Contribution of the Double Layer to Transient Faradaic Processes

13442

J. Phys. Chem. C 2010, 114, 13442–13450

Contribution of the Double Layer to Transient Faradaic Processes: Implications for Hydrodynamic Modulated Voltammetry of Nanostructures Jekaterina Kuleshova,† Peter R. Birkin,*,† and Joanne M. Elliott‡ School of Chemistry, UniVersity of Southampton, Southampton SO17 1BJ, and Department of Chemistry, UniVersity of Reading, Reading RG6 6AD, United Kingdom ReceiVed: March 14, 2010; ReVised Manuscript ReceiVed: June 8, 2010

The electrochemistry of Pt nanostructured electrodes is investigated using hydrodynamic modulated voltammetry (HMV). Here a liquid crystal templating process is used to produce platinum-modified electrodes with a range of surface areas (roughness factor 42.4-280.8). The electroreduction of molecular oxygen at these nanostructured platinum surfaces is used to demonstrate the ability of HMV to discriminate between faradaic and nonfaradaic electrode reactions. The HMV approach shows that the reduction of molecular oxygen experiences considerable signal loss within the high pseudocapacitive region of the voltammetry. Evidence for the contribution of the double layer to transient mass transfer events is presented. In addition, a model circuit and appropriate theoretical analysis are used to illustrate the transient responses of a time variant faradaic component. This in conjunction with the experimental evidence shows that, far from being a passive component in this system, the double layer can contribute to HMV faradaic reactions under certain conditions. Introduction High surface area electrodes hold considerable benefit for the investigation of surface-limited processes.1-5 However, increasing the area of an electrode will also increase background processes associated with the interface. These include doublelayer charging, underpotential deposition/stripping, and oxide formation steps, etc.6-8 This can impose limitations in the type and number of electrochemical techniques which are able to study the reactions of interest without interference from these background processes. This situation is particularly true if dynamic experiments are attempted with high surface area electrodes. Here we attempt to use hydrodynamic modulated voltammetry9-11 (HMV) to overcome some of these difficulties. HMV offers the advantage of discrimination between solutionphase faradaic processes and nonfaradaic (for example, surfacebound electrode reactions) processes.12-15 Hence, it would be expected that this approach should enable the reactions of interest (e.g., solution-phase species) to be studied in isolation from the surface-dependent processes. However, limitations, reported here, are found for this technique. To illustrate these limitations, an HMV investigation of the electrochemical reduction of molecular oxygen at a set of nanostructured (mesostructured) Pt electrodes is reported.16 Mesostructured microelectrodes produced by the “true liquid crystal templating” technique have been investigated in a number of studies. These materials have a regular repeating 3D architecture.17-21 Clearly, the intrinsic high surface area of such electrodes offers a significant advantage during the study of surface-limited processes. Unfortunately, these high surface areas can also be a disadvantage. This is due to the large currents associated with the electrochemical double-layer charging and with the formation/stripping of oxide and hydride species, masking the solution-phase electrochemistry of interest. For * To whom correspondence should be addressed. E-mail: prb2@ soton.ac.uk. Phone: +44 2380 594172. Fax: +44 2380 593781. † University of Southampton. ‡ University of Reading.

example, it has been shown that although modified Pt microelectrodes were catalytically active for oxygen reduction, relatively slow sweep rates (on the order of 2 mV s-1) were required to observe the appropriate voltammetry in the absence of detrimental distortion.1 Clearly, the application of an HMV approach to these systems would be beneficial. Here we explore the HMV technique and suggest general limitations to this experimental approach beyond the system reported here. In the following section a brief outline of the available HMV approaches is described as well as the oscillating jet system used here. There are many studies of HMV using a variety of different approaches. However, in general they can be divided into two basic strategies. In the first, flow to the electrode is modulated in a periodic manner. This may involve modulation of the rotation rate of a rotating disk electrode (RDE) or alteration of the flow to a stationary electrode by “chopping” or oscillating the hydrodynamics in a suitable manner.14,15,22,23 In the second, the modulation of the signal required is generated by the mechanical oscillation of an electrode.12,13,24 All these approaches have advantages (for example, the RDE system has known analytical solutions that may be applied) and disadvantages (limited frequency regime and/or mechanical restrictions).12,25-28 It should also be noted that the modulation frequency can be an important parameter. The technique of electrohydrodynamic impedance (EHD) utilizes modulated transport phenomena at different frequencies to gain valuable insight into processes which occur over different time scales.11,29-33 However, in this study we employ a fixed frequency oscillating jet as the method of generating hydrodynamic modulation and a stationary jet/ electrode arrangement. In this case a small mechanical oscillation of a large piston produced the desired periodic fluid motion from a jet (diameter 2 mm) using a conical section which enhances fluid flow at the orifice.34 This approach was shown to be reproducible and suitable for the study of high surface area electrodes, specifically nanostructured Pt electrodes (RF (roughness factor) ) 42.4).35 In this paper we show how such an approach may be extended and applied to a range of high

10.1021/jp102308p  2010 American Chemical Society Published on Web 07/22/2010

Contribution of the Double Layer to Faradaic Processes

J. Phys. Chem. C, Vol. 114, No. 32, 2010 13443

surface area electrodes. In addition, perturbations away from the expected response of these electrodes are reported. The mechanisms responsible for the experimental observations are investigated in detail and explained with the use of a simple equivalent circuit model. The results of this study are now reported and suggested to have widespread implications for all HMV systems. Experimental Section The general experimental arrangement used in this work has been reported previously.34 This consisted of a ∼3.5 cm radius membrane attached to the base of an inverted funnel with a 2 mm diameter jet orifice. A piston or disklike structure was then used to drive fluid motion. A mechanical shaker (model V4, Signal Force, Data Physics Ltd.) was attached to the center of the piston, which was glued to a Viton (500 µm thickness, Altec Products Ltd.) sheet. This sheet was attached to both the base plate and the inverted funnel to act as a flexible seal. A mechanical coupling incorporating a single-axis accelerometer (model 3100B, Dytran Instruments, Inc., sensitivity 99.3 mV g-1) was included to assess the magnitude of motion of the piston. The accelerometer signal was conditioned with an amplifier (model 4105C, Dytran Instruments, Inc.) and recorded on an oscilloscope (Techtronixs, TDS 2014, 1 GS/s, 100 MHz). The shaker was driven by an amplifier (Signal Force 30 W power amplifier, model PA 30E, Data Physics Ltd.), which was in turn supplied by a function generator (TGA12101 100 MHz arbitrary waveform generator, TTi Ltd.). In all cases the frequency of oscillation of the membrane, and hence jet, was 16 Hz. The electrodes employed (Pt, 0.5 mm diameter) were fabricated in-house and were sealed in glass (diameter 5.0 mm). Positioning of the electrode with respect to the jet orifice was controlled using an XYZ stage (Zaber, 60 mm travel, resolution 0.1 µm, TLA 60A actuators connected to TSB 60-M stages). Data analysis (lock-in experiments) and positioning were attained through in-house-written software (VB6).36 The electrodes were initially hand polished to a mirrorlike finish in a conventional manner. A three-electrode system (using mercury/mercurous sulfate, MMS, as the reference electrode and a Pt counter electrode) was employed in all experiments. Electrochemical data were acquired on an in-house-constructed potentiostat interfaced to a PC through an ADC card (computer board type PCI-DAS1602/16). Software, to determine either conventional cyclic voltammetry or the HMV signal, was developed in-house. Solutions were prepared using a Purite Select Fusion 160 (Ondeo) water purification system (resistivity typically >15 MΩ cm and a TOC < 10 ppb). H2SO4 (98%, Fisher Scientific) was used as received. The Pt nanostructured electrodes were deposited on a set of 0.5 mm diameter Pt disk electrodes, a 50 µm diameter Pt microdisk electrode, or commercially available RRDEs (with either the ring only modified or the ring and the disk modified). The preparation of the mesoporous electrodes followed the procedure previously described.16 After deposition, the electrodes were removed from the cell and allowed to soak in deionized water, which was regularly replaced to remove the surfactant. Voltammetry of the electrodes in sulfuric acid as described previously was used to determine the roughness factor (reported in the appropriate figure).37 To complement and explain the electrochemical experimental data, a model circuit was constructed to mimic rapid changes in the faradaic component such as those experienced in HMV experiments. This circuit was controlled using digital lines from

Figure 1. Schematic representation of the model circuit and experimental arrangement used to measure the currents flowing in each part of the equivalent circuit. Here WE represents the working electrode, R/C represents the reference and counter electrodes, Ru represents the uncompensated resistance, FR1 and FR2 represent the faradaic resistances, Cdl represents the double-layer capacitance, S1 and S2 represent switches operated by a 0-5 V signal, FG represents the function generator controlling the mass transfer step, UGDA represents the unity gain differential amplifier, and Amp(×100) represents the amplifier used to increase the capacitance signal for measurement purposes.

an ADC card, a function generator, and a PC. Figure 1 shows a schematic of the circuit and the experimental arrangement. This circuit enabled a set of three different capacitances (as well as no capacitance) to be selected as required. Switching between different faradaic resistances was controlled by a potential square wave from a function generator (TGA12101 100 MHz arbitrary waveform generator, TTi Ltd.). The solid-state switch employed had an “on” resistance of ∼5-8 Ω and is included in the modeling of the data. The current flowing in and out of the capacitor (the double-layer equivalent) was monitored by the potential drop across a 1 Ω resistor placed in the circuit in series with the capacitance. The potential across the 1 Ω resistor was then measured with a unity gain differential amplifier (INA105KP). The resultant voltage signal from this component was then amplified (×100) before being recorded. The capacitive (doublelayer) current, the total current supplied by the potentiostat, and the current flowing through each of the faradaic resistors were recorded simultaneously on a PC through an ADC card and bespoke software (VB6). Normally 200 transients were recorded in each experiment and averaged to improve the signal-to-noise ratio; this was particularly necessary for measuring the current passed from the double-layer capacitance. Note that, under the conditions employed, the voltage drop across the 1 Ω resistor (chosen to be as minimally invasive in the circuit as possible) was on the order of 0.4 mV at its maximum value. Results and Discussion Figure 2 shows the data obtained for a nanostructured platinum electrode with a roughness factor of 281. The HMV response of this electrode to molecular oxygen reduction was found to be broadly similar to the results presented previously. However, when scanning was done below -0.35 V vs MMS, an anomalous effect was observed. It was noted that as the electrode entered the hydride region the HMV signal dropped by ca. 70% of its maximum value. The hysteresis in the molecular oxygen signal was also affected (see Figure 2, IHMV reverse scan, red dashed line). Interestingly, the averaged current

13444

J. Phys. Chem. C, Vol. 114, No. 32, 2010

Figure 2. Time-averaged current signal (Iav) and HMV signal (IHMV) as a function of the electrode potential recorded at a 0.5 mm diameter nanostructured Pt electrode (RF ) 280.8) in aerobic 1 mol dm-3 sulfuric acid solution. Note the experimental data were gathered with the jet on. The sweep rate was 20 mV s-1. The oscillating jet was modulated at a frequency of 16 Hz and with a piston displacement amplitude (zeroto-peak) of 0.011 ( 0.001 mm. The insets show a series of current-time traces recorded at different potentials. The temperature of the solution was 18-22 °C.

signal (Iav, blue solid line) does not show the current drop-off observed for the HMV data. The current-time response of the electrode is illustrated in the insets in Figure 2. These show how the amplitude of the signal varies at different potentials over the range of interest. Clearly, there is no ac signal observed at the potential +0.4 V vs MMS (see Figure 2, inset A) because of the absence of any solution-phase redox processes in this potential region. This potential region corresponds to the platinum oxide region on polycrystalline platinum. However, as the electrode potential progresses negatively, the electrochemical reduction of molecular oxygen is initiated. The amplitude of this signal reaches a maximum at ∼-0.3 V vs MMS, and the periodic nature of the signal can be clearly seen (see Figure 2, inset B). This corresponds to periodic forced convection of the solution as a result of the pulsating jet employed. However, the signal from the pulsating jet almost disappears as the electrode potential enters the -0.3 to -0.6 V vs MMS region. This can be seen in Figure 2, inset C, where the electrode potential is sufficiently negative for the reduction of molecular oxygen to be expected at the mass transfer limited rate. However, a significantly smaller 16 Hz can be observed. Interestingly, the time-averaged current (Figure 2, blue solid line) recorded simultaneously with the HMV signal shows no such signal perturbation within the same potential region. Indeed, this signal shows the classic surface electrochemistry for polycrystalline platinum expected under the conditions employed. In addition, a small contribution from forced mass transfer of molecular oxygen was also observed as expected (see previous papers). The unusual loss in signal in this potential region is intriguing and merits further discussion. First, we will consider the mechanisms that are known to perturb the voltammetry of molecular oxygen on a polycrystalline platinum surface. Second, we will consider the effect of double-layer capacitance on transient faradaic electrochemical events. Turning to the mechanistic possibilities, two possible explanations should be considered. The first mechanistic consideration involves pH perturbations (in this case consumption of protons)

Kuleshova et al. associated with the surface electrochemistry of polycrystalline platinum over this potential range. The second mechanistic consideration considers the effect of a change in the apparent number of electrons consumed in the reduction of molecular oxygen. Considering the first mechanistic explanation (pH), it should be noted that the electrochemical removal of the platinum oxide layer and the formation of platinum hydride (underpotential deposition (UPD) of atomic hydrogen on the surface of the platinum) both consume protons. Hence, it is reasonable to consider the possibility of a local pH increase to be the cause of the perturbation in the reduction of molecular oxygen observed on this nanostructured Pt surface. However, as we shall argue here, this effect cannot be responsible for the perturbation observed in the HMV data for a number of different reasons. First, the experiment was performed in a convective solution containing 1 mol dm-3 H2SO4. This provides a considerable reservoir of H+ ions within the porous structure and adjacent to the electrode surface. Again the voltammetry shown in Figure 2 is instructive. If we integrate the time-averaged voltammetry (blue solid line, Figure 2) between +0.3 and -0.1 V vs MMS, a charge of 0.28 mC can be determined for the platinum oxide stripping process. This is more than that of the PtHUPD process (0.21 mC), which occurs between -0.3 and -0.65 V vs MMS. Hence, one would suggest that the pH perturbation as a result of oxide stripping is of a greater magnitude than that produced by the formation of the PtHUPD. However, the severe perturbation in the oxygen signal is most significant within the PtHUPD region. These observations suggest that a pH perturbation cannot be responsible for the loss in HMV signal observed. Further to this argument, the structure of the PtHUPD region (in the potential region -0.35 to -0.65 V vs MMS) in the time-averaged data is also illustrative. In this case the positions of the hydride formation and stripping peaks (which are known to be sensitive to localized pH changes) are essentially the same for both the forward and reverse sweeps. Hence, the shape of the timeaveraged signal and consideration of the solution constituents imply that a localized pH change is not responsible for the perturbations observed. The second possible mechanistic explanation is associated with a reduction in the number of electrons exchanged on reduction of molecular oxygen. The electrochemical reduction of molecular oxygen may be considered as two parallel reaction pathways with H2O2 formation as an intermediate species. The production of H2O2 decreases the molecular oxygen reduction signal from a maximum of four electrons per molecule of oxygen for complete reduction to water to two electrons if hydrogen peroxide is the sole product. Clearly, the anomalous current drop-off (see Figure 2) could be caused by the production of hydrogen peroxide within the hydride region. In the following section we assess H2O2 production at both polished and nanostructured Pt substrates using a rotating ring disk electrode (RRDE) in an attempt to clarify the issue. Damjanovic et al. introduced a way of using the RRDE to distinguish between H2O2 as an intermediate in the reduction of O2 to water.38 To investigate the apparent number of electrons exchanged for oxygen reduction, a similar RRDE experiment was performed. However, in this case a nanostructured platinum disk and a polished disk were compared for their ability to produce hydrogen peroxide during molecular oxygen reduction in sulfuric acid. Note that in this experiment molecular oxygen was reduced at the disk’s surface, which was swept through an appropriate potential range. The “downstream” Pt ring (which has been nanostructured to ensure good H2O2 detection char-



Id ) nappFAkmcox ) θ(2FAkmcox) + (1 - θ)(4FAkmcox) where θ is the fraction of molecular oxygen converted to H2O2, A represents the geometric electrode area, F represents Faraday’s constant, km represents the mass transfer coefficient for transport of molecular oxygen to the disk electrode surface, and cox represents the concentration of molecular oxygen in solution. Hence, the apparent number of electrons can be shown to be

napp ) 2θ + 4(1 - θ)

(1)

In addition, the value of θ can be given by

θ)

2 x+2

(2)

where x is the ratio of the four-electron current passed at the disk to the two-electron current passed at the disk.38 Damjanovic et al. reported that, under acidic conditions, the value of x could be related to the disk current, ring current, and collection efficiency:38

x) Figure 3. (a) Cyclic voltammograms recorded at a polished Pt disk in 1 mol dm-3 aerobic H2SO4 (rotation speed (red line) 0 rpm and (black line) 2500 rpm, potential scan rate 50 mV s-1). (b) Current-potential curves recorded at a nanostructured Pt ring. The ring’s potential was held at +0.4 V vs MMS. The values on the lower right y-axis represent the estimated number of electrons (napp) during oxygen reduction on the Pt disk calculated using eqs 1-3. Note that this is valid for the mass transfer limited potential region only. The temperature of the solution was 18-22 °C.

acteristics3 (see the Experimental Section for further details)) was held at a potential to detect any resulting H2O2 production. The evaluation of the ring current as a function of the disk potential should enable the apparent number of electrons (napp) associated with molecular oxygen reduction to be assessed. Figure 3a shows the voltammetry recorded at a polished platinum disk under aerobic conditions in the presence (black line) and absence (red line) of electrode rotation. At all times the ring potential was held at +0.4 V vs MMS corresponding to the mass transfer limited potential for H2O2 oxidation.3 In the absence of rotation the voltammetry shows classic surface electrochemistry. However, molecular oxygen electrochemistry is still present but masked by the relatively high surfacedependent signals. In the presence of rotation a clear voltammetric wave for molecular oxygen electroreduction was observed between +0.2 and -0.65 V vs MMS. Figure 3b shows the corresponding ring current in the absence (red line) and presence (black line) of electrode rotation. In the absence of rotation, no ring signal was observed over the entire potential range as expected. However, in the presence of rotation, H2O2 was detected from +0.1 to -0.6 V vs MMS. Note that the majority of the H2O2 signal appears when the Pt surface approaches full coverage with PtHUPD. To assess the apparent number of electrons involved in the reduction of molecular oxygen, the following protocol was adopted. The total current recorded at the disk electrode (Id) can be expressed as the sum of two- and four-electron contributions:

IdN -1 Ir

(3)

Note that only part of the intermediate H2O2 can be captured by the ring electrode and oxidized to O2. Therefore, N (the collection efficiency) has to be included. The collection efficiency for this system was determined by experiment and found to be 0.214 ( 0.001 for these electrodes.7 This is in good agreement with the value expected from the dimensions of the ring, disk, and spacer predicted by Albery and Hitchman.39 Figure 3b shows the actual napp values (see right y-axis) calculated using the method described in eqs 1-3. Note that, to calculate these numbers, the value of Id is assumed to be 178.5 µA and approximately constant over the mass transport limited range. The RRDE experiments show that while hydrogen peroxide is generated on the polycrystalline Pt surface, the value of napp is still 3.87 at the potential corresponding to the maximum perturbation observed in the HMV signal (see Figure 2). This value demonstrates that approximately 93% of the oxygen reaching the Pt disk surface is fully reduced to water through the four-electron pathway at this potential. The same series of experiments were repeated for a nanostructured disk RRDE. Figure 4a shows the voltammetry of the disk electrode. This shows the enhanced signals for PtHUPD formation and stripping and platinum oxide formation and stripping as expected. In addition, in the presence of electrode rotation (black line), a clear molecular oxygen reduction signal was observed at the disk. Interestingly, hydrogen peroxide production is only marked below -0.55 V. However, a small “pulse” of H2O2 production is seen at +0.1 V vs MMS on the cathodic scan. This presumably corresponds to the case where few surface sites are available for oxygen reduction as adsorbed oxide species stripping is initialized at the disk electrode surface. This assumption is supported by several experimental observations. First, the pulse was found to disappear if O2 was removed from the liquid by argon sparging. Second, the pulse height increased with oxygen saturation. Third, the pulse disappeared if rotation of the RRDE was terminated. However, over the entire potential region the amount of hydrogen peroxide produced is less than on the corresponding polished Pt surface.

13446


Kuleshova et al.

Figure 5. HMV signal (IHMV) as a function of the electrode potential recorded at a set of 0.5 mm diameter nanostructured Pt electrodes (RF included in the figure in the range 42.4-280.8) in aerobic 1 mol dm-3 sulfuric acid solution. Note the experimental data were gathered with the jet on. The sweep rate was 20 mV s-1. The oscillating jet was modulated at a frequency of 16 Hz and with a piston displacement amplitude (zero-to-peak) of 0.011 ( 0.001 mm. The temperature of the solution was 18-22 °C.

Figure 4. (a) Cyclic voltammograms recorded at a nanostructured Pt disk in 1 mol dm-3 aerobic H2SO4 solution (rotation speed (red line) 0 rpm and (black line) 2500 rpm, potential scan rate 20 mV s-1). (b) Current-potential curves recorded at a nanostructured Pt ring. The ring’s potential was held at +0.4 V vs MMS. The values on the lower right y-axis represent the estimated number of electrons (napp) during oxygen reduction on the Pt disk calculated using eqs 1-3. Note that this is valid for the mass transfer limited potential region only. The temperature of the solution was 18-22 °C.

This is indicated by the higher apparent number of electrons shown on the right y-axis in Figure 4b (note that Id for the mass transfer limited reduction of molecular oxygen is assumed to be ∼186 µA in this system). Indeed, the RRDE experiment shows that the value of napp at the maximum perturbation in the HMV signal (see Figure 2, -0.59 V vs MMS) is 3.98. This value demonstrates that approximately 99% of the oxygen reaching the Pt disk surface is fully reduced to water through the four-electron pathway at this potential. This is greater than that of the polished electrode. These results indicate that the nanostructured electrode shows an increased efficiency for the reduction of molecular oxygen in agreement with previous studies.1,21 Clearly, the results reported here (for Pt polished and nanostructured RRDEs) indicate that the drop in the HMV signal amplitude, shown in Figure 2, is unlikely to be attributed to a change in the oxygen electrochemistry at the Pt surface investigated. Clearly, both surfaces consume molecular O2 predominantly in a four-electron mechanism. Hence, other factors must be considered. This is the subject of the following section. An indication of the origin of this effect can be gathered from the influence of surface roughness on the perturbation of the signal. An earlier investigation of a similar electrode with a smaller roughness factor did not show any perturbation of the HMV signal in this potential region. However, increasing the roughness factor of the electrode was found to have a significant impact on the HMV amplitude of molecular oxygen reduction. To show this, a set of nanostructured platinum electrodes, with

Figure 6. Capacitance (dQ/dV, black line) and HMV current (IHMV, blue solid circles) profiles as a function of the applied potential for the hydrogen adsorption process at a platinum electrode (500 µm diameter, RF ) 280.8) surface in 1 mol dm-3 sulfuric acid solution. The HMV sweep was performed at 20 mV s-1. The jet was modulated at a frequency of 16 Hz with a piston displacement amplitude of 0.011 ( 0.001 mm.

differing surface roughness factors, were fabricated using the same liquid crystal templating technique described previously. These electrodes were prepared with a range of RFs from ∼40 to 300 (the exact values are reported in the appropriate figure). Figure 5 shows the HMV response of these platinum electrodes as a function of the electrode potential. These results show that the perturbation in the HMV molecular oxygen signal becomes more significant as the roughness factor (RF) of the electrode increases. It is also interesting to note that the shape of the signal perturbation is most pronounced in the PtHUPD adsorption/ desorption region. Clearly, further consideration of the characteristics of these electrodes (excluding those ruled out above) is necessary. It is instructive at this point to consider the shape of the perturbation and the pseudocapacitance of the nanostructured electrodes employed. Figure 6 shows a comparison of the pseudocapacitance calculated from the time-averaged voltammetry of the electrode (see Figure 2, blue solid line) plotted as a function of the electrode potential. Included on the same plot

Contribution of the Double Layer to Faradaic Processes is the HMV signal recorded at the same time. Figure 6 shows that the perturbation and shape of the HMV signal coincide with the pseudocapacitance of the electrode. Hence, further consideration of this observation is necessary. The effect of double-layer capacitance on electrochemical systems is well-known and is normally considered as paramount to the interpretation of the response of an electrode observed during a voltage perturbation (for example, during a potential step, voltammetry, or ac impedance investigations).7 In the results presented here the voltage perturbation on the system is only associated with the sweep of the electrode potential within the cyclic voltammetry technique. In addition, in the absence of an imposed potential perturbation (for example, if the scan is stopped), the HMV signal remains suppressed. Hence, the mechanism behind this phenomenon is not associated with the sweep itself. In the next section we will argue that the perturbation in the HMV signal is associated with the unusually high capacitance of the electrodes within the potential region chosen. In addition, we propose that rather than the double layer being a passive component, it can be directly involved, under appropriate physical conditions, with transient faradaic processes. It is important at this point to consider an equivalent circuit for an HMV electrochemical cell.33 Note that more complex HMV equivalent circuits can be found in the literature.40 However, here we simplify the system to simulate a step change in the hydrodynamic conditions. This matches the experimental system employed in the pulsating jet and other literature examples.33 Figure 7 shows the test circuit employed. In this system the faradaic component varies from one value to another in a periodic manner (this represents a change in the mass transfer characteristics, as in HMV, or a concentration step). Here FR(A) and FR(B) represent two differing values of the faradaic resistance. In turn, the current supplied by the potentiostat varies from I(A) to I(B). Under static conditions the double layer gives no contribution to the system. However, at the point of faradaic resistance change, a re-equilibration of charge from the double layer is necessary. This is due to the changing value of the voltage drop across the uncompensated resistor as the current value varies from I(A) to I(B) and vice versa. To test this hypothesis, a test circuit was constructed (see Figure 1). Here transient changes in the faradaic resistance were initiated by a solid-state switch controlled by a 0-5 V square wave supplied by a function generator. This particular system stepped the faradaic resistance from 2 to 1 kΩ and vice versa in a repetitive manner. During this transition the current flowing into and out of the capacitor (the double-layer analogue) was measured as a voltage drop across a 1 Ω resistor placed in series with this component. The current flowing from the potentiostat (which imposed a voltage on the circuit of 1 V) and the current flowing through each of the faradaic resistors (see Figure 1, FR1 and FR2) were also monitored simultaneously as a function of time. Figure 8 shows a collection of results obtained from this circuit. Parts a, b, and c of Figure 8 represent the responses of the circuit when the double-layer capacitance was 10, 100, and 1000 µF, respectively. Note the symbols in Figure 8 represent the experimental data, while the lines represent the calculated current. To calculate the currents flowing from the capacitor and the potentiostat, the circuit was modelled as a set of components and two voltage sources. With reference to Figure 7, the first voltage source represents the constant voltage applied by the potentiostat (Epot), while the second (Ecap(A or B)) corresponds to the voltage applied by the double-layer capacitance under the two conditions of faradaic resistance. This problem can be solved by applying Kirchhoff’s first and second


Figure 7. Representation of the equivalent circuit with the currents and potential distribution within the system as the faradaic resistance value periodically varies.

laws to the circuit.41 For example, Kirchhoff’s laws enable us to write

If ) I(A) + Icap

(4)

Epot ) I(A)Ru + (I(A) + Icap)FR

(5)

Ecap(A) ) IcapS + (I(A) + Icap)FR

(6)

where S represents the sum of the resistance of the solid-state switch (S2, see Figure 1) and the 1 Ω resistor. Solving eqs 5 and 6 simultaneously allows us to write expressions for Icap and Ipot in terms of the other components in the circuit:

Icap )

FREpot - (FR + Ru)Ecap FR2 - (FR + Ru)(S + FR) Ipot )

Epot - IcapFR Ru + FR

(7)

(8)

Finally, to calculate the currents flowing in the circuit from the point where the switch S1 is closed (to generate a new value of FR), eqs 7 and 8 are employed in conjunction with the initial potential of the capacitor prior to the switch (S1) closing. In

13448


Kuleshova et al.

Figure 9. HMV signal (IHMV, red line) and average current signal (Iav, blue line) as a function of the electrode potential recorded at a 50 µm diameter nanostructured Pt microelectrode (RF ) 941) in 1 mol dm-3 sulfuric acid solution. The plot shows the results with the jet on (J) and the jet off (NJ). The sweep was performed at 20 mV s-1. The jet was modulated at a frequency of 16 Hz and with a zero-to-peak piston displacement amplitude of 0.014 ( 0.001 mm. The temperature of the solution was 18-22 °C.

Figure 8. Response of the test circuit compared to the predicted currents. Here the symbols b, O, and ∆ represent the measured signals from the test circuit for the current measured by the potentiostat, the current flowing from the capacitor, and the current flowing through the faradaic resistors, respectively. The predicted currents are shown as a red solid line for the potentiostat, a red dotted line for the current flowing from the capacitor, and blue solid line for the faradaic resistances. Note that the values employed in the test circuit for the capacitance were 10, 100, and 1000 µF for (a), (b), and (c), respectively, while the best fit to the data was 8.5, 107, and 1080 µF for (a), (b), and (c), respectively. In all cases the value of Ru was 100 Ω and a potential of 1 V was placed across the circuit. The value of S was 6 Ω, and the faradaic resistances (FR) were stepped from 2 to 1 kΩ at time t ) 0 s.

each time step the charge expended by the capacitance is calculated and then used to determine the new potential of the capacitor (Ecap). In this way the currents flowing in each section of the circuit can be numerically calculated as the capacitor equilibrates. The value of Ecap is continuously re-evaluated after

each time step until Icap ) 0. This occurs when the condition FREpot ) (FR + Ru)Ecap is satisfied. Figure 8 shows that the currents flowing in the test equivalent circuit closely match those predicted by the method described above within the tolerances of the components employed. Figure 8c is particularly important as the values of Cdl and Ru closely match those estimated in the HMV system of the RF ) 280 nanostructured electrode. Clearly, under the conditions stated, the electrochemical system is unable to respond to the 16 Hz pulsation provided by the oscillating jet used in the HMV apparatus (note that the period of the jet is of the order of 62 ms compared to ∼350 ms for the complete response of the electrode). These observations suggest that the electrochemical reduction of molecular oxygen is maintained under mass transfer control within the potential region where the perturbation in the HMV signal was observed. However, during the HMV process, electrons are supplied not solely by the potentiostat but are continuously exchanging between the potentiostat and the double-layer equilibration process. Hence, electroneutrality is maintained at all times, and a time-averaged signal is recorded from the potentiostat. This is clearly supported by Figure 2, which shows that the time-averaged voltammetry behaves as expected under the conditions employed. If the roughness factor (and hence pseudocapacitance) of the electrode is reduced, then the HMV signal should return. This is again observed and shown in Figure 5. Finally, this argument has some interesting permutations. For example, what consequences are there for general HMV systems? We are already in a position to investigate the limitations of this technique. The capacitive damping effects, observed here, imply that large electrodes with high surface roughness and in the presence of an uncompensated resistance will not be able to respond to even modest dynamic changes in the mass transfer regime. However, if the electrode geometric area were to be reduced, then the HMV response should be restored. Figure 9 shows just such an experiment. In this case a high surface area nanostructured microelectrode has been fabricated with an impressive RF of 941. However, this was a 50 µm diameter Pt microelectrode. The HMV analysis clearly shows no damping effect for the reduction of molecular oxygen over the complete voltammetry studied (including the hydride region). This is expected as even though the roughness factor is greater by a factor of 3 compared to that of the largest 500



TABLE 1: Estimated Response Times of a Variety of Literature HMV Techniquesa estimated 1/RC

frequency range employed/s-1

HMV type

experimental

HMRDE12 porous electrode26 CF-MJE23 FT HMRDE45 vibrating microwire13

0.316 cm2 5.9 cm2 RVC disk 25 µm diameter disk 2.8 mm diameter RDE 800 µm diameter wire × 3 mm

3516-35.16 Hz 188-1.88 Hz 226-2.26 MHz 18 kHz-180 Hz 14 kHz-139 Hz

3 step change 0.67 0.02-12.6 160

vibrating planar microband46

10 µm × 2 mm 1 mm2

5.3 MHz-55 kHz 111-1.1 kHz

2-50

comments no effects expected possible as RC-like response reported no effects expected no effects expected possible for larger electrodes employed or higher uncompensated resistance; could contribute to “hydrodynamic efficiency” effects no, although a large planar electrode was quoted as not showing a modulated response; in addition, the cell configuration was quoted as either two or three electrodes

a Note that in many cases Ru values are not known (through use of either two- or three-electrode systems or unusual electrode geometries). Hence, we will give a range of 10-1000 Ω for Ru within the calculations. A typical Cdl value of 90 µF cm-2 is assumed in all cases (a roughness factor of 3 for normal electrodes).

µm diameter electrode system reported in Figure 2; the geometric surface area (and hence capacitance) is a factor of 100 smaller. Hence, under these conditions the double-layer pseudocapacitance is ∼30 times less than that for the 500 µm diameter Pt nanostructured electrodes described previously. This improves the response time of this electrode and avoids the dramatic capacitive damping observed in Figure 2. The experiments and conclusions drawn from the above discussion apply to HMV experiments, but where would these effects be observed? The results reported here imply that high surface area electrodes are limited to low mass transfer modulation frequencies in HMV applications. Also as the frequency regime of the HMV system rises, the electrode capacitance and the uncompensated resistance will be more significant. Considering these factors, it is important to consider the available literature. Table 1 lists some of the available literature and estimates of “RC” constants in comparison to the frequency regime employed. Note that the response of the electrode will not follow precisely an RC-like behavior but is used here as an estimate of the time scale of the HMV system. See eqs 7 and 8, the associated text, and the EHD literature (see Deslouis et al.29-33) for a more accurate estimation of the true response of the electrode to a change in the faradaic reaction. Table 1 indicates that, for most systems reported in the literature, the experimental conditions (frequency range, area of electrodes, and uncompensated resistance, etc.) do not allow for this “damping effect” to be observed. However, some exceptions may be noted. For example, the microwire experiments where higher frequencies and microwire electrodes have been combined may be expected to encounter this capacitive damping effect.13 In addition, experiments with large surface area porous electrodes may also be limited by this effect.26 However, further investigation of these systems is required before a definitive assignment can be made. Lastly, it should be noted that the effect of the double layer on a transient faradaic process has been noted previously.42-44 In this case electrochemically active species were generated by a transient light source in front of a rotating disk electrode. To successfully model the response of the RDE to the light pulse, the effect of the double layer on the response in combination with an appropriate kinetic model to describe the chemistry involved was invoked. However, the contribution of this capacitive damping effect to HMV systems of bare electrodes is normally ignored30 (although modified electrodes with higher capacitance, for example, poly(aniline)-modified interfaces, have been studied using EHD29,30,33). The results reported here clearly indicate that under suitable conditions (for example, high surface roughness combined with a suitable frequency domain) it is also necessary to consider the effect of the double layer on an HMV

system (or wherever transient faradaic responses are encountered). Further investigation of the consequences of this effect is currently under way. Conclusions The HMV analysis of a set of high surface area electrodes has been undertaken. An anomalous “damping” effect upon the electrochemical HMV signal for molecular oxygen reduction has been observed in the high pseudocapacitance region of platinum. Further to this, this damping effect is not caused by a change in the apparent number of electrons or a pH change. Rather the effect is due to a capacitive effect (in association with the uncompensated resistance of the system) within the electrochemical cell. Analysis of a test circuit supports this conclusion, and modelling using Kirchhoff’s first and second laws also allows a numerical prediction to validate the experimental data. Thus, the damping effect is due to the electrochemical characteristics of the cell and this suggests that the double layer is an active part of the HMV system under the conditions stated. Implications for other HMV systems are also suggested. Acknowledgment. We thank the RSC/EPSRC for funding J.K. with an analytical studentship under Grant EP/C011430/1 and Prof. Phil Bartlett for useful discussions. References and Notes (1) Birkin, P. R.; Elliott, J. M.; Watson, Y. E. Chem. Commun. 2000, 1693. (2) Antoine, O.; Durand, R. J. Appl. Electrochem. 2000, 30, 839. (3) Evans, S. A. G.; Elliott, J. M.; Andrews, L. M.; Bartlett, P. N.; Doyle, P. J.; Denuault, G. Anal. Chem. 2002, 74, 1322. (4) Schneider, A.; Colmenares, L.; Seidel, Y. E.; Jusys, Z.; Wickman, B.; Kasemo, B.; Behm, R. J. Phys. Chem. Chem. Phys. 2008, 10, 1931. (5) Stamenkovic, V. R.; Fowler, B.; Mun, B. S.; Wang, G. F.; Ross, P. N.; Lucas, C. A.; Markovic, N. M. Science 2007, 315, 493. (6) Elliott, J. M.; Birkin, P. R.; Bartlett, P. N.; Attard, G. S. Langmuir 1999, 15, 7411. (7) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and Applications, 2nd ed.; John Wiley & Sons, Inc.: New York, 2001. (8) Adams, R. N. Electrochemistry at Solid Electrodes; Marcel Dekker, Inc.: New York, 1969. (9) Wang, J. Talanta 1981, 28, 369. (10) Macpherson, J. V. Electroanalysis 2000, 12, 1001. (11) Williams, D. E.; Macpherson, J. V. Hydrodynamic modulation methods in electrochemistry. In ComprehensiVe Chemical Kineticss Applications of Kinetic Modelling; Compton, R. G., Hancock, G., Eds.; Elsevier: Amsterdam, 1999; Vol. 37, p 369. (12) Miller, B.; Bruckenstein, S. Anal. Chem. 1974, 46, 2026. (13) Schuette, S. A.; McCreery, R. L. Anal. Chem. 1986, 58, 1778. (14) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1999, 71, 4642. (15) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1999, 71, 2939. (16) Attard, G. S.; Bartlett, P. N.; Coleman, N. R. B.; Elliott, J. M.; Owen, J. R.; Wang, J. H. Science 1997, 278, 838.

13450


(17) Imokawa, T.; Williams, K. J.; Denuault, G. Anal. Chem. 2006, 78, 265. (18) Nie, M. Y.; Elliott, J. M. J. Mater. Sci. Technol. 2005, 21, 863. (19) Braun, P. V.; Osenar, P.; Stupp, S. I. Nature 1996, 380, 325. (20) Whitehead, A. H.; Elliott, J. M.; Owen, J. R. Nanostructured tin for use as a negative electrode material in Li-ion batteries. Presented at the 9th International Meeting on Lithium Batteries, Edinburgh, Scotland, 1998. (21) Jiang, J. J.; Kucernak, A. Electrochem. Solid State Lett. 2000, 3, 559. (22) Blaedel, W. J.; Wang, J. Anal. Chem. 1979, 51, 799. (23) Simjee, N.; Unwin, P. R.; Macpherson, J. V. Electroanalysis 2003, 15, 1445. (24) Pratt, K. W.; Johnson, D. C. Anal. Chim. Acta 1983, 148, 87. (25) Blaedel, W. J.; Engstrom, R. C. Anal. Chem. 1978, 50, 476. (26) Blaedel, W. J.; Wang, J. Anal. Chem. 1980, 52, 1697. (27) Miller, B.; Bruckenstein, S. J. Electrochem. Soc. 1974, 121, 1558. (28) Miller, B.; Rosamilia, J. M. Abstr. Pap.sAm. Chem. Soc. 1983, 186, 44. (29) Deslouis, C.; Musiani, M. M.; Tribollet, B. J. Electroanal. Chem. 1989, 264, 37. (30) Deslouis, C.; Musiani, M. M.; Tribollet, B. J. Electroanal. Chem. 1989, 264, 57. (31) Deslouis, C.; Tabti, N.; Tribollet, B. J. Appl. Electrochem. 1997, 27, 109. (32) Deslouis, C.; Tribollet, B. Electrochim. Acta 1990, 35, 1637.

Kuleshova et al. (33) Deslouis, C.; Tribollet, B. Flow modulation techniques in electrochemistry. In AdVances in Electrochemical Science and Engineering; Gerischer, G., Tobias, C. W., Eds.; VCH: New York, 1990; Vol. 2; p 205. (34) Kuleshova, J.; Birkin, P. R.; Elliott, J. M. J. Electroanal. Chem. 2008, 617, 185. (35) Kuleshova, J.; Birkin, P. R.; Elliott, J. M. J. Electroanal. Chem. 2009, 636, 68. (36) Kuleshova, J. Ph.D. Thesis, University of Southampton, 2008. (37) Elliott, J. M.; Attard, G. S.; Bartlett, P. N.; Coleman, N. R. B.; Merckel, D. A. S.; Owen, J. R. Chem. Mater. 1999, 11, 3602. (38) Damjanovic, A.; Genshaw, M. A.; Bokris, J. O. M. J. Electrochem. Soc. 1966, 70, 3761. (39) Albery, W. J.; Hitchman, M. L. Ring-Disc Electrodes; Clarendon Press: Oxford, U.K., 1971. (40) Martem’yanov, S. A.; Grafov, B. M. SoV. Electrochem. 1988, 24, 94. (41) Morley; A. Hughes, E. Principles of Electricity; Longmans: London, 1961. (42) Dahnke, K. F.; Fratoni, S. S.; Perone, S. P. Anal. Chem. 1976, 48, 296. (43) Fratoni, S. S.; Perone, S. P. Anal. Chem. 1976, 48, 287. (44) Fratoni, S. S.; Perone, S. P. J. Electrochem. Soc. 1976, 123, 1672. (45) Schwartz, D. T.; Stroeve, P.; Higgins, B. G. J. Electrochem. Soc. 1989, 136, 1755. (46) Williams, D. E.; Ellis, K.; Colville, A.; Dennison, S. J.; Laguillo, G.; Larsen, J. J. Electroanal. Chem. 1997, 432, 159.

JP102308P

Contribution of the Double Layer to Transient Faradaic Processes

Recommend Documents