Electrical double layer Debye-Hiickel approximation

For studying the stability of colloidal particles in suspension (Chapter 13) or for determining the potential at the surface of particles (Chapter 12), one often needs expressions for potential distributions around small particles that have curved surfaces. Solving the Poisson-Boltzmann equation for curved geometries is not a simple matter, and one often needs elaborate numerical methods. The linearized Poisson-Boltzmann equation (i.e., the Poisson-Boltzmann equation in the Debye-Hiickel approximation) can, however, be solved for spherical electrical double layers relatively easily (see Section 12.3a), and one obtains, in place of Equation (37),... 

Even allowing for the fact that the Debye-Hiickel approximation applies only for low potentials, the above analysis reveals some features of the electrical double layer that are general and of great importance as far as stability with respect to coagulation of dispersions and electrokinetic phenomena are concerned. In summary, three specific items might be noted ... 

Figure 1.4 shows y(x) for several values of yo calculated from Eq. (1.37) in comparison with the Debye-Hlickel linearized solution (Eq. (1.25)). It is seen that the Debye-Hiickel approximation is good for low potentials (lyol< 1). As seen from Eqs. (1.25) and (1.37), the potential i//(x) across the electrical double layer varies nearly... 

The Debye-Hiickel assumption, discussed earlier in this chapter, is often used when we make simplifications - approximations in the theory of the electrical double layer as many equations are largely simplified if we use this assumption. This approximation means that the surface potential should be much lower than 25 mV. The surface potential can, however, in reality for colloidal systems of practical interest be much higher (see also Figure 10.22). 

In the earlier section, we have assumed constant potential distribution of electric potential inside the electric double layer for the estimation of EO velocity. Let us use the Debye-Hiickel approximation for potential distribution as... 

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