The Application of disc-ring electrodes to the kinetics of reactions in solution

The ring-disc electrode consists of a central disc electrode which has an insulating annulus around it, forming the gap, and this in turn is surrounded by a ring electrode. The usefulness of this system lies in the fact that a reactant can be generated on the disc, and then it can be monitored at the ring as it is transported outwards by radial convection and diffusion.
The first chapter of this thesis discusses the importance of the ring-disc electrode and reviews its development and application to the study of electrode processes, to solution kinetics, and to analytical problems. Most of the work prior to 1966 was of a qualitative or semi-quantitative nature owing to the lack of exact solutions to the problem of the transport of a species from the disc to the ring. This was largely resolved by the publication of a series of papers by Albery and Bruckenstein (1), who presented a new approach to the theory and in particular obtained solutions for cases where the intermediate is consumed by first- or by second-order kinetics. The work described in this thesis has been directed towards testing and applying these theories.
Experiments with the ring-disc electrode usually involve the simultaneous and independent measurement of the ring electrode and disc electrode currents, while maintaining the potential of one electrode constant with respect to a reference potential. This is most readily achieved by the use of operational amplifiers, and Chapter 2 of this thesis describes the design, construction and use of a multi-purpose, operational amplifier, electrochemical control unit; experiments on the amplifiers used in the unit were carried out to test their suitability for use in D.C. electrochemical control circuits and this is dealt with in an Appendix to the thesis. The other apparatus used throughout this work together with other essential experimental details are dealt with in the third chapter.
A fundamental parameter for the ring-disc electrode is the collection efficiency, N. This is a function only of electrode geometry and the theoretical value is obtained by calculating the limiting ring current for a given disc current; a resumandeacute; of this theory is contained in Chapter 4. The value of N for each of the two electrodes used in this research was determined with. a number of different redox systems - Brandminus;/Br2, Fe(CN)4andminus;6/Fe(CN)3andminus;6, Fe3+/Fe2+ - and in all cases very good agreement between theory and experiment was obtained.
If an intermediate generated on the disc electrode decomposes homogeneously in its passage from the disc to the ring, then the collection efficiency will fall. Chapter 5 deals with the theory for the decomposition of the intermediate by a first-order reaction, This theory relates the kinetic collection efficiency, Nn, to the parameter:
n = (k1/D)andhalf;.(D/C)1andfrasl;3,
where k1 is the first-order rate constant for the decomposition of the intermediate, D is its diffusion coefficient and C is the convection constant (2). The exact form of the relationship depends generally upon the size of n and two cases are considered. For n~or andlt; 1 and n andlt;0.3 the theory is based upon thin-gap, thin-ring assumptions, and since the electrodes used did not fulfil these conditions with sufficient rigour it was found necessary to modify the theoretical expression in each case by a factor N1/N2; this is the ratio of the non-kinetic collection efficiency N1 calculated without making any assumptions about electrode geometry to that calculated assuming thin-gap, thin-ring conditions. When this modification is made the results obtained from measurements on the bromination of two anisoles under pseudo first- order conditions with two electrodes for which N1 and N2 differ by about 10% and 30% respectively, are in good agreement with each other; the extension of the theory is useful since electrodes with wide rings which are capable of better polarographic separation can now be used. The results also show good agreement with those reported by Dubois and Aaron (3),(4) for the same reactions. The salt effects upon the rate of reaction between bromine and anisoles were also investigated and the results are discussed.
Experiments carried out on the bromination of anisole alone with the conditions adjusted to make nandgt;~3.5 gave results which failed to agree with theory; this is discussed, but no satisfactory explanation for the discrepancy can be given.
The ring-disc electrode can be used as the basis of a rapid and sensitive analytical technique, in which a titration reaction is carried out inside the diffusion layer at the electrode surface. The principle of the method is that one of the reactants is generated on the disc electrode and then the ring electrode is used to detect when excess of this reagent has been produced. Chapter 6 gives the theory for these diffusion layer titrations and the results of the experiments carried out on the reactions of bromine with allyl alcohol and As(III) are reported. The particular importance, from the kinetic point of view, of these titrations is that for solutions of known concentration they enable the average diffusion coefficient for the two reactants to be measured; for second-order kinetic studies the value of this diffusion coefficient is needed in the calculation of the rate constant.
Chapter 7 considers the case when the disc electrogenerated intermediate, B, reacts rapidly with a reagent, A, of comparable concentration to its own. In this situation the solution is divided into an A dominated region and a B dominated region, but because of finite kinetics there is some interpenetration of A and B into each other's region. Thus the ring electrode detects the presence of B at lower disc currents than predicted by diffusion layer titration theory, which assumed an infinitely fast reaction. By defining a reaction surface where [A] = [B] one can calculate the disc current required to place this surface on the inside edge of the ring electrode, and the kinetic theory then enables one to obtain a particular relationship between the ring current arising from this kinetic penetration and the second-order, rate constant. The ratio of this ring current to the disc current at r = r2 gives the kinetic collection efficiency Nn , and it is shown that in general for the same position of the reaction surface systems with the same value of n give equal values of Nn. The theory was tested for two electrodes with the bromination of allyl alcohol and the results are in agreement with those previously reported by Bell and Atkinson (5). The general theory is shown to hold throughout the whole experimental range of observed n values, but the particular theory breaks down at low n; the reasons for this failure are discussed at length.
The kinetics of the oxidation of As(ill) by bromine were also investigated and rate constants in the range (0.5 .- 1.0) x 108 M-1sec-1 were measured. Experiments at varying [Br-] gave kBr2 = (1.13 andpm; 0.03) x 108 M-1sec-1 and kBrandminus;3 = (4.65 andpm; 0.28) x 108 M-1sec-1. The one disturbing feature about the Br2/As(III) system is the breakdown of the general conclusion at low n values, and possible reasons for this are suggested and discussed in Chapter 8. This chapter also deals with the oxidation of Fe(II) by Ce(IV), a system where one of the products of reaction, Ce(III), interferes with the detection of the intermediate, Fe(II), at the ring electrode. Although it is not possible to obtain a rigorous solution to the problem of working out the contribution to the ring current of the electrochemical oxidation of Ce(III), an approximate solution is obtained which shows that if the same conditions are set up both in the presence and absence of kinetics, and Ce(III) is generated at the disc electrode with a current equal to the kinetic disc current, then the ring current for the oxidation of Ce(III) is the same in both cases. The method is applied to the Fe(II)/Ce(IV) system and it is found to be reasonably successful in explaining the observed kinetic results.
The final chapter of the thesis discusses the range of first- and second-order rate constants measurable with the ring- disc electrode, the various advantages and disadvantages of the technique and possible future applications to homogeneous kinetic studies.