar solvent after a sudden switch-off of a strong external dc field is evaluated in the context of the anisotropic noninertial rotational diffusion model. On solving the differential-recurrence equations for the statistical moments (expectation values of Wigner's D functions), the decay transients of the birefringence and dielectric relaxation are obtained. The solutions (valid for arbitrary strengths of an external electric field) are given in a closed form suitable for comparison with experiment and Brownian dynamics simulations.

Reorientational dynamics of the pseudonematic domains studied with nonlinear dielectric spectroscopy

Nonlinear dielectric spectroscopy was used for studies of the reorientational dynamics of the pseudonematic domains in the isotropic phase of the mesogenic substance in the vicinity of the isotropic to nematic phase transition. The results were interpreted in the frame of the Landau-de Gennes theory.

Dynamics of the nonlinear dielectric properties of a nematogenic compound dissolved in a nonpolar medium

The nonlinear dielectric spectra of 4-(trans-4'-n-hexylcyclohexyl)isothiocyanatobenzene (C6H13CyHx Ph NCS, 6CHBT) in benzene solutions were recorded in the whole concentration range up to an appearance of the two-phase isotropic and nematic region (0.82 mole fraction of 6CHBT, at 25 degrees C). Two electric fields: (i) the field of high strength (110 kV/m) and low frequency (85 Hz) causing the dielectric nonlinearity, and (ii) the probing field of low strength and high frequency (100 kHz-3 GHz), were used. At about of 0.2 mole fraction of 6CHBT the nonlinear dielectric increment becomes positive. With increasing of 6CHBT concentration the dynamics of the increment shows a critical-like behavior, which can be interpreted in terms of the reorientation of the growing pseudonematic domains in the solutions studied.