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

Abstract

The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the orientational correlation times τ_l vary as [l(l+1)]^-1, where l is the rank of the orientational time 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 τ₁/τ₂ falls considerably below 3 (the Debye limit), one usually invokes a jump diffusion model to explain the approach of the ratio τ₁/τ₂ 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 τ₂/η, η being the shear viscosity of the liquid, becomes much larger than the hydrodynamic value near the I-N transition. We also analyze the breakdown of the Debye model of rotational diffusion in ratios of higher order orientational correlation times. We show that the breakdown of the DSE model is due to the growth of orientational pair correlation and provide a mode coupling theory analysis to explain the results.