An interpretation of the bifurcation of orientational relaxation processes in a supercooled liquid

Abstract

The orientational relaxation of molecules in a supercooled liquid is known to exhibit interesting dynamical behavior. As the temperature of the liquid is lowered towards its glass transition temperature, there is a bifurcation of the relaxation dynamics into primary (α) and secondary (β) processes; the former is associated with the collective motion responsible for the glass transition, while the latter is associated with single particle motion. In this paper we present a theory of orientational relaxation in a supercooled liquid. This theory provides both qualitative and quantitative descriptions of the (αβ) bifurcation phenomenon at a molecular level. The theory exploits the properties of a time dependent free energy functional which explicitly includes the effects of the collective motions in the liquid on the orientational motion of a solute (or a tagged) molecule. In the overdamped limit, this analysis leads to two coupled Smoluchowski equations for the orientation distribution function. These equations, when solved, reveal the essential features of the (αβ) bifurcation phenomenon. Explicit calculations are presented for orientational relaxation in a liquid of dipolar hard spheres, a liquid of nonpolar ellipsoids, and an orientationally disordered solid. Our calculations demonstrate the ubiquity of the (αβ) bifurcation phenomenon and they reveal many of its aspects. The relevance of the present work to current theories of glass transition is discussed briefly.