Self-motion and the alpha relaxation in a simulated glass-forming polymer: crossover from Gaussian to non-Gaussian dynamic behavior.

J Colmenero,F Alvarez,A Arbe

doi:10.1103/physreve.65.041804

Abstract

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.

Highlights

The understanding of how atoms or molecules move within a supercooled liquid and the way this liquid becomes a glass—the glass transition—is still one of the main challenges in the field of condensed matter
We calculate the density-density correlation function F(Q,t)/F(Q,0) and the secondorder autocorrelation function M 2(t) for different C-H bonds of the main chain. ␣2(t) shows a broad maximum centered at a time t*Ϸ4 ps, which corresponds to the intermediate region ofr2(t)͘ between microscopic dynamics and sublinear diffusion
In the higher Q range—not 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 ␣ relaxation

Summary

Introduction

The understanding of how atoms or molecules move within a supercooled liquid and the way this liquid becomes a glass—the glass transition—is still one of the main challenges in the field of condensed matter. Nowadays there is an increasing interest in the so-called ‘‘dynamical heterogeneity’’ of the main dynamical process in supercooled liquids: the ␣ relaxation. Dynamical heterogeneities have been directly observed in colloidal models of glass-forming systems7͔. The heterogeneous dynamics in polymer films of polymethylacrylatenear their glass-transition temperature has recently been proved by means of singlemolecule spectroscopy8͔. Many different theoretical concepts of dynamical heterogeneity are usually invoked9͔. From a general point of view, a system is considered as dynamically heterogeneous if a dynamically distinguishable subensemblee.g., ‘‘fast’’ or ‘‘slow’’ particlescan be isolated by computer simulation or experiment. Computer simulations of model systems3,5͔, as well as the experiments in colloidal systems mentioned above, show that the deviations of Gs(r,t) from the Gaussian form can be expected in the case of more complex dynamic processes as, for instance, a heterogeneous dynamics. Gs(r,t) can be evaluated in a computer simulation ‘‘experiment’’

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Discussion

Conclusion