Search

By changing the control parameters, many physical systems reach a slow dynamics regime followed by an arrested or a quasi-arrested state. Examples, among others, are gels and glasses. In this paper, we discuss some experimental and theoretical results in polymer and colloidal systems, where gel and glass transitions interfere, and use models from Mode Coupling Theory (MCT) to illustrate the rich phenomenology observed. The continuous and the discontinuous transition lines, found in the MCT models, are considered suitable to describe respectively the gel and the glass transitions, so we suggest that the interplay between gel and glass may be interpreted in terms of the $F_{13}$ MCT model, clarifying also the origin of logarithmic decays often observed in such systems. In particular, the theoretical predictions of the MCT in the $F_{13}$ model are compared with Molecular Dynamics simulations in model systems for chemical gels and charged colloids.

A long standing problem in glassy dynamics is the geometrical interpretation of clusters and the role they play in the observed scaling laws. In this context, the mode-coupling theory (MCT) of type-A transition and the sol-gel transition are both characterized by a structural arrest to a disordered state in which the long-time limit of the correlator continuously approaches zero at the transition point. In this paper, we describe a cluster approach to the sol-gel transition and explore its predictions, including universal scaling laws and a new stretched relaxation regime close to criticality. We show that while MCT consistently describes gelation at mean-field level, the percolation approach elucidates the geometrical character underlying MCT scaling laws.

We investigate the heterogeneous dynamics in a model, where chemical gelation and glass transition interplay, focusing on the dynamical susceptibility. Two independent mechanisms give raise to the correlations, which are manifested in the dynamical susceptibility: one is related to the presence of permanent clusters, while the other is due to the increase of particle crowding as the glass transition is approached. The superposition of these two mechanisms originates a variety of different behaviours. We show that these two mechanisms can be unentangled considering the wave vector dependence of the dynamical susceptibility., Comment: The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60175-x

The structural arrest of a polymeric suspension might be driven by an increase of the cross-linker concentration, which drives the gel transition, as well as by an increase of the polymer density, which induces a glass transition. These dynamical continuous (gel) and discontinuous (glass) transitions might interfere, since the glass transition might occur within the gel phase, and the gel transition might be induced in a polymer suspension with glassy features. Here we study the interplay of these transitions by investigating via event-driven molecular dynamics simulation the relaxation dynamics of a polymeric suspension as a function of the cross-linker concentration and the monomer volume fraction. We show that the slow dynamics within the gel phase is characterized by a long sub-diffusive regime, which is due both to the crowding as well as to the presence of a percolating cluster. In this regime, the transition of structural arrest is found to occur either along the gel or along the glass line, depending on the length scale at which the dynamics is probed. Where the two lines meet there is no apparent sign of higher order dynamical singularity. Logarithmic behavior typical of A3 singularity appears inside the gel phase along the glass transition line. These findings seem to be related to the results of the mode coupling theory for the F13 schematic model.

We perform molecular dynamic (MD) simulations of frictional non-thermal particles driven by an externally applied shear stress. After the system jams following a transient flow, we probe its mechanical response in order to clarify whether the resulting solid is 'fragile'. We find the system to respond elastically and isotropically to small perturbations of the shear stress, suggesting absence of fragility. These results are interpreted in terms of the energy landscape of dissipative systems. For the same values of the control parameters, we check the behaviour of the system during a stress cycle. Increasing the maximum stress value, a crossover from a visco-elastic to a plastic regime is observed., 6 pages, 9 figures, accepted in Granular Matter on 01-02-2012

The dynamical susceptibility has been introduced to characterize the dynamical heterogeneities in glass forming liquids. We have used it as a tool to investigate the slow dynamics of other disordered systems such as gels, granular media and spin glasses. We review here the results obtained via numerical simulations of different model systems. The comparative study of the behaviour of the dynamical susceptibility sheds some light on the significant differences in the complex slow dynamics of glasses, spin glasses, granular media, irreversible gels, and colloidal gels.

A system under gravity, made up of hard spheres with an internal degree of freedom, is studied on a 3d lattice under a Monte Carlo “tap” dynamics. A “jamming” transition similar to that found in real experiment is found. To understand the nature of such transition a simplified version of the model is also studied in a mean field approximation, using the statistical mechanics approach a la Edwards. A phase transition from a “fluid” to a “glassy” phase is found when crystallization is avoided. Interestingly, the nature of such a “glassy” phase turns out to be the same found in mean field models for glass formers.

We briefly review a Statistical Mechanics approach for the description of granular materials following the original ideas developed by Edwards. We show that Edwards’ assumptions works very well for a class of lattice models and we discuss some recent analytic results obtained in such a framework on their phase diagram, jamming transition and mixing/segregation properties.

We develop a novel approach that combines the ideas of inherent structures, free-volume theory and geometrical packing properties to derive a general theory to understanding the complex dynamics of glass-forming liquids, granular packings and amorphous solids. We show that the thermodynamical properties of these systems can be retrieved from the study of geometrical and topological properties of local configurations only. When applied to hard-sphere systems, the present theory describes the critical approach toward the random close-packing density with the configurational entropy that approaches zero, and the α-relaxation time that diverges according to the Vogel-Fulcher behavior following also the Adam-Gibbs relation. The equation of state derived for the stable fluid, the metastable fluid, and for the crystalline and amorphous solids, results in good quantitative agreement with the data available in the literature.

A cell theory for glassforming liquids, amorphous solids and granular packings, is developed by combining geometrical properties of local packings with the ideas of inherent structures and free volume theory. We show that for hard-spheres the present theory reproduces well the equation of state, the approach to zero of the configurational entropy and the divergence of large relaxation times following both the Vogel–Tammann–Fulcher behavior and the Adam–Gibbs relation.

We present a novel theoretical approach to understanding the complex dynamics of glass-forming liquids, granular packings and amorphous solids. This theory, which is an elaboration of the free volume and inherent structure approaches, allows one to retrieve the thermodynamical properties of these systems from studies of geometrical and topological properties of local, static configurations alone. When applied to hard-sphere systems, the present theory reproduces with a good quantitative agreement the equation of state for the crystalline and the disordered glassy phases. Moreover, we find that, as the density approaches a critical value close to the random close-packing density, the configurational entropy approaches zero and the large relaxation time diverges according to the Vogel–Fulcher behaviour, following also the Adam–Gibbs relation.

We present a study of molecular dynamics at the sol-gel transition. Application of percolation and bond-fluctuation dynamics provides critical exponents for viscoelastic properties in a strong covalent gel and shows a complex non-exponential relaxation behaviour. The results are in good agreement with experimental findings and offer interesting pointers for discussions.

We briefly review the basics ideas and results of a recently proposed statistical mechanical approach to granular materials. Using lattice models from standard Statistical Mechanics and results from a mean field replica approach and Monte Carlo simulations we find a jamming transition in granular media closely related to the glass transition in super-cooled 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 of granular materials such as the Reynolds transition., 18 pages with 6 postscript figures. to appear in J.Phys: Cond. Mat

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 .

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At the mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows one to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the ${\mathsf{F}}_{12}$ schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields predictions for dynamic relaxation exponents below an upper critical dimension of 6.

A three-dimensional (3D) spin-glass model diluted with lattice gas variables is investigated and compared with glass-forming liquids. The spin variables which play the role of internal degrees of freedom exhibit strong fluctuations. While a critical length associated to these fluctuations diverges at the glass transition, where the diffusion coefficient is found to vanish, the density fluctuations do not show any critical behaviour.

The concepts of connectivity, localization, and frustration are explored in relation to glass formation in amorphous materials. First, the concept of eigenclusters to geometrically characterize correlations in amorphous materials is introduced, and discussed in detail for both the Ising ferromagnet and Ising spin glass models. Second, a new, glass-forming percolation model that contains frustration as the essential ingredient, and exhibits two percolation transitions, is discussed. This new model gives new insights into frustrated systems, and applications to the Ising spin glass model and other glass-forming systems are discussed. In particular, we propose the possibility that the occurrence of a percolation-type transition at temperatures above the glass transition temperature may be a general feature of glass-forming systems. The important role of computer simulations in probing the mechanism of glass formation is emphasized.

The dynamical arrest of gels is the consequence of a well defined structural phase transition, leading to the formation of a spanning cluster of bonded particles. The dynamical glass transition, instead, is not accompanied by any clear structural signature. Nevertheless, both transitions are characterized by the emergence of dynamical heterogeneities. Reviewing recent results from numerical simulations, we discuss the behavior of dynamical heterogeneities in different systems and show that a clear connection with the structure exists in the case of gels. The emerging picture may be also relevant for the more elusive case of glasses. We show, as an example, that the relaxation process of a simple glass-forming model can be related to a reverse percolation transition and discuss further perspective in this direction., Published in the J. Stat. Mech. Special Issue of "The Role of Structure in Glassy and Jammed Systems "

We report recent results of molecular dynamics simulations of frictional athermal particles at constant volume fraction and constant applied shear stress, focusing on a range of control parameters where the system first flows, but then jams after a time tjam. On decreasing the volume fraction, the mean jamming time diverges, while its sample fluctuations become so large that the jamming time probability distribution P(tjam) becomes a power-law. We obtain an insight on the origin of this phenomenology focusing on the flowing regime, which is characterized by the presence of a clear correlation between the shear velocity and the mean number of contacts per particles Z, whereby small velocities occur when Z acquires higher values., Comment: 10 pages, 7 figures

Carlo computer simulations of spinodal decomposition to show that the model exhibits "pinning" of the structure factor, a behavior also seen in phase-separating polymer gels and binary alloys with impurities. The rate of strong bond formation depends on an entropic parameter 0, and we fInd both the pinned domain size and the crossover time between "normal" spinodal decomposition and the pinning scale with 0 as power laws with exponents that relate simply to the usual growth exponent. We propose a speci6c mechanism for pinning that permits the prediction of exact values for the pinning exponents. Finally, we discuss applications of the model to binary alloys with quenched disorder and polymer gels.

We investigate the relaxation process and the dynamical heterogeneities of the kinetically constrained Kob-Andersen lattice glass model and show that these are characterized by different time scales. The dynamics is well described within the diffusing defect paradigm, which suggests that we relate the relaxation process to a reverse-percolation transition. This allows for a geometrical interpretation of the relaxation process and of the different time scales.

We review some recent results relevant to colloidal systems with competing interactions. In particular we report some findings concerning the pattern formation phenomena obtained in a φ4 theory. Some of the general features are also found in an atomistic model by means of a thermodynamic approach and molecular dynamics simulations. Finally this model is shown to exhibit a structural arrest in a disordered gel-like state, once the ordered state is avoided.

We study the dynamical heterogeneities along the attractive glass line in a model for charged colloids, where short-range attraction competes with long-range repulsion. We focus on the crossover from gel-like to glassy-like regime, where the system displays both features of chemical gels and of glassy systems. The former are due to long living clusters the latter to crowding effects, which both slow down the relaxation process. We show how to separate the two effects by looking at the fluctuation of the self Intermediate Scattering Function, χ 4(k,t), for different values of wave vector k. For small values of k, χ 4(k,t) detects the dynamical behavior at large length scale, where both cluster effects and crowding effects are present. On the other hand by increasing the value of k, χ 4(k,t) detects the dynamical behavior at small length scale where the cluster effects are suppressed and only the crowding effects dominate the dynamics.

The non-equilibrium transition from a fluid-like state to a disordered solid-like state, known as the jamming transition, occurs in a wide variety of physical systems, such as colloidal suspensions and molecular fluids, when the temperature is lowered or the density increased. Shear stress, as temperature, favors the fluid-like state, and must be also considered to define the system 'jamming phase diagram' [1-4]. Frictionless athermal systems [1], for instance, can be described by the zero temperature plane of the jamming diagram in the temperature, density, stress space. Here we consider the jamming of athermal frictional systems [8-13] such as granular materials, which are important to a number of applications from geophysics to industry. At constant volume and applied shear stress[1, 2], we show that while in absence of friction a system is either fluid-like or jammed, in the presence of friction a new region in the density shear-stress plane appears, where new dynamical regimes are found. In this region a system may slip, or even flow with a steady velocity for a long time in response to an applied stress, but then eventually jams. Jamming in non-thermal frictional systems is described here by a phase diagram in the density, shear-stress and friction space.

Via molecular dynamics simulations, we unveil the hysteretic nature of the jamming transition of soft repulsive frictionless spheres, as it occurs varying the volume fraction or the shear stress. In a given range of control parameters the system may be found both in a flowing and in an jammed state, depending on the preparation protocol. The hysteresis is due to an underlying energy landscape with many minima, as explained by a simple model, and disappears in the presence of strong viscous forces and in the small $\sigma$ limit. In this limit, structural quantities are continuous at the transition, while the asymptotic values of two time quantities such as the self-intermediate scattering function are discontinuous, giving to the jamming transition a mixed first-order second-order character close to that found at the glass transition of thermal systems.

We describe the sol-gel transition by introducing an order parameter, defined as the average of local variables, and its fluctuations. It can be shown that these quantities are related to percolation quantities, but in principle they can be measured without resorting to connectivity properties. In this framework it appears that the dynamical transition associated with gelation is a real thermodynamic transition, as happens in spin glasses. The strong analogies between the sol-gel transition and the spin glass transition are also discussed.

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.

We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram' in the volume fraction/stress plane $(\phi,F)$: at low $\phi$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $\phi$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy with the glassy region of thermal systems, slow dynamics followed by kinetic arrest occurs when the ordering transition is prevented., Comment: 4 pages

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., 16 pages, 7 figures

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 present extensive molecular dynamics simulations on species segregation in a granular mixture subject to vertical taps. We discuss how grain properties, e.g., size, density, friction, as well as shaking properties, e.g., amplitude and frequency, affect such a phenomenon. Both the Brazil nut effect (larger particles on the top, BN) and the reverse Brazil nut effect (larger particles on the bottom, RBN) are found and we derive the system comprehensive ``segregation diagram'' and the BN to RBN crossover line. We also discuss the role of friction and show that particles which differ only for their frictional properties segregate in states depending on the tapping acceleration and frequency.

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., Comment: Final version, accepted for publication in Phys. Rev. Lett

In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For simplicity we have applied the theory to a lattice model and a transition with exactly the same nature of the glass transition in mean field models for usual glass formers is found. The model is also simulated in three dimensions under tap dynamics and a jamming transition with glassy features is observed. In particular two step decays appear in the relaxation functions and dynamic heterogeneities resembling ones usually observed in glassy systems. These results confirm early speculations about the connection between the jamming transition in granular media and the glass transition in usual glass formers, giving moreover a precise interpretation of its nature., Comment: 11 pages, 12 figures

We introduce and analytically study a generalized $p$-spin glasslike model that captures some of the main features of attractive glasses, recently found by mode coupling investigations, such as a glass-glass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. The model also displays features not predicted by the mode coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line.

We compare the predictions of two different statistical mechanics approaches, corresponding to different physical measurements, proposed to describe binary granular mixtures subjected to some external driving (continuous shaking or tap dynamics). In particular we analytically solve at a mean field level the partition function of a simple hard sphere lattice model under gravity and we focus on the phenomenon of size segregation. We find that the two approaches lead to similar results and seem to coincide in the limit of very low shaking amplitude. However they give different predictions of the crossovers from Brazil nut effect to reverse Brazil nut effect with respect to the shaking amplitude, which could be detected experimentally., to appear on Physical Review Letters

We address the question of the dependence of the fragility of glass forming supercooled liquids on the softness of an interacting potential by performing numerical simulation of a binary mixture of soft spheres with different power n of the interparticle repulsive potential. We show that the temperature dependence of the diffusion coefficients for various $n$ collapses onto a universal curve, supporting the unexpected view that fragility is not related to the hard core repulsion. We also find that the configurational entropy correlates with the slowing down of the dynamics for all studied n., Comment: 4 pages, 4 figures

Dynamical instabilities in fluid mechanics are responsible of a variety of important common phenomena, such as waves on the sea surface or Taylor vorteces in Couette flow. In granular media dynamical instabilities has just begun to be discovered. Here we show by means of molecular dynamics simulation the existence of a new dynamical instability of a granular mixture under oscillating horizontal shear, which leads to the formation of a striped pattern where the components are segregated. We investigate the properties of such a Kelvin-Helmholtz like instability and show how it is connected to pattern formation in granular flow and segregation., Comment: Phys. Rev. Lett. 94, 188001

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.

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 study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical mechanics model. The model is based on percolation and bond-fluctuation dynamics. 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.

The present paper proposes a Statistical Mechanics approach to the inherent states of glassy systems and granular materials, following the original ideas developed by Edwards for granular materials. Two lattice models, a diluted Spin Glass and a system of hard-spheres under gravity, introduced in the context of glassy systems and granular materials, are evolved using a ``tap dynamics'' analogous to that of experiments on granular materials. The asymptotic macrostates, reached by the system, are shown to be described by a single thermodynamical parameter, and this parameter to coincide with the temperature, called the ``configurational temperature'', predicted assuming that the distribution among the inherent states satisfies the principle of maximum entropy., Comment: revised and improved version including new results on a 3D hard-spheres model; 4 pages, 4 figures

In order to study the viscoelastic properties at the gelation transition we have introduced a percolation dynamic model. Using percolation and bond-fluctuation dynamics it is suited to study the critical behaviour of the viscoelastic properties and shows complex relaxation functions. The results obtained via numerical simulation are in good agreement with some theoretical predictions and experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.

The elastic response in polymeric gels is studied by means of a percolation dynamic model. By numerical simulations the fluctuations in the gyration radius and in the center-of-mass motion of the percolating cluster are determined. Their scaling behavior at the gelation threshold gives a critical exponent for the elastic modulus f approximately 2.5+/-0.1 in agreement with the prediction f=dnu.

The properties of a diluted spin-glass model are reviewed. This model interpolates between a spin glass and a frustrated lattice gas which displays glassy behaviour at high density. Using the effective potential introduced by Franz and Parisi, we show in the mean-field formalism that its static properties are closely related to those of the p-spin-glass models. These models are strongly related to glass-forming liquids. In the mean-field formalism they exhibit in fact a dynamical transition described by the same equations as in the schematic mode-coupling theory. Compared to the p-spin model, the frustrated lattice gas model is more appropriate for describing a supercooled liquid, being constituted essentially of diffusing particles. Numerically in three dimensions we in fact show that the frustrated lattice gas model exhibits qualitatively the properties of glass-forming liquids. Interestingly, the diffusion coefficient exhibits a sharp crossover from a power-law behaviour at low density to a Vogel-Fulcher or Arrhenius behaviour at high density, suggesting a crossover from mode-coupling behaviour to a hopping regime.

We study microscopic and macroscopic dynamical properties of a frustrated lattice gas, strictly related to usual spin glasses, showing the violation of Stokes-Einstein law. The glassy behaviors are analyzed and related with experimental results in glass former systems., 4 pages, to be published in Phys. Rev. E, Rapid Communication

We describe the contact network of granular packings by a frustrated lattice gas that contains steric frustration as essential 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.

One of the challenges in soft and condensed matter over the last few years has been understanding the phenomena of glass and jamming transitions. A recent advance in the field is the idea that the dynamical heterogeneities play here the same role as the critical fluctuations in ordinary critical phenomena. This is due to the fact that the decay of density fluctuations in glasses and jammed systems takes place thanks to the dynamically correlated motions of groups of particles. In this paper, after a brief review of the properties of the dynamical heterogeneities in glasses we analyze the cases of chemical and colloidal gels, which are still intensely debated.

A new model for polymer gelation is presented that predicts new effects that can not be derived from the conventional theory of Flory and Stockmayer. An exact solution is obtained for the Bethe lattice, and is related to recent experimental results of Tanaka. Under certain conditions, the gelation curve terminates at the consolute point; at this point, both connectivity and concentration fluctuations are critical, just as in the random magnet at the percolation threshold.

To describe the irreversible growth of linear polymers, we introduce a new type of correlated walk, related to the zero---initiator-concentration limit of the kinetic gelation model. Our model simulates real polymer growth by permitting the walker to form the next bond from the unsaturated monomers at the neighboring sites of its present location. A heuristic kinetic argument of the Flory type suggests a fractal dimension ${d}_{f}=\frac{(d+1)}{2}$, in agreement with our Monte Carlo and series expansion results (including a logarithmic correction at the upper critical dimension ${d}_{c}=3$).

A statistical-mechanical model for reversible gelation is developed. This model takes into account solvent effects, which usually are neglected in the classical theory of gelation. The exact solution of this model is given for the limiting case in which "loops" or intermolecular interactions may be neglected (Cayley tree). The general phase diagram is obtained and it is shown that, with a particular choice of a solvent, one can realize the interesting situation in which gelation point and consolute point coincide. This point has peculiar properties associated with the simultaneous divergence of "connectivity" and thermal fluctuations. The recent experimental data of Tanaka and collaborators are in good qualitative agreement with the predictions of the model.