Limiting current electron transfer

At low currents, the rate of change of die electrode potential with current is associated with the limiting rate of electron transfer across the phase boundary between the electronically conducting electrode and the ionically conducting solution, and is temied the electron transfer overpotential. The electron transfer rate at a given overpotential has been found to depend on the nature of the species participating in the reaction, and the properties of the electrolyte and the electrode itself (such as, for example, the chemical nature of the metal). 

At higher current densities, the primary electron transfer rate is usually no longer limiting instead, limitations arise tluough the slow transport of reactants from the solution to the electrode surface or, conversely, the slow transport of the product away from the electrode (diffusion overpotential) or tluough the inability of chemical reactions coupled to the electron transfer step to keep pace (reaction overpotential). 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

Let us see now what happens in a similar linear scan voltammetric experiment, but utilizing a stirred solution. Under these conditions, the bulk concentration (C0(b, t)) is maintained at a distance S by the stilling. It is not influenced by the surface electron transfer reaction (as long as the ratio of electrode area to solution volume is small). The slope of the concentration-distance profile [(CQ(b, t) — Co(0, /))/r)] is thus determined solely by the change in the surface concentration (Co(0, /)). Hence, the decrease in Co(0, t) duiing the potential scan (around E°) results in a sharp rise in the current. When a potential more negative than E by 118 mV is reached, Co(0, t) approaches zero, and a limiting current (if) is achieved ... 

FIGURE 1-7 Current-potential curve for the system O + ne - " R, assuming that electron-transfer is rate limiting, C0 = CR, and a = 0.5. Hie dotted lines show the cathodic ((.) and anodic ( ) components. 

Conversely, the use of elevated temperatures will be most advantageous when the current is determined by the rate of a preceding chemical reaction or when the electron transfer occurs via an indirect route involving a rate-determining chemical process. An example of the latter is the oxidation of amines at a nickel anode where the limiting current shows marked temperature dependence (Fleischmann et al., 1972a). The complete anodic oxidation of organic compounds to carbon dioxide is favoured by an increase in temperature and much fuel cell research has been carried out at temperatures up to 700°C. 

Figure 17.7 Electrocatalysis of O2 reduction by Pycnoporus cinnabarinus laccase on a 2-aminoanthracene-modified pyrolytic graphite edge (PGE) electrode and an unmodified PGE electrode at 25 °C in sodium citrate buffer (200 mM, pH 4). Red curves were recorded immediately after spotting laccase solution onto the electrode, while black curves were recorded after exchanging the electrochemical cell solution for enzyme-fiiee buffer solution. Insets show the long-term percentage change in limiting current (at 0.44 V vs. SHE) for electrocatalytic O2 reduction by laccase on an unmodified PGE electrode ( ) or a 2-aminoanthracene modified electrode ( ) after storage at 4 °C, and a cartoon representation of the probable route for electron transfer through the anthracene (shown in blue) to the blue Cu center of laccase. Reproduced by permission of The Royal Society of Chemistry fi om Blanford et al., 2007. (See color insert.)...

In agreement with the theory of electrolysis, treated in Sections 3.1 and 3.2, the parts of the residual current and the limiting current are clearly shown by the nature of the polarographic waves because for the cathodic reduction of Cd2+ and Zn2+ at the dme we have to deal with rapid electron transfer and limited diffusion of the cations from the solution towards the electrode surface and of the metal amalgam formed thereon towards the inside of the Hg drop, we may conclude that the half-wave potential, Eh, is constant [cf., Fig. 3.13 (a ] and agrees with the redox potential of the amalgam, i.e., -0.3521V for Cd2+ + 2e - Cd(Hg) and -0.7628 V for Zn2+ + 2e -> Zn(Hg) (ref. 10). The Nernst equation is... 

In an EC mechanism the ratio of the forward and backward reaction rates is decisive for k/ d in , the chemical follow-up reaction has no influence here, so that for a sufficiently rapid electron transfer step the limiting current remains diffusion controlled.)... 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

Back electron transfer takes place from the electrogenerated reduc-tant to the oxidant near the electrode surface. At a sufficient potential difference this annihilation leads to the formation of excited ( ) products which may emit light (eel) or react "photochemical ly" without light (1,16). Redox pairs of limited stability can be investigated by ac electrolysis. The frequency of the ac current must be adjusted to the lifetime of the more labile redox partner. Many organic compounds have been shown to undergo eel (17-19). Much less is known about transition metal complexes despite the fact that they participate in fljjany redox reactions. 

A number of metal porphyrins have been examined as electrocatalysts for H20 reduction to H2. Cobalt complexes of water soluble masri-tetrakis(7V-methylpyridinium-4-yl)porphyrin chloride, meso-tetrakis(4-pyridyl)porphyrin, and mam-tetrakis(A,A,A-trimethylamlinium-4-yl)porphyrin chloride have been shown to catalyze H2 production via controlled potential electrolysis at relatively low overpotential (—0.95 V vs. SCE at Hg pool in 0.1 M in fluoroacetic acid), with nearly 100% current efficiency.12 Since the electrode kinetics appeared to be dominated by porphyrin adsorption at the electrode surface, H2-evolution catalysts have been examined at Co-porphyrin films on electrode surfaces.13,14 These catalytic systems appeared to be limited by slow electron transfer or poor stability.13 However, CoTPP incorporated into a Nafion membrane coated on a Pt electrode shows high activity for H2 production, and the catalysis takes place at the theoretical potential of H+/H2.14... 

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