Dielectric and elastic properties of liquid crystals

The structural properties, the static and relaxation dielectric coefficients $[{\epsilon }_j$ and ${\epsilon }_j\left(\omega \right)$ $(j=\Vert ,\perp )],$ the rotational diffusion constants $D_{\perp }$ and $D_{\Vert },$ the orientational correlation times ${\tau }_{i0\mathrm{}}^1$ $\mathrm{}(i=0,1\mathrm{}),$ and the bulk elastic constants $K_i$ $\mathrm{}(i=1,2,3\mathrm{})\mathrm{}$ are investigated for polar liquid crystals, such as $4-n-\mathrm{pentyl}-4^{\prime }-\mathrm{cyanobiphenyl}$ (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 ${\epsilon }_j\left(\omega \right)$ 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 ${\epsilon }_j\left(\omega \right)$ for 5CB is obtained. The bulk Frank elastic constants $K_i$ $\mathrm{}(i=1,2,3\mathrm{}),$ for splay, twist, and bend distortion modes, as well as their ratios $K_3{/K}_1$ and $K_2{/K}_1$ are also obtained.