16-Redox_6_web - ADVANCED to fully understand POLAROGRAPHY...

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Mass transport: the Nernst-Planck equation The Cottrell Equation Sampled current voltammetry, a reversible wave: Ox + ne <-> Red SHAPE OF THE REVERSIBLE WAVE RC circuit ADVANCED: to fully understand POLAROGRAPHY
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General Statement of Mass Transport to a Planar Electrode Mass transfer to an electrode is governed by the Nernst-Planck equation . For one-dimensional mass transfer of a species i (or j ) along the x -axis: J i ( x ) =- D i C i ( x ) x - z i F RT D i C i ∂φ ( x ) x + C i v ( x ) where is the flux of species i(mol sec -1 cm -2 ) at a distance x from the surface. J i ( x ) D i is the diffusion coefficient ( cm 2 /sec) is the concentration gradient at a distance x , C i ( x )/ x is the potential gradient ∂φ ( x )/ x z i and C i are the charge and concentration of species i, respectively, v(x) is the velocity (cm/sec) with which a volume element in solution moves along the axis. 1 st term (diff) 2 nd term (migr.) 3 rd term (conv.)
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0 ) , ( ) , 0 ( = = x x t x o C o D t o J 1st Fick’s law: where: D O is a diffusion coefficient of the species “O”, in cm 2 /s, usually ca. 10 -5 cm 2 /sec. We are seeking a current vs. time relationship!
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Diffusion Fick’s Laws are Applicable in POLAROGRAPHY
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The Cottrell Experiment Ox + ne Red E 2 = E n
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2 1 * 2 1 ) ( t o C o nFAD t i = The Cottrell equation (the highest current you can get in a stagnant solution)! Predicts: an inverted t 1/2 current-time relationship at t approaching zero, the current goes to infinity current measured is always proportional to the bulk concentration of “Ox”.
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