Elasticity of Monolayers

Because of their peculiar molecular architecture, surfactants are adsorbed at the interface between oil and water. As a result, when the surfactant monolayer is deformed, it shows not only a viscous response to deformation, but also an elastic response. There are several deformation modes of the monolayer to be considered stretching, bending, shearing, and tilting. Each of the modes can be characterized by its own elastic and viscous moduli. The main interests of this chapter are the stretching and bending deformation modes in the elastic regime. 

Consider a patch of a surfactant monolayer at the interface between oil and water. The free energy of the monolayer F is proportional to the surface area of the patch. 

The most familiar contribution is the interfacial tension term, which can be presented as a difference  

On the other hand, microscopic monolayers covering the micellar interface are under zero tension. In a closed system, the molecules at the micellar interface adjust their area per molecule in such a way that the free energy is minimized. In this state, the bare oil-water interfacial tension is completely counterbalanced by the interfacial pressure  

This balance is reached at the optimum area per surfactant molecule. A. The state in which the bare oil-water interfacial tension is completely counterbalanced by the surface pressure is called the Schulman limit. The free energy has a minimum at. d, and deviations from this value cost energy, as determined by the following Hookean form  

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