Determination of orientational correlation functions in ordered fluids: Raman scattering

Thermodynamic scaling of dynamic properties of liquid crystals: verifying the scaling parameters using a molecular model

The thermodynamic scaling of molecular dynamic properties of rotation and thermodynamic parameters in a nematic phase was investigated by a molecular dynamic simulation using the Gay-Berne potential. A master curve for the relaxation time of flip-flop motion was obtained using thermodynamic scaling, and the dynamic property could be solely expressed as a function of TV(γτ) , where T and V are the temperature and volume, respectively. The scaling parameter γτ was in excellent agreement with the thermodynamic parameter Γ, which is the logarithm of the slope of a line plotted for the temperature and volume at constant P2. This line was fairly linear, and as good as the line for p-azoxyanisole or using the highly ordered small cluster model. The equivalence relation between Γ and γ(τ) was compared with results obtained from the highly ordered small cluster model. The possibility of adapting the molecular model for the thermodynamic scaling of other dynamic rotational properties was also explored. The rotational diffusion constant and rotational viscosity coefficients, which were calculated using established theoretical and experimental expressions, were rescaled onto master curves with the same scaling parameters. The simulation illustrates the universal nature of the equivalence relation for liquid crystals.

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.

Dielectric and elastic properties of liquid crystals

The structural properties, the static and relaxation dielectric coefficients [epsilon(j) and epsilon(j)(omega) (j= ||, perpendicular)], the rotational diffusion constants D( perpendicular) and D( ||), the orientational correlation times tau(1)(i0) (i=0,1), and the bulk elastic constants K(i) (i=1,2,3) are investigated for polar liquid crystals, such as 4-n-pentyl-4(')-cyanobiphenyl (5CB). epsilon(j) are calculated by a combination of the existing molecular theory and statistical-mechanical approach (SMA) that takes into account translational and orientational correlations as well as their coupling, whereas epsilon(j)(omega) are calculated by combining SMA and nuclear magnetic resonance relaxation theory, both based on a rotational diffusion model in which the reorientation of an individual molecule is assumed as stochastic Brownian motion in a potential of mean torque. Reasonable agreement between the calculated and experimental values of epsilon(j) and epsilon(j)(omega) for 5CB is obtained. The bulk Frank elastic constants K(i) (i=1,2,3), for splay, twist, and bend distortion modes, as well as their ratios K(3)/K(1) and K(2)/K(1) are also obtained.

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.

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.