Modeling the glass-liquid transition in thin films: A theoretical approach using the modified Allen-Cahn model

When thin glassy films are heated above their glass transition temperature (T g ), the mechanism by which they transform to the liquid state (“rejuvenation”) is governed by the structure of the initial glassy state, determined by the film’s preparation conditions. While the conventionally prepared glassy films rejuvenate through a spatially homogeneous process, the ultrastable glass films, typically produced by physical vapor deposition, transform differently: a mobility front originates at the free surface and moves inward at a roughly uniform speed. This speed depends on the material properties and the annealing temperature, and it scales approximately inversely with the α -relaxation time. In this work, we develop a continuum framework based on the free energy minimization, leading to a modified Allen-Cahn equation that captures both homogeneous and front-mediated relaxation dynamics. This equation is designed to represent the contrast in mobility and the associated thermodynamic driving forces, thereby linking molecular-scale relaxation behavior to mesoscopic front propagation phenomena. Although experimental evidence supports the existence of mobility fronts during the glass-to-liquid transition, the development of a predictive theoretical framework remains an open challenge. Key unresolved questions include how deposition conditions govern front velocity, the extent to which this phenomenon is universal across diverse glass-forming systems, and whether a unified model can be formulated to describe rejuvenation dynamics in a broad class of non-crystalline solid materials.