Configurational temperatures and interactions in charge-stabilized colloid

TL;DR

This paper introduces a formalism based on configurational and hyperconfigurational temperatures to analyze electrostatic interactions in colloidal monolayers, providing new self-consistency tests and a model-free method for measuring pair potentials.

Contribution

It develops a hierarchy of hyperconfigurational temperature definitions derived from the hypervirial theorem for experimental use in colloid studies.

Findings

Validated the use of configurational temperatures for probing colloidal interactions.

Provided a thermodynamic sum rule for consistency checks.

Introduced a model-free method for direct pair potential measurement.

Abstract

We demonstrate that the configurational temperature formalism can be derived from the classical hypervirial theorem, and introduce a hierarchy of hyperconfigurational temperature definitions, which are particularly well suited for experimental studies. We then use these analytical tools to probe the electrostatic interactions in monolayers of charge-stabilized colloidal spheres confined by parallel glass surfaces. The configurational and hyperconfigurational temperatures, together with a novel thermodynamic sum rule, provide previously lacking self-consistency tests for interaction measurements based on digital video microscopy, and thereby cast new light on controversial reports of confinement-induced like-charge attractions. We further introduce a new method for measuring the pair potential directly that uses consistency of the configurational and hyperconfigurational temperatures as a set of constraints for a model-free search.