Monolayers flexural properties

Next, we consider the flexural properties of surfactant adsorption monolayers, which are important for the formation of small droplets, micelles, and vesicles in the fluid dispersions. The contributions of various interactions (van der Waals, electrostatic, steric) into the interfacial bending moment and the curvature elastic moduli are described. The effect of interfacial bending on the interactions between deformable emulsion droplets is discussed. 

It should be noted that usually the energy of interfacial bending is much smaller than the energy of dilatation. That is the reason why the interfacial flexural properties are important for phase boundaries of low surface tension and/or high curvature, such as surfactant micelles, microemulsions, emulsions, as well as lipid monolayers, bilayers, and biomembranes. 

The mechanical properties of surfactant adsorption monolayers are characterized not only by the interfacial tension but also by the interfacial bending moment, which is proportional to the so-called spontaneous curvature of the interface. In addition, the variation of the interfacial bending moment with curvature is characterized by the curvature elastic moduli. These interfacial flexural properties are determined mostly by the interactions between the head groups and tails of the adsorbed surfactant molecules. In their own turn, the interfacial flexural properties influence phenomena and processes such as the formation of microemulsions, critical emulsions, holes in foam and emulsion Aims, fluctuation capillary waves, flocculation in emulsions, and so on see Sec. IV. 

In the previous section, we considered the response of a surfactant adsorption monolayer to dilatation and shear deformations. In addition, in the present section, we will focus our attention on the properties of interfaces subjected to flexural deformations (i.e., bending and torsion), see Fig. 10. Indeed, the interactions between the head groups and the tails of adsorbed surfactant molecules lead to a nonzero work of bending or torsion. 

---