Alternative Theory of Nucleation in Super-Cooled Liquids

TL;DR

This paper proposes a corrected and dimensionally consistent approach to nucleation in super-cooled liquids using the Zeldovich rate formula, introducing a new thermal evolution law for interfacial tension validated by numerical simulations.

Contribution

It introduces a dimensionally correct nucleation model based on Zeldovich's formula and establishes a new thermal law for interfacial tension near absolute zero.

Findings

Accurate fit of the thermal evolution law to numerical data.

Interfacial tension depends on scale and temperature near absolute zero.

Melting crystal volume correlates with potential attractivity.

Abstract

Having discovered a dimension mistake in two key formulas of the Classical Nucleation Theory (CNT) but wishing to remain in the style of this theory, we propose to approach nucleation on the basis of the Zeldovich unsteady rate formula, with the dimensionally correct expressions for the nucleation rate and time constant. Beforehand, the problematic status - physical size or simple parameter - of interfacial tension in CNT was audited. The results of numerical simulations on nucleation in various attraction but fixed repulsion conditions of the interaction potential have led us to motivate, then establish, a thermal evolution law for interfacial tension. Taking into account a scale dependance in the vicinity of absolute zero in temperature, this law is of stretched Arrhenius type. It works with the Zeldovich formula, notably for the determination of adjusting parameters. A remarkably accurate adjusting of this law to the numerical simulations has been obtained and led us to exhibit melting crystal volume as a measure of potential attractivity. It should allow accurate forecasts of instantaneous nucleation rate and average nucleation duration in physical or numerical super-cooled monoatomic liquids.