Colloids Huckel equation

A major remaining problem is that many systems of interest in colloid chemistry do not correspond to either of these two limiting cases. The situation is summarized in Figure 12.4, which maps the particle radii Rs and 1 1 electrolyte concentrations that correspond to various kRs values. Clearly, there is a significant domain of particle size and/or electrolyte concentration for which neither the Huckel nor the Helmholtz-Smoluchowski equations can be used to evaluate f from experimental mobility values. The relationship between f and u for intermediate values of kRs is the topic of the following section. 

Electrophoresis of nonconducting colloidal particles has been reviewed in this chapter. One important parameter determining the electrophoretic velocity of a particle is the ratio of the double layer thickness to the particle dimension. This leads to Smoluchowski s equation and Huckel s prediction for the particle mobility at the two extrema of the ratio when deformation of the double layer is negligible. Distortion of the ion cloud arising from application of the external electric field becomes significant for high zeta potential. An opposite electric field is therefore induced in the deformed double layer so as to retard the particle s migration. 

To make headway with the colloidal problem, the Poisson-Boltzmann equation must be solved in spherical coordinates. -> Debye and -> Huckel [iv] introduced the following approximation into the spherical case,... 

Attempts to improve the theory by solving the Poisson-Boltzmann equation present other difficulties first pointed out by Onsager (1933) one consequence of this is that the pair distribution functions g (r) and g (r) calculated for unsymmetrically charged electrolytes (e.g., LaCl or CaCl2) are not equal as they should be from their definitions. Recently Outhwaite (1975) and others have devised modifications to the Poisson-Boltzmann equation which make the equations self-consistent and more accurate, but the labor involved in solving them and their restriction to the primitive model electrolyte are drawbacks to the formulation of a comprehensive theory along these lines. The Poisson-Boltzmann equation, however, has found wide applicability in the theory of polyelectrolytes, colloids, and the electrical double-layer. Mou (1981) has derived a Debye-Huckel-like theory for a system of ions and point dipoles the results are similar but for the presence of a... 

The equation for the electrostatic repulsion that we see in Figure 10.18 and Equation 10.4 is valid for monodisperse spherical colloidal particles when the so-called Debye-Huckel approximation is fulfilled and when kR< 5. The Debye-Huckel approximation can be expressed as ... 

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