Conductivity ambipolar

From the theory of ambipolar conduction (see, e.g., Ref.56) it follows immediately that given an oxygen potential difference A/i0 between the lhs (u(]) and the right-hand side, an oxygen flux which is of the form... 

As the oxygen partial pressure ratio, and hence A/u0, is known, the ambipolar conductivity is readily determined from the flux. This knowledge can be further used to calculate the partial conductivities, and by knowing Ef from the transient (i.e., by also evaluating the delay time231) to derive the thermodynamic factor (i.e., the chemical capacitance). 

The physical meaning of the ambipolar conductivity relates to the correlated transport of several charge carriers, when an internal -> electrical field in the system impedes the migration of species with a higher - mobility, but enhances transfer of less mobile species. 

The phenomenon of ambipolar conduction is not limited to chemical potential gradients only, and may occur in systems with several driving forces (e.g., chemical-potential and temperature gradients in combination with external electrical field). However, this phenomenon is always related to conjugate transport of several charge carriers. 

The quantity of ambipolar conductivity is widely used for the analysis of -> electrolytic permeability of -> solid electrolytes, caused by the presence of electronic conductivity. Other important cases include transient behavior of electrochemical cells and ion-conducting solids, dense ceramic membranes for gas separation, reduction/ oxidation of metals, and kinetic demixing phenomena [iv]. In most practical cases, however, the ambipo-... 

See also - ambipolar conductivity, -> diffusion determination in solids, - Wagner factor, - insertion electrodes, -> batteries. 

The equilibrium conditions in electrochemical systems are usually expressed in terms of electrochemical potentials. For non-equilibrium systems, the gradient of chemical and/or electrochemical potential is a driving force for flux of particles i. See also Wagner equation, - Wagner factor and ambipolar conductivity, -+ On-sager relations. 

Similar approaches are used for most steady-state measurement techniques developed for mixed ionic-electronic conductors (see -> conductors and -> conducting solids). These include the measurements of concentration-cell - electromotive force, experiments with ion- or electron-blocking electrodes, determination of - electrolytic permeability, and various combined techniques [ii-vii]. In all cases, the results may be affected by electrode polarization this influence should be avoided optimizing experimental procedures and/or taken into account via appropriate modeling. See also -> Wagner equation, -> Hebb-Wagner method, and -> ambipolar conductivity. 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

Electrolytic permeability — of ion-conducting - solid materials is the transport of neutral potentialdetermining component(s) under a -> chemical potential gradient due to the presence of bulk electronic conductivity in the material, or a parameter describing this transport. As the flux of ions is charge-compensated by a simultaneous flux of electronic charge carriers, -> steady-state permeation can be achieved without external circuitry. The transport processes can be quantitatively described in terms of -> ambipolar conductivity. 

The overall permeation rate of a material is determined by both ambipolar conductivity in the bulk and interfacial exchange kinetics. For -> solid electrolytes where the electron - transference numbers are low (see -> electrolytic domain), the ambipolar diffusion and permeability are often limited by electronic transport. 

Concepts of local equilibrium and charged particle motion under - electrochemical potential gradients, and the description of high-temperature -> corrosion processes, - ambipolar conductivity, and diffusion-controlled reactions (see also -> chemical potential, -> Wagner equation, -> Wagner factor, and - Wagner enhancement factor). 

The chemical diffusion coefficient includes, as we know from the formal treatment in Section VI..3iv., both an effective ambipolar conductivity and an effective ambipolar concentration. The latter parameter is determined by the thermodynamic factor which is large for the components but close to unity for the defects. 

TqVjUo (with crs =aeonalon/cr being the ambipolar conductivity, see Section NlA.ii). Owing to its constancy the flux can be recast as (1/L) Jaod o r lus die growth rate measured by the thickness... 

Fig. 7.9 Hydrogen flux and ambipolar conductivity at different hydrogen feed pressure from the modeling results...

Fig. 7.10 The ambipolar conductivity as calculated from Eq. 7.26 based on the experimental data of Figs. 7.4 and 7.5...

Fic. 4. Calculated curves of a and Q versus 1 /r. (1) Extended-states transport modulated by potential fluctuations, (2) contribution of hopping conduction near p> (3) presence of thin, highly conducting layer, and (4) contribution of ambipolar conduction. 

This is a good point at which to look a little closer at the ambipolar transport term that we have mentioned eartier in passing. The materials property of interest here is the protonic-electronic ambipolar conductivity term, which can be written in... 

In the case discussed here, where three or more species (e.g.. A, B, C) provide charge transport, it may, as mentioned earlier, be important to keep the pairwise ambipolar conductivities in the correct form, and to be aware of the inequality ... 

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