Dynamic elasticity of adsorption layers in the presence of internal reorientation processes

It has been shown that reorganization processes in the adsorbed layer, such as the orientation of the adsorbed molecules, can play an important role in determining the equilibrium and dynamic behavior of surfactant systems. In fact, a model allowing for two possible adsorption states of the molecules, with different molar surface areas, has been successfully applied to describe the equilibrium properties and the aging of liquid interfaces. In this work, the problem of the rheological behavior of an adsorption layer in the presence of reorientation processes is addressed, which represents a rather important need to increase the insight into the properties of these surfactant systems and to support the experimental investigations. Thus, the main goal of this paper is to calculate the frequency dependence of the dynamic dilational elasticity, is an element of, within the framework of the two-state model. According to the results, the phase of is an element of is no longer a monotonic function of the frequency, as predicted by the classical Langmuir model, but suggests the presence of a local maximum. Local extrema are found also in the modulus and phase of is an element of as a function of the equilibrium surface pressure. This behavior is qualitatively in agreement with experimental observations available so far. The dynamic elasticity of insoluble monolayers is also derived as a particular case of the general approach given here.