Article pubs.acs.org/JPCC
Conductive Mesoporous Catalytic Films. Current Distortion and Performance Degradation by Dual-Phase Ohmic Drop Effects. Analysis and Remedies Claude P. Andrieux, Cyrille Costentin,* Carlo Di Giovanni, Jean-Michel Savéant,* and Cédric Tard Université Paris Diderot, Sorbonne Paris Cité, Laboratoire d’Electrochimie Moléculaire, Unité Mixte de Recherche Université - CNRS No. 7591, Bâtiment Lavoisier, 15 rue Jean de Baïf, 75205 Cedex 13 Paris, France S Supporting Information *
ABSTRACT: In the active interest aroused by catalysis of electrochemical reactions, particularly molecule activation related to modern energy challenges, mesoporous films deposited on electrodes are often preferred to catalysts homogeneously dispersed in solution. Conduction in the solid portion of the film and in the pores may strongly affect the characteristic catalytic Tafel plots, possibly leading to mechanistic misinterpretation and also degrade the catalytic performances. These ohmic drop effects take place, unlike those classically encountered with a massive electrode immersed in an electrolytic solution, in two different zones of the film, the solid bulk of the film and the pores, that are coupled together by a distributed capacitance and by the faradaic impedance representing the catalytic reaction located at their interface. A transmission line modeling allows the analysis of the capacitance charging responses as a function of only two dimensionless parameters in the framework of linear scan voltammetry: the ratio of the resistances in the two parts of the film and of the time-constant of the film. After validation with an experimental system consisting of an ionic polymer/carbon powder mixture, deposited on a glassy carbon electrode and immersed in a strong electrolyte aqueous solution, a procedure is established that gives access the key-conduction parameters of the film. On these bases, and of the predicted current−potential responses for fast catalytic reactions according to the same transition line model, it is shown how the dual-phase ohmic drop effects can be gauged and compensated. Ensuing consequences on optimization of macroelectrolysis are finally discussed.
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INTRODUCTION Modern energy challenges have triggered during recent years an intense interest in catalysis of electrochemical reactions, particularly oxidation or reduction of small molecules such as water, hydrogen, oxygen, proton, and carbon dioxide.1−7 Although homogeneous molecular catalysis may be a valuable approach to these issues,8,9 the deposition of catalytic films onto electrode surfaces is often preferred. In most cases, these films are mesoporous structures allowing the contact between reactants dispersed in the bathing solution and the catalytic molecules or nanoparticles, preferably connected to the electrode surface by an electronically conducting material such as various forms of carbon, e.g., powder, nanotubes, and so forth.10,11 The first challenge is the design and synthesis of intrinsically good catalytic materials. However, translating these propitious characteristics into large catalytic currents and/or small overvoltage may be hampered by charge transport through the system. The more so, the better the catalytic material. These drawbacks may result in energy losses and also in incorrect assignments of mechanisms and rates. Although rarely explicitly mentioned,12 the possible interplay between catalysis and conduction is potentially present in the following nonexhaustive list of heterogeneous systems catalyzing H2 evolution,13−19 O2 evolution,11,20−24 CO2 reduction,25−27 O2 reduction,28 and H2 oxidation.29 © XXXX American Chemical Society
Determining the nature and magnitude of these limitations and designing ways to circumvent or minimize them is the subject of the present contribution. Another associated reason to address these problems relates to catalysts benchmarking. Even if pretty obvious for some time, the need for a lucid benchmarking of catalysts in front of their rapidly growing number has been the object of a recent strong multiauthored statement.30 Rational benchmarking of catalysts requires that intrinsic kinetic characteristics are extracted from raw micro- and macroelectrolytic data after elimination of secondary factors related to transport and ohmic losses. Efficient methods to achieve these tasks have been proposed in the case of homogeneous molecular catalysis leading to the establishment of catalytic Tafel plots that relate the turnover frequency to the overpotential whose comparison allows the selection of the intrinsically best catalyst and the optimization of energy vs rate factors.31−36 The following discussion provides the necessary tools to extend these methods to the field of heterogeneous molecular and nanoparticular catalysis. Received: July 13, 2016 Revised: August 23, 2016
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DOI: 10.1021/acs.jpcc.6b07013 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
Figure 1. Schematic representation of the mesoporous films. The pores and the solution are in blue and the solid parts are in green. In red: potentials (ϕWE, RE, B and P: potential at the working electrode, the reference electrode, in the bulk solid parts of the film, and in the pores, respectively) and current densities (currents per working electrode unit surface area), IB, IP, and I in solid parts of the film, pores, and solution, respectively. In black, the resistance and capacitance parameters of the equivalent transmission line: rB and P: distributed resistances of the bulk of the film and pores per unit of thickness of the film and for unit of surface area of the electrode, respectively. c: distributed capacitance per unit of surface area of the electrode and unit of thickness of the film, i.e., a capacitance per unit of volume of the film. RS is the solution resistance between the working and reference electrodes. L is a self-inductance related to the instrument bandpass characteristics.35 A glossary of symbols is available in the SI.
simple system that serves at present or may serve in the next future as a versatile structuring and conducting backbone of many catalytic films in which appropriately designed catalytic molecules or nanoparticles are incorporated. With all these results in hand, it was then possible to analyze how of these dual-ohmic drop effects affect faradaic currents, and, particularly, large catalytic currents. Ensuing quantitative predictions required the extension of the theoretical analysis and the design of a numerical calculation procedure. They will concern not only linear voltammetric microelectrolytic conditions, but also, those prevailing in macroelectrolytic conditions in electrolyzers as well as in generators.
We start with a general analysis of the current−potential linear voltammetric responses in potential domains where faradaic currents are negligible so as to analyze, in a first stage, the combined capacitive and resistive responses of the system composed of solid islands of electronically conductive material intermingled with mesopores filled with a supporting electrolyte, which allows for ionic transport of the current. Two important conclusions emerge from the comparison of the ohmic drop effects in such systems with the classical case of a massive electrode immersed in an ionic solution. One is that the charging current does not follow the classical RC exponential charging behavior but is rather sensitive to the delay time resulting from capacitance distribution along the interface between the bulk of the film and the pores. The second is that the resistance involved in global ohmic drop through the film cannot be viewed as the sum of the resistances of each of these two phases. This dual-phase ohmic drop effect is not only important in the case of capacitive current charging but will have to be taken into account when a faradaic catalytic current is flowing through the system even when steady-state conditions are achieved. Understanding these dual-phase ohmic drop effects is important to minimize energy losses in macro-electrolysis catalytic conditions, in electrolyzers or fuel cells. It is also important when nondestructive techniques such as cyclic voltammetry at microelectrodes are used to characterize the catalytic system by means of catalytic Tafel plots relating turnover frequency to the overpotential, which can be derived from the current−potential responses. Such an analysis may be used as a prelude to the determination of the appropriate conditions for efficient macro-electrolyzes. It will be the occasion of investigating the possibility and limitations of positive feedback compensation of ohmic drop, as helping the microelectrolytic analyses, emphasizing the differences with the classical case of a massive electrode immersed in an ionic solution, where this approach is well documented.37−39 The next step was the choice of an experimental example illustrating the previous theoretical analysis and validating the compensation procedures. Deposition onto a glassy carbon electrode of a mixture of an ionic polymer, in this case Nafion, and of a carbon powder, in this case Vulcan, with a strong electrolyte (KNO3 or HNO3) in the aqueous phase provides a
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RESULTS AND DISCUSSION 1. Predicted Linear Voltammetric Responses in the Absence of Faradaic Reactions. Averaging the dimensions of the pores and solid parts of the mesoporous films suggests the schematic representation of Figure 1. It follows a transmission line model of the type previously proposed for volumic metal electrode40−42 and their application to supercapacitors.43 Most actual mesoporous films are likely to be more complex than this model. Pores are often tortuous and not of fixed radius and length across the film. The model we use is the result of an averaging of the local structural peculiarities. It is a powerful tool which allows the representation and treatment of many practical cases that may differ in their details, as in the case of supercapacitors40,41 as well as of catalytic films.44−49 Detailed structural features can obviously not be derived from current−potential responses, in cyclic voltammetry as well as with other electrochemical techniques. The most efficient approach of these mesoporous films proceeds actually in a reverse way: gross structural traits are used to build an averaged approximate model that will allow the analysis and characterization of the faradaic and nonfaradaic characteristics of the system, which are what we need for generator or electrolyzer applications and benchmarking. The caption of the figure defines the current and potential variables as well as the resistance and capacitance parameters in the various parts of the system (see also the glossary of symbols in the Supporting Information (SI)). The distributed resistances rB and rP have the dimensions of resistivities. They are related to the resistivities of the bulk of the film and of the pores ρB and ρP by B
DOI: 10.1021/acs.jpcc.6b07013 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C rB = γBρB ,
rP = γPρP ,
with
γB + γP = 1
features emerging from Figure 2 and from the accompanying analysis in section 1 of the SI are the following.
where γB and γP are the fractions of the base electrode surface that are covered by the bulk of the film and the pores, respectively. The current−time responses are governed by the values of a number of experimental parameters that may be grouped in a minimal number of dimensionless parameters. The variables, e.g., current and time may be adimensionalized as well. One distinct advantage of dimensionless formulations is that they make evident that a given effect may be the result of the variations of different experimental parameters. In order to put the focus on the intrinsic characteristics of the film, we examine first the case where the resistance of the solution is negligible or has been f ully compensated by means of a hypothetically perfect instrument (L = 0). The current−time responses obtained in these conditions indeed represent the intrinsic properties of the film. It can be shown, as established in section 1 of the SI, that the dimensionless current density response vs the dimensionless time (I/cvdf vs t/tf where tf = df2(rB + rP) c is the time-constant of the film) then depends on a single dimensionless parameter, namely, the ratio rP/rB. Figure 2 shows typical such I/cvdf vs t/tf dimensionless responses for several values of rP/rB. The main remarkable
I /(cvdf ) = (2/ π ) t /tf
(i) These responses seem to be almost the same whatever rP/ rB. A closer examination of the short-time portion of the responses, as scaled up in Figure 2b, however shows that they are actually different. Two limiting behaviors are reached for large (or small) values of the resistivity ratio (yellow curves in Figure 2) on the one hand and for rP/rB = 1, on the other (blue curves in Figure 2). In the first case, the I /(cvdf ) = (2/ π ) t /tf expression of the response applies at short times whereas in the second case, the tangent at the origin of the response is simply I/(cvdf) = 0.25t/tf (dashed blue curve in Figure 2b). (ii) It is also worth noting that the capacitance charging current is clearly distinct from the classical RC exponential response expected for a massive electrode immersed in an electrolyte solution having the same time constant as the mesoporous film (dashed black curve in Figure 2a). (iii) Coming back to the first limiting case in (i) (rP/rB → 0 or →∞ at short times), it should be noted the maximal possible ohmic drop compensation has then been achieved. The charging process is accordingly the fastest possible. The situation is best understood through comparison with the classical RC exponential response expected for a massive electrode immersed in an electrolyte solution in the same conditions. In the latter case, if the resistance was fully compensated by an ideally perfect positive feedback device, the capacitance charging response would be a step function rising in a vanishingly short time the plateau value. In the present case, full compensation bumps into the nonzero charging time transpiring in the I /(cvdf ) = (2/ π ) t /tf diffusion-like response. When rP/rB is close to 1, the situation may look worse in the sense that the charging delay is larger. However, part of the film resistivity can be compensated by means of positive feedback so as to reach a diffusion-like behavior at short times (black dashed line Figure 2c). As detailed in section 1 of the SI, the maximal value of the film ohmic drop that can be compensated in this way is given by SR umax rPrB r (or rB) =− ≈− P df (rP + rB) 2
The variation of Rmax u with the resistivity ratio is summarized in Figure 2d. How can we approach these ideal conditions in practice and know how much of ohmic drop remains uncompensated are the questions addressed in the next section, taking into account the bandpass limitations of the instrument and the ensuing appearance of disturbing oscillations. 2. Ohmic Drop Compensation in the Absence of Faradaic Reactions with a Nonperfect Instrument. Most micro- and macroelectrolyses are carried out with the help of three-electrode devices. The potentiostat compensates the resistance between the reference electrode and the counterelectrode but not the resistance between the working and the reference electrode, which may be compensated at least partly, by a positive feedback online device.37,50 It subtracts from the potential between working and the reference electrodes a tension proportional to an adjustable fraction of the current
Figure 2. Charging the mesoporous film shown in Figure 1 when the resistance of the solution is negligible or has been fully compensated by means of a hypothetically perfect instrument (the symbols have the same meaning as in the caption of Figure 1). (a) Variation of the dimensionless current function with the dimensionless time (tf = df2(rB + rP) c is the time constant of the film) for several values of the rP/rB ratio: 1 (blue), 2 (green), 3 (red), 5 (gray), 10 (magenta), 20 (orange), 50 (cyan), and ∞ (yellow). The black full line is the diffusion-like limiting behavior observed at short times for rP/rB (see text). The dashed black line is the classical RC exponential response expected for a massive electrode having the same time constant as the mesoporous film. (b) Blow up of the short-time response. (c) Ohmic drop compensation for films where rP/rB is close to 1 for several values of the SRu/df(rB + rP): 0 (blue), −0.1 (green), −0.2 (red), −0.24 (yellow), and −0.25 (black) The black dashed line is the limiting diffusion-like response at short time. (d) Maximal feedback compensation as a function of the resistivity ratio of the two phases. C
DOI: 10.1021/acs.jpcc.6b07013 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C flowing between the working and counter electrodes. In the case of a massive electrode immersed in an electrolytic solution, charging the double layer capacitance in the absence of faradaic current amounts to trigger the response of the an oscillating circuit composed as in Figure 1 of a self-inductance, L, representing the bandpass limitations of the instrument, a solution resistance, RS, and in which the film would be replaced by a global capacitance, representing the double layer at the interface between the massive electrode and the electrolytic solution. Typical current−time capacitance charging responses are shown in Figure 3a. As the amount of positive feedback is
short times (Figure 2). We thus expect also a different outcome upon positive feedback resistance compensation. This is indeed what is observed as detailed in Figures 3b, c for two values of the resistivity ratio. Oscillations appear as in the RC case but they appear as superimposed over the rising diffusion-like response curve (see section 1.4. of the SI for details on numerical simulations). The fact that they appear at negative values of the parameter SRu/[df(rB + rP)] simply means that overcompensation of the solution resistance occurs as the film resistance starts to be compensated. The strategy to minimize ohmic drop in this mesoporous film is thus the same as with the massive electrode−electrolytic solution systems. It consists to push positive feedback as far as the presence of oscillations remains compatible with measurement of further events. Practical examples are given in the next section. 3. An Experimental Example: Charging Response of a Carbon Powder-Nafion Mesoporous Film Immersed in a Strong Electrolyte Solution. The carbon powder (Vulcan)Nafion films we used in this purpose were prepared from a mixture of the two components in water drop-casted onto a glassy carbon electrode and dried so as to obtain films of ca. 3 μm thickness (see the SI). These film-covered electrodes were then investigated by linear scan voltammetry using a homebuild potentiostat equipped with positive feedback for ohmic drop compensation.35 The degree of positive feedback can be set as a known, adjustable, negative resistance inserted between the working and the reference electrodes. The linear scanning charging current responses recorded as functions of the carbon powder loading and of the supporting electrolyte concentration give access to the intrinsic conductivity characteristics of our mesoporous films in the framework of the transmission line description of. In a first stage of the analysis, we assumed that resistance compensation is practically achieved when the positive feedback resistance is 1 Ω less than the value at which the oscillations appear.
Figure 3. Positive feedback ohmic drop compensation in the absence of faradaic process. (a) Classical RC-response of a massive electrode immersed in an electrolytic solution for increasing value of the ohmic drop compensation from blue to red and black curves: R u/2 L /C = 0.15 (blue), 1 (red), 5 (green). (b) Capacitance charging response for mesoporous films of the type shown in Figure 1 for rP/rB = 100, the instrument being characterized by the parameter SL/[df3(rB + rP)2c] = 0.005, as a function of the degree of resistance compensation measured by the ratio SRu/[df(rB + rP)]: 1 (black), 0.5 (green), 0 (red), −0.18 (blue). (c) Capacitance charging response for mesoporous films of the type shown in Figure 1 for rP/rB = 1, the instrument being characterized by the parameter SL/[df3(rB + rP)2c] = 0.0005, as a function of the degree of resistance compensation measured by the ratio SRu/[df(rB + rP)]: 0.25 (black), 0 (green), −0.25 (red), and −0.303 (blue). The symbols have the same meaning as in the caption of Figure 1 (glossary of symbols in the SI).
Table 1
increased, i.e., as the still uncompensated resistance decreases, the RC-exponential response gradually straighten up. When the uncompensated resistance approaches zero, damped oscillations appears in line with a resonant circuit behavior. Sustained oscillations appear when the uncompensated resistance reaches zero (not shown in Figure 3a). We have seen in the preceding section that, with a perfect instrument compensating exactly the solution resistance and part of the film resistance, the capacitance charging response is quite different from an RCexponential curve but rather involves a diffusion-like behavior at
Vulcan (mg)
electrolyte
ν (V/s)
Cf (μF)
Rf (Ω)
0.6 2 5 10 2 2 2 2 2 2 2 2
KNO3 0.1 M KNO3 0.1 M KNO3 0.1 M KNO3 0.1 M KNO3 0.01 M KNO3 0.05 M KNO3 0.1 M KNO3 1 M HNO3 0.05 M HNO3 0.1 M HNO3 0.5 M HNO3 1 M
300 100 20 10 20 50 100 100 100 100 100 100
26 89 343 739 79 83 89 95.5 95.5 91 95 95
13 11 13 22 80 20 11 5 9 4
