Berlin 2024 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Statistical Physics: General

DY 41.11: Vortrag

Donnerstag, 21. März 2024, 12:15–12:30, BH-N 128

Calculation of second virial coefficients of convex bodies in D-dimensional Euclidean spaces via Brunn-Minkowski theory — •Markus Kulossa and Joachim Wagner — Institut für Chemie, Universität Rostock, 18051 Rostock, Germany

The virial series expands the compressibility factor of imperfect gases in a power series of the particle number density ϱ, where the virial coefficient of order i accounts for the contribution of interactions in an i-particle cluster to the non-ideal behavior. In the low-density limit, the second virial coefficient is the leading contribution to the departure from ideal gas behavior. For hard particles, the second virial coefficient is the orientationally-averaged mutual excluded volume per particle which is within the Brunn-Minkowski theory analytically accessible via quermassintegrals.

In this talk we present analytical formulations for the second virial coefficient of hard, convex bodies in D-dimensional Euclidean spaces R^D with emphasis on so far unknown expressions for second virial coefficients of uni-axial solids of revolution in R⁴. In addition to the effect of the aspect ratio, the detailed influence of the particle shape is analyzed. The effect of the dimensionality D is shown by comparing virial coefficients of 4D objects with their sections in lower-dimensional spaces.

Keywords: virial theorem; excluded volumes; convex particles; hard body interaction