Dynamics across a Free Surface Reflect Interplay between Density and Cooperative Length: Application to Polystyrene
Ronald P. White, Jane E. G. Lipson
Abstract
It is now generally agreed that the most dramatic influence of a free surface on local relaxation dynamics occurs over the first 10 nm from the surface. Using the cooperative free volume (CFV) rate model, we have linked a faster dynamic response to a lower density (i.e., greater available or free volume) closer to the interface. Experimental and simulation studies have shown that the relaxation profile is significantly broader than the local density profile. Here, we explain this difference using the CFV model to show that local relaxation can be enabled through accrual of a fixed amount of free volume, the value of which is a characteristic, material-dependent quantity. The process by which a relaxing segment acquires this volume involves a cooperative region whose length scale will change with density and therefore with distance from the interface. The result is a region-averaged position-dependent density profile that is significantly broadened and that links directly to the relaxation profile. Finally, we explain why these film confinement effects diminish in importance as the temperature is increased.