Annalisa Fierro

Columnar and lamellar phases in attractive colloidal systems

In colloidal suspensions, at low volume fraction and temperature, dynamical arrest occurs via the growth of elongated structures that aggregate to form a connected network at gelation. Here we show that, in the region of parameter space where gelation occurs, the stable thermodynamical phase is a crystalline columnar one. Near and above the gelation threshold, the disordered spanning network slowly evolves and finally orders to form the crystalline structure. At higher volume fractions the stable phase is a lamellar one, which seems to have a still longer ordering time.

Colloidal gelation, percolation and structural arrest

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 first increases as a power law as a function of the volume fraction 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 a 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.

Percolation, gelation and dynamical behaviour in colloids

We review some results on the dynamics of gelation phenomena, obtained via a lattice model and via molecular dynamics using a DLVO potential. This study allowed us to make a connection between classical gelation and the phenomenology of colloidal systems, suggesting that gelation phenomena in attractive colloids at low temperature and low volume fraction can be described in terms of a two-line scenario.

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 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.

A unifying model for chemical and colloidal gels

We investigate the slow dynamics in gelling systems by means of Monte Carlo 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.

Dynamical heterogeneity in a model for permanent gels : Different behavior of dynamical susceptibilities

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.

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

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.

Complex viscosity behavior and cluster formation in attractive colloidal systems

The increase in viscosity that 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 nontrivial 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.

Percolation transition and the onset of nonexponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in two and three dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the ‘‘large scale’’ effects of frustration, present below the percolation threshold. Moreover, these results are consistent with the picture suggested by Campbell et al. @J. Phys. C 20, L47 ~1987!# in the space of configurations. @S1063-651X~98!07412-1#

Cage-jump motion reveals universal dynamics and non-universal structural features in glass forming liquids

The sluggish and heterogeneous dynamics of glass forming liquids is frequently associated to the transient coexistence of two phases of particles, respectively with a high and low mobility. In the absence of a dynamical order parameter that acquires a transient bimodal shape, these phases are commonly identified empirically, which makes it difficult to investigate their relation with the structural properties of the system. Here we show that the distribution of single particle diffusivities can be accessed within a continuous time random walk description of the intermittent motion, and that this distribution acquires a transient bimodal shape in the deeply supercooled regime, thus allowing for a clear identification of the two coexisting phases. In a simple two-dimensional glass forming model, the dynamic phase coexistence is accompanied by a striking structural counterpart: the distribution of the crystalline-like order parameter becomes also bimodal on cooling, with increasing overlap between ordered and immobile particles. This simple structural signature is absent in other models, such as the three-dimesional Kob–Andersen Lennard-Jones mixture, where more sophisticated order parameters might be relevant. In this perspective, the identification of the two dynamical coexisting phases opens the way to deeper investigations of structure-dynamics correlations.