AN INTERPRETATION OF THE BIFURCATION OF ORIENTATIONAL RELAXATION PROCESSES IN A SUPERCOOLED LIQUID

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 (alpha) and secondary (beta) 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 (alpha-beta) 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 (alpha-beta) 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 (alpha-beta) bifurcation phenomenon and they reveal many of its aspects. The relevance of the present work to current theories of glass transition is discussed briefly.