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Institut für Theoretische Physik I

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- Comparing Step Potential Free Energy Approximations made with Fundamental Measure Theory
- supervised by Michael Schmiedeberg
- finished 2023-04
- [PDF]

Ways of approximating the Helmholtz free energy functional (in the context of Classical Density Functional Theory) of the step potential u(r)=hΘ(L−r) are derived, which are formulated with Fundamental Measure Theory. The first approach adds an interaction energy term to the White Bear II hard sphere gas excess free energy, where the weighted densities inserted into White Bear II are reweighted in a manner motivated by the Barker-Henderson effective hard sphere diameter. The second approach emulates Rosenfelds derivation of his original Fundamental Measure Theory, followed by a modification analogous to the changes White Bear II makes relative to Rosenfelds original functional. Both analytically reproduce White Bear II for βh→∞ and the ideal gas for βh→0. Their behaviour is probed by comparing their predicted structure function with Monte Carlo simulations and with the Percus-Yercick closure to the Ornstein-Zernike equation. The Barker-Henderson+energy approach predicts a structure function in close agreement with the Percus-Yervick closur. The emulation of Rosenfeld’s approach turns out to be sensitive to the quality of the approximation of interaction energy and in the approximations considered fails at intermediate step sizes 1<βh<3. There are indications in its qualitative behaviour however, that suggest it includes effects seen in Monte Carlo simulations, that neither Percus-Yervick closure nor the first approach encompass.