Interpreting viscosity isotherms in materials with significant structural disorder

Abstract

Numerical simulations of viscosity isotherms are presented for a model system with substantial structural disorder. The system consists of an ensemble of metastable two-level subsystems, characterized individually by an elementary activation moment μ and a double well potential with a dissipation barrier Wd=μHd and a level splitting Ws=2μHs, and collectively by a distribution of equivalent fields p(Hd,Hs)=(2πσd2Hd2)−1∕2exp{−[ln(Hd∕Hdm)]2∕2σd2}×(2πσs2)−1∕2exp(−Hs2∕2σs2). The disorder is modeled with broad dispersions σd=σs∕Hdm=1.0. Under these conditions, a typical experimental observation window 10s⩽t⩽104s reveals only a short quasilogarithmic fragment of the complete relaxation isotherm. In the current investigation, we present a prescription for evaluating the thermal fluctuation field Hf=kT∕μ based on a plot of Tln(tr∕τ0) versus Ha, where tr is the “reversal time” at which an isotherm changes sign (or passes through m=0), and we discuss the merits of this approach with respect to scaling strategies.