Experimental and Theoretical Voltammograms

The reductive and oxidative peaks shown in Fig. 7.21 are well resolved and the relative magnitude of the oxidative peak and the peak-to-peak separation increases with frequency. The theoretical reverse SWV voltammograms were fitted to the experimental data assuming both BV and MH models. As can be seen, with the Butler-Volmer formalism ( ) excellent fits are obtained between experimental and theoretical SWV curves such that the magnitude and separation of the reduction and... 

Figure 14.3.3 Experimental and theoretical cyclic voltammograms for reduction and reoxidation of 9,10-phenanthrenequinone irreversibly adsorbed on a pyrolytic graphite electrode. Fq = 1.9 X 10 mol/cm i = 50 mV/s in 1 M HCIO4. (—) experimental...

Figure 14.3.4 Experimental and theoretical linear sweep voltammograms for a system where adsorbed O is irreversibly reduced.

A recently identified problem in the kinetic analysis of steady-state IT and ET voltammograms is the lack of the unique fit between the experimental and theoretical curves. 

Fig. 2.14 Square-wave voltammograms for reduction of 1 mM Zn(II) in 1.0 M KNO3. AE = 5 mV, Esw = 25 mV. Experimental (...) and best fitting theoretical (-) currents with / in ascend-...

Normalized potential sweep voltammetry (NPSV) involves a three-dimensional analysis of the LSV wave where the normalized current (I/Ip) is taken as the Z axis, theoretical electrode potential data as the X axis, and experimental electrode potential data as the Y axis, with the potential axes defined relative to Ep/2. The method is illustrated by the voltammogram in Fig. 15. The projection of the wave on to the X—Y plane results in a straight line of unit slope and zero intercept if the theoretical and experimental data describe the same process. In practice, NPSV analysis simply involves the linear correlation of experimental vs. theoretical electrode potentials at particular values of the normalized current. 

Fig. 7.21 Experimental (solid line) and theoretical (points) SWV voltammograms obtained with Butler-Volmer (dotted) and Marcus-Hush (triangle) models. A positive sign corresponds to...

Fig. 7.38 Experimental (solid line) and theoretical (points) square wave voltammograms corresponding to the reduction of [P(W30io)4]3 at a gold microelectrode (rj = 15.1 pm) in the presence of different concentrations of the nitrite anion (indicated on the curves), f = 10 Hz, sw = 25mV, A s = 5mV, 7 = 293 K. Test solutions 0.2 mM [P(W3O10)4]3, 0.1 M in H2S04. Reproduced from [60] with permission...

Figure 16. (a) The SECM current versus distance curve and a steady-state voltammogram (inset) obtained with a 46-nm radius polished Pt electrode. Aqueous solution contained 1 mM FcCH2OH and 0.2 M NaCl. (a) Theoretical approach curve (solid line) for diffusion-controlled positive feedback was calculated from Eq. (19). Symbols are experimental data. The tip approached the unbiased Au film substrate with a 5-nms-1 speed, (b) Experimental (symbols) and theoretical (sold lines) steady-state voltammograms of 1 mM ferrocenemethanol obtained at different separation distances between a 36-nm Pt tip and a Au substrate, d = oo (1), 54 nm (2), 29 nm (3), and 18 nm (4). v = 50 mV s-1. Theoretical curves were calculated from Eq. (22). Adapted with permission from Ref. [51]. Copyright 2006, American Chemical Society. 

Then, to analyze the obtained current, a Fourier transform is applied and the responses at the fundamental, co, and harmonic, 2m, 3m, 4m,..., frequencies are obtained. Next, the current responses at the fundamental and harmonic frequencies are extracted by an inverse Fourier transform. Harmonics up to the eighth order were obtained. Analysis of the kinetic parameters is carried out by comparison of the experimental and simulated data. Theoretical ac voltammograms were simulated using classical numerical simulations of the diffusion-kinetic process using an implicit finite-difference method [658, 659] with a subsequent Fourier analysis of the simulated data. An example of the comparison of the experimental and simulated data is shown in Fig. 15.5. In this case, oxidation of ferrocenmethanol appeared reversible, and a good agreement was found with the simulated data for the reversible process. 

Figure 2,13 Contour maps for relative difference f l j between the fundamental, 4 and 7 AC harmonic components of the experimental FT AC voltammograms obtained using a 3 mm CC electrode for reduction of I mM [Ru(NHj)J in aqueous I M KCI atf=9 (a) and 219 Hz (b) and theoretical data simulated using and k° varied over 0.5-10 SI and 0.1-20 (9 Hz) or l-lOO cm s (219 Hz) ranges, respectively. Other parameters are analogous to those listed in the caption for Figure 2.12.

The case of the UPD of Cu on Au( 111) in the presence of H-iSO has been extensively studied in recent times both experimentally [136, 20, 137, 138, 120, 121, 1, 139, 140, 122] and theoretically [123], We should also mention that two recent studies of the kinetics of this system [141, 142] clearly indicate that in the shape of the voltammogram the first peak can be derived from equilibrium considerations, as was done in our earlier work, while in the second the kinetics is much slower and therefore observable from the analysis of the voltammogram. 

Figure 8.30 Comparison between experimental RDE voltammograms (symbols) and theoretical curves simulated with the indicated kinetic parameters. Tafel plots normalized to the ratio f = [SnLH"]j/[SnLH"](, are shown in the inset.

FIGURE 6.3 Experimental (symbols) and theoretical (solid lines) steady-state voltammograms of ImM FcMeOH obtained at different separation distances between the 36nm Pt tip and An substrate. d= >, 54, 29, and 18 mn from the top to the bottom. Scan rate, 50mV/s. (Reprinted with permission from Sun, P. and Mirkin, M.V., Kinetics of electron-transfer reactions at nanoelectrodes, AwaZ. Chem., 78, 6526-6534, 2006. Copyright 2006 American Chemical Society.)... 

Fig. 4.16 Experimental voltammograms (solid lines) obtained at a 1.5-pm-radius Pt SECM tip at distances of L=0.12, 0.15, 0.20, 0.30, 0.54 and oo from a 1-mm-radius Pt-disk substrate. The solution was 9 mM [FcCimim][N(Tf)2] in [C2mim][N(Tf)2] and the substrate potential was -0.6 V vs. Ag/Ag+. The theoretical voltammograms at each distance (open circles) were calculated using Eq. (4.14) in the text. Reprinted with permission from Taylor, A W Qiu, F L Hu, J P Licence, P Walsh, D A (2008) J. Phys. Chem. B 112 13292-13299. Copyright 2008 American Chemical Society...

From Eq. (68), following a procedure similar to that described for chronoamperograms and voltammograms, theoretical coulovoltagrams were obtained as a function of the variables studied. The results189 can be observed in Fig. 67. Some new effects can be deduced from these experimental curves, which will allow us to provide a complete description of the electrochemistry of conducting polymers. 

The theory for catalytic reaction has been verified by studying the reductions of Ti + in presence of NH2OH and CIO and the reduction of Fe + in presence of NH2OH. In these stndies the mercury electrode has been applied [53]. The properties of the experimental voltammograms confirm the theoretical predic-... 

Fig. 15. A normalized potential sweep voltammogram showing the linear projection of theoretical (X) and experimental (V) electrode potential data onto the X—Y plane.

Figure 5.13 Forward, reverse, and difference current DNP voltammograms of 9.9 pm (2.05 ppm) Pb2+ in 0.5 M CH3COOH/0.5 M CH3 COONa. Conventional NP volt-ammogram is also shown (dotted line) t, = tp = 50 ms ts = 16.67 ms tdday = 0.4 s Edday = -300 mV AE = -25 mV T = 20°C. Solid lines are experimental curves. Dotted line is theoretical response. [From Ref. 42, reprinted with permission.]...

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