Mathematical models of surface tension as a function of solute concentration are needed for predicting the behavior of surface processes relevant to the environment, biology, and industry. Current aqueous surface tension-activity models capture either solutions of electrolytes or those of nonelectrolytes, but a single equation has not yet been found that represents both over the full range of compositions. In prior work, we developed an accurate model of the activity-concentration relationship in solutions over the full range of compositions by extending the BET (Brunauer, Emmett, Teller) and GAB (Guggenheim, Anderson, de Boer) isotherms to multiple monolayers of solvent molecules sorbed to solutes. Here, we employ similar statistical mechanical tools to develop a simple equation for the surface tension-activity relationship that differs remarkably from prior formulations in that it (1) works equally well for nonelectrolyte and electrolyte solutes and (2) is accurate over the full range of concentrations from pure solvent to pure solute.
Keywords: interfacial processes; statistical thermodynamics; surface films.