Out-of-equilibrium dynamics of a fractal model gel.

Using molecular dynamics computer simulations we investigate the dynamics of a gel. We start from a fractal structure generated by the diffusion limited cluster aggregation-deflection algorithm, onto which we then impose an interaction potential consisting of a short-range attraction as well as a long-range repulsion. After relaxing the system at zero temperature, we let it evolve at a fixed finite temperature. Depending on the temperature T we find different scenarios for the dynamics. For T approximately > 0.2 the fractal structure is unstable and breaks up into small clusters which relax to equilibrium. For T approximately < 0.2 the structure is stable and the dynamics slows down with increasing waiting time. At intermediate and low T the mean squared displacement scales as t(2/3) and we discuss several mechanisms for this anomalous time dependence. For intermediate T, the self-intermediate scattering function is given by a compressed exponential at small wave vectors and by a stretched exponential at large wave vectors. In contrast, for low T it is a stretched exponential for all wave vectors. This behavior can be traced back to a subtle interplay between elastic rearrangements, fluctuations of chainlike filaments, and heterogeneity.

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.

Mode-coupling theory for heteropolymers.

We study the Langevin dynamics of a heteropolymer by means of a mode-coupling approximation scheme, giving rise to a set of coupled integro-differential equations relating the response and correlation functions. The analysis shows that there is a regime at low temperature characterized by out-of-equilibrium dynamics, with violation of time-translational invariance and of the fluctuation-dissipation theorem. The onset of aging dynamics at low temperatures gives insight into the nature of the slow dynamics of a disordered polymer. We also introduce a renormalization-group treatment of our mode-coupling equations, which supports our analysis, and might be applicable to other systems.

Dynamical first-order phase transition in kinetically constrained models of glasses.

We show that the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field approximation, and numerical results for the Fredrickson-Andersen model, the East model, and constrained lattice gases, in various dimensions. This dynamical first-order transition is generic in kinetically constrained models, and we expect it to be present in systems with fully jammed states.

Anomalous dynamical light scattering in soft glassy gels.

We compute the dynamical structure factor S( q,tau) of an elastic medium where force dipoles appear at random in space and in time, due to "micro-collapses" of the structure. Various regimes are found, depending on the wave vector q and the collapse time theta. In an early time regime, the logarithm of the structure factor behaves as (q tau)(3/2), as predicted in (L. Cipelletti et al., Phys. Rev Lett. 84, 2275 (2000)) using heuristic arguments. However, in an intermediate-time regime we rather obtain a (q tau)(5/4) behaviour. Finally, the asymptotic long-time regime is found to behave as q(3/2)tau. We also give a plausible scenario for aging, in terms of a strain-dependent energy barrier for micro-collapses. The relaxation time is found to grow with the age t(w), quasi-exponentially at first, and then as t(w)(4/5) with logarithmic corrections.

Universal non-diffusive slow dynamics in aging soft matter.

We use conventional and multispeckle dynamic light scattering to investigate the dynamics of a wide variety of jammed soft materials, including colloidal gels, concentrated emulsions, and concentrated surfactant phases. For all systems, the dynamic structure factor f(q,t) exhibits a two-step decay. The initial decay is due to the thermally activated diffusive motion of the scatterers, as indicated by the q(-2) dependence of the characteristic relaxation time, where q is the scattering vector. However, due to the constrained motion of the scatterers in jammed systems. the dynamics are arrested and the initial decay terminates in a plateau. Surprisingly, we find that a final, ultraslow decay leads to the complete relaxation of f(q,t), indicative of rearrangements on length scales as large as several microns or tens of microns. Remarkably, for all systems the same very peculiar form is found for the final relaxation of the dynamic structure factor: f(q,t) approximately exp[-(t/tau s)p], with p approximately equal to 1.5 and tau s approximately q(-1), thus suggesting the generality of this behavior. Additionally, for all samples the final relaxation slows down with age. although the aging behavior is found to be sample dependent. We propose that the unusual ultraslow dynamics are due to the relaxation of internal stresses, built into the sample at the jamming transition, and present simple scaling arguments that support this hypothesis.