Potential distribution across a surface charge layer

2 Potential Distribution Across a Surface Charge Layer 

If the thickness of the surface layer d is much greater than the Debye length 1/k, then the potential deep inside the surface layer becomes the Donnan potential Adon, which is obtained by setting the right-hand side of Eq. (4.15) to zero, namely. 

When ZN/zn ICl, Eq. (4.18) gives the following linearized Donnan potential  

Also we term lAo = (0) (which is the potential at the boundary between the surface layer and the surrounding electrolyte solution), the surface potential of the polyelectrolyte layer. 

If we take the limit in Eq. (4.25), keeping the product Nd constant, that 

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In Chapter 1, we have discussed the potential and charge of hard particles, which colloidal particles play a fundamental role in their interfacial electric phenomena such as electrostatic interaction between them and their motion in an electric field [1 ]. In this chapter, we focus on the case where the particle core is covered by an ion-penetrable surface layer of polyelectrolytes, which we term a surface charge layer (or, simply, a surface layer). Polyelectrolyte-coated particles are often called soft particles [3-16]. It is shown that the Donnan potential plays an important role in determining the potential distribution across a surface charge layer. Soft particles serve as a model for biocolloids such as cells. In such cases, the electrical double layer is formed not only outside but also inside the surface charge layer Figure 4.1 shows schematic representation of ion and potential distributions around a hard surface (Fig. 4.1a) and a soft surface (Fig. 4.1b). 

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See also in sourсe #XX -- [ , ]

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