Complete breakdown of the Debye model of rotational relaxation near the isotropic-nematic phase boundary: Effects of intermolecular correlations in orientational dynamics

TL;DR

This study investigates the failure of the Debye model of rotational relaxation near the isotropic-nematic phase boundary, revealing the role of intermolecular correlations and providing a mode coupling theory explanation.

Contribution

It demonstrates the breakdown of the Debye model in liquid crystals near the phase transition and links this to growing intermolecular correlations using simulations and mode coupling theory.

Findings

The ratio τ₁/τ₂ drops below one near the I-N transition.

The ratio τ₂/η exceeds hydrodynamic predictions near the transition.

The breakdown is due to increased orientational pair correlations.

Abstract

The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the rotational correlation times $\tau_{l}$ vary as $[l(l+1)]^{-1}$, where $l$ is the rank of the orientational correlation function (given in terms of the Legendre polynomial of rank $l$). One often finds significant deviation from this prediction, in either direction. In supercooled molecular liquids where the ratio $\tau_{1}/\tau_{2}$ falls considerably below three (the Debye limit), one usually invokes a jump diffusion model to explain the approach of the ratio $\tau_{1}/\tau_{2}$ to unity. Here we show in a computer simulation study of a standard model system for thermotropic liquid crystals that this ratio becomes much less than unity as the isotropic-nematic phase boundary is approached from the isotropic side. Simultaneously, the ratio $\tau_2/\eta$ (where $\eta$ is the shear viscosity of the liquid) becomes {\it much larger} than hydrodynamic value near the I-N transition. We have also analyzed the break down of the Debye model of rotational diffusion in ratios of higher order rotational correlation times. We show that the break down of the DSE model is due to the growth of orientational pair correlation and provide a mode coupling theory analysis to explain the results.