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

Dynamic heterogeneities in attractive colloids

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 figure

Reentrant phase diagram and pH effects in cross-linked gelatin gels

Experimental results have shown that the kinetics of bond formation in chemical crosslinking of gelatin solutions is strongly affected not only by gelatin and reactant concentrations but also by the solution pH. We present an extended numerical investigation of the phase diagram and of the kinetics of bond formation as a function of the pH, via Monte Carlo simulations of a lattice model for gelatin chains and reactant agent in solution. We find a reentrant phase diagram, namely gelation can be hindered either by loop formation, at low reactant concentrations, or by saturation of active sites of the chains via formation of single bonds with crosslinkers, at high reactant concentrations. The ratio of the characteristic times for the formation of the first and of the second bond between the crosslinker and an active site of a chain is found to depend on the reactant reactivity, in good agreement with experimental data.Comment: 8 pages, 8 figure

Kinetics of bond formation in crosslinked gelatin gels

In chemical crosslinking of gelatin solutions, two different time scales affect the kinetics of the gel formation in the experiments. We complement the experimental study with Monte Carlo numerical simulations of a lattice model. This approach shows that the two characteristic time scales are related to the formation of single bonds crosslinker-chain and of bridges between chains. In particular their ratio turns out to control the kinetics of the gel formation. We discuss the effect of the concentration of chains. Finally our results suggest that, by varying the probability of forming bridges as an independent parameter, one can finely tune the kinetics of the gelation via the ratio of the two characteristic times.Comment: 8 pages, 9 figures, revised versio

Correlated rigidity percolation and colloidal gels

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation

Columnar and lamellar phases in attractive colloidal systems

In colloidal suspensions, the competition between attractive and repulsive interactions gives rise to a rich and complex phenomenology. Here, we study the equilibrium phase diagram of a model system using a DLVO interaction potential by means of molecular dynamics simulations and a thermodynamical approach. As a result, we find tubular and lamellar phases at low volume fraction. Such phases, extremely relevant for designing new materials, may be not easily observed in the experiments because of the long relaxation times and the presence of defects.Comment: 5 pages, 5 figure

Viscoelasticity near the gel-point: a molecular dynamics study

We report on extensive molecular dynamics simulations on systems of soft spheres of functionality f, i.e. particles that are capable of bonding irreversibly with a maximum of f other particles. These bonds are randomly distributed throughout the system and imposed with probability p. At a critical concentration of bonds, p_c approximately equal to 0.2488 for f=6, a gel is formed and the shear viscosity \eta diverges according to \eta ~ (p_c-p)^{-s}. We find s is approximately 0.7 in agreement with some experiments and with a recent theoretical prediction based on Rouse dynamics of phantom chains. The diffusion constant decreases as the gel point is approached but does not display a well-defined power law.Comment: 4 pages, 4 figure

Nutrient Digestibility, Ruminal Fermentation Activities, Serum Parameters and Milk Production and Composition of Lactating Goats Fed Diets Containing Rice Straw Treated with Pleurotus ostreatus

The study evaluated replacement of Egyptian berseem clover (BC, Trifolium alexandrinum) with spent rice straw (SRS) of Pleurotus ostreatus basidiomycete in diets of lactating Baladi goats. Nine lactating homo-parity Baladi goats (average BW 23.80.4 kg) at 7 d postpartum were used in a triplicate 33 Latin square design with 30 d experimental periods. Goats were fed a basal diet containing 0 (Control), 0.25 (SRS25) and 0.45 (SRS45) (w/w, DM basis) of SRS. The Control diet was berseem clover and concentrate mixture (1:1 DM basis). The SRS45 had lowered total feed intake and forages intake compared to Control. The SRS25 and SRS45 rations had the highest digestibilities of DM (p = 0.0241) and hemicellulose (p = 0.0021) compared to Control which had higher (p<0.01) digestibilities of OM (p = 0.0002) and CP (p = 0.0005) than SRS25 and SRS45. Ruminal pH and microbial protein synthesis were higher (p<0.0001) for SRS25 and SRS45 than Control, which also had the highest (p<0.0001) concentration of TVFA, total proteins, non-protein N, and ammonia-N. All values of serum constituents were within normal ranges. The Control ration had higher serum globulin (p = 0.0148), creatinine (p = 0.0150), glucose (p = 0.0002) and cholesterol (p = 0.0016). Both Control and SRS25 groups had the highest (p<0.05) milk (p = 0.0330) and energy corrected milk (p = 0.0290) yields. Fat content was higher (p = 0.0373) with SRS45 and SRS25 groups compared with Control. Replacement of BC with SRS in goat rations increased milk levels of conjugated linoleic acid and unsaturated fatty acids compared with Control. It was concluded that replacing 50% of Egyptian berseem clover with SRS in goat rations improved their productive performance without marked effects on metabolic indicators health. (Key Words: Fungus, Goats, Milk, Spent Rice Straw

Dynamics of gelling liquids: a short survey

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium, its critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.Comment: 21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some reference

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 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 percolation threshold.Comment: 11 pages, 14 figure