Effective pair potentials in fluids in the presence of three-body forces |
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| Authors: | G. Casanova R.J. Dulla D.A. Jonah J.S. Rowlinson G. Saville |
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| Affiliation: | 1. Department of Chemical Engineering and Chemical Technology , Imperial College of Science and Technology , London, S.W.7;2. Department of Physics , University of Genoa , Italy;3. Department of Mathematics , University of Sierra Leone |
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| Abstract: | The physical properties of a fluid in which there is only a two-body potential, uαβ , can be expressed in terms of the total correlation function, h 12, which is a sum of all connected graphs with root-points on molecules 1 and 2, whose links are f bonds, where fαβ = exp (-uαβ/κT) - 1. It is shown that the total correlation function in the presence of a weak three-body potential, uαβγ , is h 12*, where h 12* is the sum of all two-body connected graphs in which each f bond is replaced in turn by an f* bond, where  and where ? is a sub-set of the elementary graphs each of which contains one fαβγ link. We call this sub-set the line-irreducible graphs, and its leading term is a graph discussed by Rushbrooke and Silbert. The three-body potential is set equal to the dipole-dipole-dipole potential of Axilrod and Teller, and the analytic properties and numerical values of the first term ?1 examined in detail. Other effective potentials have been defined and the relations between them are elucidated. In particular it is shown that the first term in ? cannot be used to obtain the effective link f* at liquid densities, but that it can be compared with the dependence on density of the effective potential u* obtained by Mikolaj and Pings from the x-ray diffraction of compressed argon. |
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