Direct Measurements of Colloid Crystal Nucleation Barriers and Rates Comply with A Priori Classical Theory Predictions

According to classical models, the nucleation of crystals is hindered by a barrier due to the excess free energy of their interface with the crystallization medium. Measurements of absolute crystal nucleation rates, however, severely diverge from quantitative model predictions and have cast doubt over the power of classical theory to interpret crystal nucleation. We design a suspension of attractive colloid particles in which crystals form at low particle number density, mimicking molecular solutions. The particles interact with an isotropic pair potential with a single attractive minimum. Empowered by the particles' large size and slow diffusion, we directly observe the dynamics between solute particles and quasi-two-dimensional hexagonal crystals during nucleation. Crystal nuclei assemble directly from suspended particles, fully complying with the classical scenario. The depth of the pair potential between two particles, the bond strength, predicts the volume fraction of suspensions at equilibrium with crystals and, using classical nucleation theory (CNT), the measured sizes of the critical nucleus and the free energy barrier for nucleation. A model based on the diffusion limit of the reaction between a particle and a nucleus, justified by the lack of barriers for particle association in the pair interaction potential, reproduces the prefactor in the nucleation rate law. We highlight two deviations from classical behaviors. The nucleation rate law prefactor is faster than the CNT prediction for nuclei larger than one particle, for which multiple-body interactions matter. At elevated supersaturations, the nucleation rate decouples from supersaturation, indicating a shift to a spinodal-like regime. Our results reveal the power of CNT to predict both the thermodynamic and kinetic behaviors during crystal nucleation in simple systems and emphasize that the numerous nonclassical crystal nucleation pathways are not due to failures of classical theory but to the complexity of real biological, geological, and engineered systems.