Configurational Temperatures and Interactions in Charge-Stabilized Colloid

Yilong Han [1] and David G. Grier [2]
[1] Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd St., Philadelphia, PA 19104
[2] Department of Physics and Center for Soft Matter Physics, New York University, 4 Washington Place, New York, NY 10003

Date: October 1, 2004

Abstract:

A system's temperature can be defined in terms of its constituents' instantaneous positions rather than their momenta. Such configurational temperature definitions offer substantial benefits for experimental studies of soft condensed matter systems, most notably their applicability to overdamped systems whose instantaneous momenta may not be accessible. 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 propose 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.