Nicholson-Shain theory

By using cyclic voltammetry, Schiffrin and coworkers [26, 186, 187, 189] studied electron transfer across the water-1,2-dichloroethane interface between the redox couple FefCNls /Fe(CN)6 in water, and lutetium(III) [186] and tin(IV) [26, 187] diphthalocyanines and bis(pyridine)-me50-tetraphenylporphyrinato-iron(II) or ru-thenium(III) [189] in the organic solvent. An essential advantage of these systems is that none of the reactants or products can cross the interface and interfere with the electron transfer reaction, which could be clearly demonstrated. Owing to a much higher concentration of the aqueous redox couple, the pseudo-first order electron transfer reactions could be analyzed with the help of the Nicholson-Shain theory. However, though they have all appeared to be quasireversible, kinetic analysis was restricted to an evaluation of the apparent standard rate constant o. which was found to be of the order of 10 cm s [186, 189]. Marcus [199] has derived a relationship between the pseudo-first-order rate constant for the reaction (8) and the rate... 

On the other hand, adsorption can have serious negative effects on analytical response. Adsorbed reactants will increase the current over that predicted from theory based on diffusion-controlled mass transport. Thus the usually powerful methods based on Nicholson/Shain voltammetric theory are seriously perturbed by adsorption, particularly at high scan rates. In addition, the adsorption of nonelectroactive impurities or reaction products can eventually deactivate the electrode, thus requiring electrode renewal. 

R. S. Nicholson and 1. Shain. Theory of stationary electrode polarography. Single scan and cychc methods applied to reversible, irreversible, and kinetic systems. Anal. Chem. 36, 706-23 (1964). 

The theory for cyclic voltammetry was developed by Nicholson and Shain [80]. The mid-peak potential of the anodic and cathodic peak potentials obtained under our experimental conditions defines an electrolyte-dependent formal electrode potential for the [Fe(CN)g] /[Fe(CN)g]" couple E°, whose meaning is close to the genuine thermodynamic, electrolyte-independent, electrode potential E° [79, 80]. For electrochemically reversible systems, the value of7i° (= ( pc- - pa)/2) remains constant upon varying the potential scan rate, while the peak potential separation provides information on the number of electrons involved in the electrochemical process (Epa - pc) = 59/n mV at 298 K [79, 80]. Another interesting relationship is provided by the variation of peak current on the potential scan rate for diffusion-controlled processes, tp becomes proportional to the square root of the potential scan rate, while in the case of reactants confined to the electrode surface, ip is proportional to V [79]. 

Bard AJ, Faulkner LR (1980) Electrochemical Methods. John Wiley Sons, New York. Nicholson RS, Shain I (1964) Theory of Stationary Electrode Polarography. Anal Chem 36 706-723. 

Nicholson, R.S., and Shain, 1. 1964. Theory of stationary electrode polarography. Analytical Chemistry 36, 706-723. 

Nicholson RS, Shain I. Theory of stationary electrode polarogr hy. Single Scan and Cyclic Methods Applied to Reversible, Irreversible, and Kinetic Systems. Anal Chem 1964 37 706-723. 

Research into this area is dominated by microelectrodes. At short times, the diffusion layer thickness is much smaller than the microelectrode radius and the dominant mass transport mechanism is planar diffusion. Under these conditions, the classical theories, e.g., that of Nicholson and Shain, can be used to extract kinetic parameters from the scan rate dependence of the separation between the anodic and cathodic peak potentials. Using this approach, the standard heterogeneous electron transfer rate constant, k°, may be determined from the published working curves relating AEp to a kinetic parameter The variation of AEp with o is determined and, from this, T is calculated. k° is then determined by the following equation ... 

Reinmuth has examined chronopotentiometric potential-time curves and proposed diagnostic criteria for their interpretation. His treatment applies to the very limited cases with conditions of semi-infinite linear diffusion to a plane electrode, where only one electrode process is possible and where both oxidized and reduced forms of the electroactive species are soluble in solution. This approach is further restricted in application, in many cases, to electrode processes whose rates are mass-transport controlled. Nicholson and Shain have examined in some detail the theory of stationary electrode polarography for single-scan and cyclic methods applied to reversible and irreversible systems. However, since in kinetic studies it is preferable to avoid diffusion control which obscures the reaction kinetics, such methods are not well suited for the general study of the mechanism of electrochemical organic oxidation. The relatively few studies which have attempted to analyze the mechanisms of electrochemical organic oxidation reactions will be discussed in detail in a following section. 

Since the 1960s, cyclic voltanunetry has been the most widely used technique for studies of electrode processes with coupled chentical reactions. The theory was developed for numerous mechanisms involving different combinations of reversible, quasi-reversible, and irreversible heterogeneous ET and homogeneous steps. Because of space limitations, we will only consider two well-studied examples—(i.e., first-order reversible reaction preceding reversible ET) and E Ci (i.e., reversible ET followed by a first-order irreversible reaction)—to illnstrate general principles of the coupled kinetics measurement. A detailed discussion of other mechanisms can be found in Chapter 12 of reference (1) and references cited therein, including a seminal publication by Nicholson and Shain (19). 

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