(475d) Direct 3D Measurement of Homogeneous Nucleation of Hard-Sphere Colloids

Understanding crystal nucleation from the liquid phase is crucial to both fundamental and applied materials science, impacting diverse systems from metallic alloys to biomolecular condensates. Colloidal suspensions uniquely allow direct observation of nucleation at the particle level, yet even in well-studied hard-sphere systems, significant discrepancies persist between experiment and theory, especially at lower densities in the liquid-solid coexistence region. To address these discrepancies, we integrate advanced three-dimensional confocal microscopy experiments with large-scale Brownian dynamics simulations to systematically study the classic problem of homogeneous nucleation of nearly hard-sphere colloids in real space and time.

In the experiments, surfaces are engineered to prevent heterogeneous nucleation at the walls. We track the positions and compute structural order parameters of over two million colloids in real time and confirm that nucleation occurs homogeneously throughout the bulk. We measure the evolution of local volume fraction during crystal nucleation and growth and find that phase boundaries deviate from the ideal hard-sphere prediction. To explain subtle experimental deviations from ideal hard-sphere behavior, we formulate an inverse problem to determine accurate particle interaction potentials that account for particle softness. Using massively parallel GPU simulations, we systematically test candidate potentials, identifying a precise, non-attractive slightly soft potential that matches experimental phase behavior and enables us to develop accurate custom equations of state.

With these refined equations of state alongside experimental and simulation data, we directly calculate key thermodynamic variables – pressure and chemical potential. Using these to define precise driving forces, we find that classical nucleation theory yields interfacial energies in accordance with earlier macroscopic simulations. Measurements of critical nucleus sizes and nucleation rates show excellent agreement at higher densities between experiments and simulations. Structural analyses reveal distinct branched-to-spherical growth transitions that differ between experiments and simulations, suggesting subtle but significant non-equilibrium, perhaps hydrodynamic, effects that are not captured in current models and influence nucleation rates at the lowest densities.

Our results highlight the utility and importance of precisely characterizing particle interactions to bridge long-standing gaps between experiments and theory, even in this extensively studied model system. By directly reconciling these discrepancies, we are able to make quantitative calculations of state variables and make meaningful comparisons between experiments and simulations, revealing fundamental new insights. To conclude the talk, we will highlight ongoing efforts to apply our methodology to more complex interactions, such as depletion-induced colloidal gelation, promising deeper understanding and further resolution of experimental-theoretical mismatches.