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

The force-level elastically collective nonlinear Langevin equation (ECNLE) theory of activated relaxation in glass-forming free-standing thin films is revisited to improve its treatment of collective elasticity effects. The naive cutoff of the isotropic bulk displacement field approximation is improved to explicitly include some aspects of 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 T_g. The theory is applied to thin films and also (for the first time) semi-infinite thick films to address qualitatively 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 surprisingly minor effect on changes of the film-averaged T_g 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 monotonically as the vapor surface is approached. Larger reductions of the absolute value of T_g 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 T_g shifts of polystyrene and polycarbonate are in reasonable accord with the theory, including a nearly 100 K suppression of T_g in 4 nm polycarbonate films. Predictions are made for polyisobutylene thin films.