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Identifying the necessary conditions for the onset of rigidity in a gel remains a challenge. It has been suggested that local particle coordination could be used to establish such conditions, but rigid gels occur for various coordination numbers. Combining simulations, oscillatory rheology, and a percolation analysis, for particles where the valence can be controlled, we find that the onset of rigidity coincides with the percolation of particles with three or more bonds, which arises after the connectivity percolation. We show that the rigidity results from an interplay of bonding and non-bonding interactions, providing insight into low-valence colloidal gel rigidity.

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., Comment: 11 pages, 14 figures

Experimental results have shown that the kinetics of bond formation in chemical crosslinking of gelatin solutions is 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 reentrant phase diagram, namely gelation can be hindered either by loop formation, at low reactant concentrations, or by saturation of active sites of the chains via formation of single bonds with crosslinkers, at high reactant concentrations. The ratio of the characteristic times for the formation of the first and of the second bond between the crosslinker and an active site of a chain is found to depend on the reactant reactivity, in good agreement with experimental data., Comment: 8 pages, 8 figures

We investigate the gel formation from the equilibrium sol phase in a simple model that has the characteristics of (colloidal) gel-forming systems at a finite temperature. At low volume fraction and low temperatures, particles are linked by long-living bonds and form an open percolating network. By means of molecular dynamics simulations, we study the lifetime of bonds and nodes of the gel network in order to relate these quantities to the complex relaxation dynamics observed., Comment: in press, J. Non-Newtonian Fluid Mech. (2007), Proceedings of the International Workshop on Mesoscale and Multiscale description of Complex Fluids 2006

We study the formation of a colloidal gel by means of Molecular Dynamics simulations of a model for colloidal suspensions. A slowing down with gel-like features is observed at low temperatures and low volume fractions, due to the formation of persistent structures. We show that at low volume fraction the dynamic susceptibility, which describes dynamic heterogeneities, exhibits a large plateau, dominated by clusters of long living bonds. At higher volume fraction, where the effect of the crowding of the particles starts to be present, it crosses over towards a regime characterized by a peak. We introduce a suitable mean cluster size of clusters of monomers connected by "persistent" bonds which well describes the dynamic susceptibility., Comment: 4 pages, 4 figures

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., Comment: 9 pages, 3 figures

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 intermediate scattering functions: In the sol phase close to the percolation threshold, we find that this dynamical 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., Comment: 4 pages, 4 figures

In chemical crosslinking 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 bonds crosslinker-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., Comment: 8 pages, 9 figures, revised version

In colloidal suspensions, the competition between attractive and repulsive interactions gives rise to a rich and complex phenomenology. Here, we study the equilibrium phase diagram of a model system using a DLVO interaction potential by means of molecular dynamics simulations and a thermodynamical approach. As a result, we find tubular and lamellar phases at low volume fraction. Such phases, extremely relevant for designing new materials, may be not easily observed in the experiments because of the long relaxation times and the presence of defects., Comment: 5 pages, 5 figures

We use molecular dynamics computer simulations to investigate the relaxation dynamics of a simple model for a colloidal gel at a low volume fraction. We find that due to the presence of the open spanning network this dynamics shows at low temperature a non-trivial dependence on the wave-vector which is very different from the one observed in dense glass-forming liquids. At high wave vectors the relaxation is due to the fast cooperative motion of the branches of the gel network, whereas at low wave vectors the overall rearrangements of the heterogeneous structure produce the relaxation process., Comment: 4 pager, 4 figures, revised version

The increase of the viscosity, which is observed in attractive colloidal systems by varying the temperature or the volume fraction, can be related to the formation of structures due to particle aggregation. In particular we have studied the non trivial dependence of the viscosity from the temperature and the volume fraction in the copolymer-micellar system L64. The comparison of the experimental data with the results of numerical simulations in a simple model for gelation phenomena suggests that this intriguing behavior can be explained in terms of cluster formation and that this picture can be quite generally extended to other attractive colloidal systems., Comment: 5 pages, 4 figures

By means of molecular dynamics, we study a model system for colloidal suspensions where the interaction is based on a competition between attraction and repulsion. At low temperatures the relaxation time $\tau$ first increases as a power law as a function of the volume fraction $\phi$ and then, due to the finite lifetime of the bonded structures, it deviates from this critical behavior. We show that colloidal gelation at low temperatures and low volume fractions is crucially related to the formation of spanning long living cluster. Besides agreeing with experimental findings in different colloidal systems, our results shed new light on the different role played by the formation of long living bonds and the crowding of the particles in colloidal structural arrest., Comment: new version, 5 pages, 9 figures

We here discuss the results of 3d MonteCarlo simulations of a minimal lattice model for gelling systems. We focus on the dynamics, investigated by means of the time autocorrelation function of the density fluctuations and the particle mean square displacement. We start from the case of chemical gelation, i.e. with permanent bonds, we characterize the critical dynamics as determined by the formation of the percolating cluster, as actually observed in polymer gels. By opportunely introducing a finite bond life time $\tau_b$ the dynamics displays relevant changes and eventually the onset of a glassy regime. This has been interpreted in terms of a crossover to dynamics more typical of colloidal systems and a novel connection between classical gelation and recent results on colloidal systems is suggested. By systematically comparing the results in the case of permanent bonds to finite bond lifetime, the crossover and the glassy regime can be understood in terms of effective clusters., Comment: 14 pages, 13 figures, to appear in Physical Review E

We investigate the slow dynamics in gelling systems by means of MonteCarlo simulations on the cubic lattice of a minimal statistical mechanics model. By opportunely varying some model parameter we are able to describe a crossover from the chemical gelation behaviour to dynamics more typical of colloidal systems. The results suggest a novel connection linking classical gelation, as originally described by Flory, to more recent results on colloidal systems., Comment: 7 pages, 4 figures

Within a recently introduced model based on the bond-fluctuation dynamics we study the viscoelastic behaviour of a polymer solution at the gelation threshold. We here present the results of the numerical simulation of the model on a cubic lattice: the percolation transition, the diffusion properties and the time autocorrelation functions have been studied. From both the diffusion coefficients and the relaxation times critical behaviour a critical exponent k for the viscosity coefficient has been extracted: the two results are comparable within the errors and are in close agreement with the Rouse model prediction and with some experimental results. In the critical region below the transition threshold the time autocorrelation functions show a long time tail which is well fitted by a stretched exponential decay., Comment: 14 pag., RevTex, 9 figures