Toward the Rational Benchmarking of Homogeneous H₂-Evolving Catalysts

Abstract

Molecular electrocatalysts for H₂ evolution are usually studied under various conditions (solvent, proton sources) that prevent direct comparison of their performances. We provide here a rational method for such a benchmark based on (i) the recent analysis of the current-potential response for two-electron-two-step mechanisms and (ii) the derivation of catalytic Tafel plots reflecting the interdependency of turnover frequency and overpotential based on the intrinsic properties of the catalyst, independently of contingent factors such as the cell characteristics. Such a methodology is exemplified on a series of molecular catalysts among the most efficient in recent literature.

Introduction

Transition towards a post-oil economy depends on our capacity to find new sustainable solutions for exploiting renewable energies such as sun or wind.¹ In this context, the production of fuels is appealing since their stability and mass energetic content are orders of magnitude higher than those of batteries or supercapacitors.^2,3 Hydrogen (H₂) has been set as the first target for such solar- or electro-fuels in the perspective of the dawn of the hydrogen economy.⁴

Hydrogen production from water is a multi-step two-electron process which requires catalysis to occur both at fast rates and near thermodynamic equilibrium, these two conditions being mandatory for efficient power to chemical energy transduction. While platinum and other noble metals already meet the above mentioned specifications as H₂-evolving electrocatalysts, the development of earth-abundant electrocatalysts^5,6,7 is a requisite for this approach to become economically viable. Many molecular compounds based on Ni,^8,9 Fe,6^,10,11 Co¹² or Mo^13,14,15 complexes, often inspired from the structure or function of the active sites of hydrogenases,^16,17 have been reported in the past 15 years as active catalysts for H₂ evolution. However, the conditions used for assessing activity are almost as varied as the catalysts themselves and it is urgent to establish a rational way to benchmark homogeneous H₂-evolving catalysts. Several previous attempts in that direction focused on the notion of “onset” or “operating” potential, which has the interest of providing a quick estimate of the maximal (in reductions) or minimal (in oxidations) electrode potential at which catalysis takes place. Several definitions of the onset/operating potential have been proposed.^{18,19,20, 21,22,23,24} However, comparison between catalysts does not only require the definition of the potential at which catalysis takes place but also some measure of the catalytic rate at this electrode potential. In this respect, it seems natural to rely on a classical notion of homogeneous catalysis, namely the turnover frequency (TOF). This has however to be adapted to the homogeneous catalysis electrochemical contextin two ways. One is to take into account the fact that the catalyst molecules that effectively partake to catalysis are not all the molecules present in the cell compartment but only those contained in a thin reaction-diffusion layer adjacent to the electrode, whose thickness is a decreasing function of the catalysis rate. The catalysis rate thus governs the TOF both in determining the rate at which the substrate is transformed and also the number of catalyst molecules actually involved, a specific feature of electro-assisted catalysis.²⁵ The second adaptation derives from the dependence of the TOF thus defined on the electrode potential, and therefore from the overpotential, classically defined as the absolute value of the difference between the electrode potential and the apparent standard potential of the reaction to be catalyzed.^25,26 The “catalytic Tafel” plots relating the TOF to the overpotential thus provide a means of comparing the catalysts though their intrinsic properties, independently from the characteristic of the electrochemical cell. Without neglecting another important factor of merit of a catalyst, viz, its stability, we focus in the following on benchmarking the catalyst by comparison of their catalytic Tafel plots.^{25, 26, 27} We first provide reminders on the foundations needed to establish such “catalytic Tafel plots” for homogeneous electrocatalysts and then illustrate the application of this approach by examples of previously reported H₂-evolving catalysts for which consistent, reliable and relevant data can be found in the literature.

Results and Discussion

1. Turnover frequency and overpotential

The turnover number is defined as the number of catalytic cycles achieved by a single catalyst. The total turnover number (tTON) is defined as the TON achieved before full degradation of the catalyst.

The turnover frequency (TOF) is the number of turnovers achieved in a unit of time, during the period of time where degradation of the catalyst remains negligible. TOF may then be obtained from the ratio $\mathit{TOF}=\frac{N_{\mathit{product}}}{N_{\mathit{active}\mathit{cat}}}$ of the number of moles of product, generated per unit of time to the number of moles of the catalyst.

The determination of TON and TOF always requires the knowledge of the number of catalytic active sites, which is often an issue in the case of heterogeneous catalysis. This problem does not exist in homogeneous catalysis but, in this case, it is necessary to know the amount of catalyst active in the immediate vicinity of the electrode that effectively participate to catalysis as discussed in more detail later on.

The overpotential (η) is a thermodynamic quantity simply equal to the difference between the electrode potential E and the apparent standard potential of the reaction to be catalyzed. In the case of reduction of protons, the overpotential is written as follows:

$$\eta =E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^{0,\mathit{ap}}-E$$

The determination of $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^{0,\mathit{ap}}$ has been the subject of several reports.^20,22,28 This value is generally computed from two tabulated values, $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^0$, the standard potential of the H⁺/H₂ couple in the solvent used for the study and the pK_a of the proton source in the same solvent:

$$E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^{0,\mathit{ap}}=E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^0-0.059\mathit{pK}$$

The pK_a values for a number of acids are known,²⁹ albeit in a restricted number of solvents. The same is true for the standard potential of the H⁺/H₂ couple, which is only known in CH₃CN, DMF and DMSO (Table 1 of reference 22). Of note, an initially reported value³⁰ has been corrected to account for the stoichiometry of the reaction²² and the new value was confirmed by measurements carried out on a bidirectional homogeneous electrocatalysts for H⁺/H₂ interconversion.³¹ More recently an electrochemical method was reported that allows the direct determination of $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^{0,\mathit{ap}}$, provided the H⁺/H₂ equilibrium can be reached at the working electrode plunged in the solvent of the study in the presence of the proton source and H₂ gas.³² Within the 50 mV error range of this method, the $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^{0,\mathit{ap}}$ values thus obtained are similar to those obtained from tabulated values in CH₃CN and DMF.²² This method, that requires the use of a special Pt electrode annealed under H₂, is nevertheless valuable to get values of $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^{0,\mathit{ap}}$ for specific solvent/proton source combinations for which no tabulated values are available.

Acids (AH) and their conjugate base (A⁻) often form stable adducts (AHA⁻) through hydrogen bonding.^33,34 This phenomenon, called homoconjugation,³⁵ depends on the concentration of the acid. It is very frequent in acetonitrile, and present to a lesser extent in DMF.²⁹ The influence of homoconjugation on $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^{0,\mathit{ap}}$ has been described in detail and is used in this study.²²

2. Catalytic Tafel plots

Molecular homogeneous catalysis of H₂ evolution is a multi-electron multi-step process. It is nevertheless useful to recall basic notions that are easier to introduce with the help of a simplified one-electron-one step reaction scheme such as the one depicted in Scheme 1.^36,37

Scheme 1.

Simplified catalytic scheme

If the catalytic reaction is fast and irreversible, a steady-state situation is established by mutual compensation between catalytic reaction and diffusional transport. It results in “pure kinetic conditions” implying that the concentration profiles of both forms of the catalyst are confined within a thin reaction-diffusion layer, whose thickness is of the order of $\sqrt{D_{\mathit{cat}}∕k_{\mathit{cat}}}(D_{\mathit{cat}}$ is the diffusion coefficient of the catalyst). This entails that, in the definition of the catalyst turnover number (TON) and turnover frequency (TOF), the number of moles of catalyst that are actually involved are those contained in the reaction layer rather than in the whole solution.³⁸ If the substrate is in such excess that its consumption may be neglected and if the electrode electron transfer that generates the active form of the catalyst is so fast that the Nernst law is obeyed, an S-shaped current potential response will be observed:

$$i=\frac{i_{\mathit{pl}}}{1+\exp \left[\frac{F}{\mathit{RT}}\left(E-E_{1∕2}\right)\right]}$$ (1)

with a half-wave potential

$$E_{1∕2}=E_{\mathit{cat}}^0$$ (2)

and with a plateau current, independent of scan rate:

$$i_{\mathit{pl}}={\mathit{FSC}}_{\mathit{cat}}^0\sqrt{D_{\mathit{cat}}}\sqrt{k_{\mathit{cat}}{C}_{\mathit{subst}}^0}$$ (3)

(S is the electrode surface area and the C⁰_s, the bulk concentrations of the subscript species).^37,36 These equations apply not only to non-destructive electrochemical techniques, such as cyclic voltammetry, but also, if the catalyst is stable enough, under preparative-scale conditions regardless of the cell-time response.³⁹

During the period of time where the catalyst remains stable, the turnover frequency, TOF, may then be obtained from the ratio:

$$\mathit{TOF}=\frac{N_{\mathit{product}}}{N_{\mathit{active}\mathit{cat}}}$$

of the number of moles of product, generated per unit of time to the maximal number of moles of the active forms of the catalyst contained in the reaction-diffusion layer. TOF has thus the dimension of (time)⁻¹.

It follows that:^25,26,27

$$\mathit{TOF}=\frac{{\mathit{TOF}}_{\mathit{max}}}{1+\exp \left[\frac{F}{\mathit{RT}}\left(E-E_{1∕2}\right)\right]}$$ (4)

with:

$$\text{with}:{\mathit{TOF}}_{\mathit{max}}=k_{\mathit{cat}}{C}_{\mathit{subst}}^0$$ (5)

Introducing the overpotential η (as already define above), the catalytic Tafel plot is thus obtained as:

$$\mathit{TOF}=\frac{{\mathit{TOF}}_{\mathit{max}}}{1+\exp \left[\frac{F}{\mathit{RT}}\left(E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^0-E_{1∕2}\right)\right]\exp \left(-\frac{F}{\mathit{RT}}\eta \right)}$$ (6)

to be plotted in logarithmic form as shown schematically in Figure 1. The resulting characteristic curve is most conveniently derived from non-destructive experiments such as CV recordings. It is however important to check that preparative-scale experiments, in which the potential or the current are imposed and the resulting current or potential are measured, leads to concordant results. Such preparative-scale data are pictured as stars in Figure 1.

Fig. 1.

An example of catalytic Tafel plot for the simplified reaction scheme (Scheme 1). The solid line is a graphical representation of equation (6) as can be derived from the values of TOF_max and E_1/2 resulting, e.g., from cyclic voltammetry measurements. The stars pictured the data that can be obtained from a series of preparative-scale experiments as a check of the predictions bases on cyclic voltammetric data. These electrolyses also allow one to test the stability of the catalyst.

What changes when the catalytic process involves several electron transfers and several chemical steps, e.g., two electron transfers and two chemical steps as is the case with hydrogen evolution catalysts? The various types of reaction mechanisms can be categorized according to the succession of electron transfer steps, E, and chemical steps, C (at least one of which involves a proton transfer in the present case). In this context, a C step is not necessarily a single elementary step. It may well consist in an association of elementary steps, reversible or not, the whole reaction being globally irreversible and characterized by an apparent rate constant. A couple of illustrating examples of this categorization is shown in Scheme 2.

Scheme 2.

Two examples of two-electron-two-step catalytic reaction schemes^a

a: M ^J: metal complex at the oxidation degree J, AH: proton donor, A⁻: conjugate base. $E_1^0$, $E_2^0$: standard potentials. k₁, k₂ : second order rate constants.

In both cases, equations (1), (4), (6) still hold, whereas equations (2), (3) and (5) are replaced by:²⁷

$$\mathrm{EECC}:E_{1∕2}=E_2^0+\frac{\mathit{RT}}{F}\ln \left(1+\sqrt{\frac{k_1}{k_2}}\frac{1}{1+\sqrt{\frac{k_1}{k_2}}}\right)$$ (7)

$$\mathrm{ECEC}:E_{1∕2}=E_1^0+\frac{\mathit{RT}}{F}\ln \left(1+\sqrt{\frac{k_1}{k_2}}\right)$$ (7′)

$$\mathrm{EECC}:i_{\mathit{pl}}=2{\mathit{FSC}}_{\mathit{cat}}^0\sqrt{D_{\mathit{cat}}}\frac{\sqrt{k_1\left[\mathrm{AH}\right]}}{1+\sqrt{\frac{k_1}{k_2}}\frac{1}{1+\sqrt{\frac{k_2}{k_1}}}}$$ (8)

or

$$\text{or}:\frac{i_{\mathit{pl}}}{i_p^0}=4.48\frac{\sqrt{k_1\left[\mathit{AH}\right]}}{1+\sqrt{\frac{k_1}{k_2}}\frac{1}{1+\sqrt{\frac{k_2}{k_1}}}}\sqrt{\frac{\mathit{RT}}{F\nu }}$$

where $i_p^0$ is the peak current of a one-electron reversible

$$\text{Nernstian wave}:i_p^0=0.446{\mathit{FSC}}_{\mathit{cat}}^0\sqrt{D_{\mathit{cat}}}\sqrt{\frac{F\nu }{\mathit{RT}}}$$

$$\mathrm{ECEC}:i_{\mathit{pl}}=2{\mathit{FSC}}_{\mathit{cat}}^0\sqrt{D_{\mathit{cat}}}\frac{\sqrt{k_1{k}_2\left[\mathrm{AH}\right]}}{\sqrt{k_1}+\sqrt{k_2}}$$ (8′)

or:

$$\text{or}:\frac{i_{\mathit{pl}}}{i_p^0}=4.48\frac{\sqrt{k_1{k}_2\left[\mathrm{AH}\right]}}{\sqrt{k_1}+\sqrt{k_2}}\sqrt{\frac{\mathit{RT}}{F\nu }}$$ (8′′)

Then, in both cases,

$$\text{Then},\text{in both cases},{\mathit{TOF}}_{\mathit{max}}=\frac{k_1{k}_2}{k_1+k_2}\left[\mathrm{AH}\right]$$ (9)

The other cases are analyzed in reference 27 and procedures to set up the catalytic Tafel plots are proposed, based on the determination of the two standard potentials and the two apparent rate constants. As in the simplified case, points located in the top left zone of the logTOF - η plane represent the best catalysts and vice versa for the bottom right zone.

We examine in the next section the behavior of several examples of H₂-evolving catalysts described in current literature. There were selected among more numerous cases on the basis that enough data were available to determine the characteristic rate constants and potentials and, from there, the logTOF - η plots featuring each of them. In this endeavor, difficulties, related to “side-phenomena,” are often encountered, which make the CV responses peak-shaped and scan rate dependent when a scan-rate independent S-shaped response is expected. As discussed in detail elsewhere, these side phenomena may have various origins — consumption of the substrate (here the acid AH), inhibition by products,^40,25 deactivation of the catalyst and, more generally, phenomena that parallel the efficiency of catalysis.²⁵Among them, the easiest to treat is the case where the consumption of the catalyst occurs and, occurs alone. The zone diagram in Figure 2, recalls the way in which substrate consumption may influence the CV responses, still taking as example the simplified reaction scheme (Scheme 1). On the top of the diagram, where the pure kinetic conditions are achieved as they are for fast catalytic processes, the system passes, upon increasing the catalytic rate constant and decreasing the excess of substrate over catalyst, from the canonical S-shape to the “total” catalysis situation. In all cases then, the characteristics of the CV responses are known and can be used to derive the relevant rate constant and therefrom, the turnover frequency. We will see in Section 2 how these procedures can be extended to two-electron-two-step processes in each case that will be treated.

Fig. 2.

Catalytic zone diagram for the simplified reaction scheme ( Scheme 1) ^37,41

Other side-phenomena, which may occur at the same time or instead of substrate consumption, are much more difficult to identify and treat. One way out of these difficulties is to focus on the foot of the CV wave where the contributions of all side-phenomena are minimal.^25,26,42 Another way is to raise the scan rate so as to decrease the charge passed during the experiment and thus minimize all the side-phenomena. These two strategies may also be applied simultaneously.

In the above discussion we have only considered heterolytic mechanisms, i.e., mechanisms in which dihydrogen results from the reaction of a metal-hydride on the acid, rather than from the reaction of two molecules of the metal-hydride during which two hydrogen atoms combine to give hydrogen, as it occurs in homolytic mechanisms. The reason for this simplification is that, as shown recently,⁴³ heterolytic pathways predominate over homolytic pathways for strong or moderately strong acids as in the examples we discuss in the next section.

3. Examples of benchmarking of some homogeneous H₂-evolving catalysts

Establishing a catalytic Tafel plot for a given catalyst derives from the application of equation (6), which implies knowing E_1/2 and TOF_max. All potentials involved are preferably referred to the Fc⁺/Fc couple in the solvent as is the value of $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^0$. TOF_max and all TOF values are reported in s⁻¹ as second order kinetic constants taken for 1 M of acid. Estimation of these two parameters requires the value of the rate constants k₁ and k₂ (equation 9).

The methodology presented here is general and can be applied to benchmark any H₂-evolution catalyst provided (i) it has been characterized in a solvent from which overpotential values can be reliably determined and (ii) kinetic data pertaining to a relevant mechanistic scheme are available. In the course of this study, we examined the vast literature on molecular H₂-evolving catalysts and in many cases, could not find all data required for the construction of catalytic Tafel plots. In most cases indeed, kinetic data are extracted using equation (3) while the system is not in the “pure kinetic” regime which precludes utilization of such data for benchmarking purposes. We finally selected only a few systems, listed in Table 1 for which we could extract reliable data for the construction of catalytic Tafel plots. Data in Table 1, and the ensuing catalytic Tafel plots in figure 4 therefore do not intend to cover all reported homogeneous H₂-evolving catalysts but simply to serve as examples of benchmarking procedures based on the intrinsic properties of the catalysts freed of the particular specifications of the electrolysis cell that was used.

Table 1.

Examples of data treatment for some examples of literature H₂-evolving catalysts

Catalyst g	acid	solvent	$E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^0$ a,b	Standard potentials a $E_1^0$, $E_2^0$	Rate constants c k1, k2	E1/2, a,f	TOFmax ([H+]= 1M)	Reaction scheme or TOF estimation	Ref.
FeIITPP g	Et3NH+	DMF	−1.20	− 1.45, −2.16	2×108, 4×105d	−2.08	4×105	EECC	44
CoII(dmgH)2py g				−1.53, $E_2^0$ > $E_1^0$	104, k2>>k1d	−1.53	104	ECEC	18
[NiII(PPh2NPh)2]2+	DMFH+	MeCN	−0.50h	−1.16, $E_2^0$ > $E_1^0$	7.5×104, k2>>k1	−1.16	7.5×104	ECEC	48
[NiII(PPh2NC6H4X2)2]2+ X= CH2P(O)(OEt)2	DMFH+			−0.84, $E_2^0$ > $E_1^0$	1.3×103, k2>>k1	0.84	1.3×103	ECEC	49
H	TfOH		−0.26	−0.85, $E_2^0$ > $E_1^0$	8×102, k2 >> k1	−0.85	8×102		21

^a:in V vs. Fc⁺/Fc;

^b:calculated for 1M proton concentration from reference 23, taking the homoconjugation effect into consideration, see text;

^c:In equations (7) - (9), $k_1^{\mathit{ap}}=k_1\left[\mathrm{AH}\right]$ and $k_2^{\mathit{ap}}=k_2\left[\mathrm{AH}\right]$, unless otherwise stated. k₁, k₂ in M⁻¹s⁻¹;

^d:from the analysis of CV responses taking into account acid consumption in conditions of “total catalysis” or close to these conditions (see Figure 2);

^e:from the estimated plateau current when the CV responses are S-shaped or close to be S-shaped;

^f:E_1/2 may have two different meanings. It is either the observed half-wave potential of the CV response in the case depicted by footnote e. It is then used, together with the plateau current to derive by means of equations (7) and (8), the two rate constants. It may conversely be a calculated value when the two rate constants have been accessed in a different manner as in footnote e, serving to establish the TOF - η relationship according to equations (6), (7) and (9).

^g:H₂TPP: tetraphenylporphyrin, dmgH₂: dimethylglyoxime, py: pyridine; Co^II(dmgH)₂py is obtained from Co^III(dmgH)₂pyCl after reductive elimination of Cl⁻.¹⁸

^h:the presence of equimolar amount of the conjugate base DMF has been taken into consideration for the calculation of $E_{{\mathrm{H}}^{+}∕{\mathrm{H}}_2}^0$ in a similar way as described in reference 22: in this specific case, the value of ε_D should be set at 17±5 mV.

Fig. 4.

Catalytic Tafel plots for the various electrocatalysts listed in Table 1. Black: Fe^IITPP, DMF, Et₃NH⁺. Blue: Co^II(dmgH)₂py, DMF, Et₃NH⁺. Green: [Ni(P^Ph₂N^Ph)₂]²⁺, MeCN, DMFH⁺. Orange: [Ni^II(P^Ph₂N^C6H4X₂)₂]²⁺, MeCN, X= CH₂P(O)(OEt)₂, DMFH⁺, (dots), X= H, TfOH (triangles).

In the case of Fe^IITPP,⁴⁴ the reaction pathway was shown to be of the EECC type. Besides the values of the standard potentials, one can thus use the reported values of k₁ and k₂, which were derived from analysis of the CV responses at low acid concentrations, where the “total catalysis” conditions (see top left zone in figure 2) are fulfilled. These values are gathered in Table 1. TOF_max was then obtained by application of equation (6) with [AH] = 1 M and E_1/2 from equation (7).

The Co^II(dmgH)₂py complex (dmgH₂ = dimethylglyoxime, Py: pyridine)¹⁸ is another interesting case. It was originally analyzed in the framework of a ECCE mechanism, in conditions close to pure kinetic behavior. Re-examination of the data showed however that an ECEC mechanism leads to better fit of the CV data in agreement with the prediction ^45,46,47 that the standard potential for the reduction of the first protonated intermediate ($E_2^0$ in lower Scheme 2) is more positive than the standard potential of the initial electron transfer step ($E_1^0$ in lower Scheme 2). The values of the various parameters, thus obtained are listed in Table 1, leading to corresponding Tafel plot in figure 3.

Fig. 3.

Catalysis of H₂ evolution from the reduction of DMFH⁺ and TfOH in acetonitrile by Ni^II(P^Ph₂N^C6H4X₂)₂].Variation of the normalized plateau with the concentration of acid. Left: X = CH₂P(O)(OEt)₂. Dots: experimental data (from figure 3 in reference 49; data measured at 50 mV/s).). Solid line: proportionality to $\sqrt{\left[{\mathrm{DMFH}}^{+}\right]}$ with a proportionality factor of 114 M^−1/2. Right: X = H. Dots: experimental data (from figure 3 in reference 21; data measured at 50 mV/s). Solid line: proportionality to $\sqrt{\left[\mathrm{TfOH}\right]}$ with a proportionality factor of 92.

A different approach was used for the other catalysts of the list. It was based on CV responses pertaining to the S-shaped canonical behavior (top right corner of the zone diagram in figure 2). A first example in this category is [Ni(P^Ph₂N^Ph)₂]²⁺ represented in Chart 1.⁴⁸ S-shaped waves, independent of scan rate, are observed for this catalyst in the presence of DMFH⁺ in acetonitrile at the level of the Ni^II/Ni^I wave.

Chart 1.

Examination of the data in figure 4 of reference 48 shows that the E_1/2 is very close to the standard potential of the Ni^II/Ni^I couple. The most likely mechanism, in line with previous analysis,⁹ thus belongs to the ECEC category (Scheme 2), with the second proton transfer being faster than the first, and the second electron transfer easier than the first. This is confirmed by the proportionality of the apparent rate constant $k_1^{\mathit{ap}}$ to the acid concentration (figure S8 of reference 48). From the reported value of $i_{\mathit{pl}}∕i_p^0=38$ for [AH] = 0.43 M and 10 V/s, k₁ =7.5×10⁴ M⁻¹.s⁻¹ is derived from equation (8′′), considering that k₂>>k₁. TOF_max is then obtained from equation 9 for [AH] = 1M, which leads to the catalytic Tafel plot in figure 4.

A similar behavior is observed with another catalyst in a similar albeit different series, [Ni^II(P^Ph₂N^C6H4X₂)₂]²⁺, in which X = CH₂P(O)(OEt)₂.⁴⁹ Here too, k₁ is proportional to the acid concentration as results from the variation of the normalized plateau current with the acid concentration, showing no saturation kinetics (figure 3, left). From the proportionality factor between $i_{\mathit{pl}}∕i_p^0$ and $\sqrt{\left[{\mathrm{DMFH}}^{+}\right]}$, the values of k₁ can be derived from equation (8′′) considering again that k₂>>k₁. TOF_max reported in Table 1 ensues as well as the resulting Tafel plot in figure 4.

Another example in the same series with X = H, but with a different acid (TfOH), is also very similar (figure 3, right), leading to the values in Table 1 and the Tafel plot in figure 4.²¹

Conclusions

Good electrocatalysts are defined by fast turn-over at low overpotential. In other words, catalysts displaying high turnover frequencies at the expense of large overpotentials will not allow for a good power-to-chemical conversion yield while those exhibiting low catalytic rates, even near the thermodynamic equilibrium, will not allow for the development of powerful electrocatalytic devices for the production of solar- or electro-fuels. Catalytic Tafel plots provide a unified way to assess that these two properties are observed simultaneously with traces associated to the best catalysts appearing in the top-left corner of these graphs.

This rational way of benchmarking homogeneous H₂-evolving catalysts under the form of catalytic Tafel plots that relate properly defined turnover frequency to the overpotential, renders the comparison between catalysts independent from the characteristics of the particular electrochemical cell used and allows comparing catalysts assayed under distinct experimental conditions (solvent, proton source), viz. without defining standard conditions of measurement.⁵⁰ Such plots can be acquired conveniently by non-destructive methods such as CV and then be used to optimize the preparative scale conditions, trading the balance between speed and energy consumption. This approach should be supplemented by testing comparatively the stability of the catalyst.