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Mapping concentration profiles within the diffusion layer of an electrode
www.elsevier.nl/locate/elecom Electrochemistry Communications 2 (2000) 353–358
Mapping concentration profiles within the diffusion layer of an electrode Part III. Steady-state and time-dependent profiles via amperometric measurements with an ultramicroelectrode probe Christian Amatore *, Sabine Szunerits, Laurent Thouin, Jean-Stephane Warkocz ´ ´ Ecole Normale Superieure, Departement de Chimie, UMR CNRS 8640 ‘PASTEUR’, 24 rue Lhomond, 75231 Paris Cedex 05, France Received 10 February 2000; received in revised form 22 February 2000; accepted 22 February 2000
Abstract A platinum-disk ultramicroelectrode is used to monitor amperometrically the concentrations of the electroactive substrate and of its electrogenerated product(s) inside the diffusion layer created by a larger working electrode. This allows a direct monitoring of the target species concentration profiles without any assumption even when diffusion coefficients differ significantly. The validity of the method is established experimentally through the study of the one-electron reversible oxidation of the Fe(CN)63y/Fe(CN)64y couple in aqueous KCl, under steady-state or under transient diffusion conditions. Under steady-state conditions, the results compare excellently with those we obtained by means of the potentiometric method reported in Part II of this series. Under transient diffusion conditions, the measured concentration profiles match perfectly those predicted for planar diffusion, which demonstrates the interest of the method for the analysis of dynamic diffusion-kinetic problems. The validity of the method in a complex diffusional situation is established as previously (Part II) by the investigation of the effect of a conproportionation reaction taking place during the second reduction of tetracyanoquinodimethane (TCNQ) in DMF. q2000 Elsevier Science S.A. All rights reserved. Keywords: Concentration profile; Conproportionation; Nernst layer approximation; Amperometry; Ultramicroelectrode
1. Introduction In this series of paper we examine several ways to record precise concentration profiles near an active surface. Indeed, concentration profiles are obviously crucial in electrochemistry since they command the electrode current through their gradients at the electrode surface. However, they are also determinant in many other instances in chemistry and physics where an active interface exchanges chemicals or energy with a solution. For example, this is obvious in heterogeneous catalysis, phase transfer catalysis, liquidNliquid interfaces, etc. Therefore, monitoring concentration profiles which build up near a working electrode is not only of importance in electrochemistry, but is also the paragon of many other chemically important situations. This explains why several attempts have already been made in the past to monitor the development of concentration profiles near an electrode surface [1–4], or liquidNliquid interfaces [5–7]. Our group contributed recently by showing * Corresponding author. Tel./fax: q33-1-4432-3863; e-mail: amatore@ ens.fr
that an unprecedented precision could be achieved through the use of confocal Raman microscopy measurements [8,9], or of potentiometric measurements recorded within the diffusion layer of an electrode with an ultramicroelectrode probe [10]. However, despite the extremely good precision of both methods that could even be used to investigate a complex mechanistic situation, we have been forced to investigate steady-state diffusion layers because in each case the time required to determine one concentration at a given distance from the working electrode was too large for transient signals to be monitored with a sufficient accuracy. This obviously prevented the investigation of transient concentration profiles. In this note, we wish to show that the use of amperometric measurements with an ultramicroelectrode probe placed within the diffusion layer of a larger working electrode is perfectly suited since it by-passes both difficulties. Thus, transient concentration profiles may be mapped, and no external assumption is required to measure absolute concentrations. Following the framework developed in Part II of this series, we will first present and establish the experimental validity of the method by investigating the composition of
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the convectively imposed steady-state layer during the oneelectron chemically and electrochemically reversible oxidation of a bulk Fe(CN)64y solution. Then, reduction of tetracyanoquinodimethane (TCNQ) on its second wave will be examined to emphasize the interest of the method in a complex kinetic situation arising from the involvement of a conproportionation reaction. Finally, we will return to the reversible oxidation of Fe(CN)64y to establish that timedependent concentration profiles can be determined with a sufficient precision and accuracy by this amperometric method.
2. Experimental Solutions of K4Fe(CN)6 (10 mM, Acros) were prepared in purified water (with Milli-Q, Millipore) with 1 M KCl (Aldrich) as the supporting electrolyte. TCNQ (Sigma) was recrystallized from acetylacetate/petroleum ether solutions before use. TCNQ solutions (10 mM) were prepared in DMF with 0.1 M tetrabutylammonium tetrafluoroborate (NBu4BF4). In all cases, the solutions were previously degassed by argon bubbling and maintained under a continuously renewed argon blanket during the experiments. In each case, the relative values of the diffusion coefficients of the electroactive species were determined both from the ratio of the steady-state current plateaus determined with a Pt-disk ultramicroelectrode (10 mm radius) and from the square of the ratio of the Cottrellian amperometric currents (one-electron reduction or oxidation accordingly) of authentic solutions of the species of interest (e.g., Fe(CN)63y, TCNQxy, or TCNQ2y) versus that of its precursor (e.g., Fe(CN)64y, or TCNQ) at identical concentration. For this purpose chemically stable solutions of the species of interest were prepared by exhaustive electrolysis of a stock solution of the precursor [10]. For Fe(CN)64y/Fe(CN)63y, we thus obtained D3ys(6.0"0.5)=10y6 cm2 sy1 (everywhere in this study the subscript designates the species by its charge) and D4y/D3ys0.95"0.05 in 1 M KCl/water. For TCNQ, Dy/D0s0.94"0.04 and D2y/D0s0.60"0.03 were obtained in 0.1 M NBu4BF4/DMF, being then extremely close from the values reported previously in acetonitrile [11]. The experimental setup was similar to the one previously described [10]. The cell, a Petri dish containing about 3 mL of solution, was placed on the stage of an inverted microscope (Axiovert 135, Carl Zeiss) equipped with a charge-coupled device video camera (VCB-3512P, Sanyo) connected itself to a video monitor (VM-2512, Sanyo). A four-electrode configuration was used with a bipotentiostat (PGStat 30, Autolab). The reference electrode (SCE, Tacussel Radiometer) was placed into the solution via a salt bridge and the counter electrode was a platinum coil of about 1 cm2 surface area. The working electrode was a Pt disk electrode of 0.25 mm diameter made by the cross section of a Pt wire (0.25 mm, Good Fellow) sealed into soft glass. The amperometric probe was a Pt disk microelectrode of 5.5"0.5 mm diameter
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made by etching a Pt wire of 25 mm diameter (Good Fellow) and sealed into a soft glass capillary [12]. It was polished at an angle of 458 over a diamond whetstone microgrinder (EG40, Narishige). Electrical contacts were performed with a drop of mercury and a nichrome wire. The working and probing electrodes were positioned within 0.5 mm precision using two three-dimensional micromanipulators (MHW-103, Narishige), the probe being located ("10 mm) on the working electrode axis. The working electrode was operated potentiostatically. The amperometric probe was wired to the potentiostat through a computer-driven mercury relay so that it was isolated except after a time delay t where it was connected during an interval of time u at the end of which the amperometric measurement was made (Fig. 1). This was essential to avoid the probe interfering with the concentration profiles. Therefore, the method presented here monitors true concentration profiles and greatly differs from another one published
Fig. 1. Principle of the amperometric measurement of concentration profiles. This is exemplified by the measurement at a distance zs50 mm from the working electrode surface of Fe(CN)63y generated during the oxidation of Fe(CN)64y (10 mM in 1 M KCl) by the working electrode. (a) Current vs. time variations for the working electrode (A, Ews0.6 V/SCE) and for the microelectrode amperometric probe (B; see enlargement in inset). The probe was connected and its potential set at E1s0.0 V/SCE at time ts40 s. (b) Variations of the probe current iprobe as a function of the sampling time u for different z values: 10 mm (circles), 20 mm (squares), 40 mm (diamonds), 60 mm (triangles) and 100 mm (crosses). The vertical dashed line shows that a sampling time us10 ms is adequate at any z value investigated here (see text for the definition of iprobe8).
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previously [1,2] in which the amperometric probe was always connected and monitored the diffusional concentration wave passing in front of it. For measurements of steady-state concentration profiles, the time delay t was chosen sufficiently large (ts40 s) so that the working electrode current had reached its steady-state limit in the unstirred solution (Fig. 1). To ensure that steady state was mostly due to interference from natural convective transport and did not contain an appreciable non-planar diffusion component [13], some experiments have been performed with a larger working electrode (1 mm diameter). These experiments, which are not reported here, afforded essentially identical results either for the time course of the working electrode current (when corrected from the surface area ratio) or for the concentration profiles. We preferred to perform most of the experiments with a 250 mm diameter working electrode to ensure a negligible ohmic drop, in particular when recording transient concentration profiles. Under our experimental conditions, this size consisted in an adequate optimum between negligible ohmic drop and negligible edge diffusion. Transient concentration profiles were recorded in a similar fashion, except that now the time delay t was fixed at much smaller values where the working electrode current still obeyed a Cottrellian behavior. In each case (transient or steady state concentration profiles) each current measurement at each z value was performed independently, after stirring the solution by argon bubbling. The current at the working electrode was recorded in each case to control the reproducibility between each run and to evaluate its Cottrellian or steady state behavior.
3. Results and discussion 3.1. Steady-state concentration profile for a one-electron reversible system Fig. 1 shows an example of the amperometric current responses obtained for a 10 mM aqueous Fe(CN)64y solution. A potential of q0.6 V/SCE was applied at the working electrode to insure the complete oxidation of Fe(CN)64y (E1/2s0.234 V/SCE) at its surface. Up to 1 s the working electrode current displayed a perfect Cottrellian behavior characteristic of planar diffusion (curve A, Fig. 1(a)) [14]. Then the current deviated slowly (at ts10 s, its value was approximately double that of its calculated Cottrellian value) and eventually reached its steady-state limit imposed by natural convection (t)30 s). Hence, the steady-state concentration profiles were recorded after a time delay t of 40 s following the application of the potential at the working electrode (Fig. 1) to ensure that steady state was achieved completely all over the solution. Before this delay, the probe was disconnected so as to avoid any generator–collector cross-talk [15,16] with the working electrode or local alteration of the solution. At time t, it was
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connected, so that its potential could be set either at E1s0.0 V/SCE, viz. on the reduction plateau of Fe(CN)63y, so as to determine the concentration of the product species, or at E2s0.6 V/SCE, viz. on the oxidation plateau of Fe(CN)64y, to determine the residual concentration of the substrate. The probe current measurements were made at time tqu. The value of u should not be too small to ensure that the probe current is not contaminated by capacitive currents, but it should not be too large to avoid a significant averaging of the concentration measured over its own diffusion layer or any cross-talk (Du
(1)
=(D 4y/D 3y)1/2 c 4y(z)/c8si probe(u,E 2 ,z)/i probe8(u)
(2)
where D4y/D3ys0.95 was determined independently (see Section 2, Experimental). Fig. 2(a) displays the ensuing steady-state concentration profiles for Fe(CN)64y and Fe(CN)63y as a function of the distance z. Each concentration profile is approximately linear over about 75% of the diffusion layer (in terms of concentration changes) corresponding to a Nernst layer thickness which is estimated at d;150 mm. Above 120 mm, a progressive deviation is observed from these linear variations so that both concentrations may tend towards their bulk values. This deviation reflects the progressive interference of natural convection. So the present results compare excellently with those we reported recently based on potentiometric measurements [10] and with the classical Nernst layer approximation. Moreover, since the probe current measurements are absolute and Eqs. (1) and (2) take into account the difference in the diffusion coefficients of Fe(CN)64y and Fe(CN)63y, the concentration profiles in Fig. 2(a) are not subjected to any assumption on the sum of Fe(CN)64y and Fe(CN)63y concentrations as for the case with potentiometric measurements [10]. Conversely, the experimental variations of this sum with z are now available (Fig. 2(b)). This shows that the mass conservation law (viz., c4yqc3ysc8) does not apply strictly here because of the difference in diffusion coefficients
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Fig. 2. Steady-state diffusion layer composition determined with the amperometric probe (ts40 s, us10 ms) during (a, b) the oxidation of Fe(CN)64y (10 mM) in 1 M KCl or (c) during the reduction of TCNQ (10 mM in DMF/0.1 M NBu4BF4) on its second wave plateau. (a) Normalized concentration of Fe(CN)63y (open circles) and Fe(CN)64y (solid circles) as a function of the distance z from the working electrode. (b) Normalized sum of the concentrations of Fe(CN)64y and Fe(CN)63y shown in (a). (c) Normalized concentrations of TCNQ (open squares), TCNQxy (solid (z-m) or open (z)m) circles; ms80 mm, see text) and TCNQ2y (open triangles).
between the substrate and the product (D4y/D3ys0.95). As expected, the maximum deviation occurs at the electrode surface and is about 5% (vide infra). This affords a precise demonstration of the precision of the method.
centration profiles have already been investigated by us either by confocal Raman microscopy [8,9] or with a potentiometric ultramicroelectrode probe [10]. In the above Fe(CN)64y/Fe(CN)63y case there was only one redox wave, so that probe currents measured on each side of the half-wave potential were representative of the only species which could be consumed electrochemically at the probe potential. Here the situation is virtually more complicated because we have three species and two half-waves. For a microprobe potential E1s0.6 V/SCE, positive to both E01 and E02, TCNQ is inert, but TCNQxy or TCNQ2y is oxidizable respectively through a one- or a two-electron process. At E2s0.0 V/SCE, located in between E01 and E02, TCNQxy is inert, but TCNQ or TCNQ2y is electroactive, giving rise respectively to a one-electron reduction or oxidation. Finally, at E3sy0.6 V/SCE, negative to both E01 and E02, TCNQ2y is inert, but TCNQxy or TCNQ is reducible respectively through a one- or a two-electron process. Mathematically speaking, the measurement of the microprobe current at any of these three potentials is then not sufficient to extract unequivocally the concentrations of each three species. In practice, the situation is less difficult because the fast conproportionation reaction (Eq. (3)) separates the diffusion layer into two distinct halves, since TCNQ and TCNQ2y cannot be present together at the same location, except at zsm where their concentrations are negligible and that of TCNQxy is maximum. The first half of the diffusion layer (z-m) contains only TCNQxy and TCNQ2y, while the second half (z)m) contains only TCNQ and TCNQxy. The above conundrum is thus easily solved provided the limit zsm is known. For z-m, the probe current measured at E2 is anodic and proportional to D2y1/2c2y, while that measured at E3 is cathodic and proportional to Dy1/2cy. Conversely, for z)m, the probe current measured at E1 is anodic and proportional to Dy1/2cy; that measured at E2 is now cathodic and proportional to D01/2c0. Then zFm: c0(z)/c8s0
(4) 1/2
cy(z)/c8s[i probe(u,E 3 ,z)/i probe8(u)]=(D 0/Dy)
(5)
c2y(z)/c8s[i probe(u,E 2 ,z)/i probe8(u)]=(D 0/D 2y)1/2
(6)
3.2. Steady-state concentration profiles in a complex kinetic situation: Reduction of TCNQ on its second wave
and
We wish to establish hereafter the interest of the method in a delicate mechanistic situation. For this we take advantage of the complex diffusional-kinetic pattern introduced by the existence of the conproportionation reaction [8–11,17–19]:
cy(z)/c8s[i probe(u,E 1,z)/i probe8(u)]=(D 0/Dy)1/2
(8)
c2y(z)/c8s0
(9)
TCNQqTCNQ
2y
™2TCNQ
xy
0
(DG <0)
(3)
which occurs between the TCNQ substrate and its dianion TCNQ2y when the working electrode potential is set on the second wave plateau of the two-wave EE reduction of TCNQ (E01s0.320 V/SCE, and E02sy0.237 V/SCE). Indeed, this system is well documented [8–11] and its peculiar con-
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zGm:
c0(z)/c8s[i probe(u,E 2 ,z)/i probe8(u)]
(7)
where iprobe8(u) is the current measured at time u with the same probe on the plateau of the first reduction wave of TCNQ in the bulk solution when the working electrode is disconnected (i.e., iprobe8(u)AD01/2c8). Application of either one of the above sets of equations requires the knowledge of m. This is easily determined by monitoring the sign of the probe current at E2 as a function of z since this is anodic for z-m (one-electron oxidation of TCNQ2y) and cathodic
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for z)m (one-electron reduction of TCNQ). Thus, zsm is the z value at which iprobe(u,E2,m)s0. Application of this method to our present case gave ms80"5 mm. The concentration profiles shown in Fig. 2(c) could then be reconstructed from the series of current measurements by application of either Eqs. (4)–(6) (zF80 mm) or Eqs. (7)– (9) (zG80 mm). Fig. 2(c) illustrates the drastic effect of the difference in diffusion coefficients of the three species. Since the fluxes are conservative, each species TCNQxy or TCNQ2y compensates its lower diffusion coefficient relative to TCNQ by a steeper concentration gradient. Note that we already observed this behavior in our previous potentiometric investigation [10], but this resulted from the external theoretical condition imposed on the variations of the sum of the three concentrations as a function of z. No external condition was imposed here, so the results in Fig. 2(c) are absolute. In this context, it is important to observe that the values of [TCNQ2y]0f1.65c8 at the electrode surface and of [TCNQxy]mf1.05c8 at its maximum (zs80 mm) are extremely close to the reciprocal ratio of their diffusion coefficients relative to TCNQ: D0/D2ys1.67"0.08, and D0/ Dys1.06"0.04. By comparison, for transient planar diffusion, one should obtain [14] [TCNQ2y]0/c8s(D0/ D2y)1/2f1.29, and [TCNQxy]m/c8s(D0/Dy)1/2f1.03. Similarly in steady state at the RDE, one should obtain [14] [TCNQ2y]0/c8s(D0/D2y)2/3f1.41, and [TCNQxy]m/ c8s(D0/Dy)2/3f1.04. Conversely, for steady-state spherical diffusion, one should obtain [9] [TCNQ2y]0/c8s(D0/ D2y)f1.67, and [TCNQxy]m/c8s(D0/Dy)f1.06. The differences in the three methods stem from the fact that, in each case, the diffusion layer thickness varies differently with the diffusion coefficient (viz., dAD1/2 in transient planar diffusion [14], dAD1/3 at the RDE [14], while d is independent of D in steady-state spherical diffusion [13]). Thus, the present results point out that under steady-state conditions driven by natural convection, the diffusion layer thickness does not vary appreciably with diffusion coefficient. This is indeed apparent in Fig. 2, and was already observed with our potentiometric measurements [10]. That and the close linearity of the concentration profiles over most of their variations bring further support to the clever Nernst layer approximation. 3.3. Transient concentration profiles The present chronoamperometric detection allows measurements at short times t. This is perfectly suited for the investigation of transient processes, such as the development of a diffusion layer with time. Fig. 3(a) illustrates this important property by presenting the Fe(CN)63y concentration profiles determined at different times t after a 0.6 V/SCE potential has been applied to the working electrode. Each concentration profile has been reconstructed by application of Eq. (1) to the probe current (us10 ms; Eprobes0.0 V/ SCE) measured at time t. This figure shows that the diffusion
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Fig. 3. Transient concentration profiles of Fe(CN)63y generated by oxidation of Fe(CN)64y (10 mM in 1 M KCl) at the working electrode, as determined by the amperometric probe (us10 ms) at different times t : 0.2 s (open circles), 0.3 s (open squares), 0.4 s (open diamonds), 0.5 s (open triangles), 1.0 s (side-up open triangles), and 40 s (steady-state profile, solid circles). (a) Experimental concentration profiles. (b) Correlation between experimental and theoretical (transient planar diffusion, Eq. (10)) concentration profiles (slope 1.002; correlation coefficient 0.996; 56 data, open symbols only). In (b) the data obtained under steady state (ts40 s; solid circles) are also represented to emphasize the effect of convective transport.
layer expands qualitatively with t1/2 (open symbols) up to the point where it begins to interfere with natural convection (dG60–70 mm). Then its progression slows down and eventually the diffusion layer collapses into the steady-state one. Fig. 3 illustrates the perfect agreement found between experimental concentrations and predicted ones when tF1 s, i.e., over the time range in which the working electrode exhibits a Cottrellian behavior. These time-dependent time concentration profiles are extremely reminiscent of those obtained previously in a similar situation based on measurements with high-resolution spatially resolved visible spectrometry [4]. This perfect agreement is adequately represented by the extremely good correlation between the experimental values of c3y(z,t)/c8 and those predicted for a pure planar diffusion [14]: c3y(z,t)/c8s(D 4y/D 3y)1/2=erfc[z/(4D 3yt)1/2]
(10)
This investigation of short time scales had to be limited
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here to ts0.2 s. Indeed, with the present size of probes used (about 15 mm diameter including the glass case), the exploration of thinner diffusion layers is prevented, since the concentration profiles would be significantly altered by the probe geometrical hindrance, even if u values short enough to avoid any cross-talk between the probe and the working electrode were used. Acknowledgements This work has been supported in part by the CNRS (UMR 8640), the French Ministry of Research and Education ´ (MENRT; Action Specifique DGRT No. 97.1502) and by ´ the Ecole Normale Superieure. G. Simonneau is cordially thanked for designing the electronic instrumentation and related software for connecting/disconnecting the probe, as well as C. Pebay for her involvement in several experiments related to the determination of diffusion coefficients. S.S. ¨ acknowledges the FWF Austria for an Erwin SchrodingerAuslandsstipendium Grant (J1840-CHE). References [1] R.C. Engstrom, M. Weber, D.J. Wunder, R. Burgess, S. Winquist, Anal. Chem. 58 (1986) 844.
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[2] R.C. Engstrom, T. Meaney, R. Tople, R.M. Wightman, Anal. Chem. 59 (1987) 2005. [3] A.J. Bard, F.F. Fan, M.V. Mirkin, in: A.J. Bard (Ed.), Electroanalytical Chemistry, vol. 18, Marcel Dekker, New York, 1994, p. 243. [4] C.C. Jan, R.L. McCreery, Anal. Chem. 58 (1986) 2771. [5] C.J. Slevin, P.R. Unwin, Langmuir 13 (1997) 4799. [6] J. Zhang, C.J. Slevin, P. Unwin, Chem. Commun. (1999) 1501. [7] C.J. Selvin, P.R. Unwin, Langmuir 15 (1999) 7361. [8] C. Amatore, F. Bonhomme, J.-L. Bruneel, L. Servant, L. Thouin, Electrochem. Commun. 2 (2000) 235. [9] C. Amatore, F. Bonhomme, J.-L. Bruneel, L. Servant, L. Thouin, J. Electroanal. Chem., in press. [10] C. Amatore, S. Szunerits, L. Thouin, Electrochem. Commun. 2 (2000) 248. [11] Z. Rongfeng, D.H. Evans, J. Electroanal. Chem. 385 (1995) 201. [12] A.A. Gewirth, D.H. Craston, A.J. Bard, J. Electroanal. Chem. Interfacial Electrochem. 261 (1989) 477. [13] C. Amatore, in: I. Rubinstein (Ed.), Physical Electrochemistry: Principles, Methods and Applications, Marcel Dekker, New York, 1995, Ch. 4, pp. 131–208. [14] A.J. Bard, L.R. Faulkner, in Electrochemical Methods, Wiley, New York, 1980. [15] C. Amatore, B. Fosset, J.E. Bartelt, M.R. Deakin, R.M. Wightman, J. Electroanal. Chem. 256 (1988) 255. [16] R.D. Martin, P.R. Unwin, Anal. Chem. 70 (1998) 276. [17] C. Amatore, M.F. Bento, M.I. Montenegro, Anal. Chem. 67 (1995) 2800. ´ [18] C.P. Andrieux, J.M. Saveant, J. Electroanal. Chem. 28 (1970) 339. [19] C. Amatore, S.C. Paulson, H.S. White, J. Electroanal. Chem. 439 (1997) 173.
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Mapping concentration profiles within the diffusion layer of an electrode Part III. Steady-state and time-dependent profiles via amperometric measurements with an ultramicroelectrode probe Christian Amatore *, Sabine Szunerits, Laurent Thouin, Jean-Stephane Warkocz ´ ´ Ecole Normale Superieure, Departement de Chimie, UMR CNRS 8640 ‘PASTEUR’, 24 rue Lhomond, 75231 Paris Cedex 05, France Received 10 February 2000; received in revised form 22 February 2000; accepted 22 February 2000
Abstract A platinum-disk ultramicroelectrode is used to monitor amperometrically the concentrations of the electroactive substrate and of its electrogenerated product(s) inside the diffusion layer created by a larger working electrode. This allows a direct monitoring of the target species concentration profiles without any assumption even when diffusion coefficients differ significantly. The validity of the method is established experimentally through the study of the one-electron reversible oxidation of the Fe(CN)63y/Fe(CN)64y couple in aqueous KCl, under steady-state or under transient diffusion conditions. Under steady-state conditions, the results compare excellently with those we obtained by means of the potentiometric method reported in Part II of this series. Under transient diffusion conditions, the measured concentration profiles match perfectly those predicted for planar diffusion, which demonstrates the interest of the method for the analysis of dynamic diffusion-kinetic problems. The validity of the method in a complex diffusional situation is established as previously (Part II) by the investigation of the effect of a conproportionation reaction taking place during the second reduction of tetracyanoquinodimethane (TCNQ) in DMF. q2000 Elsevier Science S.A. All rights reserved. Keywords: Concentration profile; Conproportionation; Nernst layer approximation; Amperometry; Ultramicroelectrode
1. Introduction In this series of paper we examine several ways to record precise concentration profiles near an active surface. Indeed, concentration profiles are obviously crucial in electrochemistry since they command the electrode current through their gradients at the electrode surface. However, they are also determinant in many other instances in chemistry and physics where an active interface exchanges chemicals or energy with a solution. For example, this is obvious in heterogeneous catalysis, phase transfer catalysis, liquidNliquid interfaces, etc. Therefore, monitoring concentration profiles which build up near a working electrode is not only of importance in electrochemistry, but is also the paragon of many other chemically important situations. This explains why several attempts have already been made in the past to monitor the development of concentration profiles near an electrode surface [1–4], or liquidNliquid interfaces [5–7]. Our group contributed recently by showing * Corresponding author. Tel./fax: q33-1-4432-3863; e-mail: amatore@ ens.fr
that an unprecedented precision could be achieved through the use of confocal Raman microscopy measurements [8,9], or of potentiometric measurements recorded within the diffusion layer of an electrode with an ultramicroelectrode probe [10]. However, despite the extremely good precision of both methods that could even be used to investigate a complex mechanistic situation, we have been forced to investigate steady-state diffusion layers because in each case the time required to determine one concentration at a given distance from the working electrode was too large for transient signals to be monitored with a sufficient accuracy. This obviously prevented the investigation of transient concentration profiles. In this note, we wish to show that the use of amperometric measurements with an ultramicroelectrode probe placed within the diffusion layer of a larger working electrode is perfectly suited since it by-passes both difficulties. Thus, transient concentration profiles may be mapped, and no external assumption is required to measure absolute concentrations. Following the framework developed in Part II of this series, we will first present and establish the experimental validity of the method by investigating the composition of
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the convectively imposed steady-state layer during the oneelectron chemically and electrochemically reversible oxidation of a bulk Fe(CN)64y solution. Then, reduction of tetracyanoquinodimethane (TCNQ) on its second wave will be examined to emphasize the interest of the method in a complex kinetic situation arising from the involvement of a conproportionation reaction. Finally, we will return to the reversible oxidation of Fe(CN)64y to establish that timedependent concentration profiles can be determined with a sufficient precision and accuracy by this amperometric method.
2. Experimental Solutions of K4Fe(CN)6 (10 mM, Acros) were prepared in purified water (with Milli-Q, Millipore) with 1 M KCl (Aldrich) as the supporting electrolyte. TCNQ (Sigma) was recrystallized from acetylacetate/petroleum ether solutions before use. TCNQ solutions (10 mM) were prepared in DMF with 0.1 M tetrabutylammonium tetrafluoroborate (NBu4BF4). In all cases, the solutions were previously degassed by argon bubbling and maintained under a continuously renewed argon blanket during the experiments. In each case, the relative values of the diffusion coefficients of the electroactive species were determined both from the ratio of the steady-state current plateaus determined with a Pt-disk ultramicroelectrode (10 mm radius) and from the square of the ratio of the Cottrellian amperometric currents (one-electron reduction or oxidation accordingly) of authentic solutions of the species of interest (e.g., Fe(CN)63y, TCNQxy, or TCNQ2y) versus that of its precursor (e.g., Fe(CN)64y, or TCNQ) at identical concentration. For this purpose chemically stable solutions of the species of interest were prepared by exhaustive electrolysis of a stock solution of the precursor [10]. For Fe(CN)64y/Fe(CN)63y, we thus obtained D3ys(6.0"0.5)=10y6 cm2 sy1 (everywhere in this study the subscript designates the species by its charge) and D4y/D3ys0.95"0.05 in 1 M KCl/water. For TCNQ, Dy/D0s0.94"0.04 and D2y/D0s0.60"0.03 were obtained in 0.1 M NBu4BF4/DMF, being then extremely close from the values reported previously in acetonitrile [11]. The experimental setup was similar to the one previously described [10]. The cell, a Petri dish containing about 3 mL of solution, was placed on the stage of an inverted microscope (Axiovert 135, Carl Zeiss) equipped with a charge-coupled device video camera (VCB-3512P, Sanyo) connected itself to a video monitor (VM-2512, Sanyo). A four-electrode configuration was used with a bipotentiostat (PGStat 30, Autolab). The reference electrode (SCE, Tacussel Radiometer) was placed into the solution via a salt bridge and the counter electrode was a platinum coil of about 1 cm2 surface area. The working electrode was a Pt disk electrode of 0.25 mm diameter made by the cross section of a Pt wire (0.25 mm, Good Fellow) sealed into soft glass. The amperometric probe was a Pt disk microelectrode of 5.5"0.5 mm diameter
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made by etching a Pt wire of 25 mm diameter (Good Fellow) and sealed into a soft glass capillary [12]. It was polished at an angle of 458 over a diamond whetstone microgrinder (EG40, Narishige). Electrical contacts were performed with a drop of mercury and a nichrome wire. The working and probing electrodes were positioned within 0.5 mm precision using two three-dimensional micromanipulators (MHW-103, Narishige), the probe being located ("10 mm) on the working electrode axis. The working electrode was operated potentiostatically. The amperometric probe was wired to the potentiostat through a computer-driven mercury relay so that it was isolated except after a time delay t where it was connected during an interval of time u at the end of which the amperometric measurement was made (Fig. 1). This was essential to avoid the probe interfering with the concentration profiles. Therefore, the method presented here monitors true concentration profiles and greatly differs from another one published
Fig. 1. Principle of the amperometric measurement of concentration profiles. This is exemplified by the measurement at a distance zs50 mm from the working electrode surface of Fe(CN)63y generated during the oxidation of Fe(CN)64y (10 mM in 1 M KCl) by the working electrode. (a) Current vs. time variations for the working electrode (A, Ews0.6 V/SCE) and for the microelectrode amperometric probe (B; see enlargement in inset). The probe was connected and its potential set at E1s0.0 V/SCE at time ts40 s. (b) Variations of the probe current iprobe as a function of the sampling time u for different z values: 10 mm (circles), 20 mm (squares), 40 mm (diamonds), 60 mm (triangles) and 100 mm (crosses). The vertical dashed line shows that a sampling time us10 ms is adequate at any z value investigated here (see text for the definition of iprobe8).
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previously [1,2] in which the amperometric probe was always connected and monitored the diffusional concentration wave passing in front of it. For measurements of steady-state concentration profiles, the time delay t was chosen sufficiently large (ts40 s) so that the working electrode current had reached its steady-state limit in the unstirred solution (Fig. 1). To ensure that steady state was mostly due to interference from natural convective transport and did not contain an appreciable non-planar diffusion component [13], some experiments have been performed with a larger working electrode (1 mm diameter). These experiments, which are not reported here, afforded essentially identical results either for the time course of the working electrode current (when corrected from the surface area ratio) or for the concentration profiles. We preferred to perform most of the experiments with a 250 mm diameter working electrode to ensure a negligible ohmic drop, in particular when recording transient concentration profiles. Under our experimental conditions, this size consisted in an adequate optimum between negligible ohmic drop and negligible edge diffusion. Transient concentration profiles were recorded in a similar fashion, except that now the time delay t was fixed at much smaller values where the working electrode current still obeyed a Cottrellian behavior. In each case (transient or steady state concentration profiles) each current measurement at each z value was performed independently, after stirring the solution by argon bubbling. The current at the working electrode was recorded in each case to control the reproducibility between each run and to evaluate its Cottrellian or steady state behavior.
3. Results and discussion 3.1. Steady-state concentration profile for a one-electron reversible system Fig. 1 shows an example of the amperometric current responses obtained for a 10 mM aqueous Fe(CN)64y solution. A potential of q0.6 V/SCE was applied at the working electrode to insure the complete oxidation of Fe(CN)64y (E1/2s0.234 V/SCE) at its surface. Up to 1 s the working electrode current displayed a perfect Cottrellian behavior characteristic of planar diffusion (curve A, Fig. 1(a)) [14]. Then the current deviated slowly (at ts10 s, its value was approximately double that of its calculated Cottrellian value) and eventually reached its steady-state limit imposed by natural convection (t)30 s). Hence, the steady-state concentration profiles were recorded after a time delay t of 40 s following the application of the potential at the working electrode (Fig. 1) to ensure that steady state was achieved completely all over the solution. Before this delay, the probe was disconnected so as to avoid any generator–collector cross-talk [15,16] with the working electrode or local alteration of the solution. At time t, it was
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connected, so that its potential could be set either at E1s0.0 V/SCE, viz. on the reduction plateau of Fe(CN)63y, so as to determine the concentration of the product species, or at E2s0.6 V/SCE, viz. on the oxidation plateau of Fe(CN)64y, to determine the residual concentration of the substrate. The probe current measurements were made at time tqu. The value of u should not be too small to ensure that the probe current is not contaminated by capacitive currents, but it should not be too large to avoid a significant averaging of the concentration measured over its own diffusion layer or any cross-talk (Du
(1)
=(D 4y/D 3y)1/2 c 4y(z)/c8si probe(u,E 2 ,z)/i probe8(u)
(2)
where D4y/D3ys0.95 was determined independently (see Section 2, Experimental). Fig. 2(a) displays the ensuing steady-state concentration profiles for Fe(CN)64y and Fe(CN)63y as a function of the distance z. Each concentration profile is approximately linear over about 75% of the diffusion layer (in terms of concentration changes) corresponding to a Nernst layer thickness which is estimated at d;150 mm. Above 120 mm, a progressive deviation is observed from these linear variations so that both concentrations may tend towards their bulk values. This deviation reflects the progressive interference of natural convection. So the present results compare excellently with those we reported recently based on potentiometric measurements [10] and with the classical Nernst layer approximation. Moreover, since the probe current measurements are absolute and Eqs. (1) and (2) take into account the difference in the diffusion coefficients of Fe(CN)64y and Fe(CN)63y, the concentration profiles in Fig. 2(a) are not subjected to any assumption on the sum of Fe(CN)64y and Fe(CN)63y concentrations as for the case with potentiometric measurements [10]. Conversely, the experimental variations of this sum with z are now available (Fig. 2(b)). This shows that the mass conservation law (viz., c4yqc3ysc8) does not apply strictly here because of the difference in diffusion coefficients
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Fig. 2. Steady-state diffusion layer composition determined with the amperometric probe (ts40 s, us10 ms) during (a, b) the oxidation of Fe(CN)64y (10 mM) in 1 M KCl or (c) during the reduction of TCNQ (10 mM in DMF/0.1 M NBu4BF4) on its second wave plateau. (a) Normalized concentration of Fe(CN)63y (open circles) and Fe(CN)64y (solid circles) as a function of the distance z from the working electrode. (b) Normalized sum of the concentrations of Fe(CN)64y and Fe(CN)63y shown in (a). (c) Normalized concentrations of TCNQ (open squares), TCNQxy (solid (z-m) or open (z)m) circles; ms80 mm, see text) and TCNQ2y (open triangles).
between the substrate and the product (D4y/D3ys0.95). As expected, the maximum deviation occurs at the electrode surface and is about 5% (vide infra). This affords a precise demonstration of the precision of the method.
centration profiles have already been investigated by us either by confocal Raman microscopy [8,9] or with a potentiometric ultramicroelectrode probe [10]. In the above Fe(CN)64y/Fe(CN)63y case there was only one redox wave, so that probe currents measured on each side of the half-wave potential were representative of the only species which could be consumed electrochemically at the probe potential. Here the situation is virtually more complicated because we have three species and two half-waves. For a microprobe potential E1s0.6 V/SCE, positive to both E01 and E02, TCNQ is inert, but TCNQxy or TCNQ2y is oxidizable respectively through a one- or a two-electron process. At E2s0.0 V/SCE, located in between E01 and E02, TCNQxy is inert, but TCNQ or TCNQ2y is electroactive, giving rise respectively to a one-electron reduction or oxidation. Finally, at E3sy0.6 V/SCE, negative to both E01 and E02, TCNQ2y is inert, but TCNQxy or TCNQ is reducible respectively through a one- or a two-electron process. Mathematically speaking, the measurement of the microprobe current at any of these three potentials is then not sufficient to extract unequivocally the concentrations of each three species. In practice, the situation is less difficult because the fast conproportionation reaction (Eq. (3)) separates the diffusion layer into two distinct halves, since TCNQ and TCNQ2y cannot be present together at the same location, except at zsm where their concentrations are negligible and that of TCNQxy is maximum. The first half of the diffusion layer (z-m) contains only TCNQxy and TCNQ2y, while the second half (z)m) contains only TCNQ and TCNQxy. The above conundrum is thus easily solved provided the limit zsm is known. For z-m, the probe current measured at E2 is anodic and proportional to D2y1/2c2y, while that measured at E3 is cathodic and proportional to Dy1/2cy. Conversely, for z)m, the probe current measured at E1 is anodic and proportional to Dy1/2cy; that measured at E2 is now cathodic and proportional to D01/2c0. Then zFm: c0(z)/c8s0
(4) 1/2
cy(z)/c8s[i probe(u,E 3 ,z)/i probe8(u)]=(D 0/Dy)
(5)
c2y(z)/c8s[i probe(u,E 2 ,z)/i probe8(u)]=(D 0/D 2y)1/2
(6)
3.2. Steady-state concentration profiles in a complex kinetic situation: Reduction of TCNQ on its second wave
and
We wish to establish hereafter the interest of the method in a delicate mechanistic situation. For this we take advantage of the complex diffusional-kinetic pattern introduced by the existence of the conproportionation reaction [8–11,17–19]:
cy(z)/c8s[i probe(u,E 1,z)/i probe8(u)]=(D 0/Dy)1/2
(8)
c2y(z)/c8s0
(9)
TCNQqTCNQ
2y
™2TCNQ
xy
0
(DG <0)
(3)
which occurs between the TCNQ substrate and its dianion TCNQ2y when the working electrode potential is set on the second wave plateau of the two-wave EE reduction of TCNQ (E01s0.320 V/SCE, and E02sy0.237 V/SCE). Indeed, this system is well documented [8–11] and its peculiar con-
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zGm:
c0(z)/c8s[i probe(u,E 2 ,z)/i probe8(u)]
(7)
where iprobe8(u) is the current measured at time u with the same probe on the plateau of the first reduction wave of TCNQ in the bulk solution when the working electrode is disconnected (i.e., iprobe8(u)AD01/2c8). Application of either one of the above sets of equations requires the knowledge of m. This is easily determined by monitoring the sign of the probe current at E2 as a function of z since this is anodic for z-m (one-electron oxidation of TCNQ2y) and cathodic
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for z)m (one-electron reduction of TCNQ). Thus, zsm is the z value at which iprobe(u,E2,m)s0. Application of this method to our present case gave ms80"5 mm. The concentration profiles shown in Fig. 2(c) could then be reconstructed from the series of current measurements by application of either Eqs. (4)–(6) (zF80 mm) or Eqs. (7)– (9) (zG80 mm). Fig. 2(c) illustrates the drastic effect of the difference in diffusion coefficients of the three species. Since the fluxes are conservative, each species TCNQxy or TCNQ2y compensates its lower diffusion coefficient relative to TCNQ by a steeper concentration gradient. Note that we already observed this behavior in our previous potentiometric investigation [10], but this resulted from the external theoretical condition imposed on the variations of the sum of the three concentrations as a function of z. No external condition was imposed here, so the results in Fig. 2(c) are absolute. In this context, it is important to observe that the values of [TCNQ2y]0f1.65c8 at the electrode surface and of [TCNQxy]mf1.05c8 at its maximum (zs80 mm) are extremely close to the reciprocal ratio of their diffusion coefficients relative to TCNQ: D0/D2ys1.67"0.08, and D0/ Dys1.06"0.04. By comparison, for transient planar diffusion, one should obtain [14] [TCNQ2y]0/c8s(D0/ D2y)1/2f1.29, and [TCNQxy]m/c8s(D0/Dy)1/2f1.03. Similarly in steady state at the RDE, one should obtain [14] [TCNQ2y]0/c8s(D0/D2y)2/3f1.41, and [TCNQxy]m/ c8s(D0/Dy)2/3f1.04. Conversely, for steady-state spherical diffusion, one should obtain [9] [TCNQ2y]0/c8s(D0/ D2y)f1.67, and [TCNQxy]m/c8s(D0/Dy)f1.06. The differences in the three methods stem from the fact that, in each case, the diffusion layer thickness varies differently with the diffusion coefficient (viz., dAD1/2 in transient planar diffusion [14], dAD1/3 at the RDE [14], while d is independent of D in steady-state spherical diffusion [13]). Thus, the present results point out that under steady-state conditions driven by natural convection, the diffusion layer thickness does not vary appreciably with diffusion coefficient. This is indeed apparent in Fig. 2, and was already observed with our potentiometric measurements [10]. That and the close linearity of the concentration profiles over most of their variations bring further support to the clever Nernst layer approximation. 3.3. Transient concentration profiles The present chronoamperometric detection allows measurements at short times t. This is perfectly suited for the investigation of transient processes, such as the development of a diffusion layer with time. Fig. 3(a) illustrates this important property by presenting the Fe(CN)63y concentration profiles determined at different times t after a 0.6 V/SCE potential has been applied to the working electrode. Each concentration profile has been reconstructed by application of Eq. (1) to the probe current (us10 ms; Eprobes0.0 V/ SCE) measured at time t. This figure shows that the diffusion
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Fig. 3. Transient concentration profiles of Fe(CN)63y generated by oxidation of Fe(CN)64y (10 mM in 1 M KCl) at the working electrode, as determined by the amperometric probe (us10 ms) at different times t : 0.2 s (open circles), 0.3 s (open squares), 0.4 s (open diamonds), 0.5 s (open triangles), 1.0 s (side-up open triangles), and 40 s (steady-state profile, solid circles). (a) Experimental concentration profiles. (b) Correlation between experimental and theoretical (transient planar diffusion, Eq. (10)) concentration profiles (slope 1.002; correlation coefficient 0.996; 56 data, open symbols only). In (b) the data obtained under steady state (ts40 s; solid circles) are also represented to emphasize the effect of convective transport.
layer expands qualitatively with t1/2 (open symbols) up to the point where it begins to interfere with natural convection (dG60–70 mm). Then its progression slows down and eventually the diffusion layer collapses into the steady-state one. Fig. 3 illustrates the perfect agreement found between experimental concentrations and predicted ones when tF1 s, i.e., over the time range in which the working electrode exhibits a Cottrellian behavior. These time-dependent time concentration profiles are extremely reminiscent of those obtained previously in a similar situation based on measurements with high-resolution spatially resolved visible spectrometry [4]. This perfect agreement is adequately represented by the extremely good correlation between the experimental values of c3y(z,t)/c8 and those predicted for a pure planar diffusion [14]: c3y(z,t)/c8s(D 4y/D 3y)1/2=erfc[z/(4D 3yt)1/2]
(10)
This investigation of short time scales had to be limited
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here to ts0.2 s. Indeed, with the present size of probes used (about 15 mm diameter including the glass case), the exploration of thinner diffusion layers is prevented, since the concentration profiles would be significantly altered by the probe geometrical hindrance, even if u values short enough to avoid any cross-talk between the probe and the working electrode were used. Acknowledgements This work has been supported in part by the CNRS (UMR 8640), the French Ministry of Research and Education ´ (MENRT; Action Specifique DGRT No. 97.1502) and by ´ the Ecole Normale Superieure. G. Simonneau is cordially thanked for designing the electronic instrumentation and related software for connecting/disconnecting the probe, as well as C. Pebay for her involvement in several experiments related to the determination of diffusion coefficients. S.S. ¨ acknowledges the FWF Austria for an Erwin SchrodingerAuslandsstipendium Grant (J1840-CHE). References [1] R.C. Engstrom, M. Weber, D.J. Wunder, R. Burgess, S. Winquist, Anal. Chem. 58 (1986) 844.
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[2] R.C. Engstrom, T. Meaney, R. Tople, R.M. Wightman, Anal. Chem. 59 (1987) 2005. [3] A.J. Bard, F.F. Fan, M.V. Mirkin, in: A.J. Bard (Ed.), Electroanalytical Chemistry, vol. 18, Marcel Dekker, New York, 1994, p. 243. [4] C.C. Jan, R.L. McCreery, Anal. Chem. 58 (1986) 2771. [5] C.J. Slevin, P.R. Unwin, Langmuir 13 (1997) 4799. [6] J. Zhang, C.J. Slevin, P. Unwin, Chem. Commun. (1999) 1501. [7] C.J. Selvin, P.R. Unwin, Langmuir 15 (1999) 7361. [8] C. Amatore, F. Bonhomme, J.-L. Bruneel, L. Servant, L. Thouin, Electrochem. Commun. 2 (2000) 235. [9] C. Amatore, F. Bonhomme, J.-L. Bruneel, L. Servant, L. Thouin, J. Electroanal. Chem., in press. [10] C. Amatore, S. Szunerits, L. Thouin, Electrochem. Commun. 2 (2000) 248. [11] Z. Rongfeng, D.H. Evans, J. Electroanal. Chem. 385 (1995) 201. [12] A.A. Gewirth, D.H. Craston, A.J. Bard, J. Electroanal. Chem. Interfacial Electrochem. 261 (1989) 477. [13] C. Amatore, in: I. Rubinstein (Ed.), Physical Electrochemistry: Principles, Methods and Applications, Marcel Dekker, New York, 1995, Ch. 4, pp. 131–208. [14] A.J. Bard, L.R. Faulkner, in Electrochemical Methods, Wiley, New York, 1980. [15] C. Amatore, B. Fosset, J.E. Bartelt, M.R. Deakin, R.M. Wightman, J. Electroanal. Chem. 256 (1988) 255. [16] R.D. Martin, P.R. Unwin, Anal. Chem. 70 (1998) 276. [17] C. Amatore, M.F. Bento, M.I. Montenegro, Anal. Chem. 67 (1995) 2800. ´ [18] C.P. Andrieux, J.M. Saveant, J. Electroanal. Chem. 28 (1970) 339. [19] C. Amatore, S.C. Paulson, H.S. White, J. Electroanal. Chem. 439 (1997) 173.
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