Fluid Membranes and Surfactants

In this chapter, we use the term membrane to denote a thin film of one material that separates two similar (bilayer membrane) or dissimilar (mono-layer membrane) materials. We focus on fluid membranes (where there is no in-plane shear modulus and the only in-plane deformations are compres-sions/expansions), which are important in industrial applications such as encapsulation and cleaning. Furthermore, some fluid membranes are prototypes of biological systems, although it should be noted that true biological membranes often have several components and sometimes, even a solidlike underpinning that can give the membrane a shear rigidity. 

Flexible, solid membranes, are also of interest. However, they are experimentally much less prevalent and are somewhat more complicated to treat since in addition to the membrane shape one must include the effects of shear. Their curvature energy is discussed in the problems at the end of this chapter. Another type of system that has received much theoretical attention is that of a tethered membrane which may describe polymerized, but not crystalline sheets. While a single fluid membrane that is unconstrained by walls or other membranes is strongly affected by thermal fluctuations ( crumpled ), solid membranes, particularly if self-avoidance of the membrane is included, tend to be more weakly affected by fluctuations and are hence flattef . 

Surfactant molecules, or amphiphiles consist of molecules that combine both polar and nonpolar parts (see Fig. 6.1). Because of the hydrophobic interactions discussed in Chapter 5, these molecules tend to form monolayer films at polar-nonpolar e.g., water-oil) interfaces with the polar part of the molecule solvated in the water and the hydrocarbon part of the molecule in the oil. In this case, the properties of the film are, in general, not symmetric with respect to the interface. In a single solvent e.g., water), these molecules tend to form bilayers where the hydrocarbon parts of each monolayer are aggregated in the middle of the bilayer to reduce the contact between the water and the nonpolar parts of the molecule. When composed of a single species, the properties of such bilayer films are symmetric with respect to their two sides. Lipid molecules are surfactant-like entities that generally have a polar head 

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