Formal Treatment of Electrochemical Internal Reactions

If local point defect equilibrium prevails and space charge effects can be neglected, one finds from the condition of electroneutrality that 

Equation (9.26) can be rewritten by defining q cv = (c0)2 and ch ce = (c°)2 from the Frenkel and electron-hole product relations as 

The steady state condition of the polarized cell provides two kinetic equations /i(= -j ) = 0 and I/F = j° = 1 /F- Zk jk- From the first condition, one derives immediately 

Equation (9.30), in combination with Eqn. (9.28), describes the charge transport in the polarized Pt/AgBr/Ag cell if no internal reactions occur. Limiting cases can be solved analytically. If, for example, c° c° and q=q, = c°, it follows that /°= -Dh-(Ach/Aif). In combination with the equilibrium conditions at the two electrodes which require that A p between the two electrodes is At/= (A/ih/F) = (RT/F) In ch/ch (A 4), one obtains 

If the anodic potential of the polarized electrode is now increased until a (h -Ag ) junction zone is formed in the interior of the electrolyte, AgBr will decompose internally provided the nucleation barrier can be overcome. This is shown 

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