Models for Porous Electrodes - de Levie

 

 

 

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Interest in fuel cells and supercapacitors has lead to renewed attention to porous electrodes.

The de Levie Model

One of the first treatments of a porous electrode was by de Levie in the late 60's (Ref 1). He assumed cylindrical pores in a metallic electrode. The solution in the pores is assumed to be homogeneous so that its conductivity does not depend on the distance down the pore. 

Transmission line model of the de Levie impedanceThe figure to the left shows a schematic for a transmission line model of the de Levie impedance. The electrolyte resistance through the pore is Ro ohm/cm and the interfacial impedance is ZIF ohm-cm2. For a small length of the pore, dx, the electrolyte resistance, dR, and interfacial impedance, dZ are given by the equations, below.  The radius of the pore is r cm, and the resistivity of the electrolyte is rho ohm-cm. Zo is the impedance at the pore wall-electrolyte interface for a unit length of pore.

equations for dR and dZ

de Levie equation for Zporede Levie showed that the impedance of a single pore of length l had an impedance given by ZPORE. This equation holds for any type of interfacial impedance as long as the interfacial impedance does not depend upon the position in the pore.

Note !The astute observer will note that if the interfacial impedance, Zo, is simply the double-layer capacitance, then Zo=1/jomegaC. Substituting into the equation for ZPORE, above, gives an equation of the same form as that for the T element!

If all of the n pores in an electrode are identical (radius r and length l) the equation for ZPORE can be used to obtain the total experimental electrode impedance if the interfacial impedance ( ZIF ) is known (Ref 2).

Impedance of a porous electrode

Barcia, et. al.( Ref 2 ) applied this equation to the cast iron corrosion in water and copper dissolution in HCl. In both cases, fairly complicated models were used for ZIF.  They also point out that, although the pores are not all of uniform radius and depth, average radii and depth can be extracted from the EIS data.

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REFERENCES
(1) R De Levie, Adv. Electrochem. Electrochem. Eng., 6 (1967) 329.
(2) "Application of the impedance model of de Levie for the characterization of porous electrodes", OE Barcia, E D'Elia, I Frateur, OR Mattos, N Pebere, B Tribollet, Electrochimica Acta, 47 (2002), 2109. doi:10.1016/S0013-4686(02)00081-6
 

 

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