Abstract
This chapter reviews the physics of surfactant systems, and presents the study of their microstructure by small-angle scattering, focusing on interfaces, shapes, fluctuations, and interactions. The self-assembly of amphiphilic molecules in selective solvents (typically water) leads to a variety of molecular aggregates at thermodynamic equilibrium, namely micelles, wormlike (cylindrical) micelles, and bilayers. The driving force of the transitions from one to the other is the spontaneous curvature of the surfactant monolayer, which depends on concentration, interactions, and external parameters like temperature. Moreover, topologically different bilayer phases – lamellar, vesicle, or sponge phases – are commonly observed, and the generic phase diagram at low concentration is discussed in the light of the bending energy expressed by the Helfrich Hamiltonian. At higher concentration, liquid crystalline phases form. The competition for the hydration water changes the headgroup interactions, and thus the spontaneous curvature. This results in transition between crystals of different symmetries, recognizable by their characteristic scattering peaks. The second part of this chapter is dedicated to a conceptually simple analysis of form and structure factors, based on intuitive representations of correlation functions in terms of mass distribution in space. This approach is then applied to the highly symmetric and thus rather simple shapes of surfactant assemblies. The latter serves as illustrations, and shall be useful as a guide to structural analysis by scattering of more complex experimental systems, based on “key features” of scattered intensities combined with knowledge of contrasts and concentrations: absolute intensity values, observable power laws and characteristic sizes, specific surface, and – depending on the concentration regime – interaction peaks, or pure form factors, with information on mass and mass distribution, including possible swelling by solvent. Understanding scattered intensities with such simple concepts narrows down the large variety of possible structures, and finally paves the way to more detailed modeling, and finally unravelling of microstructures.