Orientational relaxation in a dispersive dynamic medium : Generalization of the Kubo-Ivanov-Anderson jump diffusion model to include fractional environmental dynamics

TL;DR

This paper generalizes the Ivanov-Anderson jump diffusion model to include fractional environmental dynamics, explaining non-Debye relaxation behaviors observed in complex liquids through algebraic waiting times and combined jump mechanisms.

Contribution

It introduces a fractional waiting time distribution into the jump diffusion model and combines small and large jumps, advancing the theoretical understanding of orientational relaxation.

Findings

Power law decay in orientational correlation functions

Reproduction of non-Debye dielectric relaxation features

Small jumps influence long-time decay and exponential-like relaxation

Abstract

Ivanov-Anderson (IA) model (and an earlier treatment by Kubo) envisages a decay of the orientational correlation by random but large amplitude molecular jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion. Recent computer simulation studies on water and supercooled liquids have shown that large amplitude motions may indeed be more of a rule than exception. Existing theoretical studies on jump diffusion mostly assume an exponential (Poissonian) waiting time distribution for jumps, thereby again leading to an exponential decay. Here we extend the existing formalism of Ivanov and Anderson to include an algebraic waiting time distribution between two jumps. As a result, the first and second rank orientational time correlation functions show the same long time power law, but their short time decay behavior is quite different. The predicted Cole-Cole plot of dielectric relaxation reproduces various features of non-Debye behaviour observed experimentally. We also developed a theory where both unrestricted small jumps and large angular jumps coexist simultaneously. The small jumps are shown to have a large effect on the long time decay, particularly in mitigating the effects of algebraic waiting time distribution, and in giving rise to an exponential-like decay, with a time constant, surprisingly, less than the time constant that arises from small amplitude decay alone.