Cooperative Strings and Glassy Interfaces

Abstract

We introduce a minimal theory of glass formation based on the ideas of molecular crowding and resultant string-like cooperative rearrangement, and address the effects of free interfaces. In the bulk case, we obtain a scaling expression for the number of particles taking part in cooperative strings, and we recover the Adam-Gibbs description of glassy dynamics. Then, by including thermal dilatation, the Vogel-Fulcher-Tammann relation is derived. Moreover, the random and string-like characters of the cooperative rearrangement allow us to predict a temperature-dependent expression for the cooperative length $\xi$ of bulk relaxation. Finally, we explore the influence of sample boundaries when the system size becomes comparable to $\xi$. The theory is in agreement with measurements of the glass-transition temperature of thin polymer films, and allows to quantify the temperature-dependent thickness $h_{\textrm{m}}$ of the interfacial mobile layer.