Weak-field Debye-Hiickel solution

While no exact analytical solution to Eq. [292] is available, approximate nonlinear expressions corresponding to the PGC and NLDH solutions as well as the weak-field Debye-Hiickel solution are given below. 

Incomplete Dissociation into Free Ions. As is well known, there are many substances which behave as a strong electrolyte when dissolved in one solvent, but as a weak electrolyte when dissolved in another solvent. In any solvent the Debye-IIiickel-Onsager theory predicts how the ions of a solute should behave in an applied electric field, if the solute is completely dissociated into free ions. When we wish to survey the electrical conductivity of those solutes which (in certain solvents) behave as weak electrolytes, we have to ask, in each case, the question posed in Sec. 20 in this solution is it true that, at any moment, every ion responds to the applied electric field in the way predicted by the Debye-Hiickel theory, or does a certain fraction of the solute fail to respond to the field in this way In cases where it is true that, at any moment, a certain fraction of the solute fails to contribute to the conductivity, we have to ask the further question is this failure due to the presence of short-range forces of attraction, or can it be due merely to the presence of strong electrostatic forces ... 

The purpose of this chapter is to get a better insight of the first problem listed above, i.e., the polarization of interfaces (colloidal particles) during their interaction. Because of tutorial reasons, the electrolyte solution will be described using a rather simple, mean field approximation, that, however, allows to obtain an analytical solution of the problem. It is clear that this elaboration can easily be followed, and one can extend our model on more advanced situations. This model is identical with so-called weak-coupling theory for point ions treated in a course of the Debye-Hiickel approximation. Before going to make an elaboration for two interacting macrobodies immersed into an electrolyte solution, we would like to introduce a method, which is usually used to model this polarization, and to compute the electrical field next to a polarized medium. Then we will also discuss consequences of the polarization for the ion distribution at the particle-solution interface. 

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