Assume that the current-potential curves of a system are given by Eqs. (10.17) and (10.20). Calculate...

 

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Assume that the current-potential curves of a system are given by Eqs. (10.17) and (10.20). Calculate the effective transfer coefficients defined by: α = KT In ja eo Ən kT In jel eo θη References 115 Their values depend on the overpotential. Show that for n = 0: a + ß ‡ 1. This (small) error arises because the Fermi-Dirac distribution has been replaced by a step function. A good approximation to the current-potential curve is obtained by re- placing the Fermi-Dirac distribution with a step function: which results in: (10.17) where A kox = Aerfc- 2ħ A-con (4XkT)¹/2 erfe(a) = exp(-y²) dy = 1 – erf(x) = 1 //*exp(-y²) dy is the compliment of the error function erf(x). Equation (10.17) is a good. approximation in the region con»kT. In particular we obtain at very large overpotentials a limiting rate: = I = A- for con >>> X 2ħ' which is independent of the applied potential. The corresponding expressions for the reduction are: 1/2 Kred = A (KT) ¹/² exp(-1+2) kred Aerfc (4XKT)1/2 for leon <A for leon » KT (10.18) (10.19) (10.20) Assume that the current-potential curves of a system are given by Eqs. (10.17) and (10.20). Calculate the effective transfer coefficients defined by: α = KT In ja eo Ən kT In jel eo θη References 115 Their values depend on the overpotential. Show that for n = 0: a + ß ‡ 1. This (small) error arises because the Fermi-Dirac distribution has been replaced by a step function. A good approximation to the current-potential curve is obtained by re- placing the Fermi-Dirac distribution with a step function: which results in: (10.17) where A kox = Aerfc- 2ħ A-con (4XkT)¹/2 erfe(a) = exp(-y²) dy = 1 – erf(x) = 1 //*exp(-y²) dy is the compliment of the error function erf(x). Equation (10.17) is a good. approximation in the region con»kT. In particular we obtain at very large overpotentials a limiting rate: = I = A- for con >>> X 2ħ' which is independent of the applied potential. The corresponding expressions for the reduction are: 1/2 Kred = A (KT) ¹/² exp(-1+2) kred Aerfc (4XKT)1/2 for leon <A for leon » KT (10.18) (10.19) (10.20)

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The effective transfer coefficients and are defined as kTe ln j kTe lnj where j is the current d... View the full answer