Igniting homogeneous nucleation

TL;DR

This paper analyzes transient homogeneous nucleation in large critical size limits, characterizing three eras of nucleation, and provides improved analytical formulas that align well with numerical solutions and experimental data.

Contribution

It introduces a detailed characterization of transient nucleation eras and derives improved analytical formulas for nucleation rate and time lag.

Findings

Three distinct eras of transient nucleation are identified.

The thermally driven diffusivity model aligns better with experimental data.

Analytical formulas match numerical solutions closely.

Abstract

Transient homogeneous nucleation is studied in the limit of large critical sizes. Starting from pure monomers, three eras of transient nucleation are characterized in the classic Becker-D\"oring kinetic equations with two different models of discrete diffusivity: the classic Turnbull-Fisher formula and an expression describing thermally driven growth of the nucleus. The latter diffusivity yields time lags for nucleation which are much closer to values measured in experiments with disilicate glasses. After an initial stage in which the number of monomers decreases, many clusters of small size are produced and a continuous size distribution is created. During the second era, nucleii are increasing steadily in size in such a way that their distribution appears as a wave front advancing towards the critical size for steady nucleation. The nucleation rate at critical size is negligible during this era. After the wave front reaches critical size, it ignites the creation of supercritical clusters at a rate that increases monotonically until its steady value is reached. Analytical formulas for the transient nucleation rate and the time lag are obtained that improve classical ones and compare very well with direct numerical solutions.