MIT10_626S11_lec27b

# MIT10_626S11_lec27b - V Electrostatics Lecture 27b Diffuse...

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V. Electrostatics Lecture 27b: Diffuse charge in membranes MIT Student In last lecture we discussed the effect of diffuse charge on Faradaic reaction kinetics at an electrolyte/electrode interface. Today, we start to study diffuse charge effect on membrane/electrode interface. 1. Basic Physics Membrane allows transport of ions but not of electrons. In membrane, only one type of ion is mobile with the other type of ions fixed as a background charge, e.g., C_. The background charge ensures a high conductivity (or low resistance) carried mostly by a mobile counterions, e.g. C+(x). Let’s consider a cation exchange membrane Nafion as an example, protons will hop through very small pores in the polymer membrane, with positive transference number t+=1 and negative transference number t_=0. [Transference number denotes the fraction of current carried by a certain type of ion]. The resistance of the membrane is small, and can be treated as a constant Rm. 2. Current –Voltage Relation First we discuss two limiting cases for membrane-electrode assembly with Frumkin-Butler- Volmer kinetics and stern boundary conditions. Fig. 1 Membrane-electrode assembly

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Lecture 28 10.626 Electrochemical Energy Systems (2010) Bazant If (Helmholtz limit), we will recover traditional Butler-Volmer kinetics without diffuse charge effect. For example, if symmetry factor is taken to be 1/2, and assume only one active cation participate in the reaction (n=1), then voltage can be expressed as
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MIT10_626S11_lec27b - V Electrostatics Lecture 27b Diffuse...

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