The Journal of Physical Chemistry, Vol. 83, No. 23, 7979
Electrochemical Transfer Coefficient
Acknowledgment. Support of this work by the American Cancer Society and the Computer Center of the University of Illinois a t Chicago Circle is gratefully acknowledged. The authors also thank Dr. Charles Duke for providing the CNDO/S3 program and Mr. Terrence 0'Donne11 for computational assistance.
References and Notes (1) J. C. Arcos, M. F. Argus, and G. Wolf, "Chemical Induction of Cancer", Vol. 1-111, Academic Press, New York, 1968-1974; A Dipple, ACS Monogr., No. 173 (1976); D. J. McCaustland, D. L. Fischer, K. C. Kolwyck, W. P. Duncan, J. C. Wiley, Jr., C. S. Menon, J. F. Engel, J. K. Selkirk, and P. P. Roller in "Carcinogenesis", Vol. I, "Polynuclear Aromatic liydrocarbons: Chemistry, Metabolism and Carcinogenesis", R. I.Freudenthal and P. W. Jones, Ed., Haven Press, New York, 1976. (2) A. Pullman, C . R. Acad. Sci., 221, 140 (1945); 236, 2318 (1953); A. Pullman, C . R . SOC.Biol., 139, 1056 (1945); A. Pullman, Ann. Chim. (Paris), 2, 5 (1947); A Pullman and 8. Pullman, Adv. Cancer Res., 3, 117 (1955); A. Pullman, Buii. SOC. Chim. (Fr.), 21, 595 (1954); M. A. Mainster and J. D. Memory, Biochem. Biophys. Acta, 146, 605 (1967). (3) I. B. Weinstein, A. M. Jeffrey, K. W. Jenette, S. H. Blobstein, R. G. Harvey, C. Harris, H. Autrup, H. Kasai, and K. Nakanishi, Science, 193, 592 (1976); A. M. Jeffrey, K. W Jennette, S. H. Blobstein, I. B. Weinstein, F. A. Beland, R. G. Harvey, H. Kasai, I.Miura, and K. Nakanishi, J . Am. Chem. Soc., 98, 5714 (1976); M. R. Osborne, F. A. Beland, R. G. Harvey, and P. Brookes, Int. J . Cancer, 16,362 (1976). (4) R. T. Morrison and R. N. Boyd, "Organic Chemistry", 3rd ed, Allyn and Bacon, Boston, 1973, Chapter 17. (5) D. M. Jerina, R. E. Lehr, H. Yagi, 0. Hernandez, P. M. Dansette, P. G. Wislocki, A. W. Wood, R. L. Chang, W. Levin, and A. H. Conney in "In Vitro Metabolic Activation in Mutagenesis Testing", F. J. de Serres, J. R. Bend, and R. M. Philpot, Ed., Elsevier, Amsterdam, 1976; L. L. Shipman in "Polynuclear Aromatic Hydrocarbons", P. W. Jones and P. Leber, Ed., Ann Arbor Science, Ann Arbor, in press. (6) R. Boschi and W. Schmidt, Tetrahedron Lett., 2577 (1972); R. Boschi, E. Clar, and W. Schmidt, J . Chem. Phys., 60, 4406 (1974). (7) S.Peng, A. Padva, and P. R. LeBreton, Roc. M t i . Acad. Sci. U.S.A., 73, 2966 (1976). (8) C. Yu, S.Peng, I.Akiyama, J. Lin, and P. R. LeBreton, J. Am. Chem. Soc., 100, 2303 (1978). (9) R. G. Harvey, J. Pataki, R. N. Wilke, J. W, Flesher, and S. Soedizdo, Cancer Lett., 1, 339 (1976). (10) R. G. Harvey, S.H. Goh, and C. Cortez, J . Am. Chem. Soc., 97, 3468 (1975); C. Cortez and R. G. Harvey, Org. Syn., in press. (11) F. A. Beland and R. G. Harvey, J. Chem. SOC.,Chem. Commun., 84 (1976); P. P. Fu and R. G. Harvey, TetrahedronLett., 2059 (1977); R. G. Harvey and P. P. Fu in "Polycyclic Hydrocarbons and Cancer: Chemistry, Molecular Biology and Environment", Vol. I, H. V. Gelboin
3003
and P.O.P. T'so, Ed., Academic Press, New York, 1978, p 131. (12) A Schweig and W. Thiel, Chem. Phys. Lett., 21, 541 (1973); R. R. Corderman, P. R. LeBreton, S. E. Buttrill, Jr., A. D. Williamson, and J. L. Beauchamp, J. Chem. Phys., 65, 4929 (1976). (13) E. J. McAlduff and K. N. Houk, Can. J . Chem., 55, 318 (1977). (14) D. W. Turner, C. Baker, A. D. Baker, and C. R. Brundle, "Molecular Photoelectron Spectroscopy", Wiley-Interscience, New York, 1970. (15) H. Basch, M. B. Robin, N. A. Kuebler, C. Baker, and D. W. Turner, J . Chem. Phys., 51, 52 (1969). (16) J. P. Maier and D. W. Turner, Chem. Soc., Faraday Discuss., 54, 149 (1972). (17) C. P. Brock, M. S.Kuo, and H. A. Levy, Acta Crystallogr., Sect. B , 34, 981 (1978); A. Hargreaves and S.H. Rizvl, Acta Crystaiiogr., 15, 365 (1962); 0. Bastiansen and M. Treatterberg, Tetrahedron, 17, 147 (1962). (18) V. Eck, A. Schweig, and H. Vermeer, Tetrahedron Lett., 2433 (1978); A. D. Baker, D. P. May, and D. W. Turner, J. Chem. SOC.E , 22 (1968); T. P. Debies and J. W. Rabalais, J . Nectron Spectrosc., 1, 355 (1973). (19) R. Boschi, J. N. Murrell, and W. Schmidt, Schmidt, Chem. Soc., Faraday Discuss., 54, 116 (1972). (20) G. Bieri, F. Burger, E. Heilbronner, and J. P. Maier, Helv. Chim. Acta, 60, 2213 (1977). (21) N. 0. LipariandC. B. Duke, J. Chem. fhys., 63, 1748, 1758, 1768 (1975); C. B. Duke, W. R. Salaneck, t. J. Fabish, J. J. Ritsko, H. R. Thomas, and A. Paton, Phys. Rev. 8 , 18, 5717 (1978); C. B. Duke, Int. J. Quantum Chem., in press. (22) J. Del Bene and H. H. Jaffe, J . Chem. Phys., 48, 4050 (1968). (23) J. Trotter, Acta Crystaliogr., 16, 605 (1963). (24) J. P. Giusker, H. H. Carrell, D. E. Zacharias, and R. G. Harvey, Cancer Biochem. Biophys., 1, 44 (174). (25) A. Camerman and J. Trotter, Acta Crystallogr., 18, 636 (1965). (26) J. Iball, S. N. Scrimegour, and D. W. Young, Acta Crystallogr., Sect. 6 ,328 (1976). (27) J. Trotter, Acta Crystaliogr., 14, 1135 (1961). (28) 2. Smith and D. A. Kohl, J . Chem. Phys., 60, 4920 (1974); C. Foces-Foces, F. H. Cano, and 5.Garcia, Acta Crystailogr., B , 33, 3521 (1977). (29) G. E. Bacon, N. A. Curry, and S. A. Wilson, Proc. R. SOC.London, Ser. A , 279, 98 (1964). (30) D. W. J. Cruickshank, Acta Crystaliogr., 10, 504 (1957); R. Mason, ibid., 17, 547 (1964). (31) I.N. Rabinowitz and J. Kraut, Acta Crystaliogr., 17, 159 (1964); "Tables of Interatomic Distances and Configurations In Molecules and Ions", The Chemical Society, Burlington House, London, 1965. (32) C. A. Bear, D. Hall, J. M. Waters, and T. N. Waters, J. Chem. Soc., Perkin Trans. 2, 314 (1973). (33) A. Padva, S. Peng, J. Lin, M. Shahbaz, and P. R. LeBreton, Bopolymers, 17, 1523 (1978). (34) S. Peng, J. Lin, M. Shahbaz, and P. R. LeBreton, Int. J. Quantum Chem., Quantum Bioi. Symp., No. 5, 301 (1978). (35) F. P. Lessing in "Mass Spectrometry", C. A. McDowell, Ed., McGraw-Hill, New York, 1963.
Potential Dependence of the Electrochemical Transfer Coefficient. An Impedance Study of the Reduction of Aromatic Compounds D. Garreau, J. M. Saveant,* and
D. Tessier
Laboratoire d'Electrochimie de i'Universit6 de Paris VII-2, place Jussieu-75 22 1 Paris, Cedex 05, France (Received March 5, 1979) Publication costs assisted by Laboratoire d' Electrochimie de I' Universit6 de Pari. VII
The electrochemical electron transfer rate of five aromatic compounds (nitromesitylene, nitrodurene, terephthalonitrile, phthalonitrile, p-diacetylbenzene) have been determined in DMF as a function of the dc electrode potential by using an ac impedance technique with frequencies ranging from 1000 to 20 000 Hz. The transfer coefficient was observed to vary with potential beyond experimental uncertainty in all cases. The magnitude of the variation is on the same order as that predicted by the Marcus theory of outer-sphere electron transfers. This behavior observed for various solvents and functional groups appears as a general phenomenon in the reduction of organic molecules in aprotic solvents, i.e., in the case where charge transfer is fast and mainly governed by solvent reorganization.
Introduction The present theories of electron transfer a t electrodes (ref 1and references therein), based on harmonic approximation, predict a linear dependence of the transfer coefficient, a , upon the electrode potential. During the last 0022-3654/79/2083-3003$01 .OO/O
15 years there have been several attempts to detect such a dependence experimentally (ref 2-4 and references therein). In most cases, however, the results were not actually conclusive owing mainly to the large magnitude of the double layer correction and the uncertainties about 0 1979 American
Chemical Society
3004
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979
its determination. Recently, more reliable conclusions have been arrived at with two types of systems involving uncharged or weakly charged reactants, hence giving rise to small double layer corrections. With one of these systems, involving chromium c ~ m p l e x e sit, ~was found that CY does not vary appreciably with potential. Experimental accuracy and extension of the explored potential range were such that there is little doubt that if an CY variation of the magnitude predicted by the Marcus theory had occurred it would have been detected unambiguously. With the other type of systems, involving the reduction of the nitro compounds tert-nitrobutane, nitromesitylene, and nitrodurene in acetonitrile and dimethylformamide (DMF), a distinct variation of a with potential was f o ~ n d It . ~is~clearly ~ beyond experimental uncertainty and its magnitude matches the prediction of the Marcus theory. These two series of results may not be as conflicting as they look a t first sight. In the first case, charge transfer is slow ( k s lo4 cm s-l) and involves, therefore, besides solvent reorganization, a very significant ligand-metal vibrational contribution. In the second case, charge transfer is much faster (ks in the range 10-2-1 cm s-l) and involves mainly solvent reorganization. Anharmonicity is thus likely to be encountered in the first case much more than in the second. It is tempting to anticipate from this that significant a variations should be generally observed with relatively fast charge transfers such as those occurring with organic aromatic molecules in nonaqueous solvent^.^ It was the main purpose of the work reported here to investigate this point by extending the analysis to the reduction in DMF of other aromatic compounds than the
Garreau, Saveant, and Tessier
two previously mentioned nitroaromatics, namely, terephthalonitrile, phthalonitrile, and p-diacetylbenzene. On the other hand, the previous study of the electron transfer kinetics of the latter two compounds was carried out by using convolution potential sweep voltammetry. This technique appears to be perfectly suited to the investigation of the kinetics of moderately fast charge transfers as, e.g., tert-nitrobutane in acetonitrile and DMF, and nitromesitylene and nitrodurene in a c e t ~ n i t r i l e It . ~is, ~ ~however, at the limit of its performance in the case of the reduction of the two last compounds in DMF and this leads to rather poor accuracy in the determination of CY variations. This is the reason why we used an ac impedance technique in the present work for investigating the reduction of the two nitriles and p-diacetylbenzene as well as the reduction of nitromesitylene and nitrodurene in DMF. The fundamental harmonic characteristics of the kinetics of a charge transfer reaction A+le@B in the general case where the potential dependence of the rate constant is not a priori specified i / F S = k(E)[(C.& - ( C B )exp(F/RT)(E ~ - E")]
(i is the current, E the electrode potential, S the electrode surface area, Eo the standard potential of the A/B couple, k ( E )the potential-dependent rate constant, and (CJO and (CB)oare the concentrations of A and B at the electrode surface) are obtained by a modification6 of the theory developed in the case of Volmer-Buttler behavior.' In this
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979
Electrochemical Transfer Coefficient
3005
LOG,, k ( Edc) 1 . e
,to
C
0
6 b
b
.t
.1
. B
OB
+ D
* t 6
a C 0
4D
& E
O E 4
0
0.
0.8
t
.c
L 4
t
t
0.1
E-E"/V
-
-d
0.8
C
E-E'/V
0
r *
I
. . b b
0.1
I
0.2
0.2
0
E-E"/V
0.1
0
E-E"/V
Figure 2. Charge transfer rate and transfer coefficient as functions of the dc potential: (c) 0.95 mM terephthalonitrile; (d) 0.94 mM phthalonitrile. Frequency: (9)2500, (C) 5000, (D)10000, (E) 20000 Hz.
context, k(EDc)is obtained from the Faradaic resistance (Rf) and capacitance (C,) according to log [ ~ ( E D ~ ) / D A = -log " ~ ] [(R&$G- 1) x [ l + exp{(F/RT)(EDc - E1pr)ll/ ( 2 ~ ) ' / ~ 1 ( D A is the diffusion coefficient of A, w the angular frequency of the superimposed ac signal, EDc the electrode dc potential, and the reversible half-wave potential of the A/B system). DA and E1pr are provided by the height and location, respectively, of the minimum of the Faradaic capacitance as a function of the dc potential l/C@ = [4RT/FSCo(2wDA)'J2]cosh2 [ (F/2RT) ED^ - El/{)] where Co is the initial concentration of A. Rf and Cf are themselves extracted from the in-phase and out-of phase components of the fundamental harmonic current response taken into account the values of the cell resistance and the double layer capacitance as determined from a blank experiment. k(EDc)is thus obtained for a series of frequencies of the ac signal. The range of usable frequencies depends upon the magnitude of the charge transfer rate; for fast electron transfer low frequencies give rise to a diffusion-controled situation and the determination of k (EDc)becomes impossible. The rate constants of the systems investigated in the present work were relatively high which led to use frequencies ranging between 1000 and 20000 Hz. Since we were interested in detecting and evaluating variations of LY with potential, another requirement to be met by the experimental technique was to determine Rf and Cf for a large number of values of the dc potential on both sides of the half-wave potential. In
this purpose, the in-phase and out-of-phase component of the ac current were converted into digital form then stored and treated in an on-line computer. A detailed description of the instrumentation and procedures used is given elsewhere.G
Experimental Section The experiments were carried out at 22 " C in freshly distilled DMF containing 0.5 M Bu,NI (Fluka) as supporting electrolyte. The working electrode was a mercury drop of known surface area hanging on a small platinum disk plated with goldsG The reference electrode was an aqueous saturated calomel electrode. In the following, all the potentials will be referred to this electrode without further mention. The non-Faradaic resistance, cell resistance, and sampling resistance was about 220 D and the double layer capacitance about 0.2 pF. The Faradaic resistance and capacitance ranges between 44 and 1200 Q and between 0.04 and 1.1pF, respectively. Most of the substrates were from commercial origin and were used as received: nitromesitylene, phthalonitrile (Fluka), terephthalonitrile (Merck), p-diacetylbenzene (Eastman). Nitrodurene was prepared from dinitrod ~ r e n e(Fluka). ~,~ Results Figures 1-3 show the log k(EDc)vs. EDc plots obtained with each compound for a series of frequencies, using the procedure described above. They appear as bent toward the potential axis in each case thus showing that the apparent transfer coefficient aap= -(RT/F) a In h(EDc)/aEDc
3006
No. 23, 1979
The Journal of Physical Chemistry, Vol. 83,
Garreau, Saveant, and Tessier
151 l""NIOn U
0 0 0 0 0 0 0 0 0 0
??????????
,to
~ 0 0 0 0 0 0 0 0 0 0
.to
I
c
0.1
I gI
+I
A'
t1 tl +I +I
+I
t! t' +I
E- E"/V
0
gap
0.8
+'
*+
dririridri
>
0
0
0
c\Ic\Ic\I
0
0
0
0000000000 tl +I
tl
tl
tl
tl
+I
t' +I
+I
~mcclmooorimffiu5
?r ri no?or no? o? ron ?o?o? o 0
0.2 --
0.1
E-E"/V
0
.I.-
r v ? - m m o m
Figure 3. Charge transfer rate and transfer coefficient as functions of the dc potential: 1.0 mM pdiacetylbenzene. Frequency: (B) 2500, (C) 5000, (D) 10000 Hz.
varies with potential.1° These variations are represented on the same figures with least-squares straight lines passing through the experimental points. Figure 4 shows the variations of the potential difference between the outer Helmoltz plane (OHP) and the solution, 42,with the dc potential as derived'l from the double layer capacitance obtained by ac impedance analysis of the DMF + 0.5 M Bu4NC104solution not containing the substrate. The point of zero charge was derived from the maximum of the electrocapillary curve obtained in the same solution. The transfer coefficient is related to its apparent value through the following relationships: a = a a p / ( l - a@r/d%c)
+
aa/aEDC = [1/(1- a4r/aEDC)l(daa,/itED,)
asp[ (a2d'r/aEDC2) / (1- ad%/aEDC)'] where q5 is the potential difference between the reaction site and the solution. Assuming that the reaction site is located a t the OHP (c#J~= &) one can see that the variations of 42with potential are too small to be responsible for the apparent variation of the transfer coefficient with potential. When deriving the transfer coefficient from its apparent values aa , the variation of 42with potential can even be neglected A comparison of the observed d variations with those predicted by the Marcus theory is summarized in Table I for two opposed working hypotheses regarding the estimation of the potential at the reaction site: dr = 0 and 4 = The following procedure13 was utilized to carry out this comparison: Introducing a second form of the transfer coefficient 01 = [ a + &(E" &)]/2
+
~ ( E D= c )ks,ap exp[-&'/RT)(EDc
-
Eo)]
which is used to derive the apparent standard rate constant
7
?????"?
c\I
I
v10000000(90?
i 0
Q,
0
0
I?
2
tl
+
Q,
W
tl
?
?
? i
d
0
0 0
0
Q,
Tr
0
m
Lc
0 0
m
m
0
0 Q,
~
~
~
~
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979 3007
Electrochemical Transfer Coefficient
TABLE 11: K i n e t i c Characteristics a r o u n d E”
R,N+ reactant
concn, temp, k s , a p r M “ C c m s-’
a(E”)
0.5a
30 22 2’2
0.15 0.093 0.1 5
0.50 0.49 0.45
O.la O.la O.lb 0.5a
30 22 25 22
0.28 0.20 0.43 0.29
0.50 0.52 0.50 0.51
0.5‘“ 0.5a
22 22
0.68 0.82
0.54 0.48
0.5a 0.v
22 22
1.4 2.0
0.60 0.62
O.la
nit r o d u r e n e
0.1a nitromeaitylene
ref
14 4 this work
14 4 12 this
work terephthalonitrile
phthalonitrile -0.5
-1,5
ECV)vs SCEI
J
Figure 4. OHP potential and first and second derivative as functions of the electrode potential.
ks,apfrom the log k(EDc) - ED^ plots (Figures 1-3), taking E” = Eljzr.The standard rate constant, k,, is then derived from
k , = ks,ap exp(-a&F/RT) in each of the two cases (0, = 0 and 4 , = The reorganization factor h is further obtained from k , according to k , = Zelexp(-h/4RT) Z, = ( R T / ~ T M )(~M/ is ~ the molar mass) being the electrochemical collision frequency. The predicted potential dependency of a with potential is finally obtained from aa/aEDc = F/4X
Discussion Four of the five compounds considered here have already been investigated in DMF as far as determination of the kinetic characteristics at the standard potential are con~ e r n e d . ~These J ~ previous data are compared with our own results in Table 11. The agreement is excellent taking into account that in some cases there are differences in temperature, nature, and concentration of the supporting electrolyte. Turning back to the central point of the present work, it can be concluded from the results shown in Table I that the transfer coefficient does vary with potential in each of the five cases we have studied. The results obtained with nitrodurene and nitromesitylene in DMF confirm and reinforce the observations made on the same compounds with convolution potential sweep ~ o l t a m m e t r y .The ~ accuracy of the present ac determinations is indeed markedly better than with the convolution technique which was close to the upper limit of its performances for the reduction of these two compounds in DMF. Although the agreement is not excellent, the magnitude of the observed a variations are on the same order as predicted by the Marcus theory in all cases (Table I). It is not understood for the moment why the two nitro compounds give rise to a difference between the observed and the predicted a variations clearly larger than with the other compounds. The concordance between theory and experiment can, however, be considered as satisfactory when taking into account the
‘“
R = Bu.
5 this work
5 this work
R = Et.
crudeness of the Marcus harmonic model. Rather than an unexpected quantitative agreement, the important point is indeed that the a variations are experimentally significant indicating a definite curvature of the potential energy surfaces. One consequence is that the experimental observation on an a value significantly differing from 0.5 may soundly serve to evaluate the proximity of the transition state to either the reactant or the product along the reaction coordinate (Hammond postulate) in the context of outer-sphere electron transfer reactions. Joining the results obtained in this work, which regard aromatic compounds bearing different functional groups, to the similar observations previously made with tertnitrobutane in acetonitrile and DMF,2#4 nitrodurene and nitromesitylene in acetonitrile4and benzaldehyde in ethanolI5 allows us to conclude that the potential dependence of the transfer coefficient appears as a general feature of organic molecules at least those for which the electron-delocalizing ability is such as to result in fast and solvation controlled charge transfer.
Acknowledgment. This work was supported in part by the CNRS (Equipe de Recherche AssociBe No. 309 “Electrochimie MolBculaire”). References and Notes Schmidt, P. P. Spec. Period. Rep. Electrochem. 1974, 5, 21. SavBant, J. M.; Tessier, D. J . flectroanal. Chem. 1975, 65, 57. Weaver, M. J.; Anson, F. C., J. Phys. Chem. 1976, 80, 1861. SavBant, J. M.; Tessier, D. J. Phys. Chem. 1977, 87, 2192. Kojima, H.; Bard, A. J. J . Am. Chem. SOC. 1975, 9 7 , 6317. Garreau, D.; SavBant, J. M.; Tessier, D. J . Nectroanal. Chem. I n press. Smith, D. E. In “Electroanalytical Chemistry”, Bard, A. J., Ed.; Marcel Dekker: New York, 1966; Vol. 1, pp 26-33. Birtles, R. H.; Hampson, G. C. J . Chem. SOC.1937, 70, 1. Illuminati, G. J . Am. Chem. SOC.1952, 7 4 , 4951. I n a recent ac study of nitromesitylene” in acetonitrile and DMF it was stated that a does not vary with potential. However, this conclusion was not drawn from a systematic determination of a as a function of the dc potential but merely from the fact that a was found to be close to 0.5 at Eo $2. Delahay, P. In “Double Layer and Electrode Kinetics”; Interscience: New York; 1965, pp 33-35. Fawcett. W. R.; Lasia, A. J. Phys. Chem. 1978, 82, 1114. Marcus, R. A. J . Chem. Phys. 1965, 43. 679. Peover, M. E.; Powell, J. S. J. flectroanal. Chem. 1969, 20, 427. Savgant, J. M.; Tessier, D. J. Phys. Chem. 1978, 82, 1723.
+
