
316 Perturbation Theories for Fluids and Solids
parameter determined from the exact condition that βP must be equal to the average
density ρ(σ/2) of HS in contact with the wall, as shown by Reiss et al. (1959), that is
βP = ρ
σ
2
. (9.102)
The theory was shown to provide good agreement with simulations for the density
profiles of LJ and SHS fluids confined between two hard walls.
Several approximations, based on truncating either the perturbation series (9.23)
or the (9.24) one and introducing in the last considered term a density, different from
the bulk density ρ
0
, to correct in some way for the neglected terms, have been devised
by Zhou (2002, 2003a,b, ...