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.

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 the 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 the percolation threshold.

We study a model for the gel degradation by an enzyme, where the gel is schematized as a cubic lattice, and the enzyme as a random walker, that cuts the bonds over which it passes. The model undergoes a (reverse) percolation transition, which for low density of enzymes falls in a universality class different from random percolation. In particular, we have measured a gel fraction critical exponent beta=1.0+/-0.1, in excellent agreement with experiments made on the real system.

In chemical cross-linking of gelatin solutions, two different time scales affect the kinetics of the gel formation in the experiments. We complement the experimental study with Monte Carlo numerical simulations of a lattice model. This approach shows that the two characteristic time scales are related to the formation of single bond cross-linker-chain and of bridges between chains. In particular, their ratio turns out to control the kinetics of the gel formation. We discuss the effect of the concentration of chains. Finally our results suggest that by varying the probability of forming bridges as an independent parameter, one can finely tune the kinetics of the gelation via the ratio of the two characteristic times.

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.

We compare the slow dynamics of irreversible gels, colloidal gels, glasses and spin glasses by analyzing the behavior of the so called non-linear dynamical susceptibility, a quantity usually introduced to quantitatively characterize the dynamical heterogeneities. In glasses this quantity typically grows with the time, reaches a maximum and then decreases at large time, due to the transient nature of dynamical heterogeneities and to the absence of a diverging static correlation length. We have recently shown that in irreversible gels the dynamical susceptibility is instead an increasing function of the time, as in the case of spin glasses, and tends asymptotically to the mean cluster size. On the basis of molecular dynamics simulations, we here show that in colloidal gelation where clusters are not permanent, at very low temperature and volume fractions, i.e. when the lifetime of the bonds is much larger than the structural relaxation time, the non-linear susceptibility has a behavior similar to the one of the irreversible gel, followed, at higher volume fractions, by a crossover towards the behavior of glass forming liquids.

Modeling free radical polymerization processes in the presence of cross-linkers is a challenging problem that has been addressed using numerous techniques for over more than half a century. However, a model providing a comprehensive description of the phenomenon has not been proposed yet. In this work, we implement a simple free-radical polymerization scheme of a monovinyl (difunctional) monomer and a divinyl (tetrafunctional) cross-linker in a Monte Carlo (MC) scheme, which describes polymer dynamics using a bond-fluctuation model. MC simulations allow us to follow the entire polymerization kinetics and the formation of a percolating network (gel phase) by realistically taking into account diffusion limitations, to extract scaling information at the percolation threshold and to recover the distribution of number of monomer units between two successive fully cross-linked units, from which the extent of swelling can be computed. The predictions of MC simulations are also successfully compared to a kinetic model based on numerical fractionation, with kinetic constants used as fitting parameters. MC data and kinetic simulations are compared to some experimental data on the swelling behavior of polyacrylamide hydrogels and of poly(methyl methacrylate) (PMMA) gels, exhibiting good agreement. We conclude that the proposed MC simulation scheme represents a powerful tool from which precious and experimentally inaccessible information on polymerization processes in the presence of cross-linkers can be extracted.

Experimental results have shown that the kinetics of bond formation in chemical cross-linking of gelatin solutions are strongly affected not only by gelatin and reactant concentrations but also by the solution pH. We present an extended numerical investigation of the phase diagram and of the kinetics of bond formation as a function of the pH, via Monte Carlo simulations of a lattice model for gelatin chains and reactant agent in solution. We find a re-entrant phase diagram, namely, gelation can be hindered either by loop formation at low reactant concentrations, or by saturation of chain active sites via formation of single bonds with a cross-linker at high reactant concentrations. The ratio of the characteristic times for the formation of the first and the second bond between the cross-linker and an active site of a chain is found to depend on the reactant reactivity, in good agreement with experimental data.