Surface effects in nucleation

TL;DR

This paper extends classical nucleation theory to nanoscale nuclei by incorporating surface effects and curvature-dependent surface tension, providing more accurate predictions of nucleation rates and surface parameter fluctuations.

Contribution

It introduces a multivariable nucleation theory considering the transition region as a surface phase and derives equations accounting for curvature effects on surface tension.

Findings

Curvature significantly affects nucleation rates, potentially by several orders of magnitude.

The curvature effect depends on the positive limiting value of the Tolman length at zero radius.

Surface parameter fluctuations can be quantitatively estimated using the derived quadratic form.

Abstract

The classical nucleation theory (CNT) concept of a nucleus as a fragment of the bulk new phase fails for nanosized nuclei. An extension of CNT taking into account the properties of the transition region between coexisting bulk phases is proposed. For this purpose, the finite-thickness layer method which is an alternative to Gibbs one is used; the transition region is considered as a separate (surface) phase. An equation for the nucleation work is derived which is basic for the multivariable theory of nucleation. Equations of equilibrium following from it are employed for considering the dependences of surface tension on radius and temperature for droplets; Kelvin formula for the equilibrium vapor pressure is extended to small radii. It is shown that the ratio of the isothermal nucleation rate to that of CNT can achieve several orders of magnitude due to the curvature effect (the dependence of surface tension on curvature). The analysis of different dependences of the Tolman length on radius, d(R), suggests that (i) the curvature effect is determined by the value of d(0) which is positive and relates to the limiting (spinodal) vapor supersaturation and (ii) the function d(R) decreases with increasing radius; at the same time, this effect is weakly sensitive to the form of the function d(R) and its asymptotic value. The second differential of the work is obtained as a quadratic form with contributions from both the bulk and surface phases. It is used for calculating the fluctuations of surface layer parameters such as the surface tension and the specific surface area as well as the fluctuations of nucleus parameters.