Equilibrium and dynamics of adsorption of surfactants at fluid-fluid interfaces

Abstract

Surfactant adsorption at fluid-fluid interfaces is modeled with respect to both equilibrium and dynamic behavior. A thermodynamic treatment is developed wherein the surface concentration of ionic surfactants is distinguished from their surface excess concentration by the contribution from the electrical double layer. Only the surface concentrations are assigned to the dividing surface and the electrical double layer is considered to be a part of the aqueous phase. A general adsorption isotherm is derived by including non-idealities in the bulk as well as at the dividing surface. The corresponding equation of state is derived using the Gibbs adsorption isotherm. Several well-known adsorption isotherms and equations of state arise as limiting cases of the general equations of this model. The model is shown to correlate with several published surface and interfacial tension measurements on ionic surfactant systems with or without indifferent electrolytes. Ideal behavior is observed at the interfaces of all liquid-liquid systems investigated. Surface non-idealities are observed only in gas-liquid systems. It is concluded that the non-idealities do not arise from the electrical interactions but rather from the attractive interactions between the hydrophobic tails of the adsorbed surfactant. This approach is superior to the approaches based on a Gibbsian dividing surface since it is readily applicable to the treatment of electrostatic and electrokinetic phenomena as demonstrated by a remarkable correlation achieved between the calculated values of interfacial potentials and observed electrophoretic mobilities. The model is extended using phenomenological considerations to the case of systems not at equilibrium. A continuum treatment of adsorption dynamics is formulated wherein surfactant transport in the bulk phases is described using transport equations with constant coefficients. Activation energy barriers to solute exchange between the bulk and the dividing surface are represented by kinetics of a reversible reaction. The kinetic expression corresponding to the general adsorption isotherm is derived from phenomenological considerations.