Viscosity critical behaviour at the gel point in a 3d lattice model

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 figure

On mean coordination and structural heterogeneity in model amorphous solids

We propose a simple route to analytically evaluate the average coordination of model disordered solids with maximally homogeneous distribution of the particles in space. The model yields the average number of contacts (z) as a function of volume fraction (phi) of a hard-sphere connected system and recovers the critical jamming point of hard spheres (z=6 at phi=0.64). Numerical simulations of Lennard-Jones glasses with a varying attraction range are used to investigate the volume fraction dependence of the average coordination in the presence of attraction. It is observed that upon decreasing phi below 0.6, structural heterogeneity is reflected in values of the coordination number which are higher than those predicted by the model for a statistically homogeneous distribution of particles in space due to the attraction-induced local aggregation. Thus the model can be usefully employed as a quantitative reference to assess the degree of structural heterogeneity in glasses in terms of a directly accessible structural parameter such as the mean number of contacts

Static and dynamic heterogeneities in a model for irreversible gelation

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 figure

Complex viscosity behavior and cluster formation in attractive colloidal systems

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 figure