Interaction Between Two Dissimilar Soft Spheres

Consider the electrostatic interaction between two dissimilar spherical soft spheres 1 and 2 (Fig. 15.3). We denote by and the thicknesses of the surface charge layers of spheres 1 and 2, respectively. Let the radius of the core of soft sphere 1 be a and that for sphere 2 be a. We imagine that each surface layer is uniformly charged. Let Zi and N, respectively, be the valence and the density of fixed-charge layer of sphere 1 and Z2 and N2 for sphere 2. 

FIGURE 15.3 Interaction between two soft spheres 1 and 2 at separation H. Spheres 1 and 2 are covered with surface charge layers of thicknesses di and CI2, respectively. The core radii of spheres 1 and 2 are and a2, respectively. 

Equations (15.49) and (15.50), respectively, agrees with the expression for the electrostatic interaction energy between two parallel hard plates at constant surface charge density and that for two hard spheres at constant surface charge density [4] (Eqs. (10.54) and (10.55)). 

FIGURE 15.4 Scaled electrostatic interaction energy V p(/T)= (oi+ 2)/ Usp(W) between two dissimilar soft spheres with fixed charges of like sign as a function of scaled sphere separation calculated with Eq. (15.44) at various values of Kd = Kd2 — Kd, where and C2 (defined hy Eqs. (15.46) and (15.47)) are kept constant at a2ld = 0.5. From Ref. [3]. 

5 Scaled electrostatic interaction energy V p(/7) = fir oK (fli+ 2)/, (H) between two dissimilar soft spheres with fixed charges of unlike sign as a 

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