Elastic properties of surfactant films

Surfactants form semiflexible elastic films at interfaces. In general, the Gibbs free energy of a surfactant film depends on its curvature. Here we are not talking about the indirect effect of the Laplace pressure but a real mechanical effect. In fact, the interfacial tension of most microemulsions is very small so that the Laplace pressure is low. Since the curvature plays such an important role, it is useful to introduce two parameters, the principal curvatures 

Following Helfrich we can express the Gibbs free energy of curvature by an integral over the area considered [557]  

Co is called the spontaneous curvature. The spontaneous curvature is a more general parameter than the surfactant parameter Ns, defined by Eq. (12.4). It makes it easier to discuss the phase behavior of microemulsions because we get away from the simple geometric picture. 

It is independent of the radius It does not depend on the radius because the bending energy per unit area increases but the surface area decreases. Both effects just compensate each other. See also exercise 6. 

What are typical values for the parameters k and kl The bending rigidity of surfactant films is typically of the order of 1-20 kBT at room temperature. Factors that reduce k are short alkyl chains, cosurfactants, double-chain surfactants with unequal chains, and cis-unsaturated bonds. For the saddle-splay modulus only few measurements have been done. It tends to be negative with an amount much smaller than the bending rigidity for the same system. 

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