Initial condition of the string relaxation equation of the string model for glass transition: part-I

TL;DR

This paper addresses the initial condition problem of the string relaxation equation in the string model for glass transition, developing a recursive method to accurately determine it, which is crucial for understanding glassy dynamics.

Contribution

A recursive calculation method was developed to exactly determine the special initial condition of the string relaxation equation in the glass transition model.

Findings

Recursive method allows exact calculation of initial condition

Direct calculation method found impractical

Results will aid future solutions for stochastic string configurations

Abstract

The string relaxation equation (SRE) of the string model for the glass transition contains the well-known Debye and Rouse-Zimm relaxation equations. However, its initial condition, necessary to the model predictions of glassy dynamics, such as the mechanism of the universal primary alpha- and Johari-Goldstein beta-relaxations in glassformers, has not been solved. In this paper, the special initial condition (SIC) of the SRE of straight strings for dielectric spectrum technique, which is one of the most common methods to measure the glassy dynamics, was tentatively calculated by a direct calculation method, finding that the method has not any practical feasibility. However, a recursive calculation method was developed that allows to obtain the SIC exactly. It should be expected that the obtained SIC would benefit the thorough solution of the general initial condition of the SRE of the string model for stochastically spatially configurating strings, as will be described in separate publications.