Oxidation Reactions of a Series of Benzidines: Electrochemical

J. Phys. Chem. C 2007, 111, 5805-5811

5805

Oxidation Reactions of a Series of Benzidines: Electrochemical Detection of Dimerization of Cation Radicals and Examples of Potential Inversion Caused by Very Small Steric Effects Norma A. Macı´as-Ruvalcaba and Dennis H. Evans* Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721 ReceiVed: January 30, 2007; In Final Form: February 21, 2007

It has been previously reported that cation radicals of some benzidines undergo dimerization. In the present work dimerization equilibrium constants have been determined by UV-visible absorption spectroscopy for the cation radicals of benzidines 1a-d. This dimerization reaction was shown to produce subtle but significant effects in cyclic voltammograms recorded for oxidation of the benzidines. It is shown that cyclic voltammetry is a simple and rapid technique to detect such reactions, whose quantitative evaluation must, however, be accomplished by other means. The oxidation of certain N-peralkylated benzidines having substituents in the 3 and 3′ positions, 1e-i, occurs in a single, two-electron oxidation process due to the fact that the two standard potentials for oxidation to the cation radical and dication, respectively, are very similar. In several cases, potential inversion occurs. That is, the potential for removal of the second electron is less positive than that for removal of the first. Causes of this potential inversion are discussed.

1. Introduction

CHART 1

Benzidines, 1, are prime examples of simple redox systems which, in nonaqueous media, undergo stepwise oxidation to form the cation radical and dication forms.1,2 In a recent study of o-dianisidine (1a, R ) R2 ) H; R1 ) OCH3), the two standard potentials for the cation radical/neutral couple (E°1) and for the dication/cation radical couple (E°2) were found to show normal ordering of potentials with E°1 - E°2 ≈ -0.2 V, i.e., it was more difficult to remove the second electron compared to the first. By contrast, the N-permethylated derivative (1e: R ) CH3; R1 ) OCH3; R2 ) H) displayed a single, two-electron oxidation peak, i.e., the potentials were either inverted or strongly compressed.3 The ethyl derivative (1f: R ) C2H5; R1 ) OCH3; R2 ) H) also showed a single oxidation peak but this was interpreted as being due to one-electron oxidation.3 In that work it was reported that oxidation of o-dianisidine (1a: R ) R2 ) H; R1 ) OCH3) at the first oxidation peak in dichloromethane resulted in the formation of the cation radical perchlorate salt.3 A similar salt has been isolated from 3,3′,5,5′tetramethylbenzidine (1d) and it is described as the salt of a dimer of the cation radical, which is a singlet (with a lowlying triplet state). This dimer of the cation radical, A22+, where A is the benzidine, was also shown to exist in solution.4 The dimer is thought to be a π-bonded species with a stacking interaction between the two biphenyl ring systems. Thus, oxidation of compounds such as o-dianisidine (1a) or 3,3′,5,5′tetramethylbenzidine (1d) should produce a mixture of monomeric cation radicals and their dimers. Will this weak interaction of the product of the electrode reaction cause discernible changes in the current-voltage response? In this work we have shown for the first time that the rapid, reversible π-dimerization of the cation radicals of five different benzidines can be readily detected by cyclic voltammetry and values of the dimerization equilibrium constant can be extracted from the data. * To whom correspondence should be addressed. E-mail: dhevans@ email.arizona.edu.

Theory for cyclic voltammetry with a fully reversible dimerization following electron transfer has previously been presented and discussed5,6 but it was more convenient for us to analyze our data by digital simulation. Another type of association reaction of cation radicals has been reported, especially

10.1021/jp070801p CCC: $37.00 © 2007 American Chemical Society Published on Web 03/24/2007

5806 J. Phys. Chem. C, Vol. 111, No. 15, 2007 for cation radicals of aromatic hydrocarbons. This reaction is the association of the cation radical with the neutral starting material to form what is often called a “cation radical dimer”, A2•+.7 These “dimers” are often isolated as insoluble salts but they are also present in solution.7h We are not aware of examples of the detection of A2•+ by voltammetric wave shape analysis, but hope to investigate the matter in future work. The majority of cases where reversible dimerization has been shown to follow electron transfer are those in which σ-bonded dimers are formed.8 In most such cases, the dimer can be detected, under appropriate conditions, through its separate oxidation or reduction peak whose magnitude can ideally give information about the dimerization equilibrium and rate constants. In the case of the π-bonded dimers described in this work, the formation and dissociation of the dimers is so rapid that separate voltammetric peaks for the dimer cannot be detected. Instead, the fact that a dimer is formed is signaled via subtle changes in the voltammetric peak shape. As stated earlier, the N-permethylated derivative of odianisidine (1e: R ) CH3; R1 ) OCH3; R2 ) H) shows a single two-electron oxidation peak indicating that the potentials are strongly compressed or perhaps inverted with E°1 - E°2 > 0.9 In the present work we have determined the extent of inversion for five substituted benzidines and have shown that the structural changes that underlie the inversion are quite subtle and depend on very minor steric factors. In this paper we report our first results on fast, reversible dimerization reactions. Studies of other systems will be reported later. 2. Experimental Section 2.1. Chemicals and Reagents. The solvent was acetonitrile and the electrolyte was tetrabutylammonium hexafluorophosphate (Bu4NPF6). Sources and treatment of solvent and electrolyte have been described.10 For preparation of the cation radical salts, dichloromethane (99.8%, anhydrous (400 °C dec. Anal. Calcd for C12H10Cl3N2O4: C 40.88; H 2.86; Cl 30.17; N 7.95; O 18.15. Found: C 39.74; H 3.24; Cl 30.90; N 7.30; O 20.31. The cation radical perchlorate of 1b (1b•+ClO4-) was prepared as follows. o-Tolidine (1b) (150 mg) was electrolyzed at 0.4 V vs Ag/AgNO3 under the same experimental conditions as described above. A dark blue solid was obtained in 65.3% yield. mp >400 °C dec. Anal. Calcd for C14H16ClN2O4: C 53.94; H 5.17; Cl 11.37; N 8.99; O 20.53. Found: C 54.12; H 5.09; Cl 11.30; N, 8.98; O 20.34. The cation radical perchlorate salts of 1a (1a•+ClO4-) and 1d (1d•+ClO4-) were prepared following the same procedure as described above for 1b•+ClO4- and 1c•+ClO4-. The preparation and identity of these radicals has been previously reported by Douadi et al.3 and Awano and Ohigashi,11 respectively. 2.2. Electrochemical Cells, Electrodes, and Instrumentation. In general, this equipment was the same as described earlier.10 The working electrode was a 0.3-cm diameter glassy carbon electrode whose area was determined to be 0.0814 cm2. The reference electrode was a silver wire immersed in 0.10 M Bu4NPF6/0.010 M AgNO3 in acetonitrile. The potential of this reference electrode was periodically measured with respect to the reversible ferrocene/ferrocenium potential in acetonitrile, and all potentials reported in this work are with respect to ferrocene. The temperature of the jacketed cell was controlled with a circulating bath. The reference electrode was at room temperature (nonisothermal operation). Voltammograms with only solvent and supporting electrolyte were recorded and subtracted from the voltammograms of the compounds to obtain backgroundcorrected data. All voltammetric experiments were conducted in acetonitrile containing 0.10 M Bu4NPF6. The determination of the magnitude of the solution resistance and its compensation were carried out as described.10 The resistance compensation was achieved as follows (total solution resistance, resistance electronically compensated, resistance used in simulations): 25 °C (140 Ω, 120 Ω, 20 Ω), 0 °C (190 Ω, 130 Ω, 60 Ω), -18 °C (220 Ω, 200 Ω, 20 Ω). Variation of the scan rate, V, was done in such a way that there was an approximately linear variation in log V. Thus, for scan rates between 0.1 and 30 V/s, the values chosen were 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10, 20, and 30 V/s (log V ) -1, -0.699, -0.523, -0.301, 0, 0.301, 0.477, 0.699, 1, 1.301, 1.477). Controlled potential coulometry was conducted as described earlier.12 2.3. Determination of the Dimerization Equilibrium Constant for the Cation Radicals of 1a-d. Measurements were performed with a Spectral Instruments, Inc., CCD array UVvis spectrophotometer equipped with a fiber-optic dip cell with a path length of 1.03 ( 0.03 cm. The absorption measurements were made at the λmax of the dimer (646-715 nm), in 0.10 M Bu4NPF6, Omnisolve acetonitrile (EMD) at 25, 0, and -18 °C. Equation 1 was fit to the apparent molar absorptivities,  ( ) A/C where A is the observed absorbance at total concentration of cation radical, C), as a function of C.

[ (

 ) 0.5 -

)]

-0.5 + x0.25 + 2KdimC D + 4KdimC

[

]

-0.5 + x0.25 + 2KdimC M (1) 2KdimC

Here Kdim is the dimerization equilibrium constant, D is the molar absorptivity of the dimer, and M is the molar absorptivity

Oxidation Reactions of a Series of Benzidines

J. Phys. Chem. C, Vol. 111, No. 15, 2007 5807

Figure 2. Spectra of 1.15 × 10-4 M o-dianisidine cation radical perchlorate (1a•+ClO4-) in acetonitrile as a function of temperature: -18, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, and 35 °C.

Figure 1. Cyclic voltammogram of 2.00 mM 3,3′-dichlorobenzidine, 1c, at 1.00 V/s and 25 °C (full curve). (A) Points: Digital simulation based on simple, stepwise two-electron oxidation. Simulation parameter values: E°1 ) 0.368 V, R1 ) 0.50, ks,1 ) 104 cm/s (reversible limit); E°2 ) 0.599 V, R2 ) 0.50, ks,2 ) 0.42 cm/s; Kdisp ) 1.2 × 10-4, kf,disp ) 380 M-1 s-1, kb,disp ) 3.1 × 106 M-1 s-1; DA ) 1.89 × 10-5 cm2 s-1; DA+ ) DA2+ ) 1.15 × 10-5 cm2 s-1. (B) Points: Digital simulation based on stepwise two-electron oxidation with fast, reversible dimerization of the cation radical. Simulation parameter values: E°1 ) 0.406 V, R1 ) 0.50, ks,1 ) 0.16 cm/s; E°2 ) 0.559 V, R2 ) 0.70, ks,2 ) 0.23 cm/s; Kdisp ) 2.7 × 10-3, kf,disp ) 1.0 × 105 M-1 s-1, kb,disp ) 4.0 × 107 M-1 s-1; Kdim ) 6.5 × 103 M-1, kf,dim ) 1.0 × 109 M-1 s-1; kb,dim ) 1.5 × 105 s-1; DA ) 1.70 × 10-5 cm2 s-1; DA+ ) DA2+ ) DAA2+ ) 1.10 × 10-5 cm2 s-1. Slow, irreversible decomposition of dication included with kf ) 0.17 s-1.

of the monomer cation radical. This equation was derived for the dimerization reaction in a manner analogous to that presented earlier for neutral/dication association.4c Owing to a slow decomposition of the cation radicals, the solutions were prepared in the following manner. Stock solutions of the cation radicals were prepared and maintained at ca. -20 °C. For experiments at -18 and 0 °C, increments of the stock solution were added to acetonitrile at the indicated temperature to prepare solutions with increasing concentrations of cation radical. Spectra were obtained quickly after each addition. For experiments at 25 °C, separate solutions were prepared from the -20 °C stock solutions and acetonitrile maintained at 25 °C and the spectra were obtained as quickly as possible after each solution preparation. 2.4. Calculations. Digital simulations were conducted with DigiElch, version 2.0, a free software package for the Digital simulation of common Electrochemical experiments (http:// www.digielch.de).13 The fitting routine in that program was used to establish the final best-fit parameter values for many of the variables. Complete geometry optimization and frequency calculations were performed according to the density functional theory (DFT), using the B3LYP/6-31G(d,p) level with the Gaussian 03 program.14 For each structure it was confirmed that there were no imaginary frequencies. For radicals, the corresponding unrestricted (UB3LYP) method was used. 3. Results and Discussion 3.1. Detection of Dimerization of Cation Radicals by Voltammetric Peak-Shape Analysis. Figure 1A is a voltammogram of 2.00 mM 3,3′-dichlorobenzidine, 1c, in acetonitrile. Apparently the process is the simple, stepwise, two-electron

Figure 3. Apparent molar absorptivity (absorbance/total concentration of 1a•+ClO4-) at 715 nm for various concentrations of cation radical for three different temperatures (filled circles). Full curves: Fits of the data according to eq 1 with molar absorptivities as shown and Kdim ) 1.76 × 103, 1.37 × 104, and 8.44 × 104 M-1 for 25, 0, and -18 °C, respectively.

oxidation of the benzidine to its cation radical and dication, according to reactions 2 and 3 (A is the benzidine, 1c).

A•+ + e- h A A2+ + e- h A•+ 2A•+ h A + A2+

E°1, ks,1, R1

(2)

E°2, ks,2, R2

(3)

Kdisp, kf,disp, kb,disp

(4)

The points in Figure 1A are from a best-fit simulation of the voltammogram, using reactions 2 and 3 along with disproportionaton reaction 4. The simulation parameters, given in the figure caption, correspond to reversible electron transfers and a rapid, reversible disproportionation reaction. Small improvements in the fit can be achieved by invoking unequal diffusion coefficients for the three species in the mechanism but the fit can never be made perfect. Although a reasonable fit between simulation and experiment was obtained in Figure 1A, some important discrepancies are apparent. The experimental current near the foot of peak Ia rises much more sharply than predicted by the simulation (points). In addition, the experimental current is less than that simulated between peaks Ia and IIa and, in general, peaks IIa, IIc, and Ic are somewhat sharper than indicated by the simulation. As mentioned in the introduction, dimerization of the cation radicals of benzidines has been detected. To determine if such a reaction

5808 J. Phys. Chem. C, Vol. 111, No. 15, 2007

Macı´as-Ruvalcaba and Evans

TABLE 1: Equilibrium Constants for the Dimerization Reaction of the Cation Radicals of Benzidines 1a-da Kdim/M-1 compd

25 °C

0 °C

-18 °C

-18 °Cb

D /M-1cm-1

M /M-1cm-1

λ/nm

1a•+ClO4 1b•+ClO4 1c•+ClO4 1d•+ClO4

1.76 × 103 6.10 × 103 6.50 × 103 5.37 × 103

1.37 × 104 1.10 × 105 4.07 × 104 1.19 × 104

8.44 × 104 5.94 × 105 1.15 × 105 3.22 × 104

6.17 × 104 4.19 × 105 9.20 × 104 2.72 × 104

1.73 × 104 4.00 × 104 3.60 × 104 3.56 × 104

500 ∼0 ∼0 160

715 646 660 661

a Determined by UV-vis spectroscopy in 0.1 M Bu4NPF6 in acetonitrile. See the Experimental Section. Three-point van’t Hoff plots give ∆H°dim ) -13.5, -16, -10, and -6 kcal/mol for 1a-d•+, respectively. Estimated indeterminate error in equilibrium constants is (10%. b Determined in the absence of Bu4NPF6.

will affect the simulation, it was added as a fast, reversible dimerization and the result is shown in Figure 1B. Clearly there is a profound improvement in the quality of the fit. It should be emphasized that the only new reaction in the mechanism used in Figure 1B compared to that in Figure 1A is the dimerization, reaction 5. This mechanism, with the parameters listed in the caption of Figure 1, was found to provide adequate fits for scan rates from 0.10 to 30 V/s.

2A•+ h A22+

Kdim, kf,dim, kb,dim

(5)

The value of Kdim used in the simulation in Figure 1B was 6.50 × 103 M-1, a value determined by spectrophotometric analysis (see below). When Kdim was allowed to vary to achieve the best fit between simulation and experiment, the result was Kdim ) 2.1 × 104 M-1. This rather large discrepancy is not unexpected in view of the relatively small adjustments in the shape of the voltammogram that are controlled by the magnitude of Kdim. The spectrophotometric determination of Kdim is a more direct measurement based, as it is, on a specific absorption band due almost entirely to the dimer. For this reason, Kdim was evaluated by spectroscopy and the values so obtained were later used in the analysis of the voltammograms. 3.2. Determination of the Dimerization Equilibrium Constants for Benzidines 1a-d. Temperature-dependent absorption spectra of the cation radical of o-dianisidine, 1a•+, are shown in Figure 2. The absorption band near 700 nm, due almost entirely to the dimer, is seen to grow from almost nil at 35 °C to prominence at -18 °C. The equilibrium constant for dimerization was measured at 25, 0, and -18 °C from studies of the absorbance at 715 nm as a function of the concentration of the cation radical, as described in the Experimental Section. The experimental results, along with fits according to eq 1, are shown in Figure 3 and the derived values of Kdim, D, and M are shown in Table 1 along with results for the cation radicals of 1b-d. Spectra for the cation radicals of 1b,c (see ref 4c for spectra of 1d•+) and plots like Figure 3 are given in the Supporting Information. As can be seen in Table 1, the λmax for the dimer falls in the narrow range of 646-715 nm and the band is entirely due to absorption by the dimer for 1b and 1c (M ≈ 0) while a minor contribution from the monomer is found for 1a and 1d. The value of Kdim for 1d•+ found at 25 °C, 5370 M-1, is in reasonable agreement with that reported (8700 M-1; recalculated according to eq 1) earlier4c but the value of ∆H° reported there (for a different range of temperatures) is more than twice that found in the present work. At -18 °C, values of Kdim were obtained in the absence and presence of 0.10 M Bu4NPF6 (Table 1). The presence of the electrolyte resulted in slightly smaller Kdim (15-30% lower). For consistency, the values in the absence of electrolyte were used in simulations of the voltammetric data at the three different temperatures.

TABLE 2: Results of Controlled Potential Coulometry for Benzidines, 1a-h and 1ja compd

Eox/V

n

Ered/V

% recovery

color of oxidized solution

1a 1b 1c 1d 1e 1f 1g 1h 1j

0.17 0.22 0.50 0.16 0.27 0.27 0.34 0.43 0.15

0.97 0.93 0.96 0.97 1.80 1.90 1.40 1.53 0.99

-0.10 -0.10 0.20 -0.10 -0.30 -0.20 -0.10 ND -0.10

40 80 43 95 22 77 24 ND 83

olive green bright green dark green bright green dark olive green dark purple dark red red-orange dark green

a

Electrolyses conducted at ambient temperature. Eox and Ered are the control potentials (vs ferrocene) for oxidation and subsequent reduction, respectively. n (Faradays per mole of reactant ) electrons per molecule of reactant) for the oxidation. % recovery is the charge recovered during the reductive electrolysis compared to charge passed in the preceding oxidation. Only in the cases of 1d and 1j was the original color restored upon reduction following oxidation. ND ) not determined.

3.3. Controlled Potential Coulometry. As the voltammetric results for 1a-d will be analyzed by a model involving initial one-electron oxidation followed by reversible dimerization of the cation radicals, controlled potential coulometry was carried out at the first anodic peak to confirm that the overall reaction was a one-electron process. The results are summarized in Table 2. For compounds 1a-d, the oxidation requires one electron within experimental error, but only in the cases of 1b and 1d was the amount of charge recovered upon subsequent reduction close to the oxidative charge. Loss of the cation radical was confirmed by cyclic voltammetric studies of the solution after oxidative electrolysis. So, it would appear that the initial oxidation reaction is formation of the cation radical, which is followed in some cases by slower decomposition reactions. Compounds 1e-h show a single two-electron oxidation process (see below). Electrolysis at potentials positive of the oxidation peak requires 1.4-1.9 electrons/molecule and the smaller percent charge recovered in the subsequent reductive electrolysis indicates that the dications are less stable than the cation radicals (Table 2). Compound 1j undergoes stepwise oxidation and electrolysis at a potential between the two oxidation peaks requires one electron per molecule and the subsequent reductive electrolysis indicates good recovery of the charge. Voltammograms of the solution after oxidative electrolysis show almost complete formation of the cation radical. Due to limited solubility, electrolysis of 1k was not attempted. 3.4. Fits of Voltammograms of 1a-d with Dimerization Equilibrium Constants Determined by Spectroscopy. Examples of fits of simulation to experimental voltammograms for 1a,b,d may be found in Figures 4-6. Each of these figures contains the experimental voltammogram (solid curve), the bestfit simulation including dimerization of the cation radical (open circles) and the best-fit simulation without dimerization (dashed curve). (Data for 1c were shown in Figure 1.) The best-fit values

Oxidation Reactions of a Series of Benzidines

Figure 4. Voltammogram of 1.30 × 10-3 M o-dianisidine, 1a, at 1.00 V/s and 0 °C (full curve). Best fit simulation for two-step oxidation without dimerization of the cation radical (dashed). Best fit simulation for two-step oxidation with fast, reversible dimerization of the cation radical with simulation parameter values as summarized in Table 3 (a full list of parameter values is given in the Supporting Information) (open circles).

J. Phys. Chem. C, Vol. 111, No. 15, 2007 5809

Figure 6. Voltammogram of 1.18 × 10-3 M 3,3′,5,5′-tetramethylbenzidine, 1d, at 1.00 V/s and 0 °C (full curve). Best fit simulation for two-step oxidation without dimerization of the cation radical (dashed). Best fit simulation for two-step oxidation with fast, reversible dimerization of the cation radical with simulation parameter values as summarized in Table 3 (afull list of parameter values is given in the Supporting Information) (open circles).

TABLE 3: Summary of the Simulation Parameter Values for the Reversible Dimerization of Benzidines 1a-d and 1j at Three Different Temperaturesa compd 1a 1b 1c 1d

Figure 5. Voltammogram of 3.52 × M o-tolidine, 1b, at 1.00 V/s and -18 °C (full curve). Best fit simulation for two-step oxidation without dimerization of the cation radical (dashed). Best fit simulation for two-step oxidation with fast, reversible dimerization of the cation radical with simulation parameter values as summarized in Table 3 (a full list of parameter values is given in the Supporting Information) (open circles). 10-3

of the principal parameters for the dimerization mechanism are summarized in Table 3. For simulations without dimerization, the dimerization reaction was simply removed from the simulation and the potentials were readjusted to obtain best fit. Examples of additional simulations, at various temperatures, scan rates, and concentrations are given in the Supporting Information along with complete tables of simulation parameters. Figures 4-6 show that the fits with dimerization are definitely superior to those without. Both fits, at any given temperature and concentration, were based on the parameter values that provided the best fits for scan rates from 0.1 to 30 V/s. That is, for any given scan rate (e.g., those shown in Figures 4-6) somewhat improved fits might be obtained by further adjustment of parameter values but such adjustments would give poorer agreement at other scan rates. For dimerization equilibrium, the fraction present as monomer is 0.5 when KdimC ) 1 (where C is the initial concentration of monomer). Thus, it is not surprising that KdimC must be greater than unity for most of the monomer to dimerize and to affect the shape of the voltammograms significantly. The values of KdimC for the simulations in Figures 4-6 are 18, 2100, and 14, respectively. By contrast when KdimC is small, the dimerization

1j

T/ °C

E°1/ V

E°2/ V

E°1 - E°2/ V

Kdim/ M-1

kf,dim/ M-1 s-1

106D/ cm2 s-1

25 0 -18 25 0 -18 25 0 -18 25 0 -18 25 0 -18

0.092 0.087 0.088 0.136 0.124 0.127 0.408 0.392 0.380 0.080 0.047 0.021 0.036 0.027 0.022

0.241 0.225 0.213 0.304 0.278 0.269 0.559 0.548 0.542 0.254 0.251 0.244 0.228 0.212 0.219

-0.174 -0.204 -0.223 -0.169 -0.154 -0.142 -0.149 -0.138 -0.126 -0.151 -0.156 -0.162 -0.192 -0.185 -0.197

1.5 × 103 1.4 × 104 8.4 × 104 6.1 × 103 1.1 × 105 5.9 × 105 6.5 × 103 4.1 × 104 1.2 × 105 5.4 × 103 1.2 × 104 3.2 × 104 0 1.3 × 102 2.1 × 102

7.0 × 107 6.0 × 108 1.7 × 109 1.3 × 108 1.6 × 109 2.3 × 1010 1.0 × 109 7.0 × 109 5.0 × 109 8.0 × 108 2.8 × 109 3.0 × 109

14.9 10.8 8.6 14.4 10.4 8.7 15.8 11.7 8.8 14.3 10.5 7.1 15.7 12.9 9.90

1.9 × 108 4.4 × 108

a E°1 and E°2 and D correspond to the average values obtained by simulation for sets of data obtained at two different concentrations of the corresponding benzidine. Kdim are the values obtained by spectrophotometric measurement and kf,dim correspond to the values that give good fits to the experimental voltammograms obtained at scan rates from 0.1 to 30.0 V/s and at two different concentrations. D is the common diffusion coefficient for A, A•+, and A2+. See the Supporting Information for DAA2+. Estimated indeterminate error for rate and equilibrium constants is (10% and (5 mV for potetntials.

scarcely affects the voltammogram. An example is given in Figure 7 for 1j where KdimC is estimated to be only 0.7 at -18 °C. The fit with dimerization included (circles) is slightly superior to that without dimerization (dashed) but there is no doubt that it would be impossible to conclude that dimerization was occurring based solely on the voltammetric peak shape. 3.5. Examples of Potential Inversion. Those N-peralkylated benzidines that also contain substituents in the 3 and 3′ positions behave differently from benzidines containing NH2 groups. Figures 8 and 9 are examples of voltammograms for 1f and 1g, respectively. In each case, the two one-electron oxidation processes seen with other benzidines are replaced by a single two-electron process with both electron transfers being relatively reversible. The points in Figures 8 and 9 are simulations based on two standard potentials, E°1 and E°2, that are quite similar. The disproportionation reaction (reaction 4) was not included as it did not affect the simulations. A summary of the simulation parameters for 1e-h and 1k is given in Table 4 and a full listing

5810 J. Phys. Chem. C, Vol. 111, No. 15, 2007

Macı´as-Ruvalcaba and Evans TABLE 4: Summary of Simulation Parameter Values for 1g-i and 1ka

Figure 7. Voltammogram of 3.48 × 10-3 M N,N,N′,N′-tetramethylbenzidine, 1j, at 1.00 V/s and -18 °C (full curve). Best fit simulation for two-step oxidation without dimerization of the cation radical (dashed). Best fit simulation for two-step oxidation with fast, reversible dimerization of the cation radical with simulation parameter values as summarized in Table 3 (a full list of parameter values is given in the Supporting Information) (open circles).

Figure 8. Cyclic voltammogram of 3.94 mM N,N,N′,N′-tetraethyl3,3′-dimethoxybenzidine, 1f, at 1.00 V/s and 25 °C (full curve). Simulation based on parameter values summarized in Table 4 (a full list of parameter values is given in the Supporting Information) (open circles).

Figure 9. Cyclic voltammogram of 3.50 mM N,N,N′,N′,3,3′-hexamethylbenzidine, 1g, at 1.00 V/s and 25 °C (full curve). Simulation based on parameter values summarized in Table 4 (a full list of parameter values is given in the Supporting Information) (open circles).

appears in the Supporting Information. The reactions are found to be simple electron transfers with relatively large electrontransfer rate constants but with small differences in standard potential, E°1 - E°2 being +0.001, -0.040, +0.045, and +0.086 V for 1e-h, respectively. In most cases where E°1 - E°2 is severely compressed or even inverted (E°1 - E°2 > 0) there are significant steric interactions in one or more of the three

compd

E°1/V

E°2/V

E°1 - E°2/V

105 D/cm2 s-1

1e 1f 1g 1h 1ib 1k

0.124 0.064 0.253 0.391 0.47 0.356

0.123 0.104 0.208 0.305 0.37 0.503

+0.001 -0.040 +0.045 +0.086 +0.10 -0.147

1.53 1.24 1.51 1.52 1.36 c

a Temperature: 25 °C. Potentials expressed with respect to the ferrocenium/ferrocene potential. Diffusion coefficients assumed to be identical for all species. With the exception of 1g, the E° and D values correspond to the average from two concentrations. See Table 3 for error estimates. b Approximate values. Poor fits at low scan rates. c Not determined as this slightly soluble compound was studied with a saturated solution.

oxidation states of the system. Structure 1e2+ shows how, in the dication, the dialkylamino groups will attempt to move into the plane of the biphenyl system thus provoking steric stress with substituents in the 3 and 3′ positions. The same tendency, but weaker, is likely to be at work in the cation radicals.

When the steric interactions in the dication are strong as in the dication of 3,6-bis(dimethylamino)durene (2), profound changes in structure occur. In the case of 22+, the N-methyl/ ring methyl interactions cause the central six-membered ring to fold into a boat-form.15 Such significant changes in structure cause large changes in orbital energies that eventually lead to the removal of the second electron being easier than the first. However, in the case of 1e2+ the calculated structure (see the Experimental Section) does not differ in major ways compared to the cation radical and neutral compound. The cation radical and dication show less pyramidalization at nitrogen than does the neutral and the dimethylamino groups tend to turn into the plane of the adjacent ring system in the cations. Also, the twist angle between the two biphenyl rings closes down in the cation radical and dication compared to the neutral. Nevertheless, the changes are small compared to the ring-folding that occurs in 22+. However, the changes in structure on going from neutral to cation radical to dication in 1e do bring about changes in the energies of the species that lead to compression of E°1 - E°2 to a value near zero (Table 4). This can be seen from the computed (DFT) gas-phase energies of disproportionation (reaction 4) for 1e as compared with 1a. These are +95.26 kcal/ mol (-4.13 V) for 1a and +73.80 kcal/mol (-3.20 V) for 1e. These gas-phase potential differences of several volts, indicative of strongly disfavored disproportionation, are reduced in the solution phase to the range of tenths of volts by the solvation energies of the three species, particularly the very large solvation energy of the dication. Thus, the gas-phase disproportionation

Oxidation Reactions of a Series of Benzidines of 1e is almost 1 V less unfavorable that that of 1a in qualitative agreement with the fact that solution-phase disproportionation is unfavored for 1a but is close to favorable for 1e (Table 4). This discussion is based on the relation ∆G°disp ) F(E°1 - E°2). Thus, even the relatively minor structural changes in 1e affect the energies of the three oxidation states such that disproportionation can become favorable, corresponding to potential inversion. 4. Conclusion In this work it has been shown that fast, reversible dimerization of the cation radicals of benzidines can be detected by cyclic voltammetry through careful analysis of wave shapes. The benzidines whose cation radicals undergo dimerization are all unalkylated at nitrogen except for N,N,N′,N′-tetramethylbenzidine for which weak dimerization is detected at low temperature. The dimerization equilibrium constants have been determined independently by UV-visible absorption spectra of solutions of cation radical salts that were synthesized in this work. For several N-peralkylated benzidines that also contain ring substituents, the individual standard potentials for the two steps of oxidation are very similar so that the benzidines are oxidized in a single, reversible, two-electron process. Reasons for this potential compression have been discussed. Acknowledgment. This research was supported by the National Science Foundation, Grant CHE 0347471. Supporting Information Available: Temperature-dependent spectra of cation radical salts of 1b and 1c, apparent molar absorptivity vs total concentration of cation radical salts of 1bd, simulation parameter values used to fit voltammograms for 1a-d and 1j, comment on the magnitude of dimerization rate constants, simulation parameter values used to fit voltammograms of 1e-h and 1k, respectively and additional examples of fits of simulation to experimental voltammograms for 1ad, 1j, and 1e-h. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Hand, R. L.; Nelson, R. F. J. Am. Chem. Soc. 1974, 96, 850-860. (2) Debrodt, H.; Heusler, K. E. Electrochim. Acta 1980, 25, 545-549. (3) Douadi, T.; Benabid, S.; Cariou, M. Electrochim. Acta 2003, 48, 2659-2665. (4) (a) Note that the material was incorrectly formulated as a chargetransfer complex between the dication and the neutral compound in the earlier work.4b,c (b) Awano, H.; Ogata, T.; Murakami, H.; Yamashita, T.; Ohigashi, H. Synth. Met. 1990, 36, 263-266. (c) Awano, H.; Ohigashi, H. Bull. Chem. Soc. Jpn. 1990, 63, 2101-2103. (d) Awano, H.; Ichihara, O.; Sawada, K.; Ohigashi, H. Ber. Bunsenges. Phys. Chem. 1996, 100, 17001705. (5) Save´ant, J. M.; Vianello, E. Electrochim. Acta 1967, 12, 15451561. (6) Shuman, M. S. Anal. Chem. 1970, 42, 521-523. (7) (a) Howarth, O. W.; Fraenkel, G. K. J. Am. Chem. Soc. 1966, 88, 4514-4515. (b) Chiang, T. C.; Reddoch, A. H.; Williams, D. F. J. Chem. Phys. 1971, 54, 2051-2055. (c) Kotowski, S.; Grabner, E. W.; Brauer, H.-D. Ber. Bunsenges. Phys. Chem. 1980, 84, 1140-1145. (d) Enkelmann, V.; Morra, B. S.; Kro¨hnke, Ch.; Wegner, G.; Heinze, J. Chem. Phys. 1982, 66, 303-313. (e) Terahara, A.; Ohya-Nishiguchi, H.; Hirota, N.; Oku, A. J. Phys. Chem. 1986, 90, 1564-1571. (f) Oyama, M.; Mitani, M.; Washida, M.; Masuda, T.; Okazaki, S. J. Electroanal. Chem. 1999, 473, 166-172. (g) Oyama, M.; Masuda, T.; Mitani, M.; Okazaki, S. Electrochemistry 1999, 67, 1211-1213. (h) Kochi, J. K.; Rathore, R.; Le Mague`res, P. J. Org. Chem. 2000, 65, 6826-6836. (i) Small, D.; Zaitsev, V.; Jung, Y.; Rosokha, S. V.; Head-Gordon, M.; Kochi, J. K. J. Am. Chem. Soc. 2004, 126, 1385013858. (j) Komaguchi, K.; Nomura, K.; Shiotani, M.; Lund, A.; Jansson, M.; Lunell, S. Spectrochim. Acta, Part A 2006, 63, 76-84. (8) (a) Yeh, L.-S. R.; Bard, A. J. J. Electroanal. Chem. 1976, 70, 157169. (b) Yildiz, A.; Baumga¨rtel, H. Ber. Bunsenges. Phys. Chem. 1977,

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