Integral equation theory of hard sphere liquids on two-dimensional cylindrical surfaces

An integral equation theory has been developed to elucidate the structure of hard sphere liquids on the two dimensional (2D) surface of a cylinder. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair correlation function is reformulated as a function of two variables to account for particles packing along and around the cylinder. Both Percus-Yevick (PY) and Hypernetted chain (HNC) closures are employed to solve the integral equation theory numerically. For dense sphere concentrations, the calculated pair correlation function displays an oscillatory structure, along and around the cylinder, due to liquid like ordering. The HNC theory predicts a more pronounced oscillatory structure than PY, and the solvation shells obtained from the HNC theory shift to smaller distances due to tighter packing, along and around the cylinder, predicted by the theory. Also, the deviation between the PY and HNC theory becomes more significant at higher densities.