Abstract
We have constructed a quantitative, force level, statistical mechanical theory for how confinement
in free standing thin films introduces a spatial mobility gradient of the alpha relaxation time as a
function of temperature, film thickness, and location in the film. The crucial idea is that relaxation
speeds up due to the reduction of both near-surface barriers associated with the loss of neighbors
in the local cage and the spatial cutoff and dynamical softening near the vapor interface of the
spatially longer range collective elasticity cost for large amplitude hopping. These two effects are
fundamentally coupled. Quantitative predictions are made for how an apparent glass temperature
depends on the film thickness and experimental probe technique, the emergence of a two-step
decay and mobile layers in time domain measurements, signatures of confinement in frequencydomain dielectric loss experiments, the dependence of film-averaged relaxation times and dynamic fragility on temperature and film thickness, surface diffusion, and the relationship between kinetic experiments and pseudo-thermodynamic measurements such as ellipsometry.