Mobility Gradients, Growing Apparent Length Scales, and Layer-Dependent Decoupling in Free Standing Films

We employ the Elastically Collective Nonlinear Langevin Equation Theory of bulk and confined supercooled liquids to study macroscopic films with a single vapor interface. An improved description of the long range elastic displacement field fluctuation required to facilitate large amplitude activated hopping events has been developed. Long range and large spatial gradients of mobility and local Tg near the interface are predicted. The effective interfacial length scale based on a return to the bulk timescale criterion grows in a nearly Arrhenius manner with cooling, and is also connected with the temperature-dependent collective elastic barrier in the bulk liquid. The scale-free nature of the elastic barrier leads to layer-dependent, effective power law decoupling of the film relaxation time relative to its bulk analog. The decoupling exponent varies as an inverse power law with distance from the surface. These novel results have a purely dynamical origin since no changes of structure or thermodynamics in confinement enter the theory. The predictions are consistent with simulations of Simmons and coworkers, and have strong implications for thinking about the question of a dynamical length scale in the bulk liquid and how it is related to its interfacial analog.