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We develop a model to describe the competition between gelation and crystallization in colloidal suspensions where particle interactions are represented by square well attractions. The competition is discussed locally in terms of the tendencies of individual particles to attain amorphous or crystalline configurations on cluster surfaces. These tendencies are dictated by three independent processes, the aggregation of particles onto, the dissociation of particles from, and the rearrangement of particles on the cluster surfaces. Models are developed to determine the rates of each of these processes. The relative magnitudes of these rates determine the probability that a particle arriving onto a cluster surface reaches a crystalline configuration, remains arrested in an amorphous configuration, or dissociates back into the suspension. These probabilities are employed to determine whether stable crystalline or amorphous clusters nucleate, resulting in predictions of the occurrence of crystallization or gelation as a function of solution conditions. Comparisons of model predictions with recent experiments on globular protein suspensions show excellent agreement, suggesting that the model captures much of the underlying physics of the competition between gelation and crystallization in attractive colloidal suspensions.

A kinetic model for the evolution of the cluster size distribution during crystal nucleation and growth is presented. The model allows one to establish precise links between model parameters and experimental measures of nucleation kinetics. This approach demonstrates the significance of several processes not accounted for in classical nucleation theories. Chief among these is that the driving force for crystal nucleation decreases rapidly due to a reduction of the background monomer concentration as crystallization progresses, resulting in a reduction of nucleation rates. This, coupled with the disparities in the definitions of measured and predicted quantities, leads to significant discrepancies between predictions of extant models and experimental estimates of nucleation rates. Accounting for these effects, calculations of the kinetic model are shown to be in good agreement with experimental estimates of nucleation rates, crystal growth velocities, and induction times during the crystallization of hard sphere colloidal suspensions.

We propose a kinetic model for describing crystal nucleation kinetics in hard-sphere colloidal suspensions. The model captures the interplay between the enhanced thermodynamic driving force and the reduced particle diffusivity in determining crystal nucleation rates as the particle density is increased in hard-sphere suspensions. Model calculations of nucleation rates and crystal growth velocities agree quantitatively with experimental observations. The dependence of the critical cluster size on volume fraction that emerges differs qualitatively from predictions of classical theories allowing for an experimental validation of the mechanism of crystal nucleation in colloidal suspensions.