Soluble surfactants undergoing surface phase transitions: A Maxwell construction and the dynamic surface tension

Abstract

The dynamic surface tension of a soluble surfactant which undergoes a surface phase transition from a gaseous to a liquid expanded state is described. The application of a Maxwell construction to the surface equation of state is used to implicitly locate C*, the bulk concentration at which the surface phase transition occurs, and the binodal surface concentrations Γ(G) and Γ(L). The dynamic surface tension is assumed to reflect the instantaneous surface concentration. The mass transfer of surfactant to the interface is modeled as being controlled by bulk diffusion, or the kinetics of adsorption-desorption, or both, in a manner that accounts for the constant chemical potential as the interface undergoes the phase change and the differing interaction energies in the surface phases. As an example, using the Frumkin equation, equilibrium data for the surfactant 7-tetradecyn-6,9- diol are fitted for the maximum surface concentration Γ(∞), the ratio of the characteristic kinetic constants for adsorption and desorption β/α, and intermolecular interaction parameter K. The Maxwell construction then dictates C*, Γ(G), and Γ(L). These constants are then used to interpret dynamic surface tension data. The binodal concentrations are discussed in terms of the characteristic area swept out by the adsorbed molecule at the interface. Finally, the surface tension evolution is shown to be consistent with diffusion-controlled adsorption.