The Effect of Slow Two‐Electron Transfers and Disproportionation on Cyclic Voltammograms

The EE mechanism (two-electron transfer) for cyclic v o l t a m m e t r y was investigated in considerable detail along with the effect of disproportionation. The theory was developed for e i ther the first or second electron transfer being slow while the other one was reversible. It was possible to develop generalized working curves for the height and shape of the wave regardless of the difference in E~ and the values of ~ and ks. This theory was then applied to the analysis of the reduction of benzil in the presence of alkal ine earth ions in dimethylformamide. The theory for reversible and i r reversible electron transfer has been examined in some detail previously for cyclic vo l tammet ry (CV). The problem of mul t i electron transfers in CV was studied first by Polcyn and Shain (1). The main quant i ta t ive emphasis was placed on the deconvolution of separated waves and only quali tat ive results were given for mul t i -e lec t ron waves. Myers and Shain (2) were able to quant i ta t ively correlate the shape and peak current funct ion of r e v e r s i b l e vol tammetr ic waves to their difference in Eo's if the Eo's were close together. It was found that the shape of the wave was independent of the relat ive values of the Eo's only if the difference in Eo's was greater than 180 mV. Otherwise, the wave will be broader than expected, even though it is still reversible. In addition, its shape and position are independent of scan rate. No correlations were made for quasireversible or i rreversible electron transfers. Mult i -e lectron transfers can put a much more s t r ingent demand on the rate of electron transfers if the wave is shifted significantly from its E o because of the second electron transfer. Ruzic (3) has shown that, for polarography, the apparent heterogeneous electron transfer rate constant, ks', for the over-al l two-elect ron transfer is less than either of the individual rate constants, k~.l or ks.2, if the second E o, E2, is more positive than the first E o, El. In particular, the rate cons tant that is calculated using conventional theory is not the individual rate constant but an apparent one. Thus, the theory for quasireversible electron transfers in CV (4) yields the value of ks'. Competing with the mult ie lectron t ransfer mechnism is the disproport ionation mechanism. If the second electron t ransfer is so slow as to not be i m p o r t a n t and if E~ is positive of El, the classical disproportionat ion mechanism can then occur. The theory for this mechanism has been developed and verified by Saveant (5). But very li t t le work has been done in t rying to assess the relative importance of the electron t ransfer mechanism (EE) as compared to the disproport ionation (DISP) mechanism. For reversible electron transfers the cyclic vol tammograms will not dist inguish between these two mechanisms. It is the purpose of this work to develop the cyclic voltammetric theory more general ly for the EE mechanism, including the possibility of disproportionation, and to verify it experimental ly. The emphasis will be placed on those cases where only one wave is observed, and either the first or second electron t ransfer is slow. Recent studies have shown several reductions that are now known to follow the EE mechanism (6). In this study, the electrochemical reduct ion of benzil in dimethyl formamide (DMF) in the presence of alkal ine * Electrochemical Society Active Member.