Self-motion and the α relaxation in a simulated glass-forming polymer: Crossover from Gaussian to non-Gaussian dynamic behavior

We present fully atomistic molecular dynamics simulations for a realistic model of a glass-forming polymer: polyisoprene. The simulations are carried out at 363 K and extend until 20 ns. We calculate the self-part of the Van Hove correlation function G(s)(r,t), the mean-squared displacement <r(2)(t)>, the second-order non-Gaussian parameter alpha(2)(t), and the incoherent intermediate scattering function F(s)(Q,t) for the main chain protons. In addition, we also calculate the density-density correlation function F(Q,t)/F(Q,0) and the second-order autocorrelation function M2(t) for different C-H bonds of the main chain. alpha(2)(t) shows a broad maximum centered at a time t(*) approximately 4 ps, which corresponds to the intermediate region of <r(2)(t)> between microscopic dynamics and sublinear diffusion. The analysis of F(s)(Q,t), F(Q,t)/F(Q,0), and M2(t) focuses on the second slow step which is associated to the alpha relaxation. Following the usual experimental procedure this decay is described in terms of a Kohlrausch-Williams-Watts (KWW) function: A exp[-(t/tau)(beta)]. In the Q range below Q(max), where Q(max) is the value at which the static structure factor shows its first maximum, the Q dependence of the KWW relaxation time of F(s)(Q,t) follows a law tau approximately Q(-2/beta). This kind of Q dependence corresponds to a Gaussian behavior of G(s)(r,t) and F(s)(Q,t). This law has been experimentally found in this Q range for different polymers. In the higher Q range-not easily accessible experimentally-strong deviations from the Gaussian behavior manifest. This crossover from Gaussian to non-Gaussian behavior can be understood in the framework of the mode coupling theory as well as in terms of a crossover from homogeneous to heterogeneous dynamics. This last interpretation opens a possible way of rationalizing the apparent contradiction between the neutron scattering and relaxation techniques results concerning dynamical heterogeneity of the alpha relaxation.