Slow dynamics and glass transition in simulated free-standing polymer films: a possible relation between global and local glass transition temperatures

We employ molecular dynamics simulations to explore the influence that the surface of a free-standing polymer film exerts on its structural relaxation when the film is cooled toward the glass transition. Our simulations are concerned with the features of a coarse-grained bead-spring model in a temperature regime above the critical temperature T-c of mode-coupling theory. We find that the film dynamics is spatially heterogeneous. Monomers at the free surface relax much faster than they would in the bulk at the same temperature T. The fast relaxation of the surface layer continuously turns into bulk-like relaxation with increasing distance y from the surface. This crossover remains smooth for all T, but its range grows on cooling. We show that it is possible to associate a gradient in critical temperatures T-c( y) with the gradient in the relaxation dynamics. This finding is in qualitative agreement with experimental results on supported polystyrene ( PS) films ( Ellison and Torkelson 2003 Nat. Mater. 2 695). Furthermore we show that the y dependence of T-c( y) can be expressed in terms of the depression of T-c(h)-the global Tc for a film of thickness h if we assume that T-c( h) is the arithmetic mean of T-c( y) and parameterize the depression of T-c( h) by T-c( h) = T-c/( 1 + h(0)/ h), a formula suggested by Herminghaus et al ( 2001 Eur. Phys. J. E 5 531) for the reduction of the glass transition temperature in supported PS films. We demonstrate the validity of this formula by comparing our simulation results to results from other simulations and experiments.