Microscopic description of nematic liquid crystal viscosity

Liquid relaxation: A new Parodi-like relation for nematic liquid crystals

We put forward a hydrodynamic theory of nematic liquid crystals that includes both anisotropic elasticity and dynamic relaxation. Liquid remodeling is encompassed through a continuous update of the shear-stress free configuration. The low-frequency limit of the dynamical theory reproduces the classical Ericksen-Leslie theory, but it predicts two independent identities between the six Leslie viscosity coefficients. One replicates Parodi's relation, while the other-which involves five Leslie viscosities in a nonlinear way-is new. We discuss its significance, and we test its validity against evidence from physical experiments, independent theoretical predictions, and molecular-dynamics simulations.

Influence of shear flow on the Fréedericksz transition in nematic liquid crystals

Within the framework of Ericksen-Leslie continuum theory we analyze the influence of shear flow on the magnetic-field-induced Fréedericksz transition in nematic liquid crystal with rodlike molecules. We consider three basic orientational configurations of a nematic planar layer in the uniform magnetic field. Conditions of rigid director coupling on the boundaries of the layer and constant shear flow gradient inside the layer are used. We exhibit some flow aligning effects for nematic liquid crystals with various ratio of rotary viscosities and investigate how unequal elastic constants (elastic anisotropy) alter the magnetic Fréedericksz transition in sheared nematics. Our calculations predict that surface boundary effects in nematic films and magnetic field action lead to existence of stationary flow regimes in the so-called nonflow aligning nematics, otherwise, surface and magnetic forces extend the range of viscous coefficient values corresponding to the flow aligning regimes. We show that imposing of shear flow on the Fréedericksz transition leads to a threshold behavior or to a "smoothing" of the transition. It depends on the orientation of the nematic layer in magnetic field and magnitudes of rotary viscous coefficients.

Agreements and disagreements between theories and experiments in nematoviscosity

In this work a set of viscosity data selected from the nematic liquid crystals literature is compared with the currently accepted microscopic (molecular) theories for the nematic viscosity. It is shown that the kinetic theory of Doi [N. Kuzuu and M. Doi, J. Phys. Soc. of Jpn. 52, 3486 (1983)] and the affine transformation theory of Hess [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] equally predict that Miesowicz's coefficients of a given sample are not independent but, as it has been believed for many years [H. Kneppe, F. Scheneider, and N. K. Sharma, Ber. Bunsenges Phys. Chem. 85, 784 (1981)], they are connected by a linear relationship. Such conjecture gains a strong positive support when it is applied to a set of experimental data that we have collected. However, when these data are used to obtain the values of the parameters used to build these theories, it is found that the values assumed by them are in flagrant disagreement with the physical interpretation that they are supposed to have.

Rotational viscosity, dynamic phenomena, and dielectric properties in a long-chain liquid crystal: NMR study and theoretical treatment

The rotational diffusion constants D(perpendicular) and D(parallel), rotational viscosity coefficients gamma(i) (i=1,2), the orientational correlation times tau(L)mn, and the dielectric permittivities for nematic liquid crystals (NLCs) are investigated. gamma(i) are calculated by a combination of existing statistical-mechanical approach (SMA) and NMR relaxation theory, both based on a rotational diffusion model. In the rotational diffusion model, it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, gamma(i) are found to be a function of temperature, density, rotational diffusion constant for tumbling motions, and the orientational order parameters. The order parameters and rotational diffusion constant are obtained from an analysis of NMR measurements. Reasonable agreement between the calculated and experimental values of gamma(i) for 4-n-octyloxy-4'-cyanobiphenyl (8OCB) is obtained. The orientational correlation times, and the longitudinal and transverse components of the real chi'(j)(omega) and imaginary chi"(j)(omega) (j= parallel, perpendicular) parts of the complex susceptibility tensor for 8OCB molecules in the nematic phase are also obtained.

Simulations of flow-induced director structures in nematic liquid crystals through leslie-ericksen equations. I. Computational methodology in two dimensions

A computational treatment of the constitutive equations of nematodynamics, based on the Leslie-Ericksen approach, is presented and discussed for a rotating planar nematic sample subjected to a constant magnetic field. The dynamics of the velocity v and director n fields is taken into account exactly. Coupled partial differential equations suitable to be solved numerically are worked out, in terms of derived functionals of v and n and of their spatial and time derivatives. Time-dependent patterns of the director are obtained using a finite-difference scheme in a spatial polar grid. Several experimental situations are analyzed, corresponding to common experimental setups: continuously rotating samples for different values of the rotational speed; 30 degrees and 90 degrees step-rotation experiments. A comparison is made to existing approximate treatments. Dependence upon the sample dimension is also discussed.

Nematic liquid crystal viscosity: inadequacies of microscopic theories

Recently Janik et al. reported measurements of the Miesowicz viscosity coefficients of the nematic liquid crystal and confronted them with the results of the available theoretical models. They found that none of them can be successfully applied for the purpose of the Miesowicz-type experiment. In this paper I present an explanation why the microscopic theories seem inadequate. In particular, I analyze the applicability and conclusions of the Osipov-Terentjev model, whose final predictions are highlighted to be the same as those of the Kuzuu-Doi theory. It has been shown that the microscopic theories can perfectly explain the behavior of the Miesowicz coefficients difference eta(3)-eta(2) but are inadequate to study their ratio eta(3)/eta(2), which is contributed by the Leslie coefficient alpha(4). A disagreement between experimental data and the theoretical results for alpha(4) is attributed to the fact that the isotropic contribution to alpha(4) in the nematic phase is beyond the scope of the theories that are based on the anisotropic orientational distributions.

Mesoscopic model for the viscosities of nematic liquid crystals

Based on the definition of the mesoscopic concept by Blenk et al. [Physica A 174, 119 (1991); J. Noneq. Therm. 16, 67 (1991); Mol. Cryst. Liq. Cryst. 204, 133 (1991)] an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the mesoscopic stress tensor, whose structure is assumed similar to the macroscopic Leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier-Stokes equation. On the basis of the correspondence between microscopic and mesoscopic scales a mean-field mesoscopic potential is introduced. It allows us to obtain the stress tensor angular velocity of the free rotating molecules with the help of the orientational Fokker-Planck equation. The macroscopic stress tensor is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic viscosities have been found. The mesoscopic analysis results are shown to be consistent with the diffusional model of Kuzuu-Doi and Osipov-Terentjev with the exception of the shear viscosity alpha(4). In the nematic phase alpha(4) is shown to have two contributions: isotropic and nematic. There exists an indication that the influence of the isotropic part is dominant over the nematic part. The so-called microscopic stress tensor used in the microscopic theories is shown to be the mean-field potential-dependent representation of the mesoscopic stress tensor. In the limiting case of total alignment the Leslie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the affine transformation model of the perfectly ordered systems. This comparison shows disagreement concerning the rotational viscosity, whereas the coefficients characteristic for the symmetric part of the viscous stress tensor remain the same. The difference is caused by the hindered diffusion in the affine model case.

Rotational viscosity in a nematic liquid crystal: a theoretical treatment and molecular dynamics simulation

The rotational viscosity coefficient gamma(1) of 4-n-pentyl-4(')-cyanobiphenyl in the nematic phase is investigated by combination of existing statistical-mechanical approaches (SMAs), based on a rotational diffusion model and computer simulation technique. The SMAs rest on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMAs, gamma(1) is found to be a function of temperature, density, rotational diffusion coefficient, and a number of order parameters (OPs). The diffusion coefficient and the OPs were obtained from an analysis of a trajectory generated in a molecular dynamics simulation using realistic atom-atom interactions. In addition, a set of experimentally determined diffusion coefficients and OPs was used for evaluation of gamma(1). Reasonable agreement between calculated and experimental values of gamma(1) is obtained. It is shown that near the clearing point gamma(1) is proportional to (-)P22, where (-)P2 is the second-rank OP. This limiting value of gamma(1) is in agreement with mean-field theory.