Theory of Contact Angles and the Free Energy of Formation of Ionizable Surfaces: Application to Heptylamine Radio-Frequency Plasma-Deposited Films

Abstract

A theoretical description is presented for the macroscopic contact angle (θ) of a solid/vapor/aqueous solution interface when the solid surface is ionizable and relatively hydrophobic. The contact angle is related to the free energy of formation of the ionizable surface in aqueous solution. Therefore, the theoretical approach takes into account the electrostatic 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 θ on pH depends on the number ofionizable surface sites per unit area, the intrinsic acid-base dissociation constant (K a i ) of the surface sites, and the background electrolyte. The negative free energy change which accompanies the acid-base reactions dominates over the positive electrostatic free energy of charging the surface ; therefore, the overall free energy of ionization is negative, and the ionized surfaces are more wettable than the uncharged surfaces. The theoretical description is applied to experimental values of θ as a function of pH, measured on heptylamine plasma polymer surfaces in the presence of either 1 or 10 mM NaCl. The theoretical fit to the advancing and sessile contact angles indicates that the plasma polymer surface contains ca. 4±1x10 17 amines/m 2 and the pK a i of the amine groups is ca. 6. The surface site density is in accord with values obtained by derivatization techniques, and the pK a i is consistent with a low effective dielectric constant for the polymer-water interfacial microenvironment.