Chapter 12 Electrostatic properties of membranes: The poisson-boltzmann theory
This chapter discusses some of the basic considerations underlying the behavior of charged membranes in aqueous solutions. The chapter also describes the electrostatic interactions of membranes. After some general considerations of charged surfaces in liquids and the derivation of the Poisson–Boltzmann equation, the chapter presents specific solutions of several electrostatic problems starting with a single flat and rigid membrane, and then generalizing it to two flat membranes. Then, it considers the possibility of having a flexible membrane in various situations: a single membrane, two membranes, and a stack of membranes. Special emphasis is given to the coupling between the electrostatic and the elastic properties. By considering the membrane as a flexible (and homogeneous) interface, the contribution of the charges to the bending moduli has been found in various electrostatic regimes. Electrostatics tends to rigidify the membranes and also suppresses the out-of-plane fluctuations of a lamellar phase composed of a stack of membranes. However, when the membrane is heterogeneous, electrostatics can induce shape instabilities in relation to a lateral segregation of the two components.