Antonio Coniglio

Gelation and Critical Phenomena

For the critical exponents near the sol-gel phase transition, classical theories like those of Flory and Stockmayer predict one set of exponents, whereas scaling theories based on lattice percolation predict different exponents. The two groups of theories differ in their treatment of intramolecular loops, space dimensionality and excluded volume effects. In this article, the differences and similarities between the results of the competing theories are reviewed. For example, a gel fraction like (p-pc)β vanishes for conversion factors p very close to the gel point pc, the weight average molecular weight diverges as (pc-p)−γ for p very slightly below pc, and the radius of macromolecules at the gel point p=pc varies as the ϱ-th power of the number of monomers in that macromolecule. Classical theories predict β=γ=1 and ϱ=1/4 whereas the percolation theory gives β ≃ 0.45, γ ≃ 1.74 and ϱ ≃ 0.40. We also generalize the percolation concept to include interaction effects and concentration fluctuations; in this case the sol-gel phase transition may be connected with a phase separation.

Random very loose packings.

We measure the number Omega(phi) of mechanically stable states of volume fraction phi of a granular assembly under gravity. The granular entropy S(phi)=logOmega(phi) vanishes both at high density, at phi approximately equal to phi_rcp, and a low density, at phi approximately equal to phi_rvlp, where phi_rvlp is a new lower bound we call random very loose pack. phi_rlp is the volume fraction where the entropy is maximal. These findings allow for a clear explanation of compaction experiments and provide the first first-principle definition of the random loose volume fraction. In the context of the statistical mechanics approach to static granular materials, states with phi

Pattern formation and glassy phase in the phi(4) theory with a screened electrostatic repulsion

We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar, and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.

A statistical mechanics approach to the inherent states of granular media

We consider a Statistical Mechanics approach to granular systems by following the original ideas developed by Edwards. We use the concept of “inherent states”, defined as the stable configurations in the potential energy landscape, introduced in the context of glasses. Under simplifying assumptions, the equilibrium inherent states can be characterized by a configurational temperature, 1/β. We link β to Edwards’ compactivity and address the problem of its experimental measure. We also discuss the possibility to describe the time dependent distribution probability in the inherent states with an appropriate master equation.

The jamming transition of granular media

A statistical mechanical approach to granular material is proposed. Using lattice models from standard statistical mechanics and results from a mean-field replica approach we find a jamming transition in granular media closely related to the glass transition in supercooled liquids. These models reproduce the logarithmic relaxation in granular compaction and reversible-irreversible lines, in agreement with experimental data. The models also exhibit aging effects and breakdown of the usual fluctuation-dissipation relation. It is shown that the glass transition may be responsible for the logarithmic relaxation and may be related to the cooperative effects underlying many phenomena exhibited by granular materials such as the Reynolds transition.

Phase transitions in granular packings

We describe the contact network of granular packings by a frustrated lattice gas that contains steric frustration as esential ingredient. Two transitions are identified, a spin glass transition at the onset of Reynolds dilatancy and at lower densities a percolation transition. We describe the correlation functions that give rise to the singularities and propose some dynamical experiments.

Dynamic phase coexistence in glass–forming liquids

One of the most controversial hypotheses for explaining the heterogeneous dynamics of glasses postulates the temporary coexistence of two phases characterized by a high and by a low diffusivity. In this scenario, two phases with different diffusivities coexist for a time of the order of the relaxation time and mix afterwards. Unfortunately, it is difficult to measure the single-particle diffusivities to test this hypothesis. Indeed, although the non-Gaussian shape of the van-Hove distribution suggests the transient existence of a diffusivity distribution, it is not possible to infer from this quantity whether two or more dynamical phases coexist. Here we provide the first direct observation of the dynamical coexistence of two phases with different diffusivities, by showing that in the deeply supercooled regime the distribution of the single-particle diffusivities acquires a transient bimodal shape. We relate this distribution to the heterogeneity of the dynamics and to the breakdown of the Stokes-Einstein relation, and we show that the coexistence of two dynamical phases occurs up to a timescale growing faster than the relaxation time on cooling, for some of the considered models. Our work offers a basis for rationalizing the dynamics of supercooled liquids and for relating their structural and dynamical properties.

Lamellar order, microphase structures, and glassy phase in a field theoretic model for charged colloids

In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation.

The compaction in granular media and frustrated Ising models

We introduce a lattice model, in which frustration plays a crucial role, to describe relaxation properties of granular media. We show Monte Carlo results for compaction in the presence of vibrations and gravity, which compare well with experimental data.

A percolation dynamic approach to the sol-gel transition

The sol-gel transition is studied introducing the bond fluctuation dynamics within the percolation model in order to investigate both static and dynamic properties. Computer simulations on a square lattice have shown that the static properties agree with the random percolation model and the self-diffusion coefficients vanish at the percolation threshold. From the self-diffusion coefficients the critical behaviour of the viscosity at the sol-gel transition is determined, giving an exponent .