Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K-1), twist (K-2), and bend (K-3) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphen yl (5CB) in the nematic liquid crystal. The calculations rest on statistica l-mechanical approaches where the absolute values of K-i (i = 1, 2, 3) are dependent on the direct correlation function (DCF) of the corresponding nem atic state. The DCF was determined using the pair correlation function by s olving the Ornstein-Zernike equation. The pair correlation function, in tur n, was obtained from molecular dynamics (MD) trajectory. Three different ap proaches for calculations of the elasticity constants were employed based o n different level of approximation about the orientational order and molecu lar correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distributio n function was used. In addition we have investigated the approximation abo ut spherical distribution of the intermolecular vectors in the nematic phas e often used in derivation of various mean-field theories and employed here for the construction of the DCF, We found that this assumption is not stri ctly valid, in particular a strong deviation from the isotropic distributio n is observed for short intermolecular distances.