Static and Dynamic Heterogeneities in a Model for Irreversible Gelation

Abstract

We study the structure and the dynamics in the formation of irreversible gels by means of molecular dynamics simulation of a model system where the gelation transition is due to the random percolation of permanent bonds between neighboring particles. We analyze the heterogeneities of the dynamics in terms of the fluctuations of the self-intermediate scattering functions: in the sol phase close to the percolation threshold, we find that this dynamic susceptibility increases with the time until it reaches a plateau. At the gelation threshold this plateau scales as a function of the wave vector k as k(eta-2), with eta being related to the decay of the percolation pair connectedness function. At the lowest wave vector, approaching the gelation threshold it diverges with the same exponent gamma as the mean cluster size. These findings suggest an alternative way of measuring critical exponents in a system undergoing chemical gelation.

Self-assembly and cooperative dynamics of a model colloidal gel network

“…First, we characterize the cooperative dynamics of the gels by means of the dynamical susceptibility χ 4 . This quantity has been extensively analyzed in numerical simulations of dense glassy systems [31], but it has been relatively less studied in gels [14,15,[32][33][34][35], in spite of the fact that experimental measures of χ 4 in colloidal gels have already been performed [15,32]. We compute χ 4 and its dependence on the scattering wave vector q in networks with varying density, discussing possible connections with experimental observations.…”

Cluster structure and dynamics in gels and glasses

“…In this case, for each value of the volume fraction, χ 4 (k min , t) reaches a plateau after a characteristic time of the order of the relaxation time. It was theoretically shown [4], and numerically verified, that, in the limit of small k, the asymptotic value of χ 4 (k, t) coincides with the mean cluster size (see Inset of Fig.1), defined as S = s 2 n(s)/ sn(s), where n(s) is the number of cluster of size s, which diverges at the gelation threshold with the random percolation exponent γ. Thus, in chemical gels, DHs are due to the presence of clusters of bonded particles.…”

“…Both ξ * and t * ξ increase as power laws of ρ ka − ρ. Fig.5b shows that the dynamical susceptibility, χ 4 …”

“…For further details on the MD simulations see Refs. [4,11]. Alternatives models have been described in Refs.…”

“…We start by discussing the case of chemical gels, where for k → 0 and t → ∞, the dynamic susceptibility χ 4 (k, t) tends to the mean cluster size, which diverges at the gelation threshold [4]. Then, we consider to what extent this scenario holds on moving from chemical to colloidal gels [5], and from colloidal gels to colloidal glasses [6], i.e.…”