Physical interpretation of the partition function for colloidal clusters

TL;DR

This paper provides a classical derivation and physical interpretation of the partition function for colloidal clusters, explaining why a molecular statistical model accurately describes their equilibrium distributions.

Contribution

It offers a classical derivation of the partition function and interprets its terms physically, connecting cluster properties to their equilibrium probabilities.

Findings

Partition function derived classically without quantum mechanics

Physical interpretation of symmetry, inertia, and vibrational effects

Model explains experimental data on colloidal cluster distributions

Abstract

Colloidal clusters consist of small numbers of colloidal particles bound by weak, short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well-described by a statistical mechanical model originally developed for molecules. To explain why this model fits experimental data so well, we derive the partition function classically, with no quantum mechanical considerations. Then, by comparing and contrasting the derivation in particle coordinates with that in center-of-mass coordinates, we physically interpret the terms in the center-of-mass formulation, which is equivalent to the high-temperature partition function for molecules. We discuss, from a purely classical perspective, how and why cluster characteristics such as the symmetry number, moments of inertia, and vibrational frequencies affect the equilibrium probabilities.