Steady-state voltammograms

the potential drop displays the demarcation between two different states of the system that are related to transitions from the state with hgand deficiency into the state with hgand excess, or vice versa. Analogous transitions are also possible at the electrode surface in two cases  

In both cases, corresponding (cathodic or anodic) overvoltage increases abruptly in a narrow range of current densities. 

For the systems where the amount of protonated ligand forms is insignificant, the equation defining such pseudo-limiting current (prewave) can be obtained [2]  

If species prevails in the system, it follows from Eq. (4.1) that FD(cl -IVcm) 

It is seen from this equation that i j 0, when Cl (anodic pseudo-limiting currencies) and 0, when (cathodic prewaves). 

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Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

FIG. 19 Dependence of the half-wave potentials for Fc (curve 1) and ZnPor (curve 2) oxidation in benzene on CIO7 concentration in the aqueous phase. In these measurements, half-wave potentials were extracted from reversible steady-state voltammograms obtained at a 25 pm diameter Pt UME. The benzene phase contained 0.25 M tetra-w-hexylammonium perchlorate (THAP) and either 5 mM Fc or 1 mM ZnPor. All potentials were measured with respect to an Ag/AgCl reference electrode in the aqueous phase. (Reprinted from Ref. 48. Copyright 1996 American Chemical Society.)... 

The shape of steady-state voltammograms depends strongly on the geometry of the microhole [13,14], Wilke and Zerihun presented a model to describe diffusion-controlled IT through a microhole [15], In that model, a cylindrical microhole is assumed to be filled with the organic phase, so that a planar liquid-liquid interface is located at the aqueous phase side of the membrane. Assuming that the diffusion is linear inside the cylindrical pore and spherical outside [Fig. 2(a)], the expression for the steady-state IT voltammo-gram is... 

The mathematical formulations of the diffusion problems for a micropippette and metal microdisk electrodes are quite similar when the CT process is governed by essentially spherical diffusion in the outer solution. The voltammograms in this case follow the well-known equation of the reversible steady-state wave [Eq. (2)]. However, the peakshaped, non-steady-state voltammograms are obtained when the overall CT rate is controlled by linear diffusion inside the pipette (Fig. 4) [3]. 

Quinn et al. studied ET at micro-ITIES supported by micropipettes or microholes [16]. The studied systems involved ferri/ferrocyanide redox couple in aqueous phase and ferrocene, dimethylferrocene, or TCNQ in either DCE or o-nitrophenyl octyl ether. Sigmoidal, steady-state voltammograms were obtained for ET at the water-DCE interface supported at a micropipette. The semilogarithmic plot of E versus log[(/(j — /)//] was... 

Figure 3.98 Comparison of a reversible conventional cyclic voltammogram (linear diffusion) and reversible steady-state voltammogram obtained at a single microelectrode disc where mass transport is solely by radial diffusion. Current axis not drawn to scale. From A.M. Bond and H.A.O. Hill, Metal Inns in Biological Systems, 27 (1991) 431. Reprinted by courtesy of Marcel...

Fig. 18b.4. Steady-state voltammograms when initially (a) O is present and (b) both O and R are present.

Explain the conditions under which a steady-state voltammogram is obtained. 

The steady-state voltammogram of PVI-1-coated Cu in 0.1M HClOjj, given in figure 2C, is more complex than that for BTA-coated Cu. On the positive sweep the current becomes anodic at i-45mV (SCE) and as with BTA-coated Cu, the Cu oxidation is inhibited, but to a lesser extent. The initial cathodic currents are enhanced in comparison to bare Cu and BTA-coated Cu, but the limiting oxygen reduction current is close to that for bare Cu. 

The steady-state voltammogram of UDI-coated Cu in the phosphate buffer (figure 5C) is similar to the result in pH=1 solution the curve is indistinguishable from the baseline until approximately -300mV (SCE). In the steady-state a UDI film... 

Fig. 6 Cyclic voltammograms at a 1.6-mm diameter Pt electrode (200 mV and steady state voltammograms at a 25- tm diameter Pt electrode (20 mV s ) for oxidation and reduction of 8.5 x 10 M Mn "(TPP)Cl at 241 K in 1,2-dichloroethane containing 0.1 M TBABF4 in the presence of 0-1.28 M CH3OH. The peak potential separation at 200 mV s for cyclic voltammetric reduction of Mn" (TPP)Cl at 296 K in 1,2-dichloroethane decreases from ca 220 mV in 0 M CH3OH to ca 70 mV in > 1 M CH3OH (reprinted with permission from Ref 58, Copyright 1992 American Chemical Society).

Even in the solutions of highest resistance given in Table 12.1, the ohmic drop can be calculated to be less than 1 mV for a millimolar solution of electroactive species. In a solvent that does not promote ion pairing, the value of p is, to a first approximation, inversely proportional to the supporting electrolyte concentration. Thus, the ohmic drop in steady-state voltammograms can be adjusted by changing either the concentration of the electrolyte or the electroactive species. 

Our last example does not involve the rate of a chemical reaction, but instead, the effect of temperature on diffusion rates [25]. One of the motivations for using microelectrodes as in the previous example is to allow fast experiments without appreciable iR drop. When used in the opposite extreme of very small scan rates, microdisk electrodes produce steady-state voltammograms that have the same sigmoidal shape as dc polarograms and RDE voltammograms (cf. Chap. 12). 

Fig. 3.13 Simulated (white dots) and analytical steady-state voltammograms for the reduction of a single electro-active species at a microdisc electrode for reversible, quasi-reversible, and irreversible kinetics calculated from Eqs. (3.101) (solid line) and (3.95) (dashed line).

The SECM can be used to measure the ET kinetics either at the tip or at the substrate electrode. In the former case, the tip is positioned in a close proximity of a conductive substrate (d < a). The substrate potential is kept at a constant and sufficiently positive (or negative) value to ensure the diffusion-controlled regeneration of the mediator at its surface. The tip potential is swept linearly to obtain a steady-state voltammogram. The kinetic parameters (k°, a) and the formal potential value can be obtained by fitting such a voltammogram to the theory [Eq. (22)]. A high value of the mass transfer coefficient (m) is achieved under steady-state conditions when d rate constants (k° > 1 cm-1 s) were measured with micrometersized SECM tips [92-94]. 

Figure 16. (a) The SECM current versus distance curve and a steady-state voltammogram... 

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. 

When the solutions are contaminated with water (even in a level of a few tens of ppm), the following features are seen in the steady state voltammograms ... 

Figure 32 Steady state voltammogram for the surface in Figure 31A showing the complementarity of peaks A-A and B-B. Other conditions are the same as those specified in Figure 31. (From Ref. 54.)...

A steady state is independent of the details of the experiment used in attaining it. Thus, under conditions where a steady state is attained, e.g., under convective conditions in an - electrochemical cell, the application of a constant current leads to a constant potential and similarly the application of a constant potential leads to the same constant current. Voltammetric steady states are most commonly reached using linear potential sweeps (or ramps) in a single or cyclic direction at a UME or RDE. A sigmoidally shaped current (l)-potential (E) voltammogram (i.e., a steady-state voltammogram) is recorded in the method known as steady-state voltammetry as shown in the Figure. Characteristics of the... 

Steady state — Figure. Steady-state voltammogram at a 25 micrometer diameter Pt disk UME in a solution of 1 mM ferrocenemethanol in 0.1 M KC1 electrolyte. The potentials are given with respect to Ag/AgCl. The potential was swept linearly at 10 mV/s from -0.1 V to 0.4 V and then back to -0.1 V... 

The shape of the steady-state voltammogram shown in Fig. 1 is typical of steady-state systems. The limiting current can be written generally as... 

Figure 5 represents an ideal reversible one-electron transfer process in the absence of drop or capacitative charging current, although in real experiments contributions to the response from both these terms are unavoidable. Figure 6 shows the effect of uncompensated resistance for both transient and steady-state voltammograms, whilst Fig. 7 shows the influence of double layer capacitance on a cyclic voltammetric wave. Note that for steady-state voltammetric techniques only very low capacitative charging... 

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