**Shiqi Zhou ^{a} and Andrej Jamnik^{b}**

^{a}Institute of Modern Statistical Mechanics, Hunan, University of Tehcnology,
Wenhua Road, Zhuzhou city,
412008, P. R. China

^{b}University of Ljubljana, Faculty of Chemistry and Chemical Technology,
Aškerčeva 5,
SI-1001 Ljubljana, Slovenia

Absrtract

A recently developed third order+second
order perturbation density functional approximation (DFA) is briefly described.
The applicability of this theory is demonstrated in the study of the density
profiles of Lennard-Jones (LJ) fluid next to a large hard sphere (mimicking a
colloidal particle) of various sizes. The accuracy of DFA predictions is tested
against the results of a grand canonical ensemble Monte Carlo simulation. The
chosen density and potential parameters for the equilibrium bulk LJ fluid
correspond to the conditions situated at ‘dangerous’ regions of the phase
diagram, i.e. near the critical temperature or close to the gas-liquid
coexistence curve. It is found that the DFA theory performs successfully for
both supercritical and subcritical temperatures. It is also shown that the
‘universality’ of the adjustable parameter associated with this theory holds
also in the present case of a large spherical particle as a source of external
potential. Here the term universality means independence of this parameter on
the particular external field responsible for the generation of a non-uniform
density profile of the fluid. This DFA results can be used as a useful starting
point for further investigation of solvent-induced excess potential of mean
force in the similar systems.

**Key words:** perturbation density
functional theory, Monte Carlo simulation, inhomogeneous systems