Static and dynamic heterogeneities in a model for irreversible gelation

Effect of Polymer and Crosslinker Concentration on Static and Dynamic Gelation Behavior of Phenolic Resin Hydrogel

The application results of profile control and water plugging technology are highly related to the gelation time and strength of phenolic resin hydrogel. In this work, a hydrogel solution was prepared by fully mixing the prepared polymer solution with a crosslinker. The static gelation process of PFR hydrogel in ampoule bottles and porous media was analyzed by changes in the viscosity and residual resistance coefficient. Then, the dynamic gelation of the PFR hydrogel in porous media was tested using a circulating flow device, and the changes in viscosity and injection pressure were analyzed during the dynamic gelation process. Finally, the effects of the polymer concentration and crosslinker concentration on dynamic gelation were analyzed. The initial gelation time and final gelation time in porous media were 1-1.5 times and 1.5-2 times those in ampoule bottles under static conditions, respectively. The initial dynamic gelation time in porous media was 2-2.5 times and 1.5-2 times the initial static gelation times in ampoule bottles and porous media, respectively. The final dynamic gelation time was four times and two times the initial static gelation times in ampoule bottles and porous media, respectively. The production after dynamic gelation in porous media comprised hydrogel aggregates and water fluid, leading to a high injection pressure and low viscosity of the produced liquid. As the concentration of polymer and crosslinker increased, the dynamic gelation time was shortened and the gel strength was increased. In the dynamic gelation process in porous media, the phenol resin hydrogel could migrate deeply, but it was limited by the concentrations of the polymer and crosslinker. The results of subsequent water flooding showed that the polymer hydrogel had a good plugging ability after dynamic gelation. The deep reservoir could only be blocked off in the subsequent water flooding process when the migration of hydrogel happened in the dynamic gelation process.

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Dynamical arrest: interplay of glass and gel transitions

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.

Self-assembly and cooperative dynamics of a model colloidal gel network

We study the assembly into a gel network of colloidal particles, via effective interactions that yield local rigidity and make dilute network structures mechanically stable. The self-assembly process can be described by a Flory-Huggins theory, until a network of chains forms, whose mesh size is on the order of, or smaller than, the persistence length of the chains. The localization of the particles in the network, akin to some extent to caging in dense glasses, is determined by the network topology, and the network restructuring, which takes place via bond breaking and recombination, is characterized by highly cooperative dynamics. We use NVE and NVT molecular dynamics as well as Langevin dynamics and find a qualitatively similar time dependence of time correlations and of the dynamical susceptibility of the restructuring gel. This confirms that the cooperative dynamics emerge from the mesoscale organization of the network.

Complete set of types of phase transition in generalized heterogeneous k-core percolation

We study heterogeneous k-core (HKC) percolation with a general mixture of the threshold k, with k(min) = 2 on random networks. Based on the local tree approximation, the scaling behaviors of the percolation order parameter P(∞)(p) are analytically obtained for general distributions of the threshold k. The analytic calculations predict that the generalized HKC percolation is completely described by the series of continuous transitions with order parameter exponents β(n) = 2/n, discontinuous hybrid transitions with β(H) = 1/2 or β(A)(4)) = 1/4, and three kinds of multiple transitions. Simulations of the generalized HKC percolations are carried out to confirm analytically predicted transition natures. Specifically, the exponents of the series of continuous transitions are shown to satisfy the hyperscaling relation 2β(n) + γ(n) = ν(n).

Relaxation process and dynamical heterogeneities in chemical gels: critical behavior of self-overlap and its fluctuation

We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.

Slow dynamics, dynamic heterogeneities, and fragility of supercooled liquids confined in random media

Using molecular dynamics simulations, we study the slow dynamics of supercooled liquids confined in a random matrix of immobile obstacles. We study the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms of the density correlation function, the mean square displacement, the nonlinear dynamic susceptibility, the non-gaussian parameter, and the fragility. We find the cooperative and spatially heterogeneous dynamics to be suppressed as the obstacle density increases, leading to a more Arrhenius-like behavior in the temperature dependence of the relaxation time. Our findings are qualitatively consistent with the results of recent experimental and numerical studies for various classes of spatially heterogeneous systems. We also investigate the dependence of the dynamics of mobile particles on the protocol used to generate the random matrix. A re-entrant transition from the arrested phase to the liquid phase as the mobile particle density increases is observed for a class of protocols. This re-entrance is explained in terms of the distribution of the volume of the voids that are available to the mobile particles.

Identifying anomalous diffusion and melting in dusty plasmas

Anomalous diffusion in liquids and the solid-liquid phase transition (melting) are studied in two-dimensional Yukawa systems. The self-intermediate scattering function (self-ISF), calculated from simulation data, exhibits a temporal decay, or relaxation, with a characteristic relaxation time. This decay is found to be useful for distinguishing normal and anomalous diffusion in a liquid, and for identifying the solid-liquid phase transition. For liquids, a scaling of the relaxation time with length scale is found. For the solid-liquid phase transition, the shape of the self-ISF curve is found to be a sensitive indicator of phase. Friction has a significant effect on the timing of relaxation, but not the melting point.

Non-Gaussian dynamics in smectic liquid crystals of parallel hard rods

Using computer simulations, we studied the diffusion and structural relaxation in equilibrium smectic liquid-crystal bulk phases of parallel hard spherocylinders. These systems exhibit a non-Gaussian layer-to-layer diffusion due to the presence of periodic barriers and transient cages and show remarkable similarities with the behavior of out-of-equilibrium supercooled liquids. We detect a very slow interlayer relaxation dynamics over the whole density range of the stable smectic phase which spans a time interval of four time decades. The intrinsic nature of the layered structure yields a hopping-type diffusion which becomes more heterogeneous for higher packing fractions. In contrast, the in-layer dynamics is typical of a dense fluid with a relatively fast decay. Our results on the dynamic behavior agree well with that observed in systems of freely rotating hard rods but differ quantitatively as the height of the periodic barriers reduces to zero at the nematic-smectic transition for aligned rods, while it remains finite for freely rotating rods.

Dynamical heterogeneities in irreversible gels: analogy with spin glasses

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.

Elasticity of arrested short-ranged attractive colloids: homogeneous and heterogeneous glasses

We evaluate the elasticity of arrested short-ranged attractive colloids by combining an analytically solvable elastic model with a hierarchical arrest scheme. This new approach allows us to discriminate the microscopic (primary particle-level) from the mesoscopic (cluster-level) contribution to the macroscopic shear modulus. The results quantitatively predict experimental data in a wide range of volume fractions and indicate in which cases the relevant contribution is due to mesoscopic structures. On this basis we propose that different arrested states of short-ranged attractive colloids can be meaningfully distinguished as homogeneous or heterogeneous colloidal glasses in terms of the length scale which controls their elastic behavior.

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.

Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and spans at least five decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.

Formation of double helical and filamentous structures in models of physical and chemical gels

This discusses two recent models, one that captures physical network formation starting from the molecular architecture of its constituents and another that contains the basic features of phase separation in cross-linked polymer gels: A) the Janus chain (multibead bead-spring type) model exhibiting semiflexibility and induced curvature and B) a stretched elastic network of Lennard-Jones particles. The length scales and related structures predicted by the two generic models are different. Model B, a generic soft solid model, exhibits hysteresis and the formation of filamentous structures in two dimensions. The Janus chain model A is able to describe the process of the formation of double helical superstructures, will be operated in three dimensions, and its internal parameters are directly deduced from atomistic simulation. Both models rely on classical ingredients which have been separately studied extensively: i) the Lennard-Jones particle system, ii) the elastic solid, and iii) the FENE-B model for semiflexible, finitely extendable nonlinear elastic (FENE) polymer chains. While model A combines i) and iii), model B combines i) and ii). This aspect of technical simplicity, however, is contrasted by the rich phenomenology observed for these models. The Janus model even resolves structure formation on the molecular scale. Intriguingly, the coarse dynamical models capture a wide range of superstructures known for polymeric networks and therefore clearly serve to understand their underlying physical mechanisms.

Investigation of q-dependent dynamical heterogeneity in a colloidal gel by x-ray photon correlation spectroscopy

We use time-resolved x-ray photon correlation spectroscopy to investigate the slow dynamics of colloidal gels made of moderately attractive carbon black particles. We show that the slow dynamics is temporally heterogeneous and quantify its fluctuations by measuring the variance chi of the instantaneous intensity correlation function. The amplitude of dynamical fluctuations has a nonmonotonic dependence on scattering vector q, in stark contrast with recent experiments on strongly attractive colloidal gels [Duri and Cipelletti, Europhys. Lett. 76, 972 (2006)]. We propose a simple scaling argument for the q-dependence of fluctuations in glassy systems that rationalizes these findings.