Surface charge layer

Ohshima, H Kondo, T, Electrophoretic Mobility and Donnan Potential of a Large Colloidal Particle with a Surface Charge Layer, Journal of Colloid and Interface Science 116, 305, 1987. O Neil, GA Torkelson, JM, Modeling Insight into the Diffusion-Limited Cause of the Gel Effect in Free Radical Polymerization, Macromolecules 32,411, 1999. 

Ohshima, H. and Kondo, T. (1987). Electrophoretic mobility and Donnan potential of a large colloidal particle with a surface-charge layer, J. Coll. Interf. Sci., 116, 305-311. 

In obsidian the increase of F above 450°C and the appearance of the positive surface charge between 450-630°C do not suggest a thermo-dynamically determined surface charge layer nor Na+ segregation. If Na+ segregation were the cause, the obsidian behavoir should resemble that of soft glass, e.g. FA should decrease monotonously with increasing T. 

However the formation of a surface charge layer is also possible at low carrier concentrations, for a certain amount of carriers can be bound by surface states. These surface states can exist as a result of the geometrical distortion of the lattice at the surface (5), or they can be formed by adsorption of ions from the electrolyte. While the formation of surface states by adsorption processes is an experimental fact (6), their existence at a clean semiconductor surface is doubtful (7). 

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). 

FIGURE 4.2 The scaled potential y x) as a function of the scaled distance kx across an ion-penetrahle surface charge layer of the scaled thickness Kcl for several values of kcI kcI = 0.5, 1, and 2) at NIn = 5, Z= — 1, and z = 1. The vertical dotted line stands for the position of the surface of the particle core for the respective cases. The dashed curve corresponds to the hntiting case of Kd —> oo. From Ref [4]. 

Potential Distribution Across a Surface Charge Layer... 

Thick Surface Charge Layer and Donnan Potential... 

The potential distribution outside the surface charge layer of a soft particle with surface potential j/g is the same as the potential distribution around a hard particle with a surface potential xj/g. The asymptotic behavior of the potential distribution around a soft particle and that for a hard particle are the same provided they have the same surface potential xj/o- The effective surface potential is an important quantity that determines the asymptotic behaviors of the electrostatic interaction between soft particles (see Chapter 15). 

For a plate with scaled surface potential xj/ in a symmetrical electrolyte of valence z, the asymptotic form of the potential outside the surface charge layer is derived from Eq. (4.31), namely,... 

Next we consider the case where the hxed charges in the surface charge layer are due to dissociation of dissociable groups AH in a solution containing ions of... 

The total change in the free energy density in the surface charge layer at position X and the surrounding solution is thus given by... 

FIGURE 15.2 Interaction between two parallel soft plates 1 and 2 at separation h and the potential distribution i/r(x) across plates 1 and 2, which are covered with surface charge layers of thicknesses d and d2, respectively. 

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. 

It is seen that for thick surface charge layers, P h), Vpi(/i), and Vsp(H) are always positive when Z and are of like sign while Vpi(/i) and Vsp(H) are always negative when Z and Z are of unlike sign... 

As in the case of two interacting soft plates, when the thicknesses of the surface charge layers on soft spheres 1 and 2 are very large compared with the Debye length 1/k, the potential deep inside the surface charge layer is practically equal to the Donnan potential (Eqs. (15.51) and (15.52)), independent of the particle separation H. In contrast to the usual electrostatic interaction models assuming constant surface potential or constant surface... 

We treat the case in which the number density of molecules within the surface layer is negligibly small compared to that in the particle core. The van der Walls interaction energy is dominated by the interaction between the particle cores, while the contribution from the surface charge layer can be neglected. Thus, we have (from Eq. (19.31))... 

Note that we have considered only the region H>Q, in which the surface charge layers of the interacting soft spheres are not in contact. We have to consider other interactions after contact of the surface layers, as discussed in the previous chapter. 

FIGURE 21.4 Schematic representation of a channel of two parallel similar plates 1 and 2 at separation h covered hy ion-penetrable surface charge layers of thickness d under the influence of an electric field E and a pressure gradient P and potential distribution. 

We assume that charged groups of valence Z are distributed in the surface charge layers at a uniform density N. Since end effects are neglected, the fluid velocity is in the y-direction, depending only on x, and the present system can be considered to be at thermodynamic equilibrium with respect to the x-direction. We define m(x) as the fluid velocity in the y-drrection and Pei(- ) as the volume charge density of electrolyte ions, both independent of y. 

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