Concerted Proton−Electron Transfer: Effect of Hydroxylic Additives on

16686

J. Phys. Chem. C 2009, 113, 16686–16693

Concerted Proton-Electron Transfer: Effect of Hydroxylic Additives on the Reduction of Benzophenone, 4-Cyanobenzophenone, and 4,4′-Dicyanobenzophenone Shihua Wang,†,‡ Pradyumna S. Singh,§,‡ and Dennis H. Evans*,| Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721, KaVli Institute of Nanoscience, Delft UniVersity of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands, and Department of Chemistry, Purdue UniVersity, West Lafayette, Indiana 47907 ReceiVed: May 27, 2009; ReVised Manuscript ReceiVed: July 20, 2009

The electrochemical reduction of the title compounds proceeds in two steps in N,N-dimethylformamide. The first step is a one-electron reduction to form the anion radical of the benzophenone, a reaction which is affected by the presence of hydroxylic additives such as water, ethanol, or methanol because of hydrogenbond formation between the additive and the anion radical. Formation constants for these complexes have been evaluated for both protiated and deuterated versions of the additives. It was found that the formation constants for the protiated additives were about 20% larger than for the deuterated additives. For benzophenone, the second step of reduction in the presence of water proceeds by a concerted proton-electron transfer reaction with the electron passing from the electrode to the hydrogen-bonded complex with proton transfer from water to the oxygen atom of benzophenone anion radical. This conclusion is supported by data that rule out alternative mechanisms, by the small value of the apparent value of the transfer coefficient and by agreement between experimental and calculated reorganization energies for the process. On the other hand, the second stage of reduction of 4-cyanobenzophenone proceeds by initial electron transfer followed by proton transfer from water to the dianion. The overall mechanism includes formation of 1:1, 1:2, and 1:3 dianion:water complexes with the proton transfer occurring within the 1:3 complex. 4,4′-Dicyanobenzophenone shows little evidence for proton transfer to the dianion, but the formation of the dianion:water complexes is important. Introduction Electrochemical reactions often involve the transfer of both electrons and protons. For an overall one-electron, one-proton reduction reaction, for example, there are three possible reaction paths for addition of the electron and the proton: the proton can be added first followed by insertion of the electron (PE), there can be an initial electron transfer followed by protonation (EP), and, finally, the transfer of the electron and the proton can be concerted, i.e., a concerted proton-electron transfer reaction (CPET). The first such electrochemical reaction that was characterized as a CPET was the reduction of the anion radical of 3,5-di-tert-butyl-1,2-benzoquinone in acetonitrile in the presence of water or 2,2,2-trifluoroethanol (TFE) which occurs by concerted transfer of an electron from the electrode to the anion-radical and a proton from water or TFE to the quinone.1,2 Since then a number of other electrochemical CPET reactions have been reported including a one-electron, one-proton redox couple based on an Os aquo complex,3-5 reduction of superoxide in the presence of water and alcohols,6-8 intramolecular proton transfer from a phenolic group to a pendant amine upon oneelectron oxidation of the phenol,9,10 CPET in the 2,5-dicarboxylate-1,4-hydrobenzoquinone/2,5-dicarboxy-1,4-benzoquinone couple11 and oxidation of phenols with water as a proton acceptor.12 CPET reactions have been reviewed.13 * Corresponding author. Telephone: 1-765-494-5454. E-mail: evansd@ purdue.edu. † University of Arizona. ‡ These authors contributed equally to the work. § Delft University of Technology. | Purdue University.

Electrochemical CPET reductions can either be intramolecular or intermolecular with the latter usually involving proton transfer within a hydrogen-bonded complex of the electron acceptor and a hydroxylic additive. Herein we report a new example of a CPET of the intermolecular type, the reduction of the anion radical of benzophenone in the presence of water or alcohols. We also show that the mechanism shifts from CPET to EP on going to the derivatives 4-cyanobenzophenone and 4,4′-dicyanobenzophenone. Finally, we report weak equilibrium H-D isotope effects on the formation of hydrogen-bonded complexes between anion radicals and the hydroxylic additives. Experimental Section Chemicals and Reagents. Anhydrous N,N-dimethylformamide (DMF; 99.8%, Aldrich) was dried by storing over type 4 Å molecular sieves (Fluka) and transferred into the cell via cannula under nitrogen. Benzophenone (1, 99%, Aldrich), 4-cyanobenzophenone (2, 97%, Aldrich), and tetrabutylammonium hexafluorophosphate (Bu4NPF6; 98.0%, Aldrich) were used as received. In all experiments, the concentration of the supporting electrolyte, Bu4NPF6, was 0.10 M. Anhydrous methanol (CH3OH; 99.8%, Aldrich) and anhydrous ethanol (CH3CH2OH; 99.5%, Aldrich) were used as received. Deuterated water (D2O; 99.9% D, Cambridge Isotopes), deuterated methanol (CH3OD; 99.5% D, Aldrich), and deuterated ethanol (CH3CH2OD; 99.5% D, Aldrich) were also used as received. For addition of up to 0.2 M H2O, CH3OH, or CH3CH2OH, a 10 mL stock solution was prepared by dissolving the additive in a solution of 0.10 M Bu4NPF6/DMF. Required quantities of the stock solution were then pipetted into the cell, depending upon the desired molar concentrations of the addi-

10.1021/jp904976v CCC: $40.75  2009 American Chemical Society Published on Web 09/01/2009

Concerted Proton-Electron Transfer tives. For the cases in which the desired concentrations of H2O, CH3OH, and CH3CH2OH and the deuterated forms exceeded 0.2 M, the required quantities of the pure chemicals were pipetted into the cell directly. The concentration of the benzophenone was corrected for dilution. The residual water present in the dried DMF in the electrochemical cell was estimated to be 0.01 M based on studies where this solvent was treated in the same way as in this work.14 4,4′-Dicyanobenzophenone was prepared as follows based on methods in the literature.15,16 One gram of 4-iodobenzonitrile (97%, Aldrich) and 2.1 g of cobalt carbonyl (dicobalt octacarbonyl) with 1-5% hexane (Strem Chemicals, Newburyport, MA) were placed in a three-neck flask with 40 mL of acetonitrile. Nitrogen was introduced into the flask, and it was then heated to reflux in an oil bath. After refluxing at 80-85 °C for 36 h, the reaction mixture was cooled to room temperature and filtered through a fritted glass funnel. The filtrate was purified by column chromatography on silica gel with acetonitrile as eluent, followed by recrystallization from absolute ethanol (Decon Laboratories, Inc.). The final product is a white crystal-like solid (0.26 g, 51% yield). 1H NMR δ 7.78-7.88 (in CDCl3); 13C NMR δ 116.8, 117.9, 130.5, 132.7, 140.0, 193.7 (in CDCl3); HRMS calc. mass 232.0637, found 232.0640.17 Electrochemical Cells, Electrodes, and Instrumentation. The electrochemical cell was water-jacketed, and the temperature was maintained at 25 °C. The volume of the cell used was 25 mL. The working electrode was normally a 3 mm diameter glassy-carbon (GC) electrode (Bioanalytical Systems). The counter electrode was a coil of platinum wire (99.99%). The home-built reference electrode was a silver wire in contact with a solution of 0.10 M Bu4NPF6 and 0.010 M AgNO3 in acetonitrile. The reference electrode was separated from the contents of the cell by means of a porous Vycor frit. When not in use, the reference electrode assembly was kept immersed in 0.10 M Bu4NPF6/acetonitrile to prevent drying of the frit. The working, reference, and counter electrodes were held in the same relative position in the cell throughout all the experiments to ensure that the uncompensated solution resistance remained constant. The counter electrode was especially positioned sufficiently far away from the working electrode to enable a uniform current density at the working electrode. Prior to all experiments the working electrode was polished on a polishing felt with 1.0 µm alumina paste (aqueous, Buehler) followed by 0.05 µm alumina (aqueous, Buehler). The electrode was rinsed with deionized water, rinsed with ethanol, and finally rinsed with acetone. After air-drying, the electrode was ready to use. Preconditioning the electrode led to reproducible results. Specifically, before each set of experiments, the electrode potential was scanned at 0.10 V/s about 2 times over the entire potential range used in each set of experiments. The reference electrode was frequently calibrated with reference to the ferrocenium ion/ferrocene couple (Fc+/Fc). This was accomplished by obtaining voltammograms of ferrocene using the reference electrode and determining the potential of the ferrocene couple with respect to the reference by simulation of the voltammograms. All potentials reported here are referenced to the potential of the ferrocene couple. The electrolyte solution was purged with nitrogen (Cryogenics & Gas Facility, the University of Arizona) for 20 min prior to any measurements. The nitrogen was passed through anhydrous calcium sulfate before being introduced into the cell. All experiments were performed with a model 273 EG&G Princeton Applied Research potentiostat (PAR 273).

J. Phys. Chem. C, Vol. 113, No. 38, 2009 16687 The uncompensated solution resistance, Ru, for 0.10 M Bu4NPF6 in DMF was determined from fits of simulations to voltammograms of ferrocene. The voltammograms were obtained for a series of scan rates, and simulation was performed by keeping the electron-transfer rate constant, ks, sufficiently high such that any change in peak separation, ∆Ep, could be attributed entirely to the resistance, Ru. It was determined that the resistance for the GC electrode in our cell arrangement in dry DMF at 298 K with 0.10 M Bu4NPF6 was ∼380 Ω. In this study, part of the solution resistance was compensated electronically and the remainder was included in the simulations. A similar measurement of solution resistance was made for a solution of DMF containing 1 M H2O, giving ∼390 Ω. When acquiring data at scan rates less than 1 V/s, the 5.3 Hz filter on the PAR 273 was used. Above 1 V/s, the 590 Hz filter was used. Digital simulations were performed on the backgroundcorrected data using Digisim (version 3.03b) from Bioanalytical Systems. Operating conditions for the simulation program were planar diffusion, 0.002 V step size, and 0.50 for the expanding grid factor. Electron-transfer reactions were treated by ButlerVolmer kinetics, with the standard rate constant and transfer coefficient as kinetic parameters. In the case of addition of water, the diffusion coefficients used in the simulation were adjusted due to the changed viscosity18 according to the Stokes-Einstein equation. Results and Discussion General Observations. The three compounds studied in this work are benzophenone (1), 4-cyanobenzophenone (2), and 4,4′dicyanobenzophenone (3).

Figure 1 is a representative cyclic voltammogram of 1.24 mM 1 in N,N-dimethylformamide (DMF) and in the presence of 0.40 M added water. The first cathodic peak, Ic, represents the oneelectron reduction of 1 giving the anion radical. It is followed at more negative potentials by an irreversible peak, IIc, and, on the return scan, an anodic peak, Ia, is seen which corresponds to the oxidation of the anion radical back to neutral 1. Peak IIc is irreversible at all scan rates that were used and is also irreversible in the absence of any added water. It is peak IIc that is thought to be a CPET reaction, electron transfer to a hydrogen-bonded complex between the anion radical and water. The following reactions will be discussed in this work (B represents benzophenone and its derivatives, and HA is the hydroxylic additive).

B + e- h B•-

E°1, R1, ks,1

(1)

16688

J. Phys. Chem. C, Vol. 113, No. 38, 2009

Wang et al.

Figure 1. Cyclic voltammogram of 1.24 mM benzophenone, 1, in 0.10 M Bu4NPF6/DMF with 0.41 M water. Scan rate: 0.100 V/s. Two hundred ohms of solution resistance was compensated electronically. Curve: background-corrected experimental voltammogram. Symbols: digital simulation with E°1 ) -2.22 V, R1 ) 0.50, ks,1 ) 0.049 cm/s, E°9 ) -2.37 V, R9 ) 0.36, ks,9 ) 2.4 × 10-4 cm/s, K11 ) 4.4 M-1, kf,11 ) 107 M-1 s-1, A ) 0.071 cm2, and Dall species ) 1.35 × 10-5 cm2/s. This set of parameter values provides the best average fit for eight scan rates between 0.100 and 5.00 V/s. Slight improvements can be achieved for any given scan rate by adjusting the parameter values from the averages used here.

B•- + e- h B2B•- + HA h B•-(HA) B•-(HA) + HA h B•-(HA)2

E°2, R2, ks,2 K11, kf,11, kb,11

(2) (3)

K12, kf,12, kb,12

(4) B2- + HA h B2-(HA) B2-(HA) + HA h B2-(HA)2

K21, kf,21, kb,21

(5)

K22, kf,22, kb,22

(6) B2-(HA)2 + HA h B2-(HA)3

The full curve in Figure 1 is the background-corrected experimental voltammogram, while the symbols are the result of a simulation using the parameter values listed in the caption. The parameters used to fit CPET peak IIc are R9 ) 0.36 (to account for the shape), E°9 ) -2.37 V (see below), and ks,9 ) 2.4 × 10-4 cm/s. Further discussion of the mechanism of the process responsible for peak IIc will appear in a later section. Determination of K11 and K12. Evidence for formation of B•-(H2O) is found from the dependence of the formal potential for the first step of reduction on the concentration of water. In these studies the potential window that was recorded included only peaks Ic and Ia, and the simulations were fit to the background-corrected voltammograms, thus yielding the formal potential, E°′, 1 (see the Supporting Information for examples). These formal potentials were plotted vs log(CH2O/M), and the equilibrium constant was obtained by fitting eq 10 to the data (Figure 2). Equation 10 allows for formation of 1:1 and 1:2 complexes (reactions 3 and 4) and is written for the general hydroxylic additive, HA.19

K23, kf,23, kb,23

(7) B2-(HA)3 h BH-(HA)2 + AKp, kf,p,kb,p (proton transfer) (8) B•-(HA) + e- f HB- + A-

Figure 2. Formal potential for first step of the reduction of benzophefor various concentrations of H2O or D2O. Symbols: none, E°′, 1 experimental. Curves: fit of eq 10 to the data using the equilibrium constants shown. Inclusion of nonzero values for K12 did not improve the fits.

E°9, R9, ks,9 (CPET) (9)

E°, R, and ks are the standard potential, electron-transfer coefficient, and standard heterogeneous electron-transfer rate constant for the electrode reactions, while K, kf, and kb are the equilibrium constant, forward rate constant, and reverse rate constant for the chemical reactions. The CPET reduction of the anion radical is reaction 9 wherein the electron is transferred from the electrode to the water-anion radical complex with concerted transfer of a proton from water to the benzophenone moiety giving the anion of benzhydrol, HB-, and hydroxide. Note that HB- is the anion of benzhydrol with the proton attached to oxygen whereas BH- in eq 8 is the more stable tautomer with the proton bound to carbon.

E°1′ ) E°1 +

RT 2 ] ln[1 + K11CHA + K11K12CHA F

(10)

Here E°1 is the standard potential observed in the absence of the additive. For benzophenone and water, it was found that only the 1:1 complex needed to be considered (Figure 2). We have adopted a model which attributes all of the shift of the formal potential to the formation of specific hydrogen-bonded complexes. As pointed out and discussed elsewhere, all or part of the shift may be caused by changes in solvation energies as the concentration of the hydroxylic additive is increased.19 Compounds 1-3 were studied with various additives, in both the protiated and deuterated forms, and the data are summarized in Table 1. Plots like those in Figure 2 for the other combinations can be found in the Supporting Information. One notes that the values of K11 tend to increase on going from water to ethanol and finally to methanol. This parallels the slight increase in acidity in the same sequence that has been reported for DMF: pKa ) 31.5 (water), 30.1 (ethanol), and 29.4 (methanol).20 Also, the values of K11 decreased in the order 1 > 2 > 3. The basicity of the anion radicals decreases in the same

Concerted Proton-Electron Transfer

J. Phys. Chem. C, Vol. 113, No. 38, 2009 16689

TABLE 1: Standard Potentials and Formation Constants for Hydrogen-Bonded Complexes Obtained by Fitting Eq 10 to Experimental Formal Potentials As a Function of Additive Concentrationa compound benzophenone K11,H2O/K11,D2O ) 1.19

4-cyanobenzophenone K11,H2O/K11,D2O ) 1.18 4,4′-dicyanobenzophenone K11,H2O/K11,D2O ) 1.19

additive

E°/V vs Fc

K11/M-1

H 2O D 2O CH3CH2OH CH3OH CH3OD H 2O D 2O CH3OH CH3OD H 2O D 2O CH3OH CH3OD

-2.222 -2.222 -2.222 -2.224 -2.224 -1.821 -1.821 -1.821 -1.821 -1.631 -1.631 -1.633 -1.633

4.54 3.80 6.78 9.32 7.04 1.13 0.96 1.49 1.60 0.99 0.83 1.23 0.85

K12/M-1

4.12 1.79 0.59 0.23

0.21

Σ(residual)2/V2 (N) 6.6 × 10-6 (8) 6.3 × 10-6 (8) 1.8 × 10-6 (8) 7.4 × 10-5 (18) 5.3 × 10-5 (18) 1.8 × 10-6 (8) 2.3 × 10-6 (8) 9.4 × 10-7 (8) 3.0 × 10-6 (8) 4.1 × 10-6 (8) 1.5 × 10-6 (8) 3.3 × 10-6 (7) 1.3 × 10-6 (7)

a Data for DMF with 0.10 M Bu4NPF6 at 298 K. The observed formal potential in the presence of the additive was taken as the average of the cathodic and anodic peak potentials for the reduction of the neutral compound to the anion radical. The residual amount of water in DMF, 10 mM, was added to the amount added for water and D2O (because water and D2O behave so similarly). Largest quantity added ranged from 0.3 to 1 M. No attempt has been made to correct for changes in liquid junction potential upon addition of the additive. Values of equilibrium constant were obtained by fitting eq 10 to the data. Where no entry is shown for K12, using nonzero values did not improve the fit. Σ(residual)2 is the sum of the squares of the differences between the measured formal potential and that calculated from eq 10 using the optimized parameter values. N is the number of data points.

SCHEME 1

order owing to the strong electron-withdrawing properties of the cyano groups. Thus the largest value of K11, 9.32 M-1, is seen with the most basic anion radical, 1•-, and the strongest acid, methanol. For methanol it was found that inclusion of relatively small values of K12 improved the agreement between eq 10 and the experimental data. Small differences exist between the protiated and deuterated additives. For H2O and D2O it was found that K11,H2O/K11,D2O was almost identical for the three benzophenones, being 1.19, 1.18, and 1.19 for 1, 2, and 3, respectively (Table 1). In the Supporting Information a primitive model based on differences in the zero-point energies for a free OH(D) fragment vs the form hydrogen-bonded to B•- leads to eq 11

∆EOH - ∆EOD )

[

hνOH (F - 1) 2



]

µOH (F - 1) µOD

(11)

where ∆EOH and ∆EOD are the changes in energy on going from free to hydrogen-bonded OH and OD, νOH is the vibrational frequency for free OH, and µOH and µOD are the reduced masses of OH and OD. F is the ratio of vibrational frequencies of hydrogen-bonded to free OH and OD, i.e., F ) νOH-bonded/νOH ) νOD-bonded/νOD. Note the assumption that this ratio is the same for OH and OD. To obtain an estimate of ∆EOH - ∆EOD, F was taken as the ratio of the OH stretching frequency in liquid water (ca. 3400 cm-1), which reflects extensive hydrogen bonding, and the average of the symmetric and asymmetric stretching frequencies in water vapor (ca. 3700 cm-1; assumed to be the same in DMF).21 This leads to ∆EOH - ∆EOD ) -0.11 kcal/mol or K11,H2O/K11,D2O ) 1.2 if the energy differences can be considered as free energy differences. The close agreement of this computed value with the present data is surely fortuitous, but it would appear that the H/D equilibrium isotope effect seen here arises principally from changes in zero-point energies on going from free to hydrogen-bonded water. Other authors have observed similar equilibrium isotope effects for hydrogen bonding of hydroxylic additives to anion radicals.22-24

Peak IIc for Benzophenone. Now that we have shown that the anion radical of 1 forms a hydrogen-bonded complex with water, we can now consider peak IIc which involves the further reduction of the anion radical. Calculation of the relative species concentrations shows that under the condition of Figure 1 (0.42 M water), 65% of the anion radicals formed at the electrode in peak Ic will exist as the 1:1 anion radical-water complex. It is proposed that it is this complex that is reduced at peak IIc (reaction 9), giving the anion of benzhydrol and hydroxide. There are three mechanistic possibilities: 1. A concerted proton-electron transfer reaction (CPET) as shown by the diagonal reaction in Scheme 1. 2. Proton transfer followed by electron transfer (PE), upper horizontal and right-hand vertical reactions in Scheme 1. 3. Electron transfer followed by proton transfer (EP), left-hand vertical and lower horizontal reactions in Scheme 1. Note that the form of HB- that is initially produced is the less stable tautomer of the anion of benzhydrol, so rapid tautomerization following the irreversible reduction giving rise to peak IIc is also shown. We will begin by ruling out the stepwise PE mechanism. The reduction of hydroxydiphenylmethyl, Ph2(OH)C•, (right-hand vertical reaction) is expected to proceed more readily than reduction of benzophenone itself. Thus, if proton transfer (upper horizontal reaction) occurred, the Ph2(OH)C• so formed would be immediately reduced at peak Ic, converting it into an overall two-electron process. That is not what is seen with water and

16690

J. Phys. Chem. C, Vol. 113, No. 38, 2009

Wang et al. by an EP mechanism. This is particularly true for other additives where values of Ep,IIc - E°2 as large as 0.45 V are seen. It is also true that the EP mechanism should exhibit a transfer coefficient g0.5 owing to the fact that Ep,IIc - E°2 is positive (see below). This leaves the one-step CPET reaction as the only viable alternative. Is it reasonable that reduction of the anion radical of 1 in the presence of these additives occurs in this way? One clue can be found in the drawn-out shape of IIc, the value of the apparent transfer coefficient, R9, being only 0.34 (Figure 1). Observations such as this are normally explained by invoking a large overpotential for the process, reaction 9; i.e., Ep,IIc - E°9 is large and negative. To test this point, an estimate of E°9 ) -2.37 V is provided in the Supporting Information.

Figure 3. Ep,IIc for benzophenone, 1, as a function of the concentration of the indicated hydroxylic additives. Approximately 1 mM 1 in 0.10 M Bu4NPF6/DMF at a glassy carbon electrode, 0.100 V/s.

the other hydroxylic additives studied here, so the PE mechanism can be rejected. However, when stronger acids are used, transition to a PE mechanism occurs. With 2,2,2-trifluoroethanol (TFE; pKa ) 24 in DMF20), the addition of a 10:1 mol ratio (TFE to 1) gives about a 20% increase in peak Ic, which was accompanied by virtual elimination of peak Ia, indicating transition to a PE mechanism. With the still stronger acid 4-bromophenol (pKa ) 14.3 in DMF25), addition of as little as a 5:1 mol ratio brings about complete conversion of Ic to an overall two-electron process. The second mechanistic possibility is electron transfer followed by proton transfer (EP). Jensen and Parker26 report that the standard potential for reducing the anion radical of 1 to the dianion (reaction 2) is 0.77 V more negative than E°1 in DMF.

B + e- h B•B•- + e- h B2-

E◦1 , R1, ks,1

(1)

E◦2 , R2, ks,2

(2)

Taking E°1 from Table 1, we conclude that E°2 ) -2.99 V, which is about 0.3 V more negative than Ep,IIc (Figure 1). Ep,IIc appears at even less negative potentials at higher water concentrations (see Figure 3 for data for water, ethanol, and methanol in both protiated and deuterated forms). An explanation of this potential shift could be a very fast chemical reaction following reaction 2, viz., proton transfer from water to B2-. However, there is a limit to the extent of such a kinetic shift. If the following chemical reaction is sufficiently fast, the electrontransfer (reaction 2) will become rate limiting and Ep,IIc will be that of a totally irreversible electron-transfer reaction, eq 12.27

Ep,IIc ) E◦2 -

[

( ) ( )]

R2FV D1/2 RT + ln 0.780 + ln R2F ks,2 RT

1/2

(12)

In eq 12, D is the diffusion coefficient of the anion radical of 1 and V is the scan rate. Using R2 ) 0.5, D ) 10-5 cm2/s, ks,2 ) 1 cm/s, and V ) 0.1 V/s gives the limiting value of Ep,IIc - E°2 ) 0.24 V at 298 K. The value of ks,2 is generously large in view of the fact that ks1 is only 0.51 cm/s in dimethylacetamide.28 In any case, this calculation shows that the observed position of IIc is too far removed from E°2 to be accounted for

B•-(H2O) + e- f BH- + OH-

E°9, R9, ks,9

(9) Thus Ep,IIc - E°9 from Figure 1 is -0.33 V and R9 ) 0.34. A relationship exists (eq 13) between Ep,IIc - E°9, R9, and the reorganization energy for electrode reaction 9, λ9.29 Solving for λ9 gives 1.0 eV. This compares favorably to the calculated value of 1.14 eV obtained using the formalism of Costentin, Robert, and Save´ant30 (see the Supporting Information).

R9 )

F(Ep,IIc - E°9) 1 + 2 2λ9

(13)

As seen in Figure 3, Ep,IIc depends strongly on the concentration of the hydroxylic additive. Simulations of voltammograms according to the CPET mechanism (reaction 9) were conducted for eight scan rates between 0.1 and 5 V/s and concentrations of added water ranging from 0 to 1 M (for example, see Figure 1 and the Supporting Information). In these simulations, R9 was maintained constant at 0.34 but E°9 and/or ks,9 were simply adjusted so as to put peak IIc in its observed position. Of course, the standard potential and standard electron-transfer rate constant are not expected to be functions of the concentration of the additive. In the case of the electrochemical reduction of superoxide,7 the shift in Ep,IIc can be explained by invoking the reduction of a series of complexes (1:1, 1:2, 1:3, etc.), each with its own E°, R, and ks values. We have not performed that analysis for the present data. The quality of the fits of simulation to experimental voltammograms was best at the higher scan rates and larger water concentrations. Examples are shown in the Supporting Information. In order to further test the conclusion that the process at peak IIc is a CPET reaction, attempts were made to fit the data by an EP mechanism. It was soon found that it was impossible to account for the data by simple proton transfer from water to B2-. What was required was the formation of the hydrogenbonded complexes B2-(HA), B2-(HA)2, and B2-(HA)3 (reactions 5-7) with proton transfer occurring within the 1:3 complex (reaction 8). The simulations were in reasonable agreement with the data, but the fits were definitely inferior to those obtained with the CPET mechanism. More telling was the fact that unreasonably large values of the formation constants were required to simulate the dependence of Ep,IIc on the water concentration: K21 ) 109, K22 ) 106, and K23 ) 106 M-1. As discussed earlier, formation constants for hydrogen-bonded complexes are normally many orders of magnitude smaller.

Concerted Proton-Electron Transfer

J. Phys. Chem. C, Vol. 113, No. 38, 2009 16691

TABLE 2: Comparison of Ep,IIc with the pKa of the Additive additive

pKa

(RT/F)ln Ka/V

H2 O

31.5

-1.864

EtOH

30.1

-1.781

MeOH

29.4

-1.739

delta/mVa

Ep,IIc/V

delta/mVb

-2.686 83 42

-2.582 -2.536

104 46

a (RT/F) ln Ka of lower entry minus that of upper entry. b Ep,IIc of lower entry minus that of upper entry. Ep,IIc at 1 M additive (Figure 3).

Also noted in Figure 3 is the fact that Ep,IIc is most negative for water as an additive, followed by ethanol and methanol. This may be traced principally to the value of E°9 which varies directly with (RT/F) ln(Ka) (Supporting Information). From the known pKa values (31.5, 30.1, and 29.4 for water, ethanol, and methanol, respectively20), E°9 for ethanol should be 83 mV positive of that of water (Ep,IIc at 1 M ethanol is 104 mV positive of that of water), and E°9 for methanol should be another 42 mV more positive (compared to a difference in Ep,IIc of 46 mV). These comparisons are organized in Table 2. The differences in Ep,IIc observed for the protiated and deuterated additives (Figure 3) have been interpreted as being due to a kinetic isotope effect in the CPET reaction.6,7 Since we now know that part of the difference may be due to an equilibrium H/D isotope effect on E°, 9 we have refrained from attempting to extract a kinetic isotope effect from these data. Peak IIc for 4-Cyanobenzophenone, 2. The strongly electron-withdrawing cyano substituent in 2 brings about very substantial changes in behavior compared to 1. As already noted (Table 1), E°1 for 2 has shifted to a value that is 0.40 V less negative than that of 1. However, the most interesting change is the very significant degree of reversibility seen for peak IIc (Figure 4, upper panel) as manifested in anodic peak IIa. As the water concentration is increased, the magnitude of peak IIa decreases consistent with an EP mechanism of electron transfer (reaction 2) followed by proton transfer. Thus the mechanism of the process at peak IIc is completely different from the CPET reaction seen with 1. The lower panel of Figure 4 contains simulations of the voltammograms in the upper panel. The simulation parameters are given in Table 3. The simulations do not provide an exact match with the experimental curves, but most of the features of the data are captured in the simulations. First, the position of peak IIc as a function of water concentration is well accounted for. This was accomplished by adjusting the formation constants of the 1:1, 1:2, and 1:3 complexes of water with the dianion of 2. Also, the diminution of peak IIa with increasing water concentrations is relatively well accounted for. This peak is affected not only by the proton-transfer reaction, B2-(H2O)3 f BH-(H2O)2 + OH-, but also by the limited rate of dissociation of B2-(H2O). Finally, the decreasing magnitude of peak Ia with increasing water concentration is well accounted for. The experimental data at low water concentrations contain a small shoulder preceding peak IIc. We were unable to determine the cause of this shoulder but noted that it was not present when acetonitrile was used as solvent. It should be mentioned that the simulation parameters listed in Table 3 were obtained by considering data for the water concentrations shown in Figure 4 for 0.10 V/s but also for seven other scan rates, 0.20, 0.30, 0.50, 1.00, 2.00, 3.00, and 5.00 V/s. The values shown are the values that on average provide the best agreement for all 64 voltammograms. When the experiments were conducted with addition of D2O rather than H2O, the data could be simulated using parameter

Figure 4. Upper: cyclic voltammograms of 1.05 mM 4-cyanobenzophenone, 2, in DMF with 0.10 M Bu4NPF6 with water concentrations of 0.01, 0.06, 0.11, 0.21, 0.41, 0.61, 0.81, and 1.01 M.; 0.100 V/s. Two hundred ohms of solution resistance was compensated electronically. Lower: simulations using the parameter values given in Table 3. Arrows indicate increasing water concentrations.

TABLE 3: Simulation Parameter Values for the Simulations in Figure 4, Lower Panela electrode reactions

E°/V vs Fc+/Fc

ks/cm s-1

R

B + e- H B • B• - + e- H B2B• -(H2O) + e- H B2-(H2O)

-1.823 -2.554 -2.377

0.10 0.02 0.10

0.5 0.5 0.5

chemical reactions •-

B + BH 2B B• - + H2O H B• -(H2O) B2- + H2O H B2-(H2O) B2-(H2O) + H2O H B2-(H2O)2 B2-(H2O)2 + H2O H B2-(H2O)3 B2-(H2O)3 f BH-(H2O)2 + OH2-

K

kf

kb

2.4 × 10 1 1.0 × 103 14.4

1.0 × 10 1.0 × 107 1.0 × 108 1.0 × 108

4.2 × 10-3 1.0 × 107 1.0 × 105 6.9 × 106

51.3

1.0 × 108

1.9 × 106

12

4.0 × 106

10

7.9

a Electrode area ) 0.071 cm2. In the simulations the concentration was adjusted for slight dilution due to the addition of water. The diffusion coefficients of all species were set equal to 1.006 × 10-5 cm2/s for 0.01 M water. This value was adjusted downward with increasing water concentrations due to small increases in viscosity using the Stokes-Einstein equation. The viscosities were obtained from Bernal-Garcı´a et al.18 Equilibrium constants are based on molar standard states. Units of rate constants are s-1 and M-1 s-1 for first- and second-order reactions, respectively.

values that were virtually the same as those for H2O except for the formation constant of the 1:2 complex of water with the dianion which needed to be decreased by a factor of 3 and the rate constant for proton transfer within the 1:3 complex which needed to be decreased from 7.9 to 2.2 s-1. This latter

16692

J. Phys. Chem. C, Vol. 113, No. 38, 2009

Wang et al.

Figure 5. Cyclic voltammograms of 0.917 mM 4,4′-dicyanobenzophenone, 3, in DMF with 0.10 M Bu4NPF6 with water concentrations of 0.01, 0.06, 0.11, 0.21, 0.41, 0.61, 0.81, and 1.01 M; 0.500 V/s. Three hundred ohms of solution resistance compensated electronically. Arrows indicate increasing water concentrations.

constants follow the unusual pattern of K21 being significant (31 and 24, respectively), K22 being almost zero (0.04 and 0.02), and K23 being larger than either of the first two (1200 and 1000 M-1). Thus, there is a cooperative effect associated with complexation of the second and third molecules of H2O or D2O. The site with the greatest negative charge in the dianion of 3 is the oxygen atom, and it seems likely that the first molecule forms a hydrogen bond to this site. The second molecule will interact at a site that has the next highest negative charge density. This is likely to be one of the two identical cyano groups. This delocalization into both aromatic rings means that the second molecule interacts with a site of considerably lower charge density so K22 is small. However, when the second molecule does bind, the two cyanophenyl groups are no longer identical and the binding can provoke the formation of a more localized negative charge on the cyano that is bound to the second molecule of H2O or D2O, thus greatly enhancing the addition of a third. This is illustrated in the following structure of the dianion of 3 in which putting negative charge on one cyano group is favored by turning the attached benzene ring into the plane of the carbonyl group.

Conclusions

Figure 6. Formal potential for reaction 2 as a function of the concentration of H2O or D2O. Symbols: (Ep,IIc + Ep,IIa)/2 at each concentration is the average of eight scan rates between 0.100 and 5.00 V/s. Other conditions as in Figure 5. Curves: eq 14 with parameter values as shown.

observation may be due to a H/D kinetic isotope effect on the proton transfer. Peak IIc for 4,4′-Dicyanobenzophenone, 3. Figure 5 shows voltammograms of 3 in both the absence and the presence of added water. Now the behavior is that of two successive, reversible one-electron processes (reactions 1 and 2). As water is added, the reaction responsible for peaks IIc/IIa retains its reversibility as the peaks shift in the positive direction as would be expected for formation of hydrogen-bonded complexes between water and the dianion of 3. The midpoint potential, (Ep,IIc + Ep,IIa)/2, was taken as an estimate of the formal potential for reactions 2, E°′. 2 Figure 6 shows a plot of E°′ 2 vs log(CH2O) along with a fit of eq 14 to the experimental data.19

RT × F 2 3 1 + K21CHA + K21K22CHA + K21K22K23CHA ln 1 + K11CHA

E◦2 ′ ) E◦2 +

[

]

(14)

The best-fit values of the formation constants are given in the caption of Figure 6. For both H2O and D2O, the formation

The first step of reduction of 1-3 is a reversible, one-electron reduction to form the anion radical. The anion radicals form hydrogen-bonded complexes with the hydroxylic additives water, ethanol, and methanol. Formation constants have been evaluated, and an equilibrium isotope effect has been noted by which the formation constant of the protiated additive is about 20% larger than that of the deuterated additive. The second step of reduction of 1 in the presence of added water occurs by a CPET mechanism to produce the anion of benzhydrol and hydroxide. By contrast, the second step of reduction of 2 and 3 occurs by electron transfer followed by proton transfer from the additive to the dianion. The proton-transfer reaction is very slow with 3. The position of the second reduction peak of 2 and 3 is strongly affected by the formation of 1:1, 1:2, and 1:3 complexes of the additive with the dianion. Acknowledgment. Support of the U.S. National Science Foundation, grant number CHE-0715375, is gratefully acknowledged. P.S.S. thanks Professor Leif Hammarstro¨m, Uppsala University, for initial support. Supporting Information Available: Examples of fits of simulations to experimental voltammograms for benzophenone, 1, with added water; plots of the formal potential of the neutral/ anion radical couple (reaction 1) versus the logarithm of the concentration of hydroxylic additives for benzophenone, 1, 4-cyanobenzophenone, 2, and 4,4′-dicyanobenzophenone, 3; derivation of the H/D equilibrium isotope effect in the formation of a hydrogen-bonded complex between water and an organic anion; examples of fits of simulations to experimental voltammograms for benzophenone, 1, with added water. Scans include peaks Ic, IIc, and Ia; estimation of E°9 for benzophenone, 1; estimation of the total reorganization energy for the CPET

Concerted Proton-Electron Transfer reaction of the benzophenone radical anion. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Lehmann, M. W.; Evans, D. H. J. Phys. Chem. B 2001, 105, 8877– 8884. (2) Macı´as-Ruvalcaba, N. A.; Okumura, N.; Evans, D. H. J. Phys. Chem. B 2006, 110, 22043–22047. (3) Haddox, R. M.; Finklea, H. O. J. Phys. Chem. B 2004, 108, 1694– 1700. (4) Madhiri, N.; Finklea, H. O. Langmuir 2006, 22, 10643–10651. (5) (a) Costentin, C.; Robert, M.; Save´ant, J.-M.; Teillout, A.-L. Chem. Phys. Chem. 2009, 10, 191–198. (b) Costentin, C.; Robert, M.; Save´ant, J.-M.; Teillout, A.-L. Proc. Natl. Acad. Sci. U.S.A. Published online July 7, 2009, doi: 10.1073/pnas.0905020106. (6) Costentin, C.; Evans, D. H.; Robert, M.; Save´ant, J.-M.; Singh, P. S. J. Am. Chem. Soc. 2005, 127, 12490–12491. (7) Singh, P. S.; Evans, D. H. J. Phys. Chem. B 2006, 110, 637–644. (8) Save´ant, J.-M. J. Phys. Chem. C 2007, 111, 2819–2822. (9) Costentin, C.; Robert, M.; Save´ant, J.-M. J. Am. Chem. Soc. 2006, 128, 4552–4553. (10) Costentin, C.; Robert, M.; Save´ant, J.-M. J. Am. Chem. Soc. 2007, 129, 9953–9963. (11) Costentin, C.; Robert, M.; Save´ant, J.-M. J. Am. Chem. Soc. 2006, 128, 8726–8727. (12) Costentin, C.; Louault, C.; Robert, M.; Save´ant, J.-M. J. Am. Chem. Soc. 2008, 130, 15817–15819. (13) (a) Costentin, C. Chem. ReV. 2008, 108, 2145–2179. (b) Huynh, M. H. V.; Meyer, T. J. Chem. ReV. 2007, 107, 5004–5064. (c) Mayer, J. M. Annu. ReV. Phys. Chem. 2004, 55, 363–390.

J. Phys. Chem. C, Vol. 113, No. 38, 2009 16693 (14) Hui, Y.; Chng, E. L. K.; Chng, C. Y. L.; Poh, H. L.; Webster, R. D. J. Am. Chem. Soc. 2009, 131, 1523–1534. (15) Brunet, J. J.; Taillefer, M. J. Organomet. Chem. 1990, 384, 193– 197. (16) Enquist, P.-A.; Nilsson, P.; Larhed, M. Org. Lett. 2003, 5, 4875– 4878. (17) Choe, W.; Kiang, Y.-H.; Zu, Z.; Lee, S. Chem. Mater. 1999, 11, 1776–1783. (18) Bernal-Garcı´a, J. M.; Guzma´n-Lo´pez, A.; Cabrales-Torres, A.; Estrada-Baltazar, A.; Iglesias-Silva, G. A. J. Chem. Eng. Data 2008, 53, 1024–1027. (19) Evans, D. H. Chem. ReV. 2008, 108, 2113–2144. (20) Andrieux, C. P.; Gamby, J.; Hapiot, P.; Save´ant, J.-M. J. Am. Chem. Soc. 2003, 125, 10119–10124. (21) Eisenberg, D.; Kauzmann, W. The Structure and Properties of Water; Oxford University Press: New York, 1969. (22) Wang, H.; Ingemann, S.; Ulstrup, J.; Hammerich, O. Acta Chem. Scand. 1992, 46, 178–185. (23) Svaan, M.; Parker, V. D. Acta Chem. Scand. B 1985, 39, 401–404. (24) Parker, V. D. Acta Chem. Scand. B 1984, 38, 189–193. (25) Izutsu, K. Acid-Base Dissociation Constants in Dipolar Aprotic SolVents; Blackwell Scientific Publications: Oxford, 1990. (26) Jensen, B. S.; Parker, V. D. J. Chem. Soc,. Chem. Commun. 1974, 367–368. (27) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001; p 236. (28) Fawcett, W. R.; Fedurco, M. J. Phys. Chem. 1993, 97, 7075–7080. (29) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001; p 121. (30) Costentin, C.; Robert, M.; Save´ant, J.-M. J. Electroanal. Chem. 2006, 588, 197–206.

JP904976V