Influence of multivalent counterions adsorption on Langmuir films

It has been shown recently by neutron and X-ray reflectivity that nanometer-sized multivalent counterions (Keggin salts) can assemble as a dense monomolecular sublayer beneath a charged Langmuir monolayer of opposite sign. We have conducted experiments that examine the surface pressure isotherms of docosamine surfactant monolayers under such conditions and have shown that they undergo dramatic modifications when the Keggin salts are added. We model these experimental results by a close-packed sublayer of counterions on which charged surfactants can organize and form complexes. We then provide a thermodynamic description of the surface/sublayer system by giving an expression for surface free energy and surface pressure. We compare the results of this discrete model to traditional mean-field descriptions where the counterions form a diffuse continuous layer. The new features are: i) modifications in the shape of the surface pressure isotherm; ii) appearance of a phase separation in the surfactant layer. Finally, we show that the model is in satisfactory agreement with the experimental isotherms and a best fit yields numerical estimates of the different interaction parameters.