Transient colloidal gels by Brownian dynamics computer simulation

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Abstract
Brownian dynamics, BD, simulation has been used to model the structural evolution, phase separation dynamics and rheology of transient particle colloidal gels during formation, by quenching model monodisperse attractive spherical colloidal particles from a supercritical state point into the vapour/liquid or vapour/solid parts of their phase diagrams. Calculations were performed with particles interacting via 12:6, 24:12 and 36:18 Lennard-Jones type interaction laws at sub-critical temperatures kBT/ε, where ε is the depth of the potential well, down to 0.01 and low volume fractions (φ0.2). These systems developed a gel-like morphology during the simulations, with the aggregate morphology and rheology sensitive to the range of the attractive part of the potential and the position in the phase diagram of the quench. The long-range 12:6 potential induced compact structures with thick filaments, whereas the systems generated using the shorter-ranged 24:12 and 36:18 potentials persisted in a more diffuse network for the duration of the simulations and evolved more slowly with time. The rheology of these systems was characterized using the linear shear stress relaxation function, Cs(t), computed using the Green–Kubo fluctuation formula. The rheology of many of the systems displayed gel-like viscoelastic features, especially for the long-range attractive interaction potentials, which manifested a non-zero plateau in Cs(t), the so-called equilibrium modulus, Geq, a useful indicator of a gel, which suggests also the presence of an apparent yield stress. A formal statistical mechanical definition of Geq is presented. The infinite frequency shear rigidity modulus G∞ is extremely sensitive to the form of the potential. Despite being the most short-lived, the 12:6 potential systems gave the most pronounced gel-like rheological features, which suggests that the traditional picture of a particle gel as being formed by thin filametary networks might require reconsideration.

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