Deriving the Rosenfeld functional from the virial expansion.
In this article we replace the semiheuristic derivation of the Rosenfeld functional of hard convex particles with the systematic calculation of Mayer clusters. It is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number. This extends the virial expansion of the free energy by an expansion in the loop order, with the Rosenfeld functional as its leading contribution. Rosenfeld's weight functions then follow from the derivation of the intersection probability by generalizing the equation of Blaschke, Santalo, and Chern. It is found that the 0-loop order can be derived exactly and reproduces the Rosenfeld functional. We further discuss the influence of particle dimensions, topologies, and geometries on the mathematical structure of the calculation.
Institute of Technical Thermodynamics, RWTH Aachen University, Schinkelstraße 8, 52062 Aachen, Germany. stephan.korden@rwth-aachen.de
Stephan
S
Korden
D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular
D003102:Colloids