Glassy dynamics of simulated polymer melts: Coherent scattering and van Hove correlation functions Part I: Dynamics in the beta-relaxation regime

We report results of molecular-dynamics simulations of a model polymer melt consisting of short non-entangled chains in the supercooled state above th e critical temperature T-c of mode-coupling theory (MCT). To analyse the dy namics of the system, we computed the incoherent, the collective chain and the collective melt intermediate scattering functions as well as their spac e Fourier transforms, the van Hove correlation functions. In this first par t of the paper we focus on the dynamics in the beta -relaxation regime. The final structural relaxation, the alpha -relaxation, will be studied in the following second part. The results can be summarized as follows: Without u sing any fit procedure we find evidence for the space-time factorization th eorem of MCT in real and reciprocal space, and also for polymer-specific qu antities, the Rouse modes. The critical amplitudes in real space are determ ined directly from the simulation data of the van Hove correlation function s. They allow to identify the typical length scales of the beta -dynamics, and illustrate that it is a localized process. In a quantitative analysis t he wave vector dependences of the beta -coefficients, i.e., of the non-ergo dicity parameter, the critical amplitude, and the next-to-leading order cor rection coefficients, are studied for all correlators. The beta -coefficien ts show indications of polymer-specific effects on the length scale of the chain's radius of gyration. The agreement between simulation and the leadin g-order MCT description is found to be good in the central beta -regime. Ne xt-to-leading order corrections extend the validity of the MCT approximatio ns to a greater time window and become more important at large wave vectors .