Potential distribution near planar surfaces

FIGURE 3.7 Plots of potential distributions near a charged planar surface according to Equation 3.32. (a) The charge of co-ions (ions with the same charge as the surface) is held constant (b) the charge of counterions is held constant. (Reprinted from Chen, Z., and R.K. Singh., /. Colloid. Interface. Sci., 245, 301-306, 2002. With permission.)... 

Forx a, Eq. (1.73) reduces to the potential distribution around the planar surface given by Eq. (1.19). This result implies that in the region very near the particle surface, the surface curvature may be neglected so that the surface can be regarded as planar. In the limit of k 0, Eq. (1.72) becomes... 

We calculate the self-atmosphere potential of an ion near the planar surface. Imagine a planar uncharged plate in contact with a solution of general electrolytes composed of N ionic mobile species of valence z, and bulk concentration (number density) nf (i=l,2,. . . , N) (Fig. 3.10). Let and p, respectively, be the relative permittivities of the electrolyte solution and the plate. Consider the potential distribution around an ion. By symmetry, we use a cylindrical coordinate system r(s, x) with its origin 0 at the plate surface and the x-axis perpendicular to the surface. 

The aim of this chapter is to calculate the electric potential tj) near a charged planar interface. In general, this potential depends on the distance normal to the surface x. Therefore, we consider a planar solid surface with a homogeneously distributed electric surface charge density o, which is in contact with a liquid. The surface charge generates a surface potential tJJo = tl)(3C = 0). 

From the fitted t" and r values and approximate //n, the angular frequency harmonic potential has been estimated to be of the order of 1012s-1, which corresponds to a relatively shallow potential surface, and the parameter x() characterizing the initial configuration has been evaluated to be near 0.02 nm. The fact that the experimental data are accounted with a 5-shaped initial distribution can be related to the existence of a steep minimum in the ground-state potential curve, which presents a high barrier between the planar and perpendicular geometries. 

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