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Cyclic Voltammetry Analysis of Electrocatalytic Films Cyrille Costentin, and Jean-Michel Savéant J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b02376 • Publication Date (Web): 30 Apr 2015 Downloaded from http://pubs.acs.org on May 1, 2015

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The Journal of Physical Chemistry

Cyclic Voltammetry Analysis of Electrocatalytic Films Cyrille Costentin* 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. Contemporary energy challenges require the catalytic activation of small molecules such as H2O, H+, O2 and CO2 in view of their electrochemical reduction or oxidation. Mesoporous films containing the catalyst, conductive of electron or holes and permeable by the substrate appear, when coated onto the electrode surface, as convenient means of carrying out such reactions. Cyclic voltammetry then offers a suitable way of investigating mechanistically the interplay between catalytic reaction, mass and charge transport, forming the basis of rational strategies for optimization of the film performances and for benchmarking catalysts. Systematic analysis of the cyclic voltammetric responses of catalytic films reflecting the various mechanistic scenarios has been lacking so far. It is provided here, starting with simple reaction schemes, which provides the occasion of introducing the basic concepts and relationships which will serve to the future resolution of more complex cases. Appropriate normalizations and dimensionless formulations allow the definition of actual governing parameters. The use of kinetic zone diagrams provides a precious tool for understanding the functioning of the catalytic film.

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Introduction Recent years have been marked by the intense interest aroused by molecular catalysis of electrochemical reactions in response to issues raised by modern energy challenges.

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

Catalysis is required for reductive or oxidative transformation of the small molecules involved in these issues. It mainly relies on by transition metal complexes (notably, for water, 15,16,17

9,10,11,12,13,14,

proton, 18,19,20,21,22,23 dioxygen, 24,25,26,27,28,29 and carbon dioxide 30,31,28,32,33,34,35,36,37). Cyclic

voltammetry proved to be a tool of choice for investigating the mechanism of these catalytic reactions when they take place homogeneously in the vicinity of the electrode. This success is grounded in a body of relationships and diagnostic criteria progressively established for more and more complex reaction schemes.

38,39,40,41,42,43

It also offers a rational basis for catalysts’

benchmarking by means of catalytic Tafel plots. 36,44,45,46,47,48 An advantageous practical alternative to homogeneous catalysis consists in coating the electrode with a film containing the catalytic moieties. The film has to be porous so as to allow permeation by the substrate to be reduced or oxidized. It has to conduct electrons (or holes), possibly associated with proton transport, from the electrode surface to the catalytic sites. The mechanism and kinetics characteristics of the catalytic reaction, together with the role of mass and charge transport may be investigated by analysis of the current response of the film as a function of all parameters than can be varied experimentally. So far, the electrochemical method used for this purpose has been rotating disk electrode voltammetry (RDEV) rather than cyclic voltammetry (CV). With two exceptions,49,50 the appropriate relationships and diagnostic criteria have been made available for inspection of the system only at the level of the catalytic plateau current. 51,52,53,54 ,55,56,57 Although RDEV has been successfully applied to the analysis of catalytic


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films, with however the abovementioned limitations, application of cyclic voltammetry would have the advantage of a rapid recording of the whole current-potential responses and of an easy assay of the time characteristics of the system through the effect of the scan rate. Having at disposal such an easy and rapid method of analysis of catalytic films in terms of mechanisms, kinetics, optimization, and benchmarking is a particularly timely issue in view of the present quest for efficient catalytic films. Success rests on the availability of relationships and diagnostic criteria allowing this analysis to be performed rigorously. These were not made available so far because of the particular difficulties raised by the physico-mathematical analysis of a timedependent method that scans the potential region of interest in a single experiment as does cyclic voltammetry. The present paper is devoted to the formulation of the problem through introduction of normalized variables that will allow defining the minimum number of dimensionless parameters that govern the interplay between catalytic reaction, and mass and charge transport. For the moment our analysis is restricted to one-electron/ one-step schemes. It is however the same, after introduction of an appropriate stoichiometric factor, to multi—electron/ multistep systems in which the first step is rate-determining.

42

It also applies to reactions where electron transfer is

coupled with electron transfer provided buffer concentration is large enough.

49

This approach

will then be illustrated by a simple process in which the concentration of the substrate remains constant throughout the film and the solution at all times as it is the case when the solvent happens to be the substrate. This will be the occasion to introduce the use of kinetic zone diagrams, which provides an efficient tool for understanding the functioning of the catalytic film.


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Finally, a series of thought experiments will be presented to make more concrete the strategies to be followed when the substrate is the solvent and catalysis is strong. Results and Discussion Interplay between catalytic reaction, and mass and charge transport. The various processes taking place in the catalytic film are schematically represented in figure 1 diffusion solution layer

porous electrocatalyst film

electrode

D

k

De

k

De

k

De

k

κΑ DS

DS

D

DS

Fig. 1. Schematic representation of the porous electrocatalytic film, of the catalytic reaction and of the mass (diffusion) and charge (electron hopping) transport processes. The scheme is for reductions. Transposition to oxidation is straightforward. The symbols in the scheme are selfexplaining. Their definitions are recalled in the list of symbols. We assume that the catalytic sites are not only involved in the catalytic reaction but that charge transport results from electron hopping between them, which amounts to diffusion-like propagation with an equivalent diffusion coefficient De.

58,59,60,61

The presence of a supporting

electrolyte in the pores as in the solution practically eliminates field effects. 60 The way in which the current- potential curves depends on the three phenomena taking place in the electrocatalytic film and on substrate diffusion in the solution leads to the introduction of four characteristic current densities:


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0 d f . This is the expression of the current density when the Catalytic reaction: I k = FkCP0κ A CA

catalytic reaction is the sole limiting factor. Then, besides the proportionality to the rate constant

Symbols A: substrate; P, Q: oxidized and reduce forms of the catalyst. 0 CA : bulk substrate concentration, C P0 : total concentration of accessible catalyst in the film.

D: diffusion coefficient of the substrate in the solution, De: equivalent diffusion coefficient for electron hopping charge transport, DS: diffusion coefficient of the substrate in the film. E: electrode potential, E0: standard potential of the catalyst couple, Ep: peak potential, Ep/2: half-peak potential, E1/2: half wave potential. I: current density, IA: current density characterizing substrate diffusion in the solution, Ie: current density characterizing the diffusion-like transport of charge in the film, Ik: current density characterizing the catalytic reaction in the film, Ip: peak current density Ipl: plateau current density, IS: current density characterizing substrate diffusion in the film. df: thickness of the film, k: rate constant of the catalytic reaction, le: thickness of the film normalized toward scan rate-dependent electron transport diffusion layer, t: time, v: scan rate

κA: partition coefficient of the substrate between solution and film, τ: normalized time, ξ: normalized potential.

k, one expects proportionality to the concentration of catalytic sites C P0 , to the maximal concentration of substrate inside the film, κ A CA0 and to the thickness of the film, df, insofar all catalytic centers are then participating to the reaction. C P0 is defined as the sum of the concentrations of the reduced and oxidized catalyst molecules both accessible by means of electron hoping and participating to catalyst. Other catalyst molecules may remain inaccessible. A simple way of estimating the value of C P0 thus defined is to carry out a cyclic voltammetric of


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the system in the absence of substrate. If the substrate is the solvent high scan rates have to be used to overcome the catalytic reaction.

D Hopping charge transport in the film: Ie = FCP0 e . Proportionality to the concentration of d f

electron hopping sites and to the electron-hopping equivalent diffusion coefficient is as expected. Inverse proportionality to the film thickness reflects an increasing difficulty for the electrons to hop throughout the whole film.

D 0 S Substrate diffusion in the film: I S = FκACA . Proportionality to the concentration of df substrate and to diffusion coefficient in the film is as expected. Inverse proportionality to the film thickness reflects an increasing difficulty for the substrate to diffuse in the film. Substrate diffusion in the solution: I A = FCA0 D

Fv . Proportionality to substrate concentraRT

tion, to square root of the solution diffusion coefficient and of scan rate is as expected. 62 The way in which the current-density potential response, I – E, depends on these characteristics current densities derives from the resolution of a set of second Fick’s law partial derivative equations accompanied by initial and boundary conditions, describing the diffusion of substrate through the film and the diffusion-like transport through the film. In both cases, diffusion is linear and limited to the space contained between the electrode and the film solution interface. In both cases too, the second Fick’s law equations contain a kinetic term expressing the contribution of the catalytic reaction. The diffusion of the substrate in the solution − linear and semi-infinite− is described by a simple second Fick’s law accompanied by initial and boundary conditions. The ensuing algebraic expressions are given in the Supporting information.


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In order to give a first illustration of the derivation of the current response, in the next section we simplify the problem by considering the case where the concentration of the substrate is constant in the solution and throughout the film as is the case where the solvent is the substrate. A simple illustrative case : the substrate concentration remains constant as when the solvent is the substrate There is no need to take henceforth account of the current-densities characterizing the diffusion of the substrate inside and outside the film since its concentrations are constant. Two dimensionless parameters therefore conveniently govern the I – E responses, I k / Ie , which depicts the competition between the catalytic reaction and electron propagation and

le = d f / De RT / ( Fv ) . le compares two lengths: the film thickness, d f , and the diffusion layer length of the diffusion-like charge transport − a decreasing function of the scan rate by means of its square root as expected for linear diffusion. Various limiting behaviors of the dependency of the I – E responses from the parameters may be reached for extreme values of the two above-defined dimensionless parameters. They are represented under the form of a kinetic zone diagram as shown in figure 2. Then, according to the value of the parameter le = d f / De RT / Fv , the current-potential curve takes the familiar form of a symmetrical “adsorption” wave (or “surface” wave) when le → 0 (zone A, thin film, slow scan), or, conversely the familiar form of a diffusion wave when

(

)

0 1 I k RT kκ A CA le → ∞ (zone D, thick film, fast scan). When, on the contrary, 2 = →∞, Fv l Ie e

catalysis is so fast that “pure kinetic” conditions are achieved as the result of a steady state arising from mutual compensation of the diffusion process and the catalytic reaction. This entails


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Fig. 2. Kinetic zone diagram. The symbols are defined in the text, in Table 1 and in the list of Symbols. The compass rose (in pink) allows traveling through the zone diagram upon variation of the experimental parameters, in direction and magnitude (log). The vertical red segments represent the effect of raising the scan rate in the hypothetical experimental example discussed

a canonical S-shaped catalytic wave characteristic of zone KP.


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The current-potential curves in these three zones (A, D, KP) do not depend on any competition parameter. They may be described by close form (A, KP) or integral-equation (D) expressions as given in Table 1, together with their main characteristics (peak or plateau current, half-peak or half wave potentials). Table 1. Current-potential responses in each zone Derivation a exp (ξ ) I = le 2 Ie (1 + exp (ξ ) )2

zone A le 2

AD

∂q ∂ 2 q = , qτ = 0 = q y =1 = 0, ∂τ ∂y 2

q y =0 = 1

D

KD

π

1

π

∫

∫

τ

0

 I  1 le dη =   (η ) 1 + exp ( −ξ ) τ −η  Ie 

 I  exp  − 2k (τ − η )   I  le  le I e  dη =   (η ) I 1 exp + τ −η ( −ξ )  e

τ

0

le 2 KG

1

π

∫

τ

0

 I  exp  − 2k (τ − η )  l I 1  e e  dη = 1 + exp ( −ξ ) τ −η

I  I  I e I k tanh  k   Ie 

=

1 1 + exp ( −ξ )

Ik I 1 > 1 : Ie

KPER a: ξ = −

RT Fv 0 0 , E p = E , E p /2 = E −1.77 F RT

The characteristics depend on the parameter le = d f / De RT / Fv , see working curve in figure 3a

I p = 0.446 FC P0 De

RT RT Fv E p /2 = E 0 + 1.09 , E p = E 0 − 1.11 F F RT

The characteristics depend on the parameter

(

)

I k / I e le 2 = ( RT / Fv ) kκ A C A0 , see working curve in figure 3b

-

1 I  ∂q  , =-  1 + exp ( −ξ ) I e  ∂y  y = 0

 I    (η )  Ie 

KPE+R

I p = 0.25FCP0d f

∂q ∂ 2 q I k = − q, qτ = 0 = q y =1 = 0, ∂τ ∂y 2 I e

q y =0 =

KA

1 I  ∂q  , =-  1 + exp ( −ξ ) I e  ∂y  y = 0

Characteristics

(

I IeIk

F E − E0 RT

0 Ik = FkCP0κACA df

=

1 1 + exp ( − ξ )

D Fv t , I e = FCP0 e , ) , τ = RT df

,

le =

df De

RT Fv

The characteristics depend on the parameter

(

)

I k / I e le = ( RT / Fv ) kκ A C A0 , see working curve in figure 3c 2

 = tanh  d f 0  FCP0 De kκ ACA  See variation in figure 4 Ip

0 I p = FkCP0κACA df

0  kκ ACA  , E p /2 = E 0 De  

, E p /2 = E0

0 I p = FCP0 De kκ A CA

, E p /2 = E0

Ip: peak or plateau current density, Ep/2:half peak or half wave potential,

CP0 : concentration of the catalyst in the film, C A0 : bulk substrate concentration, De : diffusion coefficient of charge transport, df: thickness of the film, k: rate constant of the catalytic reaction v: scan rate, κ A : substrate partition coefficient


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In the transition between these zero-parameter-zones the current-potential responses may depend at maximum on two parameters. In the one-parameter transition zones the expressions of later on. The curves are only indicative of the shape of the current-potential responses. Their precise expressions are given in Table 1.

the current-potential are under the form of integral equations (KA, KD) or may require the finitedifference resolution of a partial derivative equation accompanied by a set of initial and boundary conditions (AD).

(

)

0 1 I k RT kκ A CA When = → 0 (represented by a descending 1/2 slope line in figure 2), Fv l 2 Ie e

catalysis is so slow, relative to the scan rate, that it does not contribute to the current response. In the transition zones AD, KA and KD, the characteristics of the current-potential responses are functions of one dimensionless competition parameter, le = d f / De RT / Fv (AD) and

(

I k / I ele 2 = ( RT / Fv ) kκ A CA0

) (KA and KD), respectively. The corresponding working curves

are shown in figures 3. The boundaries between zones have been obtained by maximizing the extent of the zeroparameter versus the one-parameter zones, and of the latter versus the two-parameter zone, taking into account the experimental uncertainty: 5% of peak separation for the A/AD/D passage, 5% of the maximal

(

)

F E p /2 − E 0 value for the D/KD/KP and A/KA/KP passages. Criteria on RT

the peak or plateau current (5%) lead to the same frontiers. The effect of varying the experimental parameters on the location and movement of the point representing the system in the zone diagram is summarized, in direction and magnitude by the compass rose in figure 2. The most important of them, are the parameters that can be easily


10

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A-AD-D 1.4

10 2.5 9 8 2 7 1.5 6 5 1 4 0.5 3 2 0 1 -0.5 0 -1 -1

F ∆E p

I / ID p

1.2

RT

1 0.8 0.6 0.4 0.2 0

 1 log  df 

-0.2 -0.4 -1

-0.5

0

A-KA-KP

D-KD-KP 3

 RT De   Fv  0.5

1

(

F E p /2 - E 0 RT

I / I KP p

(

1.5 10

)

)

log  RT kκ ACA0 / Fv    -3

-2

-1

0

1

2

3

I / I KP p

9 8 1 7 6 5 0.5 4 3 0 2 1 0 -0.5-1

(

F E p /2 - E 0 RT

)

0.06 F ∆E p /2 0.05

0.2

RT 0.15

0.04 0.03 0.02

0.1 0.05

0.01

(

0

)

0 log  RT kκACA / Fv   

-3

-2

-1

0

1

2

-0.01

0 -0.05

3

Fig. 3. Variations of the normalized peak or plateau current density (in blue) and half-peak or half wave potential (in red) with appropriate dimensionless parameters upon crossing the zone diagram as indicated on top of each diagram. Ip: peak or plateau current density, I pD , I pKP : values of Ip in the D and KP zones respectively. E p /2 : half-peak or half-wave potential. ∆E p /2 : difference of half-peak or half-wave potentials during the onward and reverse scan. ∆E p difference of peak potentials during the onward and reverse scan. changed experimentally, viz., substrate concentration, scan rate and film thickness. In this respect, figure 4 pictures, under pure kinetic conditions (zone KP), how an increase of the film 1.2

Ip 0 FCP0 De kκ ACA

1

KPER 0.8

KPE+R

0.6

0.4

0.2

KPR

kκ ACA0 De

df

0 0

1

2

3

4

Optimal thickness

Fig. 4. Saturation of the catalytic properties of the film under pure kinetic conditions at the level of the plateau current. Dimensionless representation.


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thickness may lead to saturation of its catalytic properties at the level of the plateau current. It is therefore useless, or even counterproductive, to increase the film thickness much beyond an optimal thickness defined as shown in figure 4. In the case where the solvent is the substrate, as discussed here, the plateau current may well be impossible to reach under pure kinetic conditions when catalysis is strong. One may then resort to a foot-of-the wave strategy similar to that proposed for homogeneous catalytic reactions.

44

This is illustrated in figure 5 where it is seen

that saturation of the film catalytic properties can also be experienced upon increase of the film thickness. We also note that when the plateau current cannot be reached, the standard potential, E0, cannot be determined and, consequently, the foot-of-the wave analysis does not provide a separate determination of the catalytic rate constant, but merely leads to the value of

( )

E 0 + ( RT / F ) ln κ A kCP0  . One has to move the system out of the KP zone, by, e.g., raising   the scan rate to be able to reach a separate estimation of these two parameters. lnI

I

1

−

F E RT

−

F E RT

0 E0 +

RT  0 0  ln FCP De kκ A CA  F 

intercept

df

E0 +

RT  0 ln FkCP0κ A CA df    F

0 k κ A CA De

1

Fig. 5. Foot-of-the wave analysis under pure kinetic conditions showing saturation of the catalytic properties of the film.


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A series of thought experiments To illustrate how to analyze an electrocatalytic film in practice, we consider the typical case of a film containing an average concentration C P0 = 1 M of active sites, which thickness, df , can be varied from hundreds of nanometers to a few micrometers. The film is coated onto a 3 mm diameter electrode (0.07 cm2 surface area). Ohmic drop is minimized by means of positive feedback compensation down to a 10 Ω remaining uncompensated resistance. Consequently, if the ohmic drop is aimed to be less than 5 mV, the current has to be less than 500 µA and the current density less than 7.15 mA/cm2. Due to such limitations, it is anticipated that for fast catalytic reactions, the expected plateau will not be reached, preventing an easy determination of 0 the catalyst standard potential E 0 from the half-wave potential as well as of kκ A CA or a 0 relationship between kκ A CA and De . This is a particularly serious problem in cases where the

solvent is the substrate since experiments in absence of substrate that could lead to E 0 and De cannot be carried out. However, based on the above zone diagram, a strategy can be devised for extracting from experimental data all three parameters characterizing the catalytic film, namely

E 0 , kκ A CA0 and De . Two relationships between the three parameters can first be derived by the previously described analysis of the foot of the wave at low scan rate (i.e. in the KP zone) as a 0 function of film thickness. This is illustrated in figure 6a for kκ A CA = 10 s-1, De = 10-7 cm2s-1.

The standard potential (figure 6b) allows the determination of the optimal film thickness, E 0 =0 V for 0.2, 0.7 and 2 µm thick films. The foot of the catalytic waves may also be converted into Tafel plots (figure 6b). Then the variation of the current density at a given potential, e.g., at the standard potential (figure 6b) allows the determination of the optimal film thickness,


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(

)

Page 14 of 26

(

)

0 0 d opt f = De / kκ A CA = 1µm ) and from it the value of De / k κ A CA (when the solvent is the 0 substrate kκ A cannot be separated from CA ).

We note furthermore that increasing progressively the scan rate from 0.02 V.s-1 up to 10 V.s-1 at any of the three film thickness moves the system out of pure kinetic conditions, as represented by the three red verticals segments in the zone diagram of figure 2. This is the source of 8

-1

0.12

7

I intercept (mA/cm 2 )

log  I (mA/cm 2 )   

I (mA/cm 2 )

0.1

-2

6 5

0.08

-3 4 0.06

a

3

c

b

-4 2

0.04

1

-5

0

0.02

0

d f (µ m)

0

E − E (V)

E − E (V)

-1

0

-6 0.2

0.1

0

0.2

0.1

0

0

0.5

1

1.5

2

2.5

d opt f

0 Fig 6. a: simulation of cyclic voltammetry of catalytic films at 0.02 V.s-1 with kκ A CA = 10 s-1,

De = 10-7 cm2s-1, E 0 =0 V, C P0 = 1 M, T = 298.16 K and d f = 0.2 (blue), 0.7 (red), 2 (green) µm. b: Tafel plots. c: variation of the current density at E = E0 with film thickness. additional information to be combined with what we already know. The resulting changes in the current-potential curves are shown in figure 7 for the same system as in figure 6, where the scan is reversed before the current density reaches 7.15 mA/cm2.


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8

8

8

I (mA/cm 2 )

I (mA/cm 2 ) 6

I (mA/cm 2 )

6

4

6

4

4

0.7 µ m

0.2 µ m

2 µm

2

2

2

0

0

0

-2

-2

-2

-4

-4

-4

0

0

E − E (V)

E − E (V)

-6 0.3

0.2

0.1

E − E 0 (V)

-6 0

-6 0.3

0.2

0.1

0

0.3

0.2

0.1

0

0 Fig 7. Cyclic voltammetry of catalytic films for kκ A CA = 10 s-1, De = 10-7 cm2s-1, C P0 = 1 M, T = 298.16 K as function of scan rate (V.s-1): 0.02 (blue), 0.05 (red), 0.1 (green), 0.2 (yellow), 0.5 (grey), 1 (magenta), 2 (orange), 5 (cyan), 10 (black). The number on each diagram is the thickness of the film.

At the lower end of the scan rate range the forward and reverse trace are superimposable as expected for pure kinetic conditions. This no longer observed upon raising the scan rate together with the appearance of current reversibility during the backward scan, meaning that diffusion 6

(

I / v mA/cm 2 / V/s

)

4

2

0

E − E 0 (V) -2 0.3

0.2

0.1

0

0 Fig 8. Cyclic voltammetry of catalytic films for kκ A CA = 10 s-1, De = 10-7 cm2s-1, C P0 = 1 M, T = 298.16 K and d f = 2 µm as function of scan rate (V.s-1): 0.02 (blue), 0.05 (red), 0.1 (green),

0.2 (yellow), 0.5 (grey), 1 (magenta), 2 (orange), 5 (cyan), 10 (black).


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starts to overcome catalysis. This situation happens when the system leaves the KP zone, i.e., when the parameter

( RT / Fv ) ( kκ A CA0 ) is

approximately equal to 5, thus allowing the

0 determination of kκ A CA and hence of De . In order to refine this estimation, we may note that,

with the thicker film, system has reached zone D (see figure 2) as attested by the observation that the forward current density is then proportional to

v (as shown in figure 8), leading to an easy

determination of De and E 0 . Alternatively, if De is too large, E 0 can be obtained using a thin film and reaching zone A at high scan rates, the criterion being then that the forward current density is proportional to v . Concluding Remarks So far, the analysis of electrocatalytic film has been restricted to steady-state electrochemical techniques although cyclic voltammetry offers an advantageous alternative. In this inaugural paper, the bases have been laid for effectively using cyclic voltammetry in this purpose through normalization of parameters and variables and dimensionless formulations. A convenient way of introducing the effect of the processes involved is to define a series of current densities characterizing substrate diffusion in the film and the solution, diffusion-like charge transport and catalytic reaction. The simple case where the substrate diffusion can be ignored because its concentration is very large, as when it serves also as solvent, provided a first example of application. Kinetic zone diagrams thus appeared as a convenient tool to analyze the interplay of the various phenomena involved, leading to the expression of the dimensionless current-potential curves in each zone. It also allowed understanding how the control by one or the other of the phenomena involved changes as a function of the experimental parameters. This is in particular


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the case the film thickness, the increase of which leads to a saturation of the catalytic capabilities of the film. As a part of the conclusion it is worth coming back to the respective merits of using CV or RDEV to analyze catalytic films, comparing the respective role of scan rate in the first case and rotation rate in the second. In the second case, changing the rotation rate allows modulation of substrate transport outside the film but does not influence directly what is going on in the film. In the first case, variation of the scan rate does both allow modulation of substrate transport outside the film and also changes the time scale inside the film, which may influence each of the three processes taking place there, catalytic reaction, electron and substrate transport. Overall, procedures for analyzing the data are somewhat more complicated with CV compared to RDEV, but more information is contained in scan rate variations than in rotation rate variations. Supporting Information. Proof of the equations of Table 1. This information is available free of charge via the Internet at: http://pubs.acs.org.

Acknowledgments Partial support from the Agence Nationale de la Recherche (ANR CATMEC 14-CE05-001401) is acknowledged.

References

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TOC

optimal thickness


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Cyclic Voltammetry Analysis of Electrocatalytic Films - The Journal of

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