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Molecular Catalysis of Electrochemical Reactions. Cyclic Voltammetry of Systems Approaching Reversibility Jean-Michel Savéant ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.8b02007 • Publication Date (Web): 20 Jul 2018 Downloaded from http://pubs.acs.org on July 20, 2018
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ACS Catalysis
Molecular Catalysis of Electrochemical Reactions. Cyclic Voltammetry of Systems Approaching Reversibility Jean-Michel Savéant Université Paris Diderot, Sorbonne Paris Cité, Laboratoire d'Electrochimie Moléculaire, Unité Mixte de Recherche Université - CNRS N° 7591, Bâtiment Lavoisier, 15 rue Jean de Baïf, 75205 Paris Cedex 13, France.
[email protected],
ABSTRACT: Efforts to design catalytic schemes approaching reversibility in which, the catalyst is active for both the oxidation and reduction processes are attracting active attention boosted by recent successes. Kinetic analysis of such systems, by of electrochemical techniques such as cyclic voltammetry (CV) would contribute to establish reliable mechanisms. So far, the relationships required to achieve this task have been restrained to irreversible catalytic schemes. The purpose of the present communication is to fill this gap. As a preliminary contribution, the analysis is limited to simple on-electron-one step schemes so as to set out the main features of the competition between catalytic reaction and diffusion transport of catalyst and substrates. Emphasis is put on S-shaped CV responses, which offer the best opportunities to accessing the detailed kinetic information forming the basis of mechanisms determination.
Molecular catalysis, Electrochemical reactions, Cyclic Voltammetry, Reversible catalysis
Introduction Contemporary renewable energy challenges 1,2,3,4,5,6,7 are strong incentives to develop strategies for catalysis of electrochemical reactions. In this framework cyclic voltammetry (CV) is a particular useful tool to investigate the kinetics and mechanism of catalytic systems, and thereof to provide the bases for their benchmarking and optimization. So far, analysis of the CV responses of such reaction schemes has been restricted to cases where the catalytic reaction is irreversible. 8,9,10 This corresponds to the fact that most of the available catalysts operate at significant overpotentials. Remarkable exceptions mostly concern catalysis of H2 oxidation and of H2 production from the reduction of acids. 11,12 Kinetic and mechanistic description of such reversible or quasi-reversible systems (the holy grail of molecular catalysis) by means of cyclic voltammetry call for the establishment of analysis procedures relevant to the CV responses of catalytic reactions approaching reversibility. This is the object of the present communication, which focuses on a simple one-electron/ one step scheme (Scheme 1) Reaction to be catalyzed → B (E 0 ) A + e- ← A/B Catalytic scheme → Q (E 0 ) P + e- ← cat k
red → P+B Q + A ←
kox
in the aim of revealing the essential features of the CV responses of such catalytic reactions. As has been the case with irreversible systems, 8,9,10 further analysis of multi-electrons/ multistep quasireversible reaction schemes is expected to derive from future adaptations of the following treatment of the simple scheme considered here.
Totally reversible reaction schemes We start with a strictly reversible reaction schemes to set out the main features of the interplay between catalytic reaction and diffusion transport of catalyst and substrate. In this case: 0 0 Ecat = EA/B
k = kox and, consequently, red The best description of the outcome of this competition consists in resorting to a kinetic zone diagram inspired from those used with irreversible systems. 9,13 The kinetic zone diagram relevant to this totally reversible situation is shown in figure 1, based on the analysis given in the supporting information (SI). To ensure equilibration of the two reversible reactions of Scheme 1, a potential scanning program as shown in figure 1 is recommended. The zone diagram can be represented with the help of only two dimensionless parameters. These can be transcribed back into the experimental parameters from which they have been defined. This leads to the compass shown in red in figure 1, which shows how their variation makes the system travel from one zone to the other. These experimental parameters can be categorized into operational parameters (concentrations, scan rate) and intrinsic rate parameters. Three of the various zones shown in figure 1 as colored diagrams, bearing defined graduated axes, are worth special attention. They represent three extreme situations of particular interest, which can be diagnosed rather easily. The most trivial of these situations, represented under the heading “diffusion, no catalysis” in figure 1 corresponds to catalytic reactions that are sufficiently slow, as compared to the scan rate,
(
)
0 ( ( RT / F ) kcat Ccat / v → 0 see figure 1 caption for definition of
symbols) for the CV responses to be simply governed by the diffusion of the catalyst as if there was no catalysis at all. Such a situation is, of course, of little value as far as kinetic and mechanistic analysis of catalysis is concerned. It may however be of practical interest to reveal, by means of raising the scan rate, the essential characteristics of the catalyst couple, such as standard potential and diffusion coefficient, for the same solution composition as when catalysis is at work. Such a case is easily identified by the shape and the scan root dependency on scan rate (see the vertical axis in the corresponding diagram)
Scheme 1
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Total catalysis 0 RT kcat Ccat log F v
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5
i b FSC A DA
−
-15
0 Ccat
Fv RT
-10
-5
0
F 0 ( E − EA, cat ) RT
5
10
15
kcat 0 CA
Canonical response 0.8 i
0.6
v
0 b FSCcat Dcat CA kcat
0.4 0.2 0 -0.2 -0.4
−
-0.6
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5
-15
i 0 FSC cat Dcat
-10
-5
0
5
10
15
Fv RT
−
-15
-10
F 0 ( E − EA, cat ) RT
-5
0
F 0 ( E − EA, cat ) RT
5
10
Cb Cb log 0A = 0B C cat Ccat
15
ER
E
0 − ER
t tR
2t R
3t R
4t R
Figure 1. Totally reversible catalytic scheme. Kinetic zone diagram represented by means of the two-dimensionless parameters shown on 0 b the two axes (see text). i: current, E: electrode potential, S: electrode surface area, v: scan rate, Ccat : total catalyst concentration, CA = CBb
: bulk concentration of substrates, kcat = 2kred = 2kox : second order catalytic rate constants, diffusion coefficients of catalyst,
Dcat ( DP ≈ DQ ) , of substrate: DA ≈ DB . The red compass shows how the system travels from one zone to the other upon changing the experimental operational (concentrations, scan rate) and intrinsic (rate constants) parameters. By convention, cathodic currents are represented as positive and vice versa for anodic currents. When, at the complete opposite of this state of affairs, the catalytic reaction is so fast, as compared to scan rate, that “pure kinetic condi-
(
)
tions” are achieved ( ( RT / F ) kcat / v → ∞ ), the concentration profiles of the two forms of the catalyst couple are squeezed within a thin reaction-diffusion layer adjacent to the electrode surface.
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ACS Catalysis
(
)
(
)
b 0 0 + CBb / Ccat → 0 , the catalytic reaction is fast enough not only to ensure the achievement of If, at the same time, CA ( Fv ) / RTkcat Ccat pure kinetic conditions but also to consume all the substrate in the reaction-diffusion layer. This situation amounts to a control by substrate diffusion that would take place at the standard potential of the substrate couple. The scan rate characteristics are the same as in the nocatalysis situation but the peak current are much higher, because of the excess of substrate over the catalyst. This ideal situation, where the overpotential is nil, is very unlikely to occur in practice, since the catalytic rate is expected to decrease together with the overpotential. 14
(
)
(
)
b 0 0 + CBb / Ccat → ∞ , there is practically no consumption of the substrate durIf, still under pure kinetic conditions, CA ( Fv ) / RTkcat Ccat ing the CV scan. Under these “canonical” conditions, The CV response is an S-shaped curve independent of scan rate, as represented in the 0 0 central diagram of figure 2. The reversibility ( Ecat = EA/B and kred = kox ) of the catalytic manifests itself under these canonical conditions 0 by the fact that the cathodic and anodic branches of the CV response are perfectly symmetrical around the E = Ecat , i = 0 point. As will
be detailed in the next section, this is the most informative situation in terms of kinetic and mechanism determination. It is easy to diagnose thanks to its S-shape and its independence from scan rate. Canonical S-shaped CV responses. Approach to reversibility. We now remove the pure reversibility restriction and investigate the passage from reversibility to irreversibility, having mostly in mind the description of the approach to reversibility. The analysis is limited to canonical conditions. This requires, as previously, that the catalytic is fast, as compared to the scan rate, but that, at the same time, the A and B concentrations are constant and equal to their bulk values across the reaction-diffusion layer. These conditions results in S-shaped CV responses easily diagnosable by their shape and independence from scan rate. They are also those in which the variations of CV responses with experimental parameters provide a maximum of information concerning kinetics and mechanism of the catalytic processes. The dimensionless current-potential responses (see the axes of the diagrams in figure 2) depend on only two dimensionless parameters,
(
0 0 − EA namely: the degree of reversibility measured by − ( F / RT ) Ecat
(
) (= 0 means complete reversibility) and the relative amounts of the
)
b b / CA + CBb . Typical examples are shown in figure 2, where complete reversibiloxidized (A) and reduced (B) forms of the substrate, CA
ity corresponds to the blue diagram.
Figure 2. Passage from reversibility to irreversibility under canonical conditions. Dimensionless CV responses for several values of the
(
)
0 0 − EA reversibility parameter, − ( F / RT ) Ecat , indicated above each diagram. In each of these, the effect of changing the relative
(
b b / CA + CBb amounts of the oxidized and reduced forms of the substrate as defined by CA
(
) is represented by changes in the color of the
)
b b / CA + CBb =1 (red), 0.75 (blue), 0.5 (black), 0.25 (green), 0 (magenta). curves: CA
Most of the useful kinetic information is contained in the plateau currents of the S-shaped CV responses. Figure 3 summarizes the variations of the dimensionless plateau currents upon changing the relative amounts of the oxidized and reduced forms of the
(
The resulting working curves may serve to check the mechanism and determine the kinetic characteristics of the catalytic reaction.
)
b b / CA + CBb , for a series of values of substrate, defined by CA
the reversi
(
)
0 0 − EA bility vs. irreversibility parameter − ( F / RT ) Ecat .
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the substrate. This the most informative situation in terms of kinetics and mechanisms. The variations of the plateau current with concentration is particularly precious in this respect, allowing checking of mechanism and determination of the kinetic characteristics of the catalytic reaction
Supporting Information Detailed establishment of all the equations on which the above analysis is based.
Figure 3. Passage from reversibility to irreversibility under canonical conditions. Dimensionless plateau current as a function of the relative amounts of the oxidized and reduced forms of the sub-
(
b b / CA + CBb strate as defined by CA
reversibility parameter,
)
for several values of the
0 0 − Ecat ( F / RT ) ( EA/B )=
∞ (red), 1.11
(blue), 0 (black), -1.11 (green), 0 (magenta). Full lines: cathodic responses. Dashed lines: anodic responses.
Conclusions. Analysis of CV responses of catalytic processes approaching reversibility requires the introduction of additional parameter as compared to the totally irreversible case, namely the difference between the standard potentials of the catalyst and substrate cou-
(
0 0 − EA ple ( − ( F / RT ) Ecat
) in dimensionless term). For this rea-
son, the detailed analysis of the reaction and diffusion parameters that control the characteristics of the CV responses has been focused on the emblematic case of complete reversibility. This allowed to delineate the conditions that give rise to “canonical” Sshaped CV responses. They require a fast catalytic reaction (as compared to the scan rate) so as to produce a steady-state situation resulting from mutual compensation of reaction and diffusion. The reaction should however not be too fast, and/or the excess of substrate over catalyst be sufficient for the substrate concentration to remain constant throughout the solution. This situation is easily diagnosed by S-shape appearance of the CV response and by its independence toward the scan rate. On these bases, removal of the total irreversibility condition, allowed a complete description of the canonical response as function of the degree of reversibility and of the relative amounts of the oxidized and reduced forms of
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