Emergence of complex behavior in gelling systems starting from simple behavior of single clusters

Abstract

A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of percolation theory, under simple assumptions on the relaxation of single clusters. By neglecting the correlation between particles belonging to different clusters, the quantities of interest (such as the self intermediate scattering function, the dynamical susceptibility, the Van-Hove function, and the non-Gaussian parameter) are written as superposition of those due to single clusters. Connection between these behaviors and the critical exponents of percolation are given. The theoretical predictions are checked in a model for permanent gels, where bonds between monomers are described by a finitely extendable nonlinear elastic potential. The data obtained in the numerical simulations are in good agreement with the analytical predictions.

Non-Gaussian rotational diffusion in heterogeneous media

“…Recent theoretical and simulation studies by Fierro et al [23,32] showed that the dynamics of permanent gels was also non-Gaussian at Fickian time scales and verified systematically that such non-Gaussian dynamics could be understood as a linear combination of the Gaussian displacement distribution functions of different values of D s , where D s is the diffusion coefficient of cluster size s of permanent gels. By employing the percolation theory and assuming the relation between D s and s, they proposed a quantitative theory to explain the complex dynamic behavior of gels in terms of P (D s ) and compared the theory to their simulation results.…”

“…Such dynamic heterogeneity has been described in terms of the distribution τ or the distribution P (D) of diffusion coefficients D [22][23][24][25]. It is, however, usually formidable to obtain P (D): (1) in ergodic systems there is no distribution of D, i.e., P (D) reaches a δ function after sufficient time averaging, and (2) in nonergodic systems such as glasses the diffusion is usually too slow to estimate P (D).…”

“…Because W (t) ∼ t indicates that molecules would undergo Brownian diffusion at given time scales, the Gaussian form of G s (r,t) is usually expected. However, there have been several reports of such a seemingly Fickian but non-Gaussian dynamics in complex systems [23][24][25][27][28][29][30][31], and how the non-Gaussian G s (r,t) emerges still remains elusive. Non-Gaussian G s (r,t) has been interpreted as a linear combination of the Gaussian displacement distribution functions g(r,t|D) of each single molecule, i.e., G s (r,t) = P (D)g(r,t|D)dD.…”

Percolation approach to glassy dynamics with continuously broken ergodicity

“…To explicitly obtain the scaling function we introduce a percolation approach elaborating on the cluster formulation used to describe the sol-gel transition [13]. We posit that our reference glassy system can be described as a collection of clusters each of which decays exponentially in time over a timescale t s that increases with the cluster size s. Structure and relaxation of clusters evidently depend on the precise nature of the system interaction and the underlying microscopic dynamics.…”

Relaxation functions and dynamical heterogeneities in a model of chemical gel interfering with glass transition

“…Indeed, the chemical sol-gel transition shows the same continuous nature of the random percolation transition. Recently, it has been shown that the same cluster mechanism holds generally for gelling systems [3] and Mode Coupling Theory (MCT) schematic model A [4]. In particular, in Ref.…”