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groups both in nonaquueous solution and in the gas phase (16). The ether linkage formed is chemically and electrochemically quite stable. This linkage can offer a much shorter bonding distance between the electrode and the aromatic framework compared to the more common amide or silane linkages and, as such, is expected to facilitate electron transfer between the electrode and terminal groups. The reactive chlorides in the "bound" CC offers the possibility to attach a wide variety of terminal groups which may contain hydroxy, amine, or other nucleophilic groups. T h e versatility of CC still remains to be fully explored and tested, but preliminary experiments have shown promising results with attachment of redox reactants such as o-toludine and bis(hydroxymethy1)ferrocene to PG and t o tin and indium oxide electrodes.
ACKNOWLEDGMENT T h e authors express their gratitude to J. F. Evans for suggestions and helpful discussions during the course of this work.
LITERATURE CITED (1) B. F. Watkins, J. R. Behiing, E. Kariv, and L. L. Miller, J , Am. Chem. SOC.,97, 3549 (1975). (2) B. E. Firth, L. L. Miller, M. Mitani, T. Rogers, J. Lennox, and R. W. Murray, J . Am. Chem. SOC.,98, 8271 (1976). (3) E. E. Firth and L. L. Miller, J . Am. Chem. SOC.,98. 8272 (1976). (4) C. M. Elliot and R. W. Murray, Anal. Chem., 48, 1247 (1976). (5) D. F. Utereker, J. C. Lennox, L. M. Wier. P. R. Moses, and R. W. Murray, J . Electroanal. Chem.. 81, 309 (1977). (6) P. R. Moses, L. Wier, and R. W. Murray, Anal. Chem., 47, 1882 (1975).
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(7) P. R. Moses and R. W. Murray, J . Am. Chem. Soc., 98, 7435 (1976). (8) P. R. Moses and R. W. Murray, J . Electroanal. Chem., in press. (9) J. F. Evans, T. Kuwana, M. T. Henne, and G. P. Royer, J . Electroanal. Chem., 80, 409 (1977). (10) N. R. Armstrong, A . W. C . Lin, M. Fujihira, and T. Kuwana, Anal. Chem., 48, 741 (1976). (11) M. Fujihira. T. Matsue, and T. Osa, Chem. Lett., 875 (1976). (12) R. J. Burt, G. J. Leigh, and C. J. Pickett, J. Chem. Soc., Chem. Commun., 940 (1976). (13) S. Mayer, T. Matusinovic. and K. Cammann, J . Am. Chem. SOC..99. 3888 (1977). (14) M. Fujihira and T. Osa, Nature(London), 264, 349 (1976). (15) J. F. Evans and T. Kuwana, Anal. Chem., 49, 1632 (1977). (16) A . W. C. Lin, P. Yeh, and T. Kuwana, unpublished data. (17) G. Kay and E. M. Crook, Nature((London),216, 514 (1967). (18) G. Kay, M. D. Lilly, A. K. Sharp, and R. J. H. Wilson, Nature (London), 217, 641 (1968). (19) R. J. H. Wilson, G. Kay, and M. D. Lilly, Biochem. J . , 108, 845 (1968). (20) R. J. H. Wilson and M. D. Liliy, Biotech. Bioeng., 11, 349 (1969). (21) A. K. Sharp, G. Kay, and M. D. Lilly, Biotech. Bioeng., 11, 363 (1969). (22) E. M. Smolin and L. Rapoport, "s-Triazines and Derivatives", Interscience Publishers, New York, N.Y., 1959, pp 48-62 and 68-90. (23) P. Leow and C. D. Weis, J . Heterocyclic Chem., 13, 829 (1976). (24) S.S. Barton and B. H. Harrison, Carbon, 13, 283 (1975). (25) W. M. Clark, "Oxidation-Reduction Potentials of Organic Systems", The Williams and Wilkins Co., Baltimore, Md., 1960, p 464. (26) J. H. Scofield, J . Electron Specbosc. Relat. Phenom.. 8, 129 (1976). (27) D R. Penn, J . Electron Spectrosc. Relat. Phenom., 9, 29 (1976). (28) S. Evans and J. M. Thomas, Proc. R . SOC.London, Ser. A , 353, 103 (1975).
RECEIVED for review ,July 8, 1977. Accepted January 19, 1978. This work was supported by funds from NSF Grant Numbers C H E 73-04882, C H E 76-04911 and US PHS Grant Number 19181.
Simultaneous Determination of Reversible Potential and Rate Constant for a First-Order EC Reaction by Potential Dependent Chronoamperometry Hung-Yuan Cheng and Richard L. McCreery" Department of Chemistry, The Ohio State University, Columbus, Ohio 432 10
When potential step experiments are performed at potentials in the region of the reversible EIl2for EC type systems, the current vs. time decay is dependent both on the applied potential and the rate constant for the homogenous reaction subsequent to charge transfer. Provided charge transfer equilibrium is established rapidly relative to the chemical reaction, both the reversible E,/2 and the rate constant may be determined by applying curve fitting procedures to the current vs. time transient. A simplex optimization procedure was evaluated using the benzidine rearrangement as a test system, and the accuracies of the determinations of El,; and k compare well with other electrochemical techniques. The advantage of the present approach, in addition to the ability to determine El/; and k simultaneously, is a large expansion in experimental time frame over other methods. Experiments lasting many times longer than the homogeneous reaction half life can be used to evaluate ElIzrand k .
T h e study of homogeneous chemical reactions associated with oxidation reduction processes a t electrode surfaces has 0003-2700/78/0350-0645$01 0010
been a major endeavor of electrochemistry during the past several decades. In particular, the examination of' the mechanisms and kinetics of the reactions of electrogenerated reactive species h a been carried out with both electrochemical techniques and electrochemistry coupled with optical spectroscopy and other analytical probes. In general, three types of chemical information are desired in the study of homogeneous reactions accompanying charge transfer. First, the mechanism of the reaction of the oxidized or reduced form of the starting material may be determined with electrochemistry and ancillary analytical techniques. Second, the rate constant for reactions subsequent to charge transfer may he determined, along with pH and temperature effects and any other relevant kinetic information. Third, the reversible half wave potential, for the original redox system may be determined, an often nontrivial task given the distortion of the electrochemical response by the ensuing chemical reactions. While mechanism diagnosis is an important and useful aspect of electrochemically initiated reactions, it is not the subject of the present work. Once the mechanism is known, the kinetics of the process may be examined by a variety of C 1978 American Chemical Society
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techniques; discussed here for the so-called EC case, an irreversible pseudo first-order chemical reaction following reversible charge transfer: ox + ne- + red red
t-
products
The numerous methods for examining such systems are discussed elsewhere (1-3) but two techniques of relevance t o this work are double step chronoamperometry ( 4 ) and cyclic voltammetry ( 5 ) . In the double step approach, the reactive form (red) is generated electrochemically and, after allowing the irreversible reaction to proceed, the potential is switched to where the remaining reactive form is re-oxidized, and the rate constant is determined from the current resulting from oxidation of the reactive form. With cyclic voltammetry, the rate constant may be determined either from the ratio of the anodic to cathodic peak currents ( 5 , 6) or the shift in peak potential caused by the homogeneous reaction (5, 7). For an accurate determination of the rate constant with these and other electrochemical techniques, the time frame of the experiment must be on the same order as the half-life of the homogeneous reaction. This constraint limits the methods to reactions slow enough to be accurately monitored with these techniques, i.e., reactions with half-lives of greater than a few hundred microseconds. The problem of determining the reversible El/; for reactive systems has been addressed since a t least the 1930’s, when flowing streams were combined with potentiometric methods. Contemporary electrochemical approaches t o the problem are based on two distinct methods. In the first, the time frame of the experiment is decreased to a point where the El 2r measurement may be made before the ensuing homogeneous reaction distorts the electrochemical response. An example is a cyclic voltammetric experiment a t sufficiently high scan rate so an EC type reaction does not distort the currentpotential curve ( 5 ) . The theory for ac polarographic determination of El iLr of reactive systems has been developed and tested (8, 9) and has been used to determine the redox potentials of electrogenerated free radicals (10). Again, these methods rely on the experimental probe being significantly faster than the reaction subsequent to charge transfer. The second approach to determining involves comparison of‘ electrochemical data with theoretical curves for situations where the follow-up reaction has distorted the ideal response. The effect of EC reactions on voltammetric data has been , a simple method for determining E1,2r and calculated, (j)and rate constants from these curves has been described (11). Because of the relative insensitivity of single-sweep voltarnmetric results t o EC reactions, this method yielded rate constants accurate to about 2&50%, and the accuracy of the Ellzrvalue was not assessed. Marcoux and O’Brien (3)have presented the theory for a method for determining EC rate constants termed “potential dependent chronoamperometry”, and its experimental applicability has been verified in our laboratory (22). Consider a chronoamperometry experiment performed under potentiostatic conditions a t potentials near The ox/red ratio is therefore held constant a t the electrode surface, assuming charge transfer equilibrium. In the absence of a homogeneous reaction, the current will have the usual t-’/’ dependence, although its magnitude will depend upon the difference between the applied potential (Ea,,) and El 21. If the reduced form undergoes an irreversible homogeneous reaction, however, additional current will flow to maintain a constant Nernstian ratio. The current decay for an EC case will not have a t-’12 dependence, but will depend on both the applied potential and the rate constant for the homogeneous reaction. Given a knowledge of El/{, the homogeneous rate
-2
-I
0
LOG I k t )
ti
tz
Flgure 1. Working curves for potential dependent chronoamperornetry is the current at a particular derived by Marcoux and O’Brien (3). napD kf value divided by the diffusion limited current at the same kf value
constant can be determined from the current vs. time transient. Note that a t potentials significantly negative of where the ox/red ratio is virtually zero at the electrode surface, the reaction has no effect on the current, and the current time transient has its usual diffusion limited t-1/2 decay. Marcoux and O’Brien ( 3 , 23) solved the appropriate equations for this technique for several homogeneous reaction mechanisms, and the working curves for the EC case are shown in Figure 1. nappis the ratio of the current a t a particular time and applied potential to the current for the diffusion limited case (E,,,
