Exact Solution of the Percus–Yevick Approximation for Hard Spheres …and Beyond

Properties of the hard-sphere fluid at a planar wall using virial series and molecular-dynamics simulation

“…1 Much effort has been dedicated over the decades to obtain an accurate analytic expression of the HS fluid equation of state (EOS), which describes the dependence of the bulk pressure on density. [2][3][4][5][6][7][8][9][10][11] In the context of integral equations, the solution of the Percus-Yevick (PY) equation constitutes a key contribution in this direction. 12,13 Different approaches to the EOS included the evaluation of virial coefficients to obtain the analytic dependence at low density and simulation, using both molecular-dynamics (MD) simulation 9,10,[14][15][16][17] and Monte Carlo (MC) techniques.…”

Statistical field theory of ion-molecular solutions

“…of the hard spheres system I can use the analytical expression based on the Percus-Yevick approximation (see, for instance, 95,98 ).…”

“…However, for the systems of high molecular concentration this approximation is not valid. In this case, it is necessary to integrate numerically over k, using analytical expression for structure factor of hard sphere systems within the Percus-Yiewick approximation 98 . Moreover, we would like to note that RPA is valid at sufficiently small electrostatic interactions between charged particles 83 .…”

“…For the excess free energy F hs of the hard spheres system I can use the Percus-Yevick or the Carnahan-Starling approximations 95,98 .…”