Gas-liquid Nucleation at Large Metastability

TL;DR

This paper introduces a new theoretical framework for gas-liquid nucleation at large metastability, addressing the limitations of classical nucleation theory by considering multiple liquid-like clusters and their collective behavior.

Contribution

The authors develop an extended formalism based on multiple order parameters, deriving an analytic expression that explains nucleation behavior at high supersaturation and aligns with recent experimental observations.

Findings

Nucleation becomes collective with barrierless growth at large metastability.

The new rate expression shows weaker supersaturation dependence than CNT.

Surface tension and free energy barriers depend on interaction range.

Abstract

Nucleation at large metastability is still largely an unsolved problem, although is a problem of tremendous current interest, with wide practical value. It is well-accepted that the classical nucleation theory (CNT) fails to provide a qualitative picture and gives incorrect quantitative values for such quantities as activation free energy barrier and supersaturation dependence of nucleation rate, especially at large metastability. In this article, we present a powerful alternative formalism to treat nucleation at large supersaturation. This formalism goes over to the classical picture at small supersaturation where CNT is expected to be valid. The new theory is based on an extended set of order parameters in terms of k-th largest liquid-like clusters where k=1 is the largest cluster in the system, k=2 is the second largest cluster and so on. We derive an analytic expression for the free energy of formation of the k-th largest cluster which shows that at large metastability the barrier of growth for the few largest liquid-like clusters disappear, the nucleation becomes collective and the approach to the critical size occurs by barrierless diffusion in the cluster size space. The expression for the rate of barrier crossing predicts a weaker supersaturation dependence than that of CNT at large metastability. Such a cross-over behavior has indeed been observed in recent experiments but eluded an explanation till now. In order to understand the large numerical difference between simulation predictions and experimental results, we carried out a study of the dependence on the range of intermolecular interaction of both the surface tension of an equilibrium planar gas-liquid interface and the free energy barrier of nucleation. Both are found to depend significantly on the range of interaction for a Lennard-Jones potential, both in two and three dimensions.