On the Physical Cluster of Nucleation Theory: Generalized Hill Cluster

TL;DR

This paper generalizes Hill's physical cluster concept for nucleation, ensuring all molecules are energetically bound and correcting previous assumptions about molecular velocities, thus providing a more accurate model of cluster stability.

Contribution

It introduces a novel generalization of Hill's physical cluster for N > 2, ensuring molecules are energetically bound without implying equal velocities.

Findings

All molecules in the cluster lack sufficient kinetic energy to escape.

The new definition avoids the misconception of equal velocities among molecules.

Provides a more physically accurate model of nucleation clusters.

Abstract

The physical cluster originally conceived by Hill (J. Chem. Phys, 23, 617) is generalized for the case $N > 2$ in a novel way. Contrary to Hill's pairwise generalization, this definition assures that all constituent molecules of the cluster have insufficient kinetic energy to escape, and avoids the spurious implication of Hill's generalization that the molecular velocities are to be increasingly equal.