Benchmarking of Homogeneous Electrocatalysts: Overpotential

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Benchmarking of homogeneous electrocatalysts. Overpotential, turnover frequency, limiting turnover number. Cyrille Costentin, Guillaume Passard, and Jean-Michel Savéant J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.5b00914 • Publication Date (Web): 10 Mar 2015 Downloaded from http://pubs.acs.org on March 13, 2015

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Journal of the American Chemical Society

Benchmarking of homogeneous electrocatalysts. Overpotential, turnover frequency, limiting turnover number. Cyrille Costentin* Guillaume Passard and Jean-Michel Saveant* 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. ABSTRACT. In relation with contemporary energy challenges, a number of molecular catalysts of the activation of small molecules have been developed, mainly based on transition metal complexes. Time has thus come to dispose of tools allowing the benchmarking of these numerous catalysts. Two main factors of merit are addressed. One involves their intrinsic catalytic performances through the comparison of the “catalytic Tafel plots” relating the turnover frequency to the overpotential independently of the characteristic of the electrochemical cell. The other examines the effect of a deactivation of the catalyst during the course of electrolysis. It introduces the notion of limiting turnover number as a second key element of catalyst benchmarking. How these two factors combine to one another to control the course of electrolysis is analyzed in detail, leading to procedures that allow their separate estimation from the measure of the current, the charge passed and of the decay of the catalyst concentration. Illustrating examples from literature data are discussed.

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Introduction

Catalysis of electrochemical reactions is currently attracting an intense interest in response to issues raised by contemporary energy challenges.

1,2,3,4,5,6,7,8

The ultimate goal is to use sun light

energy to carry out the reductive or oxidative transformations of the small molecules involved in these issues. A route toward this objective is to first convert solar energy into electricity, which will then be used to electrochemically reduce or oxidized the target molecules. Catalysis is required in most cases to carry out these reactions. It calls mainly upon transition metal complexes (notably, for water,

9,10,11,12,13, 14,15,16

proton,

17,18,19,20,21,22

dioxygen,

23,24,25,26,27,28

and

carbon dioxide 29,30,27,31,32,33,34,35,36). The large number and diversity of available catalysts make it timely to dispose of reliable tools for comparing them to one another. Two factors of merit are essential in this respect. One is the expression of the intrinsic catalytic properties of the catalyst, independently from the characteristics of the electrochemical cell used in each particular case. The second has to do with the stability of the catalyst over time. These two aspects relate to the notions of overpotential (η), of turnover frequency (TOF) and of turnover number (TON). The first of these two facets of the problem has been addressed in the case where the catalysts are unconditionally stable in the framework of H2 evolution

37

and CO2 reduction into CO.

35,38,39,40,41,42

In the present

contribution, we treat the whole problem after having analyzed the benchmarking procedure to be followed within the period of time where the catalyst may be considered as stable. 43 TOF and TON will be defined later on, but we may from now define the overpotential, η, as the difference between the standard potential for the transformation of the substrate A into the 0 product, B: η = EA/B −E


2

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We start from the following basic reaction scheme (Scheme 1) where the catalytic reaction is a simple one-electron/ one-step process based on a fast redox couple P/ Q (standard potential : 0 ). The active form of the catalyst, Q, then reacts with the substrate, A, yielding the target EP/Q

Scheme 1

product, B, and regenerating the oxidized form of the catalyst, P, with a second-order rate constant k, (the reasoning is developed for reductions; transposition to oxidations is straightforward). Deactivation of the catalyst is a first order reaction giving rise to an unreactive degradation product, C, with a first-order or pseudo-first order rate constant ki. Another simplification is that we assume that the concentration of the substrate is maintained constant as when it is the solvent (e.g., oxidation or reduction of water) or when it is a constant-pressure gas (e.g., CO2, H2, O2). In cases where the substrate tends to be significantly consumed during electrolysis, devices ensuring its continuous (or even automatic) replenishment are easy to devise In most circumstances, this should not be even necessary for catalysis of H2 evolution since the cathodic reaction is advantageously associated with an anodic reaction (e.g. oxidation of water) that regenerates stoichiometrically the protons consumed at the cathode. Under these conditions, Scheme 1 also covers the case where the inactivation of the catalyst may involve the substrate, as for example CO2 or H+ that may destroy the ligand of a catalytically active metal complex). The catalytic reaction is thus pseudo-first order with a rate constant: k = k (2)CA0 .


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In sake of simplicity, we also restrict our analysis to reactions giving rise to a single product, designated by B in Scheme 1. Although catalytic reaction schemes are usually more complex in current practice, often involving two-electron/ two-step processes, the simple scheme in Scheme 1 captures the essential features of the problem and allows the pertinent notions and parameters to be put forward. Examples of adaptation to such two-electron/ two-step schemes will be given afterwards. The case of homogeneous catalysis, where the catalyst molecules are dispersed in the solution, together with the substrate, and may diffuse to or from the electrode surface, will be treated here. However, systems in which the catalyst is immobilized on the electrode surface within a porous film have also their advantages and are sometimes considered as more promising than homogeneous systems. It should however be born in mind that, dealing precisely with progressive inactivation of the catalyst, homogeneous systems possess a definite advantage over electrocatalytic films. The volume of the solution plays indeed the role of a stock of catalyst molecules able to replace those that have been inactivated during each catalytic cycle. The data treatments proposed below do not required any particular cell design and instrumentation, provided they entail compensation or minimization of ohmic drop.

Results and Discussion As a preliminary to the discussion of catalytic systems, we will first have a look on what happens in direct electrolyses, with no help of a catalyst, to see how the current flowing through the electrode is related to the transformation of the substrate into product and how this relationship depends on the physical characteristics of the electrochemical cell.


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Non-catalyzed electrolysis Figure 1 summarizes the steady-state situation for a direct, non-catalyzed, reductive electrolysis of the substrate, A, yielding the product, B. Steady state ensues from the balance between diffusion and forced convection (generated by agitation of the solution or by liquid circulation in flow cells). It is characterized by a diffusion-convection layer whom thickness, δ, is the smaller the more vigorous the rate of agitation or of liquid circulation. The boundary conditions at the electrode/ diffusion-convection layer interface and at the diffusion-convection Symbols A: substrate; P, Q: oxidized and reduce forms of the catalyst, C: inactivated form C A0 : bulk substrate concentration, CP0 : total concentration of catalyst DA: diffusion coefficient of the substrate, A, and the product, B DP: diffusion coefficient of the catalyst oxidized (P), reduced (Q) and inactivated (C) form 0 0 E: electrode potential, E P/Q : standard potential of the catalyst couple, E A/B : standard

potential of the substrate/ product couple S: electrode surface area V: volume of the solution i: current k(2): second order rate constant of the catalytic reaction, k: pseudo first order rate constant of the catalytic reaction ki: first order or pseudo order rate constant of inactivation of the catalyst t: time, tcell: time constant of the electrochemical cell, tchem: time constant characterizing the catalytic reaction and the inactivation of the catalyst x: distance from the electrode surface

δ: thickness of the diffusion-convection layer µ: thickness of the catalytic reaction-diffusion layer


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diffusion-convection layer

electrode

−

 dC  = DA  A   dx    x =0

i FS

solution

A

A CB

e−

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 dC = − DA  B  dx 

 dC = DA  A  dx 

 dCB   = − DA   dx  x =0

B C CA A

   x=δ

b CA = CA0

b  V dCB =   x =δ S dt

B

δ

x= 0

Fig. 1. Non-catalyzed reduction of the substrate A into the product B at steady state. layer/ solution interface entail the linear concentration profiles shown in red in figure 1, in the case where the substrate concentration in solution in constant or maintained constant throughout electrolysis and if, in addition, the electrode potential is set at a value negative enough for the concentration of A at the electrode surface to be nil. The way in which the time-dependent production of B is related to its flux in the steady-state diffusion-convection layer − and therefore to the current − lies in the boundary conditions at the diffusion-convection layer/ solution interface (see the equation in figure 1). It follows that (see Supplementary Information (SI)) the bulk concentration of B increases linearly with time according to: 0 CBb = CA

i=

t tcell

, where tcell =

Vδ is the time constant of the cell and the current is constant: SDA

FSDA CA0

δ

Minimizing the time constant of the cell in order to speed up electrolysis may be achieved by decreasing the ratio volume over surface area and/ or decreasing the diffusion-convection layer thickness by raising the rate of agitation or the rate of liquid circulation.


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Homogeneous catalysis with a stable catalyst Figure 2 summarizes the steady-state association between the catalytic reaction, transport of catalyst, substrate and product with all pertinent boundary conditions and the relationship according to which the product, B builds up in the bulk of the solution. As compared to the preceding situation an additional layer appears, namely a reaction-diffusion layer adjacent to the electrode surface that arises from mutual compensation of the diffusion of the active form of the catalyst, Q, and the catalytic reaction. The achievement of these “pure kinetic conditions”

44

requires that the catalytic reaction is fast as compared to diffusion, which is indeed the case for

reaction –diffusion layer

electrode

diffusion-convection layer solution

P

A

A b CA = CA0

e−

= DA

( ( ))

ii 0 C == kCkD AD P P CQQ x =x =00 FS FS = − DA

Q x=

0

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 dCA   dx

 dCA  = DA  dx   

   x =δ

b  dCB   dCB  V dCB =   dx  = − DA     dx x=δ S dt

B µ

B

δ

Fig. 2. Homogeneous catalysis of the reduction of the substrate A into the product B at steady state. catalytic systems of practical interest. The thickness of the reaction-diffusion layer, µ, is of the order of

DA / k . Pure kinetic conditions entail that the reaction-diffusion layer is much thinner

than the diffusion-convection layer (figure 2 is somewhat misleading in this respect since the size of thicknesses is inverse due to graphical constraints). Under these pure kinetic conditions and when the P/Q electron transfer is fast (thus obeying


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the Nernst equation), the catalytic current is given by (see SI) : i = kDP FS

CP0

(

)

 F  0 1 + exp  E − EP/Q  RT 

(3)

and the Q-space profile within the reaction-diffusion layer by:

( )

CQ ( x ) = CQ

 k  exp  − x  x =0 DP   

Within the time when the catalyst is stable, the turnover frequency may be defined as: dmol (B) dt TOF = mol (Q)

where dmol (B) / dt is the rate at which the number of moles of product is generated. This rate is directly related to the current by means of the boundary relationships at the three interfaces of the system − electrode/ reaction-diffusion layer/ diffusion-convection layer/ solution: dCBb dmol (B) i =V = dt dt F

mol(Q) is the number of moles of catalyst involved in the production of B. A convenient definition of mol(Q) is the maximal mole number of active catalyst (Q) that may be generated at sufficiently negative electrode potentials when all P is reduced at the electrode surface ( E

Benchmarking of Homogeneous Electrocatalysts: Overpotential

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