POTENTIAL AND PH DISTRIBUTION ACROSS A MEMBRANE WITH A SURFACE-LAYER OF IONIZABLE GROUPS

A theory is proposed for the potential distribution across a charged membrane with a surface layer of thickness d consisting of N ionizable groups of dissociation constant K. The density of membrane-fixed charges due to dissociation is determined as a functional of the potential. For d < 20 .ANG., under physiological conditions, the potential and pH distribution depends strongly on d when calculated with the product Nd (i.e. the total amount of ionizable groups in the surface layer per unit area) kept constant. When d .gtoreq. 20 .ANG. (this condition is fulfilled for practical cases), however, the potential and pH distribution depends little on d, being almost equal to that for d = .infin.. Namely, when d .gtoreq. 20 .ANG., the potential and pH distribution in practice depends not on Nd but on N. This suggests that for practical cases the density of ionizable groups rather than their total amount plays a fundamental role in the electrostatic behavior of charged membranes. The pH as well as the potential at the membrane/solution interface is shown to be much smaller than expected from the conventional model assuming d = 0. It is also observed that the dependence of the potential upon the electrolyte concentration at the membrane/solution interface when d .gtoreq. 20 .ANG. is greater than that for d = 0.