Evaluation of Bridge Function for Hard Sphere Fluid Confined in Slit Pore Via Transition Matrix Monte Carlo Mayer Sampling

Integral equation theory (IET) has been around for many years to study properties of fluids and most its related-studies were devoted to predict the properties of the bulk fluids via determining appropriate bridge functions for IET closures. In this study, we redirect the IET approach towards the prediction of thermodynamic properties of slit-pore confined fluids, of which roles find very much significance in industrial applications. As it is hard to find a direct evaluation of the confined fluid bridge function, we adopt and modify Mayer-sampling technique, which is applied to predict the properties of hard-sphere confined in hard planar walls. The simpler one-particle Ornstein-Zernike (OZ) equation with a hypernetted chain (HNC) closure is used and we have constructed Transition Matrix Monte Carlo Mayer-sampling technique to evaluate the bridge coefficients (clusters) expanded in density for this study. The calculated bridge function containing b2(r), b3(r) and b4(r) coefficients is included in iterative calculation of the closure to obtain the density profiles, which are in turn used to provide the equation of state of the target fluids.