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Fig. 1. Schematic representation of the inner region (0<x<L) ofa porous electrode consisting in a porous metal oxide film deposited on a conducting substrate. The equivalent circuit model (discussed in the text) represents a continuous branching; in the resistive transport channel r, is the resistance of the metal oxide per unit length, while the resistance of the electrolyte in the pore is neglected and the line is short circuited in the lower channel. As similar model holds if, conversely, the resistivity of the pore channels is more significant than that of the metal oxide. Elements r; and q; in the internal surface are: charge-transfer resistance, and a CPE for double-layer polarization. R, is the resistance of the bulk electrolyte. To apply the impedance model the actual geometry of the electrode need not be as regular as depicted in the scheme, but it is required that each phase be continu- ously connected along the whole electrode length L. The following relationship holds between these frequencies:

Figure 1 Schematic representation of the inner region (0<x<L) ofa porous electrode consisting in a porous metal oxide film deposited on a conducting substrate. The equivalent circuit model (discussed in the text) represents a continuous branching; in the resistive transport channel r, is the resistance of the metal oxide per unit length, while the resistance of the electrolyte in the pore is neglected and the line is short circuited in the lower channel. As similar model holds if, conversely, the resistivity of the pore channels is more significant than that of the metal oxide. Elements r; and q; in the internal surface are: charge-transfer resistance, and a CPE for double-layer polarization. R, is the resistance of the bulk electrolyte. To apply the impedance model the actual geometry of the electrode need not be as regular as depicted in the scheme, but it is required that each phase be continu- ously connected along the whole electrode length L. The following relationship holds between these frequencies:

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Fig. 2. Complex plane representation of the impedance (Z = Z'+ iZ") of the porous electrode model discussed in the text, and shown in Fig. 1. (a) R300. (b) R3 > R,. (c) R; > R3. The marked points correspond to frequencies f= a, (@) and f=«@,/2n (Ml).
Fig. 2. Complex plane representation of the impedance (Z = Z'+ iZ") of the porous electrode model discussed in the text, and shown in Fig. 1. (a) R300. (b) R3 > R,. (c) R; > R3. The marked points correspond to frequencies f= a, (@) and f=«@,/2n (Ml).
Fig. 3. Complex plane plots of the theoretical impedance with con- stant R, =1 Q, Q;=10 mF s’~! and £ =9, and varying R;. Curves 1-8: R, = 104, 100, 50, 10, 5, 1, 0.5 and 0.1 Q. The behaviour of the dc resistance Ry. is another interesting aspect of this proposed experiment in which R, would decrease exponentially with the potential while R, and C, would remain constant. From Eqs. (14) and (15), one may infer that Rj, would vary initially with the potential with the same exponent as R; (for R, « R;), but as R; decreased, a crossover would occur (at R, x R;) to a variation of Ry, with half the exponent of R, (for R,; > R;). This result is reminiscen of a well-known aspect of the theory of current—poten ial curves in porous electrodes. In that theory, it is shown that if the Tafel slope is b at low voltage then i becomes 2b at high voltage [24-26]. The doubling o he Tafel slope is related to the fact that at higher potentials the distributed ohmic drop becomes signifi- cant and the potential cannot penetrate the whole electrode length, or in other words, the electrode be- haves as semi-infinite at the higher potentials [24].
Fig. 3. Complex plane plots of the theoretical impedance with con- stant R, =1 Q, Q;=10 mF s’~! and £ =9, and varying R;. Curves 1-8: R, = 104, 100, 50, 10, 5, 1, 0.5 and 0.1 Q. The behaviour of the dc resistance Ry. is another interesting aspect of this proposed experiment in which R, would decrease exponentially with the potential while R, and C, would remain constant. From Eqs. (14) and (15), one may infer that Rj, would vary initially with the potential with the same exponent as R; (for R, « R;), but as R; decreased, a crossover would occur (at R, x R;) to a variation of Ry, with half the exponent of R, (for R,; > R;). This result is reminiscen of a well-known aspect of the theory of current—poten ial curves in porous electrodes. In that theory, it is shown that if the Tafel slope is b at low voltage then i becomes 2b at high voltage [24-26]. The doubling o he Tafel slope is related to the fact that at higher potentials the distributed ohmic drop becomes signifi- cant and the potential cannot penetrate the whole electrode length, or in other words, the electrode be- haves as semi-infinite at the higher potentials [24].
Fig. 4. Voltammetric curves of (a) Ti/IrO, and (b) Ti/IrO,—Nb,0; (20:80 mol%) electrodes registered at 100 mV s~! in a 1.0 mol dm~? HCIO, solution.
Fig. 4. Voltammetric curves of (a) Ti/IrO, and (b) Ti/IrO,—Nb,0; (20:80 mol%) electrodes registered at 100 mV s~! in a 1.0 mol dm~? HCIO, solution.
Fig. 5. Complex plane representation of the impedance of the Ti/IrO, electrode. (a) Experimental data at different potentials, the inset shows the region near the origin. Fitting of the data recorded at (b) 0.75 V, (c) 1.30 V, and (d) 1.40 V. Fig. 5b—d shows the fitting of several spectra of the Ti/IrO, electrode to Eq. (9). These spectra were selected to illustrate the three cases discussed in Section 2. In Fig. 5b the low-frequency part shows a straight line with inclination close to 90° while the complex plane plots shown in Fig. 5c and d have the arc-shaped
Fig. 5. Complex plane representation of the impedance of the Ti/IrO, electrode. (a) Experimental data at different potentials, the inset shows the region near the origin. Fitting of the data recorded at (b) 0.75 V, (c) 1.30 V, and (d) 1.40 V. Fig. 5b—d shows the fitting of several spectra of the Ti/IrO, electrode to Eq. (9). These spectra were selected to illustrate the three cases discussed in Section 2. In Fig. 5b the low-frequency part shows a straight line with inclination close to 90° while the complex plane plots shown in Fig. 5c and d have the arc-shaped
Fig. 6. Complex plane representation of the impedance of the Ti/ IrO,—Nb,O; (20:80 mol%) electrode. (a) Experimental data at differ- ent potentials, the inset shows the region near the origin. Fitting of the data recorded at (b) 1.30 V and (c) 1.40 V.
Fig. 6. Complex plane representation of the impedance of the Ti/ IrO,—Nb,O; (20:80 mol%) electrode. (a) Experimental data at differ- ent potentials, the inset shows the region near the origin. Fitting of the data recorded at (b) 1.30 V and (c) 1.40 V.
Fig. 8. Impedance parameters of Ti/IrO, electrode as a function of the applied potential for the oer in an acidic medium.
Fig. 8. Impedance parameters of Ti/IrO, electrode as a function of the applied potential for the oer in an acidic medium.
Fig. 9. Impedance parameters of Ti/IrO,-Nb,0,; (20-80 mol%) electrode as a function of the applied potential for the oer in an acidic medium.
Fig. 9. Impedance parameters of Ti/IrO,-Nb,0,; (20-80 mol%) electrode as a function of the applied potential for the oer in an acidic medium.
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