Integral equation study of hard sphere fluids near a hard cylinder macromolecule

Hard sphere fluids near a hard cylinder of infinite length are studied using the Ornstein-Zernike equation. A method of numerically solving this equation is proposed that consists of a combination of Newton-Raphson and Picard iteration approaches in Fourier space. The Percus-Yevick (PY), hypernetted chain (HNC), Martynov-Sarkisov (MS) and modified Verlet (VM) closures are used to calculate hard sphere-hard cylinder density profiles. These are tested against simulation data for the cylinder/sphere diameter ratios σ* = σcyl/σhs = 0, 1, and 2. The PY and HNC results are good at all distances except in the vicinity of closest approach. The MS results are even better, but solutions do not exist for σ* = 1 and 2 at reduced densities above 0·7. The VM theory gives excellent results for all sphere-cylinder distances at all state points considered. The same closures are used to calculate the background correlation function y(s). The PY and the MS results are considerably lower and the HNC results considerably higher than simulation data, while VM gives results that are accurate within the precision of simulations.