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.
Authors
Salez T; Salez J; Dalnoki-Veress K; Raphaël E; Forrest JA