Diffusion of charged particles

This book treats a selection of topics in electro-diffusion—a nonlinear transport process whose essence is diffusion of charged particles, combined with their migration in a self-consistent electric field. Basic equations of electro-diffusion were formulated about 100 years ago by Nernst and Planck in the ionic context [1]—[3]. Sixty years later Van Roosbroeck applied these equations to treat the transport of holes and electrons in semiconductors [4]. Correspondingly, major applications of the theory of electro-diffusion still lie in the realms of chemical and electrical engineering, related to ion separation and semiconductor device technology. Some aspects of electrodiffusion are relevant for electrophysiology. 

The diffusion of charged particles plays a very important role in solid electrolytes. Sometimes, it can be referred to as the Wagner diffusion mechanism [14], In accordance with the electrostatic laws, the following condition of electronentrality can be fulfilled in any element of the volume of solid state ... 

Figure 4-16. Universal relation between electron temperature, pressure, and discharge tube radius in the non-equilibrium discharge regime controlled by diffusion of charged particles.

Let us now consider a semi-infinite linear diffusion of charged particles from and to the electrode. The Faraday impedance is defined as the sum of the charge-transfer resistance R and the Warburg impedance W corresponding to the semiinfinite diffusion of the charged particles... 

The charge transport equation in an electrolyte with solid or stationary immobilized liquid electrolyte can be derived on the basis of charge balance and assuming steady-state diffusion of charge particles based on ohm s law as... 

We now consider the one-way diffusion of charged particles under the simultaneous action of a gradient of concentration and of an electric field. 

Remark (concerning the samples in form of a plate).- It is noted, in the case of a plate, that due to the fact of neglecting the edge effects, the laws are independent of the direction of development because the interfacial areas constantly remain equal to the initial area. In the case of a separable rate, only two laws are obtained the linear law for any interface step as the rate-determining step and the parabohc law with diffusion as the rate-determining step. Other laws are possible with special diffusions (either by diffusion of charged particles, with thin layers or obstmcted diffusions). We will discuss such laws that are highlighted especially in the case of oxidation of metals in Chapter 15. 

Gaseous ion diffusion A method of charging particles in an electrostatic precipitator. 

In region III, the discharge is maintained only by ionization in the gas phase without electron injection from the cathode. Because of the inertial effect of ions and electrons, only small part of charged particles in the gas phase can arrive on the electrode. Therefore, polymerization may be induced principally by diffused free radicals and/or ion-electron pairs ... 

Considering the track structures as spherical or cylindrical formations and using the methods of diffusion kinetics, it proved to be possible to explain many experimental facts concerning the radiolysis of water solutions, in particular, the dependence of yields on LET.361 It is owing to this that the LET was considered to be a universal qualitative characteristic of radiation, and the concentration of active particles was considered to be in direct dependence on the LET with no regard for the type of charged particle. 

Electrophoresis is the motion of charged particles relative to the electrolyte in response to an applied DC-electric field the field causes a shift in the particle counterion cloud, the counterion-diminished end of the particle attracts other counterions from the bulk fluid, counterions from the displaced cloud diffuse out into the bulk fluid, and the particle migrates. The particle velocity is predicted by the Smoluchowski equation. 

It is evident from the last equation that the effects of the gradient and the electric field can be either additive or subtractive, because each term on the right-hand side can be of either sign. In fact, a flow of charged particles produced by a chemical potential difference across a diffusion medium can lead to charge flow and the creation of an electric potential which effectively cancels the effects of the chemical potential difference... 

Electrokinetic effects — A number of effects caused by the asymmetric distribution of charged particles in the electrochemical - double layer and subsequent charge separation during relative motion of liquid and solid phase. They can occur when the diffuse double layer is thicker than the hydrodynamic boundary layer. 

Nernst-Planck equation — This equation describes the flux of charged particles by diffusion and electrostatic forces. When the ion with charge ze is distributed at concentration c in the potential, cp, it has a one-dimensional flux of the ion, / = -Ddc/dx - (zF/RT) Dcdcp/dx [i]. This can be derived from the concept that the force caused by the gradient of the electrochemical potential is balanced with frictional force by viscosity, t], of the medium. When a spherical ion with radius ro is in the inner potential, cp, the gradient of the electrochemical potential per ion is given by... 

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