Dynamical gradients, barrier factorization and interface coupling in thick and thin films of glass-forming liquids

A force-level microscopic theory is constructed for the heterogeneous dynamics of glassy polymer liquids in free standing films. The activated event involves cage scale hopping coupled with a longer range collective elastic distortion of the medium. For thick films, weaker caging constraints at the vapor surface are dynamically transferred well into the bulk, and the elastic displacement field at the surface is cut off. A double (single) exponential form of the alpha time (T_g) gradient, near factorization of the temperature and spatial location dependences of the activation barrier, and position-dependent power law decoupling of the relaxation time from its bulk analog are predicted. The ideas are generalized to thin films resulting in an interference of weakened caging constraints from the two surfaces plus a finite size confinement modification of elasticity effects. Temperature-dependent consequences with decreasing film thickness include additional acceleration and flattening at the film center of the alpha time gradient, and large reduction of the film averaged effective barrier. The results appear to be consistent with simulations and experiment. The reliability of a linear superposition approximation of exponential gradients from a thick film have been analyzed.