Systematic Improvement of Classical Nucleation Theory

TL;DR

This paper critically examines classical nucleation theory (CNT), identifies its limitations, and introduces refined models accounting for interface non-sharpness and shape fluctuations, significantly improving the accuracy of nucleation barrier and interface energy estimates.

Contribution

It systematically improves CNT by incorporating interface and shape corrections, enhancing the accuracy of nucleation barrier and interface energy calculations.

Findings

CNT estimates are generally inaccurate for solid cluster formation.

Corrections for non-sharp interfaces and shape fluctuations improve barrier predictions.

Refined models better match experimental nucleation rates in colloids.

Abstract

We reconsider the applicability of classical nucleation theory (CNT) to the calculation of the free energy of solid cluster formation in a liquid and its use to the evaluation of interface free energies from nucleation barriers. Using two different freezing transitions (hard spheres and NaCl) as test cases, we first observe that the interface-free-energy estimates based on CNT are generally in error. As successive refinements of nucleation-barrier theory, we consider corrections due to a non-sharp solid-liquid interface and to a non-spherical cluster shape. Extensive calculations for the Ising model show that corrections due to a non-sharp and thermally fluctuating interface account for the barrier shape with excellent accuracy. The experimental solid nucleation rates that are measured in colloids are better accounted for by these non-CNT terms, whose effect appears to be crucial in the interpretation of data and in the extraction of the interface tension from them.