ORIGIN OF 1-PK AND 2-PK MODELS FOR IONIZABLE WATER-SOLID INTERFACES

A discrete charge Ising model planar ionizable water-solid interface i s developed. This model treats all individual ionizable sites explicit ly and is solved with Monte Carlo simulation techniques. It is shown t hat a mean-field cluster expansion provides a very accurate scheme for the calculation of the titration curves in this system. From the firs t two iterations of this approximation scheme one recovers the classic al 1-pK and 2-pK models. In most cases, the 1-pK model provides a suff iciently accurate description of the titration behavior of the interfa ce, while in special situations the use of the 2-pK model may be requi red. The quick convergence of this approximation scheme is related to the long-range nature of the interaction potential between ionizable r esidues, a feature which is characteristic for water-solid interfaces.