Interfacial rheology of adsorbed layers with surface reaction: On the origin of the dilatational surface viscosity

A theoretical study of the phenomena, occurring in an adsorbed layer, subject to small dilatational perturbations was carried out. Two main processes, provoked by the perturbations (surface reaction and surfactant transport onto the surface) were considered. The reaction was described by means of the reaction coordinate. The derived general rheological equation for insoluble surfactants, gave as limiting cases Voight and Maxwell type equations for fast and slow reactions, respectively. Expressions for all characteristics of the process (surface elasticity, reaction elasticity, reaction relaxation time and dilatational surface viscosity) were obtained. The obtained generalized rheological equation for reactions involving soluble surfactants is a dynamic analog of Gibbs adsorption isotherms for a multi-component system with surface reaction, since similarly to Gibbs equation it relates the surface stress only to surface variables. It gives as limiting cases generalized forms for soluble surfactants of Voight and Maxwell equations. All new rheological equations were analyzed for deformations with constant rate and periodic oscillations and they were applied to three simple surface reactions (monomolecular with one product, dimerization and association). The mass transfer was analyzed initially in the absence of surface reaction. In this system the surface stress is purely elastic, but it was shown that if the adsorption perturbation is small, regardless of the type of surface perturbation and the mechanism of adsorption, the process of mass transport always obeys a Maxwell type rheological equation. For all considered processes surface viscosities were defined, but they were called “apparent”, because they stem from diffusion, rather than from interaction between the surfactant molecules and they depend not only on surface parameters, but also on the geometry of the system. The often used in the literature correlations between the lifetime of emulsions and foams and the imaginary elasticity were analyzed. It was shown that this approach lacks serious scientific foundations and could lead to erroneous conclusions. Finally, the problem for the coupling of the surfactant diffusion with the chemical reaction was analyzed and it was demonstrated on a simple example how it could be tackled.