Spatially correlated dynamics in a simulated glass-forming polymer melt: Analysis of clustering phenomena

In recent years, experimental and computational studies have demonstrated that the dynamics of glass-forming liquids are spatially heterogeneous, exhibiting regions of temporarily enhanced or diminished mobility. Here we present a detailed analysis of dynamical heterogeneity in a simulated "bead-spring" model of a low-molecular-weight polymer melt. We investigate the transient nature and size distribution of clusters of "mobile" chain segments (monomers) as the polymer melt is cooled toward its glass transition. We also explore the dependence of this clustering on the way in which the mobile subset is defined. We show that the mean cluster size is time dependent with a peak at intermediate time, and that the mean cluster size at the peak time grows with decreasing temperature T. We show that for each T a particular fraction of particles maximizes the mean cluster size at some characteristic time, and this fraction depends on T. The growing size of the clusters demonstrates the growing range of correlated motion, previously reported for this same system [C. Beneman et al. Nature (London) 399, 246 (1999)]. The distribution of cluster sizes approaches a power law near the mode-coupling temperature, similar to behavior reported for a simulated binary mixture and a dense colloidal suspension, but with a different exponent. We calculate the correlation length of the clusters, and show that it exhibits similar temperature- and time-dependent behavior as the mean cluster size, with a maximum at intermediate time. We show that the characteristic time of the maximum cluster size follows the scaling predicted by mode-coupling theory (MCT) for the beta time scale, revealing a possible connection between spatially heterogeneous dynamics and MCT.