Kinetics of ergodic-to-nonergodic transitions in charged colloidal suspensions : aging and gelation

There are two types of isotropic disordered nonergodic states in colloidal suspensions: colloidal glasses and gels. In a recent paper [H. Tanaka, J. Meunier, and D. Bonn, Phys. Rev. E 69, 031404 (2004)], we discussed the static aspect of the differences and the similarities between the two. In this paper, we focus on the dynamic aspect. The kinetics of the liquid-glass transition is called aging, while that of the sol-gel transition is called gelation. The former is primarily governed by repulsive interactions between particles, while the latter is dominated by attractive interactions. Slowing down of the dynamics during aging reflects the increasing cooperativity required for the escape of a particle from the cage formed by the surrounding particles, while that during gelation reflects the increase in the size of particle clusters towards the percolation transition. Despite these clear differences in the origin of the slowing down of the kinetics between the two, it is not straightforward experimentally to distinguish them in a clear manner. For an understanding of the universal nature of ergodic-to-nonergodic transitions, it is of fundamental importance to elucidate the differences and the similarities in the kinetics between aging and gelation. We consider this problem, taking Laponite suspension as an explicit example. In particular, we focus on the two types of nonergodic states: (i) an attractive gel formed by van der Waals attractions for high ionic strengths and (ii) a repulsive Wigner glass stabilized by long-range Coulomb repulsions for low ionic strengths. We demonstrate that the aging of colloidal Wigner glass crucially differs not only from gelation, but also from the aging of structural and spin glasses. The aging of the colloidal Wigner glass is characterized by the unique cage-forming regime that does not exist in the aging of spin and structural glasses. © 2005 The American Physical Society

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this nonequilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging. © 2007 The American Physical Society

High-bandwidth viscoelastic properties of aging colloidal glasses and gels

We report measurements of the frequency-dependent shear moduli of aging colloidal systems that evolve from a purely low-viscosity liquid to a predominantly elastic glass or gel. Using microrheology, we measure the local complex shear modulus G* (¿) over a very wide range of frequencies (from 1 Hz to 100 kHz). The combined use of one- and two-particle microrheology allows us to differentiate between colloidal glasses and gels-the glass is homogenous, whereas the colloidal gel shows a considerable degree of heterogeneity on length scales larger than 0.5 µm. Despite this characteristic difference, both systems exhibit similar rheological behaviors which evolve in time with aging, showing a crossover from a single-power-law frequency dependence of the viscoelastic modulus to a sum of two power laws. The crossover occurs at a time t0, which defines a mechanical transition point. We found that the data acquired during the aging of different samples can be collapsed onto a single master curve by scaling the aging time with t0. This raises questions about the prior interpretation of two power laws in terms of a superposition of an elastic network embedded in a viscoelastic background

Supramolecular copolymers predominated by alternating order:theory and application

We investigate the copolymerization behavior of a two-component system into quasi-linear self-assemblies under conditions that interspecies binding is favored over identical species binding. The theoretical framework is based on a coarse-grained self-assembled Ising model with nearest neighbor interactions. In Ising language, such conditions correspond to the anti-ferromagnetic case giving rise to copolymers with predominantly alternating configurations. In the strong coupling limit, we show that the maximum fraction of polymerized material and the average length of strictly alternating copolymers depend on the stoichiometric ratio and the activation free energy of the more abundant species. They are substantially reduced when the stoichiometric ratio noticeably differs from unity. Moreover, for stoichiometric ratios close to unity, the copolymerization critical concentration is remarkably lower than the homopolymerization critical concentration of either species. We further analyze the polymerization behavior for a finite and negative coupling constant and characterize the composition of supramolecular copolymers. Our theoretical insights rationalize experimental results of supramolecular polymerization of oppositely charged monomeric species in aqueous solutions