Glassy dynamics of simulated polymer melts: Coherent scattering and van Hove correlation functions

Abstract:

We report results of molecular-dynamics simulations of a model polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature T _c of mode-coupling theory (MCT). To analyse the dynamics of the system, we computed the incoherent, the collective chain and the collective melt intermediate scattering functions as well as their space Fourier transforms, the van Hove correlation functions. In this first part of the paper we focus on the dynamics in the β-relaxation regime. The final structural relaxation, the α-relaxation, will be studied in the following second part. The results can be summarized as follows: Without using any fit procedure we find evidence for the space-time factorization theorem of MCT in real and reciprocal space, and also for polymer-specific quantities, the Rouse modes. The critical amplitudes in real space are determined directly from the simulation data of the van Hove correlation functions. They allow to identify the typical length scales of the β-dynamics, and illustrate that it is a localized process. In a quantitative analysis the wave vector dependences of the β-coefficients, i.e., of the non-ergodicity parameter, the critical amplitude, and the next-to-leading order correction coefficients, are studied for all correlators. The β-coefficients show indications of polymer-specific effects on the length scale of the chain's radius of gyration. The agreement between simulation and the leading-order MCT description is found to be good in the central β-regime. Next-to-leading order corrections extend the validity of the MCT approximations to a greater time window and become more important at large wave vectors.