Electro-neutrality approximation

We shall begin with a recapitulation of the conditions under which the local electro-neutrality approximation is expected to hold or, at least, to be consistent. Furthermore, we shall postulate using intuitive arguments the conditions of conjugation for the locally electro-neutral transport variables at the surfaces of discontinuity of N(x). (Some asymptotic justification for these conditions will be provided in the next chapter.)... 

In this section we shall consider the simplest model problem for the locally electro-neutral stationary concentration polarization at an ideally permselective uniform interface. The main features of CP will be traced through this example, including the breakdown of the local electro-neutrality approximation. Furthermore, we shall apply the scheme of 4.2 to investigate the effect of CP upon the counterion selectivity of an ion-exchange membrane in a way that is typical of many membrane studies. Finally, at the end of this section we shall consider briefly CP at an electrically inhomogeneous interface (the case relevant for many synthetic membranes). It will be shown that the concentration and the electric potential fields, developing in the course of CP at such an interface, are incompatible with mechanical equilibrium in the liquid electrolyte, that is, a convection (electroconvection) is bound to arise. 

In order for the local electro-neutrality approximation to be consistent in the vicinity of the interface the following inequality must hold... 

In parallel, the simplicity of handling the locally electro-neutral case provides a convenient ground for studying the far less tractable one-dimensional version of the nonreduced system (4.1.1)-(4.1.2), asymptotically for small e. For an example of such a study we refer to [14] where the difficult question of multiplicity of steady solutions of the nonreduced system was approached through studying the multiplicity of solutions in the LEN approximation for a four layer (quadrupolar) arrangement. The theory of a bistable electronic device (thyristor) which resulted from this study will be presented in 4.3. 

For the film thickness, as a first approximation, one can take that Lf = K. Another simplifying assumption is that the viscosity changes abruptly at the boundary between the film and the solution. Estimation of the viscosity of the film as a function of potential is very difficult, since electro-neutrality is not maintained in the diffuse double layer, and it is difficult to take into account the influence of the electric field in the double layer on the viscosity of the film. Instead, the viscosity of the film, tjf, can be taken as a parameter, to fit the theoretical curve to the experimental results. To do this one substracts from the observed frequency shift the contribution of the mass effect caused by electrostatic adsorption of ions [Eq. (56)]. 

The DH model (eqs 8.45 and 8.46), can also be derived from statistical mechanics as the solution of the mean spherical approximation (MSA) for an electro-neutral mixture of point ions in a continuum solvent i.e. it is an example of a MM-level model). It represents a limiting behaviour of electrolyte solutions and breaks down quickly for concentrations higher than 0.01 mol dm the extended DH model is accurate to a 0.1 mol dm . For more concentrated solutions, it is natural to consider replacing the point ions with finite-size ions this leads to the consideration of so-called primitive models (PMs), which are MM models consisting of an electro-neutral mixture of charged hard spheres in a continuum solvent. The simplest PM is the restricted primitive model (RPM) consisting of an equimolar mixture of equal-diameter charged hard spheres in a dielectic continuum i.e. p+=p = pj2, <7+ = <7 = a). 

However, even if a consideration of the macroscopic properties of the SSE many times is useful as a first approximation for predicting the outcome of an unknown electro-organic reaction, it must be borne in mind that the composition of the electrolyte at the electrode surface and its immediate vicinity might be completely different from that of the bulk of the solution. Current theory 19>79 assumes that the electrode surface is covered by an adsorbed layer of ions and neutral molecules during electrolysis. The thickness of this layer, the electrical... 

Photo-" and especially electro-chemical pinacolizations of aromatic systems are well established routes to 1,2-diols. Furthermore, stereoselective pinacol formation is possible via both routes through control of the reaction media. For example, photopinacolization requires the use of an external hydrogen donor, usually a secondary alcohol or an amine, and stereoselection can be influenced through changes in these hydrogen donors. Thus under neutral conditions approximately 1 1 ( ) meso mixtures are... 

Figure 8.13 Schematic of a electrochromatographic installation and the representation of a small part of the packed capillary. The different attempts to separate a mixture of neutral compounds by varying the voltage, verifies to a first approximation, the relation existing between voltage and velocity of electro-osmotic flow.

In addition to showing high electrical conductivity, polypyrrole films can be repeatedly electro-chemically driven or switched between the blue-black conducting (100ohm cm ) oxidized form and a yellow nonconducting neutral. The switching rate for thin films is approximately 1 per second. 

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