Determining overpotentials for the oxidation of alcohols by molecular electrocatalysts in non-aqueous solvents †

Molecular electrocatalysts for energy-related transformations oﬀer unique opportunities to elucidate mechanistic principles that contribute to improved rates and energy eﬃciency. New catalysts for electrochemical alcohol oxidation in non-aqueous conditions have been developed recently, but it is diﬃcult to make meaningful performance comparisons between them because the diﬀerent conditions used for each catalyst result in unquantified diﬀerences in driving force. The present report outlines an approach to determine the equilibrium potential for the oxidation of alcohols in organic solvents or solvent mixtures. These equilibrium potentials are then used to determine the overpotentials for a series of molecular electrocatalysts. Overall, the methodology outlined herein provides a foundation for future advances in this field and enables comparison of electrocatalyst performance under aqueous and non-aqueous reaction conditions.


Introduction
Alcohol oxidation is a fundamental functional group transformation that is of interest in both synthetic and energy-related contexts. As an anode reaction in fuel cells, it is imperative that oxidation takes place at an electrode potential close to the thermodynamic potential of the reaction. Although this is less critical in the context of synthetic alcohol oxidation, the energetic requirements for a process can impact reaction selectivity and, potentially, economic viability. Thus, it is important to know not only the operating potential of an alcohol oxidation catalyst, but also how that potential is related to the thermodynamic potential of the overall reaction under the catalytic conditions. Overpotential (Z) is generally defined as the difference between the equilibrium potential of the reaction being catalyzed and the potential at which a catalyst operates at a specific current. 1 In other words, overpotential is an indicator of the excess electrochemical driving force for catalysis at a given rate. It is therefore essential to report the electrocatalytic rate and the corresponding overpotential together since each can be improved at the cost of the other.
To determine an overpotential, both the catalytic potential and equilibrium potential must be well-defined. For molecular electrocatalysts, the catalytic wave typically occurs near a redox couple of the parent complex and reaches a steady-state current (i cat ) at sufficiently anodic potentials (or cathodic potentials, for reduction reactions). The selection of a catalytic potential can be somewhat subjective because similar values of i cat are observed over a range of potentials. The overpotential of a molecular catalyst is therefore frequently reported at the catalytic half-wave potential (E cat/2 ), defined as the potential at which the current of the catalytic wave reaches half of i cat . 1,2 This concept is illustrated in Fig. 1 for the electrocatalytic oxidation of 1-butanol to butanal using 4-acetamido-TEMPO (ACT, TEMPO = 2,2,6,6-tetramethylpiperidine-N-oxyl). 3 By using this approach, the current and potential are well-defined and coupled to each other. The equilibrium potential for a catalytic reaction (E1 0 ) is determined from the standard potential (E1) by accounting for non-standard state reaction conditions, specifically for temperatures other than 298 K and any reactant or product that does not have a solution concentration of 1 M (or 1 atm for gases). Buffering is recommended any time an overpotential is determined in order to provide a stable, well-defined thermodynamic potential, but is particularly important when the overpotential is low. 1 The ability to accurately define the thermodynamic potential for a reaction under each set of catalytic conditions is crucial to enable meaningful comparisons of overpotentials with different catalysts. Direct experimental measurement of E1 requires an electrode that can reversibly and rapidly perform the electrochemical reaction of interest. In cases like alcohol oxidation where no such electrode exists, E1 may be calculated from the free energies of formation of the substrate(s) and product(s). Using this method, the standard potentials of many redox reactions have been reported in aqueous solution. 4 However, molecular electrocatalysts are often studied in organic solvents or solvent mixtures in which standard potentials are not known.
In this manuscript, we report a method for determining the thermodynamic potentials for the oxidation of alcohols under non-aqueous conditions, including the 2e À /2H + interconversion of several common aldehydes and ketones with the corresponding alcohol, the 4e À /4H + oxidations of primary alcohols to esters and carboxylic acids, and the 6e À /6H + oxidation of methanol to CO 2 . These potentials allow, for the first time, a direct quantification of the overpotential for alcohol oxidation with molecular electrocatalysts in organic solvents.
Calculation of standard potentials for the oxidation of alcohols A crucial advance in evaluating overpotentials in organic solvents and solvent mixtures came with the application of open-circuit potential (OCP) measurements for the direct determination of the equilibrium potentials for the hydrogen evolution reaction (eqn (1)) in organic solvents, measured vs. the ferrocenium/ ferrocene (Fc +/0 ) couple (E BH+/H 2 (org) ). 5 In this method, E BH+/H 2 (org) is determined by measuring the OCP of buffered mixtures of an acid and its conjugate base under 1 atm H 2 using a Pt electrode freshly annealed in a H 2 flame. In solvents with an established absolute pK a scale, the OCP method can also be used to determine the standard hydrogen couple E Hþ=H 2 ðorgÞ via eqn (2).
Using this approach, values of E Hþ=H 2 have been reported in several solvents (see Table S3, ESI †), including MeCN ðE Hþ=H 2 ðMeCNÞ ¼ À0:028 V vs: Fc þ=0 Þ. 5 We note that the value reported in THF 6 ðE Hþ=H 2 ðTHFÞ ¼ À0:343 V vs: Fc þ=0 Þ was calculated using an absolute pK a scale 7 which is different from the most commonly used pK a scale in THF (sometimes referred to the pK a scale). 8 Although only a few absolute pK a values have been directly determined, pK a values, which have been reported for a wide variety of bases, can be used to calculate approximate pK a values (see ESI, † Section 2a for a more detailed discussion).
Based on E BH+/H 2 (org) , thermochemical cycles can be constructed to determine the thermodynamic potentials for reactions involving transfer of H 2 equivalents. This approach has been previously used to establish standard potentials for reduction of gaseous small molecules (O 2 , CO 2 , and N 2 ) in organic solvents 9,10 as well as for oxidation of a limited number of alcohols in water or MeCN. [11][12][13] A thermochemical cycle for determination of standard potentials for 2-electron oxidation of alcohols ðE R 2 CO=R 2 CHOH org ð Þ Þ is shown in Fig. 2. 14 The cycle starts from E Hþ=H 2 ðorgÞ and the gas-phase free energy for aldehyde or ketone hydrogenation DG þH 2 ðgÞ , which can be calculated from the difference in the gas-phase free energies of formation DG fðgÞ of the pure aldehyde or ketone and alcohol. It also involves the difference in solvation free energy between the alcohol and aldehyde or ketone DDG solv À Á . Although solvation free energies for common alcohols, aldehydes, and ketones are known in aqueous solution, few have been reported in the organic solvents commonly used in electrochemical studies of alcohol oxidation. However, since an alcohol and the corresponding aldehyde or ketone have nearly identical sizes and only modest differences in polarity, DDG solv is likely to be a relatively small contributor to the potential. In support of this assumption, the contributions of solvation free energy terms to the aqueous standard potentials for the oxidation of ethanol, 2-propanol, and benzyl alcohol are between 20 and 50 mV (see ESI † Section 4a for the complete analysis). In the solvents typically used in electrochemical experiments with organometallic and inorganic complexes, the magnitude of DDG solv is likely to be similar to or smaller than the value in water (see ESI † Section 4b). Based on its very limited contribution to the potential, DDG solv can be omitted when solvation free energies are not available. In these cases, E R 2 CO=R 2 CHOH org ð Þ is calculated using eqn (3), shown at the bottom of Fig. 2. Values of E R 2 CO=R 2 CHOH org ð Þ in water, MeCN, and THF are provided in Table 1 for several common alcohols.
The same approach can be used for the 4 e À oxidation of alcohols to esters or carboxylic acids (see ESI † Sections 5 and 6 for complete analysis). 16 We note that there is a greater degree of uncertainty in the values for carboxylic acids and carboxylates because in organic solvents these species are prone to aggregation, including homoconjugation, dimerization, and ion pairing, which perturbs solution equilibria and changes the driving force for the overall reaction. The impact of aggregation can be included if all of the relevant equilibrium constants are known. When they are not known, the influence of aggregation can be minimized by conducting measurements of E cat/2 in buffered solutions containing the acid, base, alcohol, and carboxylic acid. 1 An analogous thermochemical scheme for determination of the standard potential for the 6 e À oxidation of methanol to CO 2 is discussed in the ESI † (Section 7). Because CO 2 has a gas-phase standard state, a correction for its solvation free energy is not included. The solvation free energy term for the alcohol therefore makes a slightly larger contribution to the potential compared to the 2-electron and 4-electron cases. When solvation free energies are not available, a better estimate of E CO 2 =MeOH org ð Þ can be obtained based on E CO 2 =MeOH aq ð Þ (see ESI, † Section 7c) following the approach described in ref. 9.    15 See ESI Section 4a for further discussion. b These values correspond to the standard potential for the oxidation of methanol to formaldehyde. As discussed in more detail in ESI Section 4a, significant additional driving force for methanol oxidation is likely provided by condensation and oligomerization. Values calculated using this standard potential therefore correspond to a lower limit on the overpotential. c Values were calculated including an estimate for DDG solv . See ESI Sections 5, 6, and 7 for more details. d Under basic conditions where pK a (HBase + ) 4 pK a (RCO 2 H), the thermodynamic potential for the carboxylate/alcohol pair is calculated as

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We note that the thermodynamic potentials calculated using the above schemes involve several approximations. In addition to neglecting the contribution from solvation free energies, the analysis described above assumes ideal solutions (i.e., that the activities of all species are equal to their nominal concentrations). While the impacts on the thermodynamic potentials are expected to be small, the resulting overpotentials, particularly when they are low, should be interpreted with these sources of uncertainty in mind.

Calculation of equilibrium potentials under catalytic conditions
The values of E1 discussed above correspond to standard-state conditions of 1 M solvated H + , 1 M alcohol, and 1 M oxidized product at 298 K. Electrochemical experiments are rarely performed under standard-state conditions, however, and it is necessary to determine the equilibrium potential (E1 0 ) under the conditions employed in the experiment. The following discussion explains how to calculate E1 0 for 2 e À oxidation of alcohols. The same approach may be used for 4 e À and 6 e À oxidations of alcohols.
Under non-aqueous conditions, alcohol oxidation is generally conducted in the presence of an organic base. In solvents with an established pK a scale, the value of E1 0 can be calculated from E1 and the pK a of the protonated form of the organic base using eqn (4), shown at the bottom of Fig. 3. In solvents or solvent mixtures in which a pK a scale has not been established or E Hþ=H 2 ðorgÞ is not known, E1 0 can instead be calculated from E BH+/H 2 (org) (determined via OCP measurements using the same acid/base pair employed in the catalytic conditions) and DG þH 2 ðgÞ (see ESI, † Section 2b). The analysis in Fig. 3 indicates that the choice of base has a substantial impact on the value of E 0 R 2 CO=R 2 CHOH org ð Þ . Fig. 4 shows the range of thermodynamic potentials for bases that have been used in reports of electrocatalytic oxidation of benzyl alcohol in MeCN and 2-propanol in THF. Use of the organic bases triethylamine (NEt 3 ) and N-methyl imidazole (NMI) in MeCN, rather than standard-state conditions (i.e., solvated H + ), results in an B1 V shift in the thermodynamic potential for the PhCHO/BnOH redox equilibrium. Studies in THF have used even stronger phosphazene bases, leading to shifts of up to 2.2 V from standard-state potentials.
Electrocatalytic measurements are also often performed on solutions containing only alcohol and base. Under these conditions, the thermodynamic potential is ill-defined because the ln(Q) term in the Nernst equation contains terms with initial values of zero. Therefore, the solution composition at the electrode surface, and the corresponding electrode potential, change substantially as soon as electrocatalysis begins. If the measurement is instead performed using a buffered solution (containing a base, its conjugate acid, an alcohol, and the Fig. 3 Calculation of the thermodynamic potential for 2 e À oxidation of an alcohol in the presence of an acid/base pair E 0 R 2 CO=R 2 CHOH org ð Þ from E R 2 CO=R 2 CHOH org ð Þ (see Fig. 2) and pK a (HBase + ).  Table 1) and pK a (H-Base + ) using eqn (4).

Perspective
Energy & Environmental Science corresponding aldehyde or ketone), the relative change in ln(Q) and correspondingly in the thermodynamic potential will be small. The most straightforward method for establishing a stable potential is to perform electrocatalytic reactions in solutions containing 1 : 1 ratios of base to conjugate acid and alcohol to conjugate aldehyde or ketone. The resulting potential is the same as that calculated from eqn (4), despite the deviation from standard state conditions. If ratios other than 1 : 1 are used, E 0 R 2 CO=R 2 CHOH org ð Þ must be modified via the Nernst equation (eqn (5)) to account for the non-standard state concentrations.
Evaluation of overpotential for known electrocatalysts for oxidation of alcohols Molecular catalysts for electrochemical alcohol oxidation have been reviewed recently. [17][18][19] Here, we focus on a subset of catalysts for which electrochemical two-electron oxidation of alcohols was performed in THF or MeCN using bases with known pK a values, which allows the determination of overpotentials ( Fig. 5 and Table 2). As discussed in the previous section, catalyst performance should be evaluated under buffered conditions. Such conditions are rarely employed in practice, and it is difficult to accurately predict what impact buffering will have on the observed catalytic rate and potential. To illustrate the impact of buffering, the oxidations of BnOH and i PrOH catalyzed by [Ni(P tBu 2 N tBu 2 ) (MeCN) 2 ][BF 4 ] 2 were examined under unbuffered conditions (only alcohol and Et 3 N) and buffered conditions (alcohol, PhCHO or Me 2 CO, Et 3 N, and Et 3 NH + ). As shown in Fig. S7 and S8 (ESI †), for this specific catalyst buffering results in a small (B50 mV) positive shift in E cat/2 and an approximately two-fold decrease in rate. The precise changes will not be generalizable across catalysts, but this example shows that measuring under buffered conditions can result in a change in catalytic performance in some cases. This approach has not been used for the other systems in Fig. 5; the reported performance for these catalysts should be interpreted with this discrepancy in mind, especially for the values in THF that are expected to be more significantly impacted by the effects of ion pairing. To illustrate how the catalyst properties contribute to both overpotential and rate, the proposed catalytic cycles for several of these systems are discussed in detail below.
Under the buffered conditions described above, [Ni(P tBu 2 N tBu 2 ) (MeCN) 2 ] 2+ catalyzes the oxidation of BnOH at E cat/2 = À0.71 V vs. Fc +/0 , corresponding to an overpotential of 0.39 V. As shown in Fig. 6, the catalytic cycle is proposed to involve generation of an alkoxide complex as the rate-limiting step. 21 This species undergoes b-hydride elimination to release benzaldehyde. Oxidation of the resulting Ni(II) hydride, which is the potential determining step, occurs at a mild potential because of the presence of the pendant amine, which provides a pathway for intramolecular proton transfer. 29,30 Although the Ni(II) hydride could not be isolated, this hypothesis is supported by comparison to related bis(diphosphine) Ni(II)-H complexes. For example, the oxidation of [HNi(depp) 2 ] + (depp = 1,3-bis(diethylphosphino)propane) occurs 0.6 V more positive than the oxidation of a corresponding complex that contains a pendant amine ([HNi(Et 2 PCH 2 NMeCH 2 PEt 2 ) 2 ] + ). 31 The presence of the pendant amine is therefore crucial to achieving a low overpotential in this system. An analogous catalytic cycle was proposed for [Co(P 3 )(MeCN) 2 ] 2+ , but the Co(II)-H is oxidized at a  Fig. 4) and the white circles represent E cat/2 . The length of the colored bars corresponds to the overpotential (see also Waymouth and co-workers have reported several electrocatalysts for the oxidation of 2-propanol based on thermal catalysts that were originally used for acceptorless alcohol dehydrogenation and transfer hydrogenation reactions. [32][33][34][35] The proposed catalytic cycle for [Ir(PNP)(H) 2 ] is shown as a representative example in Fig. 7A. This complex dehydrogenates 2-propanol via a mechanism involving proton transfer to the PNP ligand amide group and hydride transfer to the Ir center to produce acetone and [Ir(PN(H)P)(H) 3 ]. 24,35 This species is oxidized at À0.65 V vs. Fc +/0 and then deprotonated by phosphazene P 2 -Et. The strong base makes a large contribution to E1 0 , which results in a high overpotential of 1.5 V. Oxidation of 2-propanol by [Fe(PNP)(CO)(H)] follows an analogous mechanism. 23 Although the E cat/2 is slightly more modest for the Fe complex, the use of a strong base (phosphazene P 2 -Et) results in a high overpotential of 1.1 V.
The overpotential of the Ir catalyst can be decreased by addition of a phenol/phenoxyl radical electron-proton transfer mediator, 36 which performs two successive formal H-atom abstractions to regenerate [Ir(PNP)(H) 2 ] (Fig. 7B). 24 The mediator a pK a refers to the conjugate acid of the indicated base. pK a values in MeCN were taken from the literature. 8,28 pK a values in THF 8 were converted 7 to absolute pK a values (see ESI section 2a). b Measurements were conducted on buffered solutions (see ESI Section 9). c No electrocatalytic activity was observed on the CV timescale, but bulk electrolysis at an applied potential of À0.63 V produced PhCHO with 97% Faradaic efficiency. Z was estimated based on the Co(II/I) E 1/2 (À0.78 V vs. Fc +/0 ). d Measurements were not conducted under buffered conditions which increases the uncertainty in Z. Values are therefore reported to the nearest 100 mV. e Rate not determined due to overlap of catalytic wave with background base oxidation by the electrode.  is then regenerated electrochemically through deprotonation of the phenol by P 2 -Et and oxidation of the phenoxide at À1.07 V vs. Fc +/0 . Since this oxidation occurs at a milder potential than the oxidation of [Ir(PN(H)P)(H) 3 ], the overpotential is decreased to 1.0 V. Similarly, the addition of [Ru(acac) 2 (pyimN)] to [Ru(H)(CNN)(dppb)] lowers the overpotential for 2-propanol oxidation from 1.6 V to 1.1 V with phosphazene P 4 -t Bu as the base. 25,26 The origin of the decrease in overpotential is less clear in this case, but has been proposed to involve H-atom abstraction by [Ru(acac) 2 (pyimN)].
Organic aminoxyls, such as TEMPO and ACT, have been widely used as molecular electrocatalysts for alcohol oxidation. 37 As a representative example, the oxidation of benzyl alcohol occurs via reaction of the alcohol with TEMPO + (Fig. 8A) to give TEMPOH and benzaldehyde. 27,38 TEMPOH is then deprotonated and re-oxidized to TEMPO + at a potential of +0.24 V vs. Fc +/0 in MeCN. The overpotential for this reaction is 1.2 V when NMI is used as the base. The addition of a Cu co-catalyst, which was originally developed to support aerobic alcohol oxidation, 39 has also been shown to enhance electrocatalytic alcohol oxidation. In this case, [Cu(bpy)] 2+ and TEMPO mediate alcohol oxidation by a different mechanism in which the Cu II and TEMPO species act cooperatively to achieve net hydride abstraction from a Cu-coordinated alkoxide (Fig. 8B). Formation of the Cu-alkoxide complex is the rate-limiting step in this reaction. The [Cu(bpy)] 2+ species also promotes proton-coupled oxidation of TEMPOH to regenerate TEMPO ; oxidation of [Cu(bpy)] + is the potentialdetermining step of the electrocatalytic reaction. This redox step occurs at a more moderate potential than the oxidation of TEMPO to TEMPO + , resulting in a lower overpotential of 0.8 V.

Comparison of overpotentials for the oxidation of alcohols
Using the approach described above, overpotentials for electrocatalytic alcohol oxidation can be meaningfully compared across solvents and conditions, as illustrated in Fig. 9A The well-defined overpotentials discussed above for catalysts that operate in organic solvents also provide a basis for clearer comparison with catalysts operating under aqueous conditions. Fig. 9B shows examples of catalysts from different classes that operate in aqueous solution. TEMPO and its analogues catalyze the oxidation of a variety of alcohols in water, although the reactions generally occur at high overpotential. For example, the overpotential for ABNO-catalyzed oxidation of 1-butanol to   butanal is 0.9 V at pH 9. 3 By modifying the pH and the identity of the nitroxyl, the overpotential can be lowered by 0.15 V, but at a cost to the rate. 40 A variety of polypyridyl Ru complexes can also catalyze oxidation of alcohols, but generally require high overpotentials (Z Z 1 V) because their mechanisms involve electrochemical generation of a Ru-oxo species at high potential. 41 50,51 For comparison, Pt/Ru alloys are among the most active heterogeneous catalysts for oxidation of alcohols and have been widely studied in direct methanol fuel cells. [52][53][54][55] Under the acidic conditions typical for proton-exchange membrane fuel cells, these alloys exhibit overpotentials as low as 0.3 V for conversion of MeOH to CO 2 . 53 Unfortunately, these catalysts are poisoned by aldehydes and carboxylic acids, limiting their utility with alcohol substrates containing C-C bonds. 54 At high pH, metal oxides such as NiOOH have been used to promote electrocatalytic alcohol oxidation, and exhibit good activity, stability, and selectivity for oxidation of primary alcohols to carboxylates. However, these reactions require potentials approaching those capable of supporting water oxidation, resulting in overpotentials for alcohol oxidation of up to 1.3 V. [56][57][58][59]

Conclusions
The methodology outlined herein provides an important foundation for future advances in the field of electrocatalytic alcohol oxidation by enabling comparisons of catalyst performance across different reaction conditions. Compared to previous studies in water, studies of reactivity and catalytic properties in organic solvents can be performed under a wider range of conditions. To date, overpotentials have not been reported for molecular electrocatalysts for the oxidation of alcohols in non-aqueous solvents because of the lack of established thermodynamic potentials, and this gap has hindered meaningful comparisons between catalysts studied under different conditions. The analysis above highlights the crucial role of both solvent and base strength on the thermodynamic potential of alcohol oxidation and shows how these two features combine with the electrochemical properties of the catalyst to establish the overpotential for electrocatalytic alcohol oxidation.
To summarize briefly, the overpotential for alcohol oxidation with a catalyst corresponds to the difference between the thermodynamic potential for the reaction under the conditions used for catalysis and the potential at which catalysis occurs at a given rate. Estimation of thermodynamic potentials for the 2 e À , 4 e À , and 6 e À oxidation of alcohols in organic solvents requires three values: (1) The equilibrium potential for the hydrogen evolution reaction (E BH+/H 2 (org) ) in organic solvent with the acid-base pair used in the catalytic reaction.
(2) Values for the gas-phase free-energies of formation DG f À Á of the alcohol and oxidized product.
(3) An approximation for the difference in solvation free energies of the alcohol and oxidized product DDG solv À Á . In solvents with an established pK a scale, E BH+/H 2 (org) can be determined from E Hþ=H 2 ðorgÞ and pK a (HBase + ). OCP measurements can also be used to directly determine this benchmark value when there is no established pK a scale for a solvent or E Hþ=H 2 ðorgÞ is not known. For the remaining two values, DG f is known for the common species of interest, and DDG solv is expected to be small (ca. 1-2 kcal mol À1 ) based on known values for relevant species. 60 The resulting uncertainty (t50 mV) is often small relative to the operating overpotentials and DDG solv can therefore be reasonably omitted in most cases.
The approach provided here has enabled comparison of the overpotentials for the oxidation of alcohols by molecular electrocatalysts in organic solvents. From this analysis, [Ni(P tBu 2 N tBu 2 ) (MeCN) 2 ] 2+ is noteworthy for its combination of good rate and comparatively low overpotential for catalysis. The lower overpotential is a result of a less positive potential for oxidation of the catalytically relevant species and the ability of the catalyst to operate with a modest base, resulting in a mild thermodynamic potential. As this field of research grows, the approach outlined here provides a basis for quantitative comparisons of catalyst performance, thereby facilitating the identification of catalyst properties that contribute to higher activities and lower overpotentials.

Conflicts of interest
There are no conflicts to declare.