Influence of Longer Range Transfer of Vapor Interface Modified Caging Constraints on the Spatially Heterogeneous Dynamics of Glass-Forming Liquids

Based on the elastically collective nonlinear Langevin equation (ECNLE) theory of bulk relaxation in glass-forming liquids, and our recent ideas of how interface-nucleated modification of caging constraints are spatially transferred into the interior of a thick film, we present a force-based theory for dynamical gradients in thick films with one vapor interface that includes collective elasticity effects. Quantitative applications to the foundational hard sphere fluid and polymer melts of diverse fragilities are presented. We predict a roughly exponential spatial variation of the total activation barrier which is nonperturbatively modified to ∼10 particle diameters into the film. This leads, to leading order, to the prediction of a reduced alpha relaxation time gradient of a double-exponential form characterized by a nearly constant spatial decay length, in qualitative accord with simulations. The relaxation acceleration at the surface grows exponentially with increasing packing fraction or decreasing temperature. The rate of increase with cooling of the alpha time strongly weakens upon approaching the vapor interface, with the top two layers remaining liquid-like down to ∼80-85% of the bulk glass transition temperature. These spatially heterogeneous changes of the temperature variation of the alpha time result in a large and long-range gradient of the local glass transition temperature. An average interfacial layer thickness relevant to ensemble-averaged dielectric and other experiments is also computed. It is predicted to be rather large at the bulk glass transition temperature, decreasing roughly linearly with heating. Remarkably, to leading order the ratio of this layer-averaged interfacial relaxation time to its bulk analogue is invariant to chemistry, volume fraction, and temperature and of modest absolute magnitude. Spatially inhomogeneous power law decoupling of the alpha relaxation time from its bulk value is predicted, with an effective exponent that decays to zero with distance from the free surface in a nearly exponential manner, trends which are in qualitative accord with recent simulations. This behavior and the double-exponential alpha time gradient are related and can be viewed as consequences of an effective quasi-universal factorization of the total barrier in films into the product of its bulk-temperature-dependent value times a function solely of location in the film.