Evaluation of bridge function for hard sphere fluid confined in a narrow slit-pore via TMMC Mayer-sampling

The bridge function required to yield a singlet integral equation (IE) up to the second order in density expansion for the hard sphere fluid confined in a slit-pore is evaluated. The slit-fluid bridge function can be divided into wall-particle bridge diagrams with h _b-bond, which were evaluated by recently proposed Transition Matrix Monte Carlo (TMMC) Mayer-sampling method. The bulk-fluid total correlation function h _b(r) used in cluster integrals is determined by solution of the bulk-fluid Ornstein–Zernike (OZ) equation with a hypernetted chain closure (HNC). The calculation is performed for the reduced density of bulk fluid in equilibrium with the fluid in slit-pores from 0.3 to 0.7 with narrow slit width of 3.0σ and 4.0σ. The quantity of the slit-fluid bridge function is assessed by comparison of the density profile obtained from the singlet IE theory and the grand canonical Monte Carlo (GCMC) simulation. Good agreement between the proposed approach and the GCMC data is observed. The reduced normal pressure is also calculated, and agrees well with the simulation data at low to medium densities but becomes a little larger at high density. It is expected that the result can be improved by adding higher order bridge coefficients. The direct evaluation of the slit-fluid bridge function seems to be practical since a great improvement of the quality of the singlet IE theory has been achieved for predicting the structural and thermodynamic properties of fluids confined in narrow slit pores.