Dynamical heterogeneity in a model for permanent gels: Different behavior of dynamical susceptibilities

Abstract

We present a systematic study of dynamical heterogeneity in a model for permanent gels, upon approaching the gelation threshold. We find that the fluctuations of the self intermediate scattering function are increasing functions of time, reaching a plateau whose value, at large length scales, coincides with the mean cluster size and diverges at the percolation threshold. Another measure of dynamical heterogeneities, i.e. the fluctuations of the self-overlap, displays instead a peak and decays to zero at long times. The peak, however, also scales as the mean cluster size. Arguments are given for this difference in the long time behavior. We also find that non-Gaussian parameter reaches a plateau in the long time limit. The value of the plateau of the non-Gaussian parameter, which is connected to the fluctuations of diffusivity of clusters, increases with the volume fraction and remains finite at percolation threshold.

11 pages, 14 figures

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• Non-Gaussian Dynamics in Smectic Liquid Crystals of Parallel Hard Rods
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• Dynamical arrest: interplay of the glass and of the gel transitions
• Anisotropic spatially heterogeneous dynamics on the $\alpha$ and $\beta$ relaxation time scales studied via a four-point correlation function
• Emergence of complex behavior in gelling systems starting from simple behavior of single clusters
• Efficient $d$-dimensional molecular dynamics simulations for studies of the glass-jamming transition
• Cluster structure and dynamics in gels and glasses
• Relaxation functions and dynamical heterogeneities in a model of chemical gel interfering with glass transition