Influence of structure on the linear response rheology of colloidal gels

Abstract

We study the linear response rheology, structure, and dynamics of colloidal gels formed by arrested phase separation with a combination of experiments and dynamic simulation, with a view toward understanding the influence of bond strength, volume fraction, and network morphology on the viscoelastic moduli. A rescaling of the data to remove the direct, equilibrium hydrodynamic, and entropic effects enables a direct comparison of experiment and simulation; the strong agreement shows that attractive forces and Brownian motion dominate relaxation, where hydrodynamic interactions play a simpler role that can be scaled out. Morphology transitions from thick, blobby strands with large solvent pores to particle-size solvent pores surrounded by concave surfaces when volume fraction increases. Unsurprisingly, generalized Stokes–Einstein relations make a poor predictor of rheology from particle dynamics. Models that connect bond dynamics to elasticity or that connect cluster dynamics to elasticity show better agreement. Prediction of age-stiffening requires a model that includes the effects of age-coarsening; surprisingly, age-stiffening is set primarily at high frequency by the dominant network length scale. A Rouse-like theory that connects dominant network length scale to elasticity provides good predictions for all volume fractions and ages, although there is an interplay between volume fraction and structural length scales. The linear viscoelastic response of the experimental system is thus well represented in a simpler computational model in which wall effects, hydrodynamics, explicit depletant molecules, and rejuvenation were neglected, suggesting that the connections between morphology, dynamics, and rheology are encoded primarily by volume fraction, attraction strength, Brownian motion, and age.