J. Phys. Chem. 1995, 99, 511-515
511
A Kinetic Method for Determination of Redox Potentials: Oxidation of Tetraarylborates Sean Murphy and Gary B. Schuster*?+ Department of Chemistry, University of Illinois, Roger Aahms Laboratory, Urbana, Illinois 61801 Received: November 4, 1994@
A method to obtain the oxidation potentials of tetraarylborates was developed which uses electron transfer rate constant measurements. The keys to the method are choosing appropriate electron acceptors, using Marcus theory of electron transfer, and independently determining the maximum rate for electron transfer. When these criteria are met, oxidation potentials of reasonable accuracy and precision are obtained.
Introduction Recently, we described a method by which the oxidation potentials of tetraarylborates are estimated from the measured electron transfer rate constants to a set of naphthalene-derived acceptors.' In the method described, the fluorescence of the naphthalenes was quenched and electron transfer rate constants were calculated using the kinetic scheme in eqs 1 and 2. The borate is D-,and the naphthalene is shown as the excited state A*. In this scheme, the donor and acceptor diffuse together ( k w ) and are also able to diffuse apart (k-diff). While they are nearest neighbors, electron transfer can occur (ket). The radical pair may transfer an electron back to the excited state (k-et), transfer an electron back to form the ground state ( k d , or diffuse apart (ksep). In most cases, back electron transfer to the ground state is much more rapid than to the excited state, so k-et can be ignored.
In the method for calculating the oxidation and reduction potentials from kinetic data, an activation energy ( A d ) for the reaction is calculated from electron transfer rate constants using the Eyring equation (eq 3) where kmax is the maximum rate constant for electron transfer and the other symbols have their standard meanings. The activation energy is converted to a free energy change of electron transfer (AG,,) using Marcus theory (eq 4). Finally, the oxidation (or reduction) potentials (Eoxor E d ) can be calculated from eq 5, where Em is the singlet energy of the acceptor, Z1 and ZZare the charge numbers of the acceptor and donor, respectively, e is the charge of an electron, €0 is the permittivity of free space equal to 8.85 x Cz/(N mz), E is the dielectric constant, and I-DA is the charge separation distance. In the present case of a neutral acceptor (Zl = 0) and an anionic donor (Zz = -l), the last term is zero because there is no Coulombic attraction in either the reactants or the products. k,, = k,,
exp(-A&IRT)
(3)
+ AGet)'/4A
(4)
AGS = (A AGet = E,, - Ered- E ,
+ (2, - 2, - l)(e2/4nc,crD,)
(5)
Current address: School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332. Abstract published in Advance ACS Absfracts, January 1, 1995. @
0022-3654/95/2099-05 11$09.00/0
TABLE 1: Tetraarylborate Structure and Oxidation Potentials abbrev substitutions" Em (V vs SCE) 0.55 4 m RI-4 = 4-methylphenyl 0.59 R1-3 = 4-methylphenyl, FQ = phenyl 3 m 0.63 2 m R1-2 = 4-methylphenyl, R3-4 = phenyl 0.68 lPTB R1= 4-methylphenyl, R2-4 = phenyl O.7lb 40TB R1-4 = 2-methylphenyl 0.71b 30TB Rl-3 = 2-methylphenyl, FQ = phenyl 0.71 20TB RI-2 = 2-methylphenyl,R3-4 = phenyl 0.75 1om RI = 2-methylphenyl, RZ-4 = phenyl R1-4 = phenyl 0.76 PHB 0.56 DMB R1-4 = 3,5-&methylphenyl 0.93 FLB R1-4 = 4-fluorophenyl 0.36 RI-4 = 4-methoxyphenyl MOB 0.33 R1-4 = 4-isopropoxyphenyl POB Borates are of the general type -BR1R2R3FQrwhere the 1-position is ipso to the boron and the 4-position is para where the R groups are phenyl rings. The 2-methyl groups hinder approach to the boron atom. In this report we follow the basic method outlined above with two important additions. The first is that we use more than one set of electron acceptors and thus obtain a more reliable measurement of the borate oxidation potentials. The second is that we have independently determined km, and found that the previous assumption that it is ca. 1 x 10" s-l is not valid. We have also obtained independent evidence that Marcus theory is a better predictor of redox potentials than other electron transfer relationships. With these modifications, we obtain reliable measures of tetraarylborate oxidation potentials spanning a range of 0.6 V.
Results and Discussion Oxidation Potentials of Tetraarylborates. The first set of oxidation potentials determined by the enhanced method are for the series of mixed borates described in the previous paper.' These borates are substituted with phenyl, o-tolyl, or p-tolyl groups (see Table 1). In addition to the methyl-substituted naphthalene acceptors used in the previous work, a set of methyl-substitutedanthracene acceptors was also employed. The two sets of electron acceptors are shown in Figure 1, and their reduction potentials, singlet energies, and fluorescence lifetimes are gathered in Table 2. The electron transfer rates (k&s) were measured by observing the quenching of acceptor fluorescence by the borate and treating the data with standard Stem-Volmer kinetic procedures. Classical Marcus theory is used to fit the observed quenching rates and obtain values for AGet. Equation 6 is derived from the kinetic expression for the quenching experiment?z the Eyring equation, and classical Marcus theory (eqs 1-5)." The 0 1995 American Chemical Society
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512 J. Phys. Chem., Vol. 99, No. 2, 1995
the unknowns in eq 6 are A and AG,,. In the calculation for AG,,, the only unknown is E,, of the borate. NAP
2NA
ANT
2AN
mea: 0Q$Q
In previous work we found that all of the borate-naphthalene combinations have essentially the same reorganization energy (A) and thus can be fit onto the same Marcus curve. The borate-anthracene combinations also have a single reorganization energy, but one that is smaller than that for the naphthalene set. Thus, when the fitting procedure is performed with the two classes of electron acceptors, the rate constants were fit to two curves. The complete data set fit to Marcus theory uses 57 quenching rate constants and 11 unknowns which are the two reorganization energies and nine oxidation potentials. The result is shown in Figure 2. The oxidation potentials are listed in Table 1, and the reorganization energies obtained are 1.85 and 1.97 eV for the anthracene and naphthalene series, respectively. The oxidation potentials are lower than previously reported,' and this is due mostly to the use of a higher maximum rate constant for electron transfer. From the reorganization energies for borate electron transfer to anthracenes and naphthalenes, the oxidation potentials for other borates can be determined from kobs. For example, tetrakis(3,5-dimethylphenyl)borate gives kobs = 8.1 x lo9, 4.4 x lo9, and 2.9 x lo9 s-l M-' for NAP, 2NA, and 23N, which gives E,, = 0.56 V vs SCE. Tetrakis(4-fluoropheny1)borate has the highest oxidation potential measured, and only one acceptor, naphthalene, could be used. In this case kobs = 1.3 x lo8 s-l M-l, which corresponds to E,, = 0.93 V vs SCE. The oxidation potentials of tetrakis(4-methoxypheny1)borate (MOB) and tetrakis(4-isopropoxypheny1)borate(POB) could not be determined accurately with the naphthalenes and anthracenes of Figure 1 because the quenching rate constants are too close to the diffusion limit. Naphthalenes with either one or two methoxy groups were developed as electron acceptors to measure these oxidation potentials. These methoxynaphthalenes are electron-rich, and thus the electron transfer rate constants are slowed to below the diffusion limit. The data describing the properties of this set are gathered in Table 2 . The methoxynaphthalene series of electron acceptors was tested with 4PTB and 3PTB using the oxidation potentials
Me
3NA
23N
9AN DMA
Me
26N
Figure 1. Electron acceptors used for determinationof the mixed borate oxidation potentials. TABLE 2: Properties of the Electron Acceptors Used for the Borate Oxidation Potential naphthalene 1-Me-naphthalene 2-Me-naphthalene 1,4-Me-naphthalene 2,3-Me-naphthalene 2.6-Me-naphthalene
1.40 1.33 1.30 1.29 1.23 1.21
-2.54d -2.57 -2.59 -2.57 -2.64 -2.62
3.94 3.90 3.89 3.86 3.87 3.83
89.5 72.1 54.5 52.9 70.5 38.1
anthracene 2-Me-anthracene 9-Me-anthracene 9.10-Me-anthracene
1.33 1.25 1.22 1.12
-1.96 -2.00 -1.97 -1.98
3.29 3.25 3.19 3.10
4.8 4.1 7.9 15.4
1-MeO-naphthalene 2-MeO-naphthalene 2,7-MeO-naphthalene 2,3-MeO-naphthalene 2,6-MeO-naphthalene
1.21 1.13 1.12 1.11 0.92
-2.65" -2.60 -2.68 -2.73 -2.60
3.86 3.73 3.80 3.84 3.52
13.5 12.5 14.4 18.8 10.0
Reduction potential of the excited state vs SCE in acetonitrile. vs SCE. Most potentials were measured in dimethylformamide. Since the dielectric constant for this solvent (36.7) is almost identical to the value for acetonitrile (36.2), the reduction potentials are the same. Fluorescence lifetime in deoxygenated acetonitrile. All methylsubstituted acceptors from ref 12 except 9,lO-Me-anthracenewhich was measured in this laboratory by X. Yang and G. B. Schuster. e Methoxysubstituted naphthalenes from ref 13. specific values for kdiff = 2 x 1O'O s-l M-I, k-dlff = 2 x 1O'O s-l, k,, = 1 x 1013 s-l, and T = 294 K are known, and thus
T 10.0
q
\
_-_ 9.5t 0
-
9.0
t 8.0 ! -1 .o
-0.9
-0.8
-0.7
, -0.6
-0.5
-0.4
AG (eV) Figure 2. Marcus theory fit to the ortho (open markers) and puru (filled markers) series. The markers are as follows: 4PTB = squares, 3PTB = diamonds, 2PTJ3 = triangles, lPTB = circles, PHB = x and the ortho series follows the same pattern.
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J. Phys. Chem., Vol. 99, No. 2, 1995 513
T
4PTB 3PTB A MOB 0 POB -MeO-naphthalenefil .- - __ - - - anthracene fit Me-naphthalenefit
10.0
9.5 YI
d
-8 9.0
0.0 -1.1
I
-1 .o
-0.9
-0.8
-0.7
-0.5
-0.6
-0.4
-0.3
AG (eV) Figure 3. Quenching of methoxynaphthalenes with borates. The solid line is the best fit of the data; the dashed line is the fit with the reorganization energy set to that observed for the anthracene-based acceptors; the dotted line is the fit with the reorganization energy set to that observed for the other naphthalene-based acceptors. TABLE 3: Quenching with Donors of Known Oxidation Potential I ,L,Lt-UUUCUIUAyUClIL.CUC
r?
9,lO-Me-anthracene 9-Me-anthracene 2-Me-anthracene anthracene
7.3 x 106 BDLb 1.2 x 108 1.8 x 109
9.7 x 7.2 x 8.7 x 1.3 x
electrochemical E,, (V) Marcus E,,, (V) Rehm-Weller E,,, (V)
1.34 1.34 1.47
1.12 1.12 1.27
108 109 109
1.5 x 1Olo 1.9 x 1Olo 2.2 x 1010
loLo
d
0.78 0.86 0.99
Quenching rate constants in acetonitrile (s-l M-l). BDL = below detection limit. All potentials vs SCE. Not measured.
determined above. These data are shown in Figure 3. From these quenching rate constants, the reorganization energy for this class of electron acceptors with borates is found to be 1.93 eV. This value is intermediate between the anthracene and naphthalene values. Using this reorganization energy, the oxidation potentials for the alkoxy-substituted borates were determined (also shown in Figure 3). The calculated oxidation potentials are collected in Table 1. Testing the Kinetic Determination of Redox Potentials. The kinetic method was tested by using it to measure the oxidation potentials of compounds that show reversible waves with standard electrochemical technique^.^ At the same time, we examined the prospect of using the empirical relationship between kobs and AGet derived by Rehm and Welle9 in place of Marcus theory. The electron donors used in this test are N,N-dimethylaniline, 1,4-dimethoxybenzene, and 1,2,4-trimethoxybenzene. The quenching data are shown in Table 3 along with the measured oxidation potentials from the electrochemical experiments as well as the kinetic method using either Marcus theory or the Rehm and Weller empirical relationship. The results show that Marcus theory correctly predicts the oxidation potentials for the methoxy-substituted benzenes but not for dimethylaniline. On the other hand, the Rehm-Weller empirical relationship overestimates the oxidation potentials in all cases. The kinetic method is unreliable for dimethylaniline because the quenching rates are close to the diffusion limit, and consequently, little information is obtained about the actual electron transfer rate constant. The fitting procedure for these test reactions was different from the procedure described above. First, since both donor
and acceptor are neutral (Zl = ZZ = 0), the Coulombic work term in eq 5 is not zero but ca. 0.1 eV. This value was calculated with E = 36.2 D (acetonitrile) and m~estimated to be 3.8 %, from molecular modeling of the compounds with PCMODEL6 using an MMX force field. A second difference is that some of these reactions occur at significantly endergonic free energies. In the kinetic scheme, this means that back electron transfer to the excited state is possible, and this complicates the calculations. In the analysis above, the reactions are sufficiently exergonic to assure that back electron transfer to the ground state is much faster than to the excited state so that eq 6 could be used. For the control reactions, eq 7 must be used.
The rate constants for the back electron transfer reactions were calculated using Marcus theory (or the Rehm-Weller relationship when testing that equation for the method) from the free energies given in eqs 8 and 9. The value for ksep was calculated to be 1.1 x lo9 s-l by an empirical equation (eq 10) from Weller,' which gives the rate constant for separation of a contact ion pair to a solvent-separated ion pair. In the equation, 7 is the viscosity of acetonitrile (0.345 cP) and d,, is the distance between charge centers in the solvent-separated ion pair (estimated as 7 A).
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514 J. Phys. Chem., Vol. 99, No. 2, 1995
AG-et = -Eox
+ ErediE, (z,- z,- l)(c?*/&EO€rDA)
AG,,, = -Eox
+ Ered- (2, - Z, - 1)(e2/4nq,crDA)
Selection of Electron Acceptors or Donors for Kinetic Determination of Redox Potentials. The most important consideration for a set of electron acceptors or donors to be used in the kinetic determination of redox potentials is control of the reorganization energy. We found that acceptor size and the type of substituent affect the reorganization energy. However, by changing only the substitution pattem on a particular aromatic hydrocarbon nucleus, the reorganization energy appears to remain constant. A second important consideration is that the range of free energies should be as large as possible. With substituted aromatic hydrocarbons, there many possible pattems which can affect redox potentials and singlet energies. The change in reorganization energy with the size of the acceptor has been noted previously by Gould, Farid, and Young.* They suggested that smaller acceptors have a larger solvent reorganization energy because the solvent is more ordered in these cases. The decrease in reorganization energy for the methoxy-substituted naphthalenes could be interpreted as an increase in the area over which negative charge is spread since a portion of the charge can reside on the oxygen atom or atoms. However, the differences in reorganization energies are only slightly larger than the experimental error, and since there are only three examples, this conclusion is tentative. Additional certainty in the kinetic determination of redox potentials comes from using more than one set of electron donors or acceptors. By forcing the computed oxidation potentials to fit two curves instead of one, the possible solutions are reduced drastically. Also, if there is a systematic error in one set which is not detected, it is unlikely that the same error will occur in another set, and the use of two sets reduces the significance of this error. Determination of the Maximum Rate. The value of k,, of 1 x l O I 3 s-l was determined from our studies of electron transfer in cyanine borate ion pairs.9 In these experiments, a cyanine dye forms a contact ion pair with a tetraarylborate. Electron transfer occurs when the cyanine is irradiated, and since the donor and acceptor are already in contact, the reaction rate is not limited by diffusion. We observe a maximum rate for these reactions of (1-2) x 1013 s-l. Since the cyanine dyes and the aromatic acceptors are both relatively flat, planar molecules, the orbital overlap with the borates should be similar. The overlap is the primary factor controlling the maximum rate. Since the aromatic acceptors can encounter the borate in a large number of orientations, whereas the cyanine is held at a close, fixed orientation, the average maximum rate in the former case may be somewhat lower because of unfavorable orientations. Uncertainty in the maximum rate led to estimation of the borate oxidation potentials which were too high in our previous report. While the maximum rate is still not known with experimental certainty (a range of 5 x 10’2 to 2 x 1013 s-’ is possible), the resulting systematic error in the oxidation potentials of the borates is only 3~0.05V. Conclusions We have shown that reliable measurements of redox potentials can be obtained from kinetic data when the standard electro-
chemical experiments give “irreversible” results. The method was demonstrated for a variety of tetraarylborates, but it should be applicable to any redox potential. The key conditions to generalizing the method are using a large set of electron transfer rate constants with more than one series of acceptors or donors, carefully controlling the structure of the acceptor or donor set, using Marcus theory, and independently estimating the maximum rate for electron transfer.
Experimental Section General. Absorption spectra were recorded with a Varian Cary 1E UV-vis spectrophotometer in quartz cuvettes in 1 cm path length. ‘H and 13C NMR spectra were measured with a Varian XL200 or a General Electric QE300 instrument as noted. A Hewlett-Packard Series 5970 mass selective detector was used for low-resolution mass spectrometry. High-resolution fast atom bombardment mass spectra employed a Fisons VG 70-SE-4F. The following solvents were freshly distilled prior to use in reaction: tetrahydrofuran (THF) from sodium benzophenone ketyl and diethyl ether from sodium benzophenone ketyl. Melting points were determined by a Biichi melting point apparatus and are uncorrected. Sodium tetraphenylborate and sodium tetrakis(4-fluoropheny1)borate were purchased from the Aldrich Chemical Co. Spectrophotometric grade acetonitrile (Aldrich) was used without further purification. The aromatic hydrocarbons used in this work were obtained from commercial sources and purified as necessary by distillation or recrystallization. Fluorescence Quenching. Quenching of fluorescence was monitored on a Spex Fluorolog F l l l fluorometer. The fluorescer sample was made up to an optical density of 0.05-0.08. All fluorescer solutions were deoxygenated by bubbling with nitrogen. Aliquots of the borate solution were added, and no significant change in the emission spectrum of the hydrocarbon was observed. After correcting for borate absorption in some cases, the data were analyzed according to the Stem-Volmer relationship. The lifetimes of the fluorescers were measured with a Photon Technology Intemational LS-100 lifetime analyzer using the stroboscopic technique. General Procedure for Tetraarylborate Salts. The synthesis is based on the method reported by Vandenberg et al.’O The tetraarylborates were prepared from the corresponding aryl magnesium bromide and sodium tetrafluoroborate. The aryl bromide was converted to the aryl magnesium bromide using approximately 1 equiv of magnesium turnings by heating a THF or ether solution at reflux. To this solution was added 0.95 equiv of sodium tetrafluoroborate, and the mixture was heated at reflux overnight. The reaction mixture was concentrated in vacuo, and the residue was dissolved in acetonitrile and water. (Approximately 40 mL of acetonitrile and 10 mL of water per gram of starting bromide were used.) This solution was extracted once with a half equal volume of hexane, and the aqueous portion was filtered to remove any undissolved salts. To the aqueous solution was added 5-10 equiv of tetramethylammonium chloride to exchange cations with the borate. The mixture was made more polar by passing a stream of nitrogen over the solution to evaporate the acetonitrile and precipitate the tetramethylammonium borate. The borate was collected by vacuum filtration, dried under vacuum, and recrystallized from acetonitrile/water if necessary. Tetramethylammonium Tetrakis(3,5-dimethyIphenyl)borate. IH NMR (200 MHz, CD3CN) 6 6.88 (s, 8 H), 6.47 (s, 4 H), 3.02 (s, 12 H), 2.11 (s, 24 H). Anal. Calcd for C36IhNB: C, 85.52; H, 9.57; N, 2.77; B, 2.14. Found: C, 85.53; H, 9.68; N, 2.93; B, 2.15.
J. Phys. Chem., Vol. 99, No. 2, 1995 515
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Tetramethylammonium Tetrakis(4-methoxypheny1)borate. The borate salt was recrystallized from ethanol. 'H NMR (300 MHz, CD3CN) 6 7.09 (m, 8 H), 6.59 (d, J = 8.6 Hz, 8 H), 3.68 (s, 12 H), 3.03 (s, 12 H). Anal. Calcd for C32&04NB: C, 74.85; H, 7.85; N, 2.73. Found: C, 74.73; H, 7.80; N, 2.72. 4-Bromoisopropoxybenene. Prepared according to the procedure of Bradley and Robinson" by heating isopropyl iodide with Cbromophenoxide foxmed from Cbromophenol and 2-propoxide in 2-propanol. From 40.2 g (0.232 mol) of phenol was obtained 35.0 g (71%) of 4-bromoisopropoxybenzeneas a clear liquid. 'H NMR (300 MHz, CDCl3) 6 7.34 (d, J = 8.8 Hz, 2 H), 6.76 (d, J = 8.8 Hz, 2 H), 4.49 (septet, J = 6.1 Hz, 1 H), 1.32 (d, J = 6.1 Hz, 6 H). MS (EI, 70 eV), d z (relative intensity) 214 (15), 216 (15). TetramethylammoniumTetrakis(4-bopropoxhenyl)borate. 'H NMR (300 MHz, CD3CN) 6 7.06 (m, 8 H), 6.56 (d, J = 8.4 Hz, 8 H), 4.43 (septet, J = 6.0 Hz, 4 H), 3.03 (s, 12 H), 1.22 (d, J = 6.0 Hz, 24 H). H R M S (FAB) d z for C&gO4N2B (borate with two ammonium cations) calcd 699.5272, obsd 699.5288. Anal. Calcd for C4oH56O4NB (+l/&O): C, 76.24; H, 9.04; N, 2.22. Found: C, 76.19; H, 9.00; N, 2.25.
Acknowledgment. This work was supported by a grant from the National Science Foundation for which we are grateful. References and Notes (1) Murphy, S. T.; Zou, C.; Mien, J. B.; Ballew, R. M.; Dlott, D. D.; Schuster, G. B. J. Phys. Chem. 1993, 97, 13152-13157. (2) Rehm, D.; Weller, A. Isr. J . Chem. 1970, 8, 259. (3) Bolton, J. R.; Archer, M. D. In Electron Transfer in Inorganic, Organic and Biological Systems; Bolton, J. R., Mataga, N.,McLendon, G. L., Eds.; Advances in Chemistry Series 228; American Chemical Society; Washington, DC,1991; pp 7-23. (4) Marcus, R. A. Discuss. Faraday SOC.1960, 29, 21. ( 5 ) Zweig, A.; Hodgson, W. G.;Jura, W. H. J. Am. Chem. SOC.1964, 86, 4124,4130. (6) Version 4.0, Serena Software, Bloomington, IN, 1990. (7) Weller, A. Pure Appl. Chem. 1982, 54, 1885-8. (8) Gould, I. R.; Farid, S.; Young, R. H. J . Phorochem. Phorobiol. A: Chem. 1992,65, 133-147. (9) Murphy, S.; Schuster, G. B. J. Am. Chem. Soc., submitted. (10) Vandenberg, J. T.; Moore, C. E Cassaretto, F. P. Org. Magn. Reson. 1973,5,57-9. Vandenberg,J. T.; Moore, C. E.; Cassaretto, F. P.; Posvic, H. Anal. Chim.Acta 1%9,44, 175-83. (11) Bradley, W.; Robinson, R. J. Chem. SOC.1926, 2356-67. (12) Streitwieser, Jr., A.; Schwager, I. J . Phys. Chem. 1962,66,231620. (13) Zweig, A.; Maurer, A. H.; Roberts, B. G. J . Org. Chem. 1%7,32, 1322-9. JP943011L
