Gelation in colloid–polymer mixtures

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Abstract
Moderate concentrations of a small non-adsorbing polymer cause a suspension of colloidal particles to phase separate into coexisting colloidal fluid and crystal via the ‘depletion’ mechanism. At higher polymer concentrations, crystallization is suppressed, and a variety of non-equilibrium aggregation behaviour is observed. We report the results of small-angle laser light scattering studies of aggregation in a model system: colloidal PMMA–polystyrene. In all cases, ‘rings’ in the small-angle scattering are observed. At intermediate times, the scattering S(Q, t) from any one sample collapses onto a master curve under the scaling ansatz S(Q)→[Qm(t)]dS[Q/Qm(t)], where Qm(t) is the (time-dependent) position of the small-angle scattering peak. Just across a ‘non-equilibrium boundary’ and at moderate colloid volume fractions (ϕ 0.1), the peak collapses continuously and completely. The exponent d was found to be 3, and the master curve takes the Furukawa form; the peak position Qm(t) scales approximately as t–1/4 and t–1 at short and long times, respectively, behaviour reminiscent of classic spinodal decomposition in fluids. At higher polymer concentrations, d decreases from 3, saturating at d≈ 1.7, the fractal dimension of aggregates formed from diffusion-limited cluster aggregation (DLCA). In the latter case, where aggregation has led to a system-spanning ‘gel’, the small-angle ring appears more or less ‘frozen’ for a finite period of time (minutes to hours). Rapid collapse of the gel structure follows and the small-angle ring disappears in a matter of seconds. At lower colloid volume fractions, ϕ≈ 0.02, and just across the non-equilibrium boundary, a latency period elapses before a small angle ring becomes visible, whose position remains roughly constant while it brightens in time, behaviour consistent with classic nucleation. We suggest that non-equilibrium behaviour is ‘switched on’ by a hidden, meta-stable gas–liquid binodal. Different regimes of aggregation behaviour are controlled by the nucleation–spinodal cross-over and the transient percolation line within this binodal.