Large deformation rheological behaviour of a model particle gel

Abstract

We report on some aspects of the large deformation rheology of model three-dimensional networked particle gels. Model gels with a particle volume fraction of 5% are formed by aggregation in a Brownian dynamics simulation from soft spherical particles incorporating flexible surface-to-surface bonds that restrict the subsequent angular reorganization and infer structural stability on the resulting percolating, fractal structure. The interaction potential allows some control over the final fractal dimension of the gel and bonds may be either breakable or essentially permanent depending on the choice of parameters. The use of continuous potentials allows the rheology to be studied at constant strain-rate and at constant stress by the incorporation of a homogeneous strain algorithm. For systems with ‘permanent’ bonds, strain hardening is observed when the strain-rate is very low compared with the structural relaxation time. At relatively high strain-rates the stress response is more nearly proportional to the strain. These systems also show strain recovery when the stress is removed. For systems with short breakable bonds, a yield stress is observed at slow constant strain. Here, we have studied the yielding behaviour of these systems by applying a steadily increasing stress and we find that, under these conditions, the structure degrades in three distinct stages. The initial breakage of bonds does not immediately disrupt the gel but allows some viscoelastic flow. This is followed by breakdown into a small number of relatively large aggregates. The ensuing viscoplastic flow causes the further rupture of aggregates that culminates in a catastrophic break-up to smaller entities at a critical point that presages true viscous flow. These transitions between viscoelastic and viscoplastic flow and between viscoplastic and viscous flow correspond to the static and dynamic yield stresses that have been observed experimentally in colloidal systems at high volume fraction. The oscillatory response for systems with permanent bonds shows non-linear behaviour expressed as overtone modes for strain amplitudes in excess of 0.05. The effective modulus for these systems also increases with strain amplitude while for systems with breakable bonds the modulus decreases or passes through a maximum as a consequence of structural decay. This behaviour compares favourably with experimental studies on chemical and physical gels.