Surface tension increment due to solute addition.

Addition of solute into solvent may lead to an increase in surface tension, such as salt in water and water in alcohol, due to solute depletion at the interface. The repulsion of the solute from the interface may originate from electrostatic forces or solute-solvent attraction. On the basis of the square-well model for the interface-solute interaction, we derive the surface tension increment Deltagamma by both canonical and grand-canonical routes (Gibbs adsorption isotherm) for a spherical droplet. The surface tension is increased linearly with the bulk concentration of the solute c(b) and the interaction range lambda. The theoretical results are consistent with those obtained by experiments and Monte Carlo simulations up to a few molarity. For weak repulsion, the increment is internal energy driven. When the repulsion is large enough, the surface tension increment is entropy driven and approaches the asymptotic limit, Deltagamma approximately c(b)k(B)Tlambda, due to the nearly complete depletion of the solute at the interface. Our result may shed some light on the surface tension increment for electrolyte solutions with concentration above 0.2M.