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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.15092 |
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Table of Contents:
- We provide analytical expressions for the second virial coefficients of hard, convex, monoaxial solids of revolution in ${\mathbb{R}^{4}}$. The excluded volume per particle and thus the second virial coefficient is calculated using quermassintegrals and rotationally invariant mixed volumes based on the Brunn-Minkowski theorem. We derive analytical expressions for the mutual excluded volume of four-dimensional hard solids of revolution in dependence on their aspect ratio $ν$ including the limits of infinitely thin oblate and infinitely long prolate geometries. Using reduced second virial coefficients $B_2^{\ast}=B_2/V_{\mathrm{P}}$ as size-independent quantities with $V_{\mathrm{P}}$ denoting the $D$-dimensional particle volume, the influence of the particle geometry to the mutual excluded volume is analyzed for various shapes. Beyond the aspect ratio $ν$, the detailed particle shape influences the reduced second virial coefficients $B_2^{\ast}$. We prove that for $D$-dimensional spherocylinders in arbitrary-dimensional Euclidean spaces ${\mathbb{R}^{D}}$ their excluded volume solely depends on at most three intrinsic volumes, whereas for different convex geometries $D$ intrinsic volumes are required. For $D$-dimensional ellipsoids of revolution, the general parity $B_2^{\ast}(ν)=B_2^{\ast}(ν^{-1})$ is proven.