Competition between crystallization and gelation: A local description

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.