Probe molecules in polymer melts near the glass transition: A molecular dynamics study of chain length effects

Molecular dynamics simulations of a dense melt of short bead-spring polymer chains containing N=5, 10, or 25 effective monomers are presented and analyzed. Parts of our simulations include also a single dumbbell (N=2) of the same type, which is interpreted to represent a coarse-grained model for a fluorescent probe molecule as used in corresponding experiments. We obtain the mean-square displacements of monomers and chains center of mass, and intermediate incoherent scattering functions of both monomers in the chains and particles in the dumbbells as function of time for a broad regime of temperatures above the critical temperature T(c) of mode-coupling theory. For both the chains and the dumbbell, also orientational autocorrelation functions are calculated and for the dumbbell time series for the time evolution of linear dichroism and its autocorrelation function are studied. From both sets of data we find that both the mode-coupling critical temperature T(c) (representing the "cage effect") and the Vogel-Fulcher temperature T(0) (representing the caloric glass transition temperature) systematically increase with chain length. Furthermore, the dumbbell dynamics yields detailed information on the differences in the matrix dynamics that are caused by the chain length variation. Deviations from the Stokes-Einstein relation are discussed, and an outlook to related experiments is given.