Approximate Analytic Expressions for Moderate Potentials

FIGURE 9.5 Comparison between the Deijaguin-Landau theory [9] and the Verwey-Overbeek theory [10]. These two theories give the same result. 

Although the choice of E is different for the Deij aguin-Landau theory and the Verwey and Overbeek theories, Eqs. (9.143) and (9.144) both give the identical result (Eq. (9.86)). 

The calculation of the potential energies V h) and h) of the double-layer interaction between two parallel plates requires numerical solutions to transcendental equations (9.105) and (9.137), respectively. In the following we give approximate analytic expressions for V (h), which does not require numerical calculation. The obtained results, which are correct to the order of the sixth power of the unperturbed surface potential i//q, are applicable for low and moderate potentials. 

DOUBLE-LAYER INTERACTION BETWEEN TWO PARALLEL SIMILAR PLATES 

FIGURE 9.6 Schematic representation of the double-layer interaction at constant surface potential between two parallel plates 1 and 2 separated by h. j/o is the potential at the midpoint between the plates. 

---

APPROXIMATE ANALYTIC EXPRESSIONS FOR MODERATE POTENTIALS 229 The surface charge density a of plate 1 is related to the potential by... 

---