Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 42: Statistical Physics (General) II
DY 42.4: Vortrag
Dienstag, 8. März 2005, 15:00–15:15, TU H3010
Morphological thermodynamics: shape dependence of free energies and density profiles — •Peter König1, Roland Roth1, and Klaus Mecke1,2 — 1MPI für Metallforschung, Stuttgart — 2Institut für theoretische Physik, Universität Erlangen-Nürnberg
We show that a thermodynamic potential of a fluid bounded by an arbitrarily shaped convex container can be calculated fully from the knowledge of only four morphometric measures. This result is based on the assumption that a thermodynamic potential is an ’additive’ functional which can be understood as a more precise definition for the conventional term ’extensive’. As a consequence, the surface tension and other thermodynamic quantities contain, beside a constant term, only contributions linear in the mean and Gaussian curvature of the container and not an infinite number of curvatures. Our findings are tested numerically in the entropic system of hard spheres bounded by a curved wall within the framework of density functional theory and by a systematic expansion of density profiles in powers of wall curvatures. The dependence of the fluid density on the wall shape for large distances from the wall can be derived analytically from Ornstein-Zernicke equation. The contact value of the fluid density and the asymptotic behaviour depend again only on the mean and Gaussian curvatures, i.e., on additive morphometric measures of the wall. Our approach can be generalised to systems with short-ranged fluid-fluid and wall-fluid interaction potentials, as long as intrinsic length scales remain small.