Kinetics of crystallization and gelation in colloidal suspensions

Theories are developed that successfully describe the kinetics of crystal nucleation and the competition between crystallization and gelation in colloidal suspensions. Crystal nucleation is treated as the result of a competition between particle aggregation and dissociation processes. Detailed descriptions of these processes are developed to account explicitly for kinetic effects arising due to the nature of particle interactions. Calculations of crystal nucleation rates for particles experiencing attractive, repulsive, isotropic, and anisotropic interactions reveal the remarkable sensitivity of nucleation kinetics to particle interactions. A population balance model is developed that predicts the time evolution of cluster size distributions during crystallization. Model calculations reveal that the concentration of single particles in suspension decreases rapidly as crystallization progresses, resulting in lower nucleation rates than predicted by extant theories where the particle concentration is assumed constant. Further, the model predicts the precise quantities measured in light scattering experiments commonly employed to study crystal nucleation in colloidal suspensions. Calculations of nucleation rates, crystal growth velocities, and induction times are in excellent agreement with experimental estimates, representing significant advances in our understanding of the kinetics of crystal nucleation in colloidal suspensions.; The competition between crystallization and gelation in colloidal suspensions is addressed as arising from three underlying processes at the particle level, viz., aggregation, dissociation, and rearrangement. Particles aggregate via Brownian encounters into clusters that have open structures. Subsequently, these particles rearrange into crystalline configurations to minimize their free energies. Simultaneously, bound particles can dissociate due to thermal motion. When particle rearrangement is rapid compared to the net rate of particle aggregation, crystalline clusters result. When rearrangement is slower, amorphous aggregates leading to gels result. With knowledge of particle aggregation, dissociation, and rearrangement processes, regions on colloidal phase diagrams where crystals occur are delineated from regions where gels result. Comparisons with recent experiments on globular protein suspensions are in excellent agreement suggesting that the model captures the underlying physics of the competition between gelation and crystallization. By establishing links between tunable interaction parameters and the resulting gelation and crystallization transitions, the present approach provides design rules for the control of colloidal phase transitions.