NUMERICAL STUDY OF A MODIFIED BBGY INTEGRAL-EQUATION FOR THE PRIMITIVE MODEL OF AN ELECTROLYTE SOLUTION

A modified Poisson-Boltzmann equation derived from the BBGY hierarchy of equations is solved numerically for the restricted primitive model of an electrolyte solution. Computations are carried out for 1: 1 and 2: 2 electrolytes, and results compared with 1: 1 Monte Carlo data and results from the Poisson-Boltzmann extensions arising from the Kirkwood hierarchy. Satisfactory agreement with the Monte Carlo results are found in the 1: 1 case, and the correct qualitative behaviour of thermodynamic properties obtained in the 2: 2 case. At low concentrations in the 2: 2 case the modified Poisson-Boltzmann equations from the Kirkwood and BBGY hierarchies predict the anomalous behaviour found in the thermodynamic properties of real electrolytes. The behaviour of the mean electrostatic potential changes from a damped exponential to a damped oscillatory form for 1.2<ka<l.3 (where k is the Debye-Huckel constant and a is an ionic diameter) in the 1: 1 case and at ka˜0.8 in the 2: 2 case for the parameters considered. © 1979 Taylor & Francis Ltd.