Monte Carlo simulation of stretched exponential relaxation near the glass transition

Abstract

The dynamical behavior of a supercooled polymer melt is studied by means of Monte Carlo simulation. The simulation uses a version of the bond-fluctuation (lattice) model in which long bond vectors are favored energetically. The expansion on the length scale of a bond also induces an increase of the chains' size and stiffness during supercooling. In a dense melt the tendency of an individual chain to stretch has to compete with that of all others. This competition between the internal energy of a chain and the density of the melt strongly slows down the structural relaxation at low temperatures. In order to analyze the dynamical behavior of this model different relaxation functions were calculated in a temperature region ranging from the normal liquid-like to the supercooled state of the melt. Among these relaxation functions are the end-to-end vector correlation function and the correlation function of the Rouse modes. Both functions exhibit a time-temperature superposition property at all times. The corre sponding superposition (relaxation) times can be fitted by a Vogel-Fulcher equation, yielding a common Vogel-Fulcher temperature of about T 0 ≈ 0.12–0.13. As in experiments, this temperature is smaller than the critical temperature of mode-coupling theory (T 0 < T c ≈ 0.15). In addition to this temperature dependence another characteristic feature of the correlation functions is that their relaxation is stretched. For the Rouse modes this stretching is unexpected from the Rouse theory. However, as the theory predicts, the modes remain statically uncorrelated for all studied temperatures.