Determination of the Intrinsic Acid−Base Dissociation Constant and Site Density of Ionizable Surface Groups by Capillary Rise Measurements

Abstract

A theoretical description is presented for the equilibrium capillary height (heq) of a solution between parallel,flat,solidsurfaceswhichcontainionizablegroups. Theheqisrelatedtothechangeingravitational potential energy, the intrinsic wettability of the un-ionized surface, and the free energy of formation of theionizablesurfaceinaqueoussolution. Thetheoreticalapproachtakesintoaccountboththeelectrostatic free energy of charging the surface and the change in the free energy associated with the acid-base reactions of the surface sites. It is shown that the dependence of heq on pH depends on the number of ionizable surface sites per unit area, the intrinsic acid-base dissociation constant (Ka i ) of the surface sites, andthebackgroundelectrolyte. Thenegativefreeenergychangewhichaccompaniestheacid-basereactions dominates over the positive electrostatic free energy of charging the surface. Consequently, the overall free energy of ionization is negative, and an ionized surface is more wettable than an un-ionized surface. The theoretical description is applied to experimental values ofheqas a function of pH, measured between two heptylamine plasma polymer surfaces in the presence of 1 mM NaCl. The theoretical fit to the data indicates that the plasma polymer surface contains ca. 1017 amines/m2 and the pKa i of the amine groups is ca. 5. The surface site density is in reasonable accord with values obtained by both derivatization techniquesandcontactanglemeasurements. ThepKa i isconsistentwithaloweffectivedielectricconstant for the polymer-water interface.