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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.1 Overvoltage μ is the change in electrode potential caused by the passage of current.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.2 Signs. This diagram conforms to the definitions of cell voltage (its sign matches that read by the voltmeter), cell current (I is positive when WE is anodic), and electrode potential (in aqueous solution only, E = ΔE + E RE(versus SHE) ; otherwise specify RE).

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.3 The four quadrants. In this example the two axes correspond to zero current density and to the cell voltage having its null value.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.4 The coordinate ℓ is in the direction of current flow. Equipotential surfaces, of which three are shown in cross section, are orthogonal (at right angles) to the coordinate and have areas A (ℓ).

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.5 In the case of a trough cell, the cross-sections of the trough, through which the current flows, are of constant area A.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.6 Small hemispherical and disk working electrodes shown in cross section. A typical equipotential surface is shown in red.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.7 Kinetic polarization depicted as a graph showing the current density associated with η kin for two values of the transfer coefficient. The shape of the green curve is that of a hyperbolic sine 1014 : i = 2i n sinh{Fη kin /2RT}

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.8 Illustrating how the transport laws, T, by providing linkage between the surface concentration and the surface flux density of each electroactive species, thereby interrelate the current density i to the transport overvoltage η trans. The letters N and F respectively represent the roles played by Nernst’s and Faraday’s laws.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.9 Current-voltage curve arising from transport polarization. If other polarizations are present, the wave becomes less steep, but the limiting-current plateaus are unaltered.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.10 Each curve corresponds to a single polarization of the working electrode for the reaction R(soln) ⇄ e – + O(soln) or O(soln) + e – ⇄ R(soln).

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.11 When an electrode is polarized by the joint action of ohmic, kinetic, and transport polarizations, there are several routes by which the current density i influences the overall overvoltage. Ohm’s law O, Faraday’s law F, transport laws T, and the Butler- Volmer equation BV, are all involved.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.12 In the black polarization curves the sole cause of overvoltage is transport polarization, with limiting currents at 6.75 and -2.89 A m –2. The other curves represent the addition of kinetic polarization (upper graph) or ohmic polarization (lower graph). Equation 10:30 was used with the following data: c b R = 0.7 mM; c b O = 0.3 mM; α = 0.6; T= T°; m R = m O = 10 –4 m s –1. In the upper graph R cell = 0; k°΄ = ∞, 100, 31, 10, 3, 1 μm s –1. In the lower graph k °΄ = ∞; A = 10 –9 m 2 ; R cell = 0, 10, 25, 50, 100, 150, 250 MΩ.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.13 The five polarizations associated with a two-electrode cell. Kinetic polarizations occur at the electrode junctions; transport polarizations arises in the narrow transport layers adjacent to the electrodes; the source of ohmic polarization is the entire ionic conductor.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.14 Division of the reference electrode into two portions, the larger now being named the counter electrode, is the principle behind three-electrode cells.

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Electrochemical Science and Technology: Fundamentals and Applications, Keith B. Oldham, Jan C. Myland and Alan M. Bond. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. Figure 10.15 A three-electrode cell, incorporating a Luggin capilliary, is controlled by the potentiostat shown as a grey box. The box reveals the features, but not the internal circuitry, of the potentiostat. The pink dashed lines represent virtual connections; that is, they join points of equal potential but prohibit current flow.

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