Debye-HOckel approximation

Figure 3.12. Charge in a spherical diffuse double layer. Electrolyte (1-1), 10 M. Temperature 25°C. The particle radius a is given. Dashed curves Debye-HOckel approximation.

The first attempt in this direction dates back to the Just-mentioned Smolu-chowski theorem. For the development of electrophoresis theory a very important contribution was made by Henryk) who systematically studied the distortion of the field by spherical and cylindrical particles. It depends on the size and shape of the particle, and on K /K as illustrated in fig. 3.84. The electrophoretic friction that is created also depends on x. For this type of theory a double layer picture is needed, but because of mathematical difficulties Henry had to limit himself to the linearized (Debye-HOckel) approximation. As a consequence, Henry s results are only valid for low Notwithstanding this... 

For spherical symmetry the Polsson-Boltzmann equation cannot be solved analytically, but numerical solutions are nowadays available. Analytical solutions exist for low potentials, that is In the Debye-HOckel (DH) approximation, already encountered in the treatment of the ionic atmosphere around Ions, sec. 1.5.2a. As compared with flat double layers, the low-potential approximation tends to become better, the smaller the particle is. The reason is that, because of the stronger divergence of the lines of force, the potential decays more rapidly a relatively larger fraction of the countercharge is therefore found in the region of low potentials. 

Let us specify the different hypotheses laid out by the Debye-HOckel model and the subsequent approximations which help one develop a means of expressing the activity coefficient of various ions in an electrolyte. Nearly all the assumptions, expressed below, are based on the fact that this theory is developed for dilute solutions ... 

Illustrating the difference between the approximation of Debye and HOckel and the theory of MtlLLER for spherical particles, xa = 0.2 = z— = z... 

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See also in sourсe #XX -- [ ]

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