Delayed Glassification Model for Free-Surface Suppression of Tg in Polymer Glasses

Suppression of the glass transition by some tens of degrees within a few tens of nanometers of a free surface in a polymer film is a technologically important, commonly observed, as-yet poorly understood phenomenon. We construct a quantitative theory of the influence of the free surface via transmission of "kinks" or "free volume" along the backbone of loops starting and ending at the free surface, following a proposal by de Gennes. Using our delayed glassification (DG) model, we predict depth-dependent values of the local T-g for both semi-infinite and freestanding film geometries, for both infinite and finite molecular weights. The qualitative features of our results are in reasonable agreement with experiment, but the averaging process inherent in connecting our results to macroscopic observations raises further issues, which we treat in the following paper.