Corrections to the Activation Energy Barrier Allow Classical Nucleation Theory to Better Predict Phase Change Kinetics in Colloidal Hard Spheres and Beyond: The Role of Thermodynamic Reference States

Despite being a century old, classical nucleation theory (CNT) remains in wide use to this day for qualitatively describing the phase change kinetics spanning a wide variety of materials relevant to both natural and commercial processes. Unfortunately, the absolute nucleation rates predicted by CNT often disagree with experimental measurements by many orders of magnitude. This discrepancy is evident even in the simplest of model systems - so-called "hard sphere (HS)" colloids - where the constituents are assumed not to interact with each other through any chemical potential. In this work, a simple thermodynamic correction, which references the volume density of the liquid fraction within the metastable coexistence region to the thermodynamically stable close-packed solid, is used to overcome the key source of error in determining the activation energy barrier of HS systems. Applying it is found to benefit CNT rate predictions by increasing the activation energy by 53% to 72%, across the three different system densities investigated. Separately, two alternative thermodynamic corrections are proposed for broader application (to also include self-interacting atoms, molecules, or colloids) by leveraging the CNT energy profile directly, thereby providing increases in the predicted activation energy barrier for steady-state nucleation of 33% to 50%. This range has particular significance in the context of previous simulations of HS systems that have indicated the (uncorrected) energy barrier predicted by CNT is 30% to 50% too low.