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Communication: Non-Hadwiger terms in morphological thermodynamics of fluids
7. H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie (Springer, Berlin, 1957).
18.These expressions for and give the leading behavior for Ri → ∞, which is the relevant limit in the present work. The full expressions for and have to be constructed such that the weight of ρi vanishes as Ri → 0.
19. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, 3rd ed. (Academic Press, London, 2006).
21.Henceforth, we use the tilde to refer to thermodynamic coefficients calculated relative to the physical wall rather than the parallel wall which defines the external potential on the solvent, see Ref. 4 for details.
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We demonstrate that the Hadwiger form of the free energy of a fluid in contact with a wall is insufficient to describe the low-density behavior of a hard-sphere fluid. This implies that morphological thermodynamics of the hard-sphere fluid is an approximate theory if only four geometric measures are included. In order to quantify deviations from the Hadwiger form we extend standard fundamental measure theory of the bulk fluid by introducing additional scaled-particle variables which allow for the description of non-Hadwiger coefficients. The theory is in excellent agreement with recent computer simulations. The fact that the leading non-Hadwiger coefficient is one order of magnitude smaller than the smallest Hadwiger coefficient lends confidence to the numerous results that have been previously obtained within standard morphological thermodynamics.
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