Nonuniformly Charged Surface Layer Isoelectric Point

6 NONUNIFORMLY CHARGED SURFACE LAYER ISOELECTRIC POINT 

Consider an ion-penetrable planar soft surface consisting of two sublayers 1 and 2 (Fig. 4.7). The surface is in equilibrium with a monovalent electrolyte solution of bulk concentration n. Note here that n represents the total concentration of monovalent cations including ions and that of monovalent anions including OH ions. Let h be the concentration in the bulk solution phase. Sublayer 2 is 

Here i//(x) is the electric potential at position x relative to the bulk solution phase, where ij/(x) is set equal to zero, Wh xp —e jj x)lkT) is the H concentration at position x. The charge density resulting from dissociated acidic groups at position x in layer 1 —d x Q) is thus obtained by multiplying Eq. (4.101) by —e, namely, 

Similarly, the charge density resulting from the dissociated basic groups at x in layer 2(x —d)is given by 

The Poisson-Boltzmann equation for i/ (x) in layer 1 is then given by 

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