MIT10_626S11_lec20

# MIT10_626S11_lec20 - IV Transport Phenomena Lecture 20...

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IV. Transport Phenomena Lecture 20: Warburg Impedance Notes by ChangHoon Lim 1. Warburg impedance for semi-infinite oscillating diffusion Warburg (Ann. Physik. 1899) is credited with the first solution to the diffusion equation with oscillating concentration at the boundary, which is related to the diffusional (or mass transfer) impedance of electrochemical systems. An interesting point made in the first part of the class is that the very same mathematical model and impedance formula also holds for capacitive charging of a porous electrode with constant electrolyte concentration (i.e. no diffusion) modeled by an RC transmission line, and this effect is often mistaken for diffusional impedance. We start by linearizing the equations for transport and electrochemical reactions to describe the response to a small oscillating voltage. Suppose equation, ) and for linear response (e.g. Nernst Also, assume quasi-equilibrium reactions at x=0 and linear diffusion. Alternating current: Therefore, Hence, ( as ) Thus, impedance is ,

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x 0 L x 0 L Now, C=C 0 is imposed on x=L , not at the infinity. At low frequency ( ), FLW acts like a resistor. This situation is depicted in above figure. Solve
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MIT10_626S11_lec20 - IV Transport Phenomena Lecture 20...

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