Influence of the Director-Density Coupling on the Orientational Dynamics in the Isotropic Phase of Nematic Liquid Crystals

Abstract

The dynamics of how the order parameter $Q_{\alpha \beta }$ of the nematic-isotropic phase transition relaxes to zero in the isotropic phase is divided into two time scales, one slow and the other fast. The slow time scale is associated to the final portion of the curve G(t), the orientational correlation function, which decays exponentially in accordance with the Landau-de Gennes prediction. The initial portion of the curve G(t), on the other side, exhibits a power-law decay given by $t^{-\alpha }$, where $\alpha$ is a temperature-independent exponent. In contrast to the slow dynamics, the fast one is yet barely understood. In this paper, a new approach for the nematodynamics in the isotropic phase is developed in order to include an energetic coupling between mass density gradients and $Q_{\alpha \beta }$. The important result here is the appearance of a new viscosity parameter $\zeta '$ that is crucial to derive the power-law behavior of G(t). We also explain why the fast dynamics is strongly coupled with density fluctuations and dominated by large momentum contributions.