Condensed Matter Physics, 2013, vol. 16, No. 4, 43001:14
DOI:10.5488/CMP.16.43001
arXiv:1312.3547
Title:
Nonmonotonic pressure as a function of the density in a fluid without attractive forces
Author(s):

D. Henderson
(Department of Chemistry and Biochemistry, Brigham Young University, Provo UT 846025700)

A simple result for the pressure of a hard sphere fluid that was developed many years ago by Rennert is
extended in a straightforward manner by adding additional terms that are of the same form as Rennert's
formula. The resulting expression is moderately accurate but its accuracy does not necessarily improve as
additional terms are included. This expression has the interesting consequence that the
pressure can have a maximum, as the density increases, which is consistent with the freezing of
the hard spheres. This occurs solely as a consequence of repulsive interactions. Only the BornGreenYvon
and Kirkwood theories show such behavior for hard spheres and they require the numerical solution of an
integral equation. The procedure outlined here is ad hoc but is, perhaps, useful just as the
popular CarnahanStarling equation for the hard sphere pressure is also ad hoc but useful.
Key words:
partition function, equation of state, pressure, hard sphere fluid, freezing transition
PACS:
05.20.y, 05.20.Jj, 64.10.+h, 64.30.+t, 64.70.Hz
