Because the positions of microscopic particles, such as atoms, are hard to measure, experimental applications of the configurational temperature have been relatively limited (5). Colloidal dispersions differ from many experimental systems in that their constituents' motions can be tracked quite easily. Unlike most macroscopic model systems, they can be thoroughly equilibrated through the particles' intimate contact with the suspending fluid. Furthermore, an effective potential between two particles often can be defined. For this reason, colloidal dispersions offer an almost ideal experimental test-bed for studying the configurational temperature and related ideas. These ideas, in turn, provide valuable new tools for assessing the microscopic state of this important state of matter.
This section describes methods for estimating the configurational and hyperconfigurational temperatures of colloidal dispersions from digital video microscopy measurements of their microscopic dynamics. Emphasis is placed on how to account for inevitable experimental errors in systems of limited size whose interactions may not be fully characterized a priori. In particular, we analyze the structure and dynamics of dilute monolayers of charge-stablized colloidal spheres confined by planar surfaces, on the one hand using convergence of different temperature expressions as a thermodynamic self-consistency test for independently measured effective pair potentials, and on the other as a new approach to measuring the pair potential directly.
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