Dynamic Gradients, Mobile Layers, Tg Shifts, Role of Vitrification Criterion and Inhomogeneous Decoupling in Free-Standing Polymer Films

TL;DR

This paper refines a theoretical model to better predict how glass transition temperature and dynamics vary in free-standing polymer films, accounting for anisotropic elasticity and spatial inhomogeneity, with results aligning well with experiments.

Contribution

It introduces an improved elasticity treatment in the Elastically Collective Nonlinear Langevin Equation theory for thin films, capturing spatial inhomogeneity and dynamic decoupling effects.

Findings

Enhanced theory predicts faster dynamics and lower Tg in thin films.

Mobile layer length scale correlates linearly with bulk relaxation time.

Quantitative agreement with experimental Tg shifts in PS and PC films.

Abstract

The force-level Elastically Collective Nonlinear Langevin Equation theory of activated relaxation in glass-forming free-standing thin films is re-visited to improve its treatment of collective elasticity effects. The naive cut off of the isotropic bulk displacement field approximation is improved to explicitly include spatial anisotropy with a modified boundary condition consistent with a step function liquid-vapor interface. The consequences of this improvement on dynamical predictions are quantitative but of significant magnitude and in the direction of further speeding up dynamics and further suppressing Tg. The theory is applied to thin films and also thick films to address new questions for three different polymers of different dynamic fragility. Variation of the vitrification time scale criterion over many orders of magnitude is found to have a minor effect on changes of the film-averaged Tg relative to its bulk value. The mobile layer length scale grows strongly with cooling and correlates in a nearly linear manner with the effective barrier deduced from the corresponding bulk isotropic liquid alpha relaxation time. The theory predicts a new type of spatially inhomogeneous "dynamic decoupling" corresponding to an effective factorization of the total barrier into its bulk temperature-dependent value multiplied by a function that only depends on location in the film. The effective decoupling exponent grows as the vapor surface is approached. Larger reductions of the absolute value of Tg shifts in thin polymer films are predicted for longer time vitrification criteria and more fragile polymers. Quantitative no-fit-parameter comparisons with experiment and simulation for film-thickness-dependent Tg shifts of PS and PC are in reasonable accord with the theory, including a nearly 100 K suppression of Tg in 4 nm PC films. Predictions are made for polyisobutylene thin films.