Grand canonical Monte Carlo and modified singlet integral equations for the density profile of a Yukawa fluid near a planar wall

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Abstract
Results for the density profile for Yukawa molecules near a hard wall and an exponential attractive wall are presented for Grand Canonical Monte Carlo (GCMC) simulations, for the singlet hypernetted chain (HNC) integral equation and for a modified version of the Lovett–Mou–Buff–Wertheim (LMBW-1) which uses the exact contact value theorem. The results of the standard singlet HNC are quite poor. If the LMBW equation is modified (but still using the bulk direct correlation function) the results at high temperature become reasonable. However, the results at low temperatures, close to the bulk coexistence curve, are only a partial improvement. The contact value of the density profile is now quite good but the profile has the incorrect oscillatory behavior predicted by the unmodified approximate equation. The GCMC simulation results show a clear effect of drying at low temperatures.