On Measuring the Characteristic Length of the Cooperative Molecular Dynamics in the Glass-Forming Liquids

Abstract

An analysis of the methods for measuring the characteristic length of the cooperative molecular dynamics in glass-forming liquids is submitted. The equations and methods for measuring the size of the cooperatively rearranging regions in post Adam-Gibbs theories are compered, and it is proved that they give one and the same number, but with different interpretation for the relaxed molecular units. The interpretation that the rearranging units defined by Wunderlich are smallest structural units, named beads, is supported by the predicted “universal” value for the cooperatively rearranging range at the glass-transition temperature, as well as from a precise modeling for the relaxations by the generalized entropy theory. It has been found that the characteristic length estimated by random first order transition theory, as well as by the “four-point” dynamic susceptibility method, measured as the number of the bead’s diameters coincide with the length of the cooperatively rearranging region in Adam-Gibbs theory extended at the molecular level.