Dissimilar Plates

In this chapter, we give exact expressions and various approximate expressions for the force and potential energy of the electrical double-layer interaction between two parallel similar plates. Expressions for the double-layer interaction between two parallel plates are important not only for the interaction between plate-like particles but also for the interaction between two spheres or two cylinders, because the double-interaction between two spheres or two cylinders can be approximately calculated from the corresponding interaction between two parallel plates via Deijaguin s approximation, as shown in Chapter 12. We will discuss the case of two parallel dissimilar plates in Chapter 10. 

Consider two parallel dissimilar plates 1 and 2 having thicknesses d and d2, respectively, separated by a distance h immersed in a liquid containing N ionic species with valence z, and bulk concentration (number density) (/ = 1, 2,. . . , N). We take an x-axis perpendicular to the plates with its origin at the right surface of plate 1, as in Fig. 10.1. We assume that the electric potential j/ x) outside the plates (—ooPoisson-Boltzmann equation ... 

ELECTROSTATIC INTERACTION BETWEEN TWO PARALLEL DISSIMILAR PLATES... 

FIGURE 10.1 Schematic representation of the potential distribution (soUd line) across two interacting parallel dissimilar plates 1 and 2 at separation h. Dotted line is the unperturbed potential distribution ath = oo. unperturbed surface potentials of plate 1 and 2, respectively. 

ELECTROSTATIC INTERACTION BETWEEN TWO PARALLEL DISSIMILAR PLATES then P is attractive for all xh and has a minimum PV,... 

We calculate the potential energy of the double-layer interaction per unit area between two parallel dissimilar plates 1 and 2 at separation h carrying constant surface charge densities cti and <12, as shown in Fig. 10.1[8]. Equation (9.116) for the interaction energy F (h) is generalized to cover the interaction between two parallel dissimilar plates as... 

The method for obtaining an analytic expression for the interaction energy at constant surface potential given in Chapter 9 (see Section 9.6) can be applied to the interaction between two parallel dissimilar plates. The results are given below [9]. 

Similarly, the interaction energy V(h) between two parallel dissimilar plates 1 and 2 per unit area in a vacuum, which have molecular densities N and N2, London-van der Waals constant Cj and C2, and thicknesses d and 2. respectively, can be obtained from Eq. (4.11)... 

---