Dielectric and elastic properties of liquid crystals

The structural properties, the static and relaxation dielectric coefficients [ε_j and ε_j(ω) (j=‖,⊥)], the rotational diffusion constants D_⊥ and D_‖, the orientational correlation times τ_i0¹ (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). ε_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 ε_j(ω) 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 ε_j and ε_j(ω) 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 K₃/K₁ and K₂/K₁ are also obtained.