Why simulated and measured hard-sphere nucleation rates disagree
In plain words
Hard-sphere colloids are the simplest crystallizing system, yet computer simulations predict crystal formation many orders of magnitude slower than experiments observe at modest supercooling, by up to roughly 10 to 20 powers of ten depending on the estimate. The cause of this gap is disputed.
Precise statement
For hard-sphere colloids at volume fractions $\phi$ of roughly $0.50\text{ to }0.53$, simulated nucleation rate densities (umbrella sampling, forward flux, brute-force MD) fall below light-scattering and microscopy measurements by roughly 10 or more orders of magnitude (up to 22 in some estimates), while agreeing at higher $\phi$. Identify the cause (polydispersity, sedimentation, solvent hydrodynamics, errors in mapping experimental to effective volume fraction, simulation method, or a deficiency in the nucleation picture itself) and reconcile simulation and experiment within statistical error.
What would settle it
Simulations and experiments on the same characterized system (polydispersity, gravity, effective $\phi$) giving rates that agree within error at low supersaturation.
Status in the literature
Unverified note
A 2025 particle-level experiment (Kale, Lederer, Schoepe, Soft Matter 2025, https://doi.org/10.1039/D5SM00776C) argues that the gap requires a revised picture of nucleation rather than a correction to simulations; no reconciliation is accepted as of 2026.