Configurational temperatures and interactions in charge-stabilized colloid

A system's temperature can be expressed 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 thermodynamic sum rule, provide previously lacking self-consistency tests for interaction measurements based on digital video microscopy, and thereby cast light on controversial reports of confinement-induced like-charge attractions. We further introduce a method to determine unknown parameters in a model potential by using consistency of the configurational and hyperconfigurational temperatures as a set of constraints. This approach, in principle, also should provide the basis for a model-free estimation of the pair potential.