Room-Temperature

Nonlinearities (instabilities) at the charged interfaces1-30 that are different from ... A hanging mercury drop electrode (area = 0.018 cm2; model CGM...
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J. Phys. Chem. B 2007, 111, 12849-12856

12849

Nonlinear Phenomena at Mercury Hg Electrode/Room-Temperature Ionic Liquid (RTIL) Interfaces: Polarographic Streaming Maxima and Current Oscillation Md. Mominul Islam, Muhammad Tanzirul Alam, Takeyoshi Okajima, and Takeo Ohsaka* Department of Electronic Chemistry, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Mail Box G1-5, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan ReceiVed: July 22, 2007

The polarographic streaming maxima and cyclic voltammetric anodic current oscillation (CVACO) at a hanging mercury drop electrode (HMDE) in room-temperature ionic liquid (RTIL) have been studied for the first time using cyclic voltammetric, potential step chronoamperometric and pulse voltammetric techniques. The reversible redox reaction of the 2,1,3-benzothiadiazole (BTD)/BTD•- (an anion radical of BTD) couple with a formal potential (E0′) of -1.36 V versus Ag/AgCl/NaCl(saturated) in 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIBF4) RTIL was typically employed for this purpose. A maximum was observed at the rising part of the normal pulse voltammogram for the reduction of BTD to BTD•- as well as of the reversed pulse voltammogram for the reoxidation of BTD•- to BTD at the HMDE. The conditions of the initiation and control of the CVACO at the HMDE in EMIBF4 were extensively investigated. Generally, the CVACO was enhanced by increasing the concentration of BTD at a given potential scan rate (υ) and was attenuated by increasing υ. An electrocapillary curve was measured using a dropping mercury electrode in EMIBF4, and the potential of zero charge was determined to be -0.23 V. On the basis of the modern theory of the polarographic streaming maxima of the first kind, the observed streaming maxima and CVACO phenomena are successfully explained to originate from the macroscopic instability at the electrode/solution interface wherein the oscillating mode creates the CVACO.

Introduction Nonlinearities (instabilities) at the charged interfaces1-30 that are different from those induced by the gravitational force31 and that are known to originate from various microscopic physicochemical perturbations owing to namely electrocrystallization, chemical reaction at the electrode vicinity, adsorption, passivation-activation, dissolution (or corrosion), and well-known polarographic streaming phenomena resulting in current (or potential) oscillation have attracted much attention.1-27 Moreover, the vortices (instabilities) in electroosmotic flow and in fluid flow of biochannels or biochips are of individual interest.28-30 For the past decade, our group has devoted tremendous effort9-18 to know the unrevealed origin of the familiar cyclic voltammetric anodic current oscillation (CVACO) observed in the redox reactions at a hanging mercury drop electrode (HMDE) in aprotic solutions.9-26 Recently, using the electrochromic redox reaction of 2,1,3-benzothiadiazole (BTD), we have successfully visualized that a novel circular motion vigorously agitates the HMDE/solution interface, resulting in an unsmooth anodic peak (i.e., oscillation).10 This motion has been shown not to be associated with the gravitational force31 or other process or experimental result (e.g., adsorption or instrumental artifact), and its origin could not be revealed from the classical theories of streaming phenomena.10,11,20,27,32-35 In addition, it has been anticipated that a suitable generation and control of this motion could permit its use as a microtransducer for a mechanical amplification device.10 These facts motivate * To whom correspondence should be addressed. Tel: +81-45-9245404. Fax: +81-45-9245489. E-mail: [email protected].

us to study the so-called CVACO more widely using different electrolytic media. In the present trend of electrochemical works, room-temperature ionic liquids (RTILs) have been advantageously used as the electrolytic media due to their dual roles as the solvent and the electrolyte required for an electrochemical solution, large electrochemical potential window (2-4 V), low vapor pressure, and reasonable thermal stability.13,36-41 The RTILs are ionic in character and highly viscous, and the concentrations of the ions (cation and anion) in RTILs are much larger than those commonly used in the electrochemical media as the supporting electrolyte.36,38 We extensively studied the redox reactions of some organic compounds at an HMDE in RTILs to verify the possibility of the occurrence of the well-known streaming phenomena and the CVACO. In the present paper, we report on the polarographic maxima and CVACO at the HMDE observed during the redox reaction of BTD in 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIBF4) RTIL using cyclic voltammetric, chronoamperometric, and normal and reversed pulse voltammetric techniques. The results obtained in this highly viscous (31.8 cP) and concentrated (6.4 M) ionic solvent (EMIBF4) are inconsistent with the classical concepts on the streaming phenomena20,27,32-35 and are very novel in the history of RTILs. The redox reaction of BTD in EMIBF4 was characterized at a gold (Au) electrode using cyclic voltametry. For a better understanding, the CVACO at the HMDE in dimethyl sulfoxide (DMSO) solution was also investigated. The conditions of the increase and decrease of the CVACO in EMIBF4 and DMSO solutions were examined. Moreover, a typical electrocapillary curve (ECC), drop time versus potential curve,10,43 in EMIBF4 was measured using a dropping mercury electrode (DME). The modern theory44,45 of

10.1021/jp075749b CCC: $37.00 © 2007 American Chemical Society Published on Web 10/18/2007

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the polarographic streaming maxima of the first kind was successfully employed to explain the streaming maxima and the CVACO at the HMDE in EMIBF4. Experimental Section Reagents. 1-Ethyl-3-methylimidazolium tetrafluoroborate with purity of more than 99% and less than 30 ppm (ca. 2.1 mM) water was used as purchased from Stella Chemifa Co. (Japan). Dimethyl sulfoxide of reagent grade was obtained from Kanto Chemical Co. Inc. and dried over activated molecular sieves (4A 1/16, Wako Pure Chemicals Industries) before use. Tetraethylammonium perchlorate (TEAP) (Kanto Chemical Co. Inc.) was used as a supporting electrolyte. Apparatus and Procedures. Cyclic voltammetric, normal and reversed-pulse voltammetric, and chronoamperometric measurements were carried out using a computer-controlled electrochemical system (model 50W, Bioanalytical Systems, Inc. (BAS)). The electrochemical cell was a conventional twocompartment Pyrex glass container with a working electrode, a spiral Pt-wire counter electrode, and a silver (Ag)/silver chloride (AgCl)/sodium chloride [NaCl (saturated)] reference electrode. A hanging mercury drop electrode (area ) 0.018 cm2; model CGME 900, BAS) or a gold (Au, area ) 0.020 cm2) electrode was used as a working electrode. In the case of the HMDE, each experiment was performed at a freshly formed mercury drop as the HMDE. Prior to use, the Au was polished with alumina powder and then washed with Milli-Q water by sonication for 10 min. The Au electrode was also electrochemically pretreated in N2-saturated 0.05 M H2SO4 solution by repeating the potential scan in the range of -0.2 to 1.5 V until the voltammogram characteristic for a clean Au electrode was obtained, and the Au electrode was dried by blowing air. To minimize the IR drop yielded across the cell and the contamination of water into the cell solution, the reference electrode was placed in a glass beaker containing NaCl-saturated aqueous solution and connected to the cell solution via a salt bridge filled with the EMIBF4 or DMSO solution containing TEAP. In the measurement of the ECC, a different reference electrode was used. The reference electrode was a Ag wire coated electrochemically with Cl- ion (i.e., AgCl), called a Ag/AgCl reference electrode,50 and this reference electrode was directly dipped into the EMIBF4 solution. The electrocapillary curve was determined with a homemade natural dropping mercury electrode in an electrochemical cell with the same arrangement of the reference and counter electrodes as described above. To construct the ECC, the mercury drop was allowed to fall through the capillary (the flow rate of Hg, m ) 1.2 mg s-1; drop time, t ) 4.9 s at the height of Hg head and h ) 69 cm in EMIBF4 solution) under different applied potentials. The other features regarding the measurement of the ECC have been well-described in our previous papers.11,50 Before measurements, N2 gas was bubbled directly into the cell to obtain the saturated solutions, and during the measurements, the gas was flushed over the cell solution. All the measurements were carried out at room temperature (25 ( 2 °C). Results Redox Reaction of BTD in EMIBF4. Figure 1 shows a typical CV obtained for the redox reaction of BTD at a Au electrode in EMIBF4 RTIL. The well-defined cathodic and anodic peaks were observed at -1.39 and -1.33 V, respectively. The observed separation between the cathodic and anodic peaks (60 mV) is comparable to the theoretical value for a one-electron reversible redox reaction (i.e., 59 mV).43 In addition, the plot

Figure 1. The typical CV obtained for the redox reaction of BTD at Au electrode in N2-saturated EMIBF4 solution. Potential scan rate: 0.05 V s-1.

of the (anodic and cathodic) peak current versus the square root of potential scan rate (υ1/2) was found to be a straight line passing through the origin, indicating that the redox reaction of the BTD is a diffusion-controlled process.43 Similar cathodic and anodic peaks (at -1.37 and -1.28 V, respectively) have been observed for the redox reaction of the BTD/BTD•- (anion radical of BTD) couple in DMSO solution containing TEAP.10-12 The number of electrons involved in the redox reactions and the peak potentials for the first redox couple of nitrocompounds (aliphatic and aromatic),39,40 aldehydes,41 and benzoquinone46 in imidazolium-cation-based RTILs (e.g., EMIBF4) have been reported to be almost comparable with those in aprotic solutions (DMSO and acetonitrile), except for the so-called ionpairing39-41,46 phenomenon [the ion-pairing process can shift predominantly the formal potential (E0′) of the second redox couple (if any) toward the positive potential39,40]. Thus, the cathodic and anodic peaks observed at -1.39 and -1.33 V (i.e., the E0′ value is the midpoint potential, -1.36 V) in EMIBF4 can be reasonably attributed to a one-electron reduction of BTD to BTD•- and the reoxidation of BTD•- to BTD, respectively; that is, the BTD/BTD•- redox couple. In this study, the BTD/ BTD•- redox couple was typically employed to study the nonlinear phenomena (i.e., polarographic streaming maxima and CVACO) at the HMDE. Current Oscillation at the HMDE in EMIBF4. Figure 2 represents the CVs obtained for the redox reaction of the BTD/ BTD•- couple at the HMDE in N2-satutrated EMIBF4 solution. The cathodic peak was observed as expected for the reduction of BTD to BTD•- (compare with Figure 1), whereas the anodic wave corresponding to the reoxidation of BTD•- to BTD was not smooth (especially in the CV shown in Figure 2b); that is, the shape of the anodic wave is not similar to that obtained at the Au electrode (Figure 1). It is noted that the position and the amplitude of the current spike(s) of the observed CVACO largely change with υ at a given concentration of BTD and that the CVACO is enhanced by increasing the concentration of BTD at a given υ (Figure 2), whereas it is diminished by increasing υ at a given concentration of BTD (Figure 3). That is, the concentration of BTD and υ exert opposite effects on the CVACO (discussed later). It has been known that the CVACO can be characteristically observed at the HMDE for the redox reaction of a compound with E0′ more negative than the potential of zero charge (PZC)

Nonlinear Phenomena at Hg Electrode/RTIL Interface

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Figure 4. CVs obtained for the BTD/BTD•- redox couple at the HMDE in N2-saturated DMSO solutions containing (a, b) 0.1 and (c,d) 0.5 M TEAP. Concentrations of BTD: (a) 0.5, (b, c) 1, and (d) 2 mM. Potential scan rate: 0.1 V s-1.

Figure 2. CVs obtained for the redox reaction of BTD at the HMDE in N2-saturated EMIBF4 solutions. Concentrations of BTD were (a) 5 and (b) 20 mM. Potential scan rates: (a) 0.03 and (b) 0.05 V s-1.

Figure 3. CVs obtained for the redox reaction of 20 mM BTD at the HMDE in N2-saturated EMIBF4 solution. Potential scan rates: (a) 0.05, (b) 0.1, (c) 0.2, and (d) 0.3 V s-1.

in aprotic solutions (e.g., acetone, acetonitrile, N,N-dimethylformamide and DMSO).10,11,14,16,20 Furthermore, the CVACO does not occur (i) at the conventional solid electrodes (e.g., platinum, Au, and glassy carbon electrodes), (ii) at a potential more positive than the PZC, (iii) at a faster υ, (iv) in the solution containing the electrolyte of high concentration, and (v) in the presence of surfactant in the solution.9,11,16-18 In the present case, the characteristics of the CVACO observed in EMIBF4 are similar to those found in the conventional aprotic solutions, but the occurrence of CVACO in the highly concentrated (6.4 M) and viscous (31.8 cP) ionic solution (EMIBF4) is worthy of remark, indeed. The CVACO in DMSO Solution. As mentioned above, the CVACO largely depends on the concentration of BTD and υ. In the case of EMIBF4, we can vary the concentration of BTD,

but unfortunately, the concentration of the so-called supporting electrolyte cannot be changed. To evaluate the effects of the concentrations of the electrolyte and redox species (BTD) and υ on the CVACO, the redox reaction of BTD at the HMDE was extensively studied in DMSO solutions. Figure 4 shows the CVs obtained for the BTD/BTD•- redox couple at the HMDE10,11 in DMSO solutions containing different concentrations of BTD and TEAP. Similarly to our previous paper,10 the current oscillatory phenomenon was observed only in the anodic peak scan. At a constant concentration of TEAP (0.1 M), when the concentration of BTD was 0.5 mM, a weak, broad current peak (oscillation) in the anodic cycle was found at ca. -1.0 V (Figure 4a), but the CVACO was enhanced when the concentration of BTD was increased to 1 mM (Figure 4b). The CVACO could be effectively attenuated with increasing the concentration of TEAP to 0.5 M (Figure 4c) while the concentration of BTD was kept at 1 mM. Interestingly, the CVACO could be retained even in the case of 0.5 M TEAP when the concentration of BTD was increased from 1 to 2 mM (Figure 4d). In addition, the CVACO in the DMSO solution could be damped completely at 0.5 V s-1 (Figure 5) or above, as observed in EMIBF4 RTIL (Figure 3). By comparing Figure 2a with Figure 4a, the current peak at ca. -1.0 V obtained with 5 mM BTD in EMIBF4 would be ascribed to the CVACO. Thus, these results clearly indicate that the concentrations of BTD and TEAP are critical experimental factors dominating the appearance of the CVACO, and the CVACO can be generally observed at threshold conditions of the concentrations of redox species and supporting electrolyte as well as υ (i.e., the time scale of the measurement). Potential-Step Chronoamperometric Response in EMIBF4. Figure 6 represents the chronoamperograms (i-t curves) obtained at the HMDE in N2-saturated EMIBF4 solution containing 20 mM BTD. Two sets of i-t curves were separately measured for the cathodic and anodic processes. For the cathodic process, the initial potential (Ei) was chosen as -0.8 V, at which no faradic process takes place (see Figure 1), and then the electrode potential was stepped to the stepping potential (Es) of -1.6 V (Figure 6A). Since the applied Es (-1.6 V) is more negative than the E0′ (-1.36 V) of the BTD/BTD•- redox couple, the reduction of BTD to BTD•- takes place with time (t). The observed characteristic decrease of the current with t

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Figure 5. CVs obtained for the redox reaction of 1 mM BTD at the HMDE in N2-saturated DMSO solution containing 0.1 M TEAP. Potential scan rates: (a) 0.05, (b) 0.1, (c) 0.2, (d) 0.3, and (e) 0.5 V s-1.

Figure 6. Chronoamperograms (i-t curves) obtained at the HMDE in N2-saturated EMIBF4 solution containing 20 mM BTD. (A) The initial potential was Ei ) -0.8 V, and the holding time at the Ei (t0) was 5 s. (B) Ei ) -1.6 V, and the values of t0 were (b1) 2, (b2) 10, (b3) 12, (b4) 15, and (b5) 20 s.

could be ascribed to the reduction of BTD to BTD•- at a diffusion-controlled condition (faradic process) at the HMDE (i.e., spherical electrode)43 (note: the unsmoothness in the limiting current region of the i-t curve is associated with the instrumental noise). In the case of the anodic i-t curves (Figure 6B), the electrode potential was held at -1.6 V (Ei) for different electrolysis time (t0) and then stepped to -1.2 V (Es) [which is within the oscillatory potential region (see Figure 2)]. Here, because the chosen Ei was more negative than the E0′ of the BTD/BTD•redox couple, the BTD•- species is electrogenerated under a diffusion-controlled condition. Conversely, after the potential step to Es, the reoxidation of BTD•- to BTD takes place,47 and thus, the i-t curves should represent the reoxidation of BTD•to BTD (i.e., a faradic process). Interestingly, the obtained i-t

Islam et al. curves are characterized by an irregular decay with current spikes or current maxima (Figure 6B). Moreover, the magnitude of the current spike (oscillation) increased and its position shifted regularly toward the larger value of the time axis as t0 was increased (discussed later). Similar characteristics were also observed in the i-t curves measured at the HMDE in DMSO solution (data are not shown), but such an oscillation was not observed on the i-t curves obtained for the anodic process at the Au electrode. Previously, we observed the characteristic oscillation on the i-t curve for the reoxidation of the electrogenerated superoxide ion (O2•-) to oxygen (O2) at the HMDE in DMSO solution.9 The present results suggest that the longer t0 is (electrolysis time); that is, the higher concentration of the BTD•- species, the larger the current oscillation at the HMDE is. This observation strongly supports the conditions in which the CVACO can be observed in the CV measurements (described above). Normal and Reversed-Pulse Voltammetry in EMIBF4. The cyclic voltammetric and chronoamperometric measurements showed that the oscillatory phenomena in EMIBF4 can characteristically occur at the HMDE. In this case, the same streaming of the mercury surface as that observed in the conventional protic and aprotic solutions is thought to be operative. In contrast, it has also been known that the adsorption-desorption process (or chemical reaction) of the redox species may initiate the current oscillation as well as polarographic maxima.9,27 According to the literature,27 the HMDE is concerned with two kinds of maxima: the intense maximum with a sharper shape at the rising part of a voltammogram and the weak maximum with a rounded shape occurring at the limiting current region are associated with streaming of the mercury surface (first kind) and the adsorption-desorption process of the redox species (third kind), respectively. Here, normal and reversed-pulse voltammetric techniques were chosen as a probing tool of the type of the process (i.e., streaming of the mercury electrode surface or chemical processes at the electrode) associated with the observed CVACO. The typical normal pulse and reversed-pulse voltammograms (NPVs and RPVs) obtained at the HMDE and the Au electrode in N2-saturated EMIBF4 solution containing 20 mM BTD are shown in Figure 7. In the case of NPVs (Figure 7A), Ei was chosen at -1.0 V, where no faradic process takes place (Figure 1). The NPV obtained at the Au electrode represents the expected S-shaped wave corresponding to the reduction of BTD to BTD•- (dashed line, Figure 7A),43,47 whereas a maximum was observed at the rising part (ca. -1.6 V) of the NPV obtained at the HMDE.27 Similarly to the case of NPV, the RPV obtained at the HMDE possesses a maximum at the rising part (solid line, Figure 7B), but such a maximum was not observed on the RPV observed at the Au electrode (dashed line, Figure 7B). In addition, the steady current (i.e., d.c. current)47 observed in the RPVs at the potential range of -1.6 to ca. -1.45 V is slightly larger at the HMDE than that at the Au electrode. In our previous study,9 the NPV and RPV for the redox reaction of the O2/O2•couple at the HMDE in DMSO solution have been obtained with the maxima of different characteristics: A weak maximum has been observed in the NPV, but in the RPV, similarly to the case of deposition of lead on the mercury electrode surface,45 an intense, broad maximum followed by a decrease of the limiting current toward the zero level of the voltammogram has been obtained. This observed unique maximum in the RPV has been ascribed to the formation-destruction (i.e., chemical reaction) of the so-called mercury-O2•- compounds.9 On the other hand, according to the above-described definition of the

Nonlinear Phenomena at Hg Electrode/RTIL Interface

Figure 7. (A) Normal and (B) reversed-pulse voltammograms obtained at the HMDE (solid lines a and a′) and a Au electrode (dashed lines b and b′) in the same solution as used in the case of Figure 6. Pulse delay, td ) 1 s; pulse period, tp) 50 ms; and sampling time, ts ) 20 ms.

maxima, the observed maxima in both NPV and RPV of the BTD/BTD•- redox couple are of the first kind and, thus, would be essentially ascribed to the streaming of the mercury surface9-11 but not to the adsorption (reaction) of BTD•- (or BTD) on the HMDE. Measurement of ECC in EMIBF4. Classically, the streaming phenomena of the mercury surface has been categorized into two types: namely, “upward” and “downward”.10,11,20,27 Furthermore, the mode of the streaming (upward or downward) of the mercury surface depends on the potential with respect to the PZC of the HMDE in a particular solution, that is, on whether the electrode potential is more negative or positive than the PZC,11,20 and the streaming is essentially absent at the potential region of the PZC.20,27 Therefore, the knowledge of the PZC is necessary to know the mode of streaming of the HMDE surface in EMIBF4. Figure 8 represents the typical ECC, which is a convex parabola with a maximum43-45,48-51 at ca. -0.3 V, measured using a DME in EMIBF4. The shape (especially the maximum part) of the ECC is slightly broad compared to that obtained in DMSO solution but is similar to those reported for various RTILs.50,51 Nanjundiah et al.51 have determined similar ECCs in three RTILs, including EMIBF4, and the maximum of the ECC in EMIBF4 has been reported to be -0.50 V versus Ag/AgCl/Cl-. Very recently, we measured the ECCs in different RTILs, and the PZC in EMIBF4 has been reported as -0.23 V.50 Discussion From the above-described results, we can see that the CVACO could be characteristically observed at the HMDE in the ionic solvent (EMIBF4), in analogy with that found in the conventional molecular solvents (e.g., DMSO) containing the supporting electrolyte. Since the PZC of the HMDE in EMIBF4 is -0.23 V, the E0′ (-1.36 V) of the BTD/BTD•- redox couple is by ca. 1.0 V more negative than the PZC (assuming that the potentials of both Ag/AgCl reference electrodes used for the CV and ECC measurements are the same; see the Experimental

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Figure 8. A typical drop time versus potential curve (an ECC) measured using a DME in N2-saturated EMIBF4.

Section). On the basis of the classical theory of the polarographic streaming maxima of the first kind,10,11,14,20,27 the CVACO may be primarily understood to be initiated by the streaming of the mercury surface as discussed elsewhere,10,11,14,20 but this theory is not competent to clarify the reason of the occurrence of (i) oscillation with “a bundle of current spikes” (see Figures 2-6) instead of the smooth maximum (see Figure 7B) in the reoxidation of BTD•- species to BTD (anodic process) and (ii) the streaming maxima only at the rising part of the voltammogram (Figure 7). This fact illustrates the need for a competent theory in this regard. Herein, the observed streaming maxima and CVACO are explained exclusively on the basis of the modern theory of the streaming maxima of the first kind.44,45 For the sake of a clear understanding of the these phenomena, first, the origin of the instability at the mercury electrode/ interface proposed in the modern theory will be purposely described below. In 1978, Aogaki et al.44 critically developed a new theory by considering various hydrodynamical and electrochemical features of the liquid mercury electrode/liquid solution interfaces. In this theory, numerous small perturbations have been considered to be endlessly amplified to macroscopic instabilities, resulting in polarographic maxima by their coupling in a cyclic chain: surface tension f surface motion f bulk motion f diffusional mass transport f surface electrochemical potential f surface tension. Figure 9 schematically illustrates the growth of the microscopic instabilities at the mercury electrode/ electrolyte solution interface, an ECC merged with a voltammogram and the diffusion patterns of the electrogenerated product (e.g., BTD•- species) at the HMDE surface. In this case, the streaming of the mercury surface has been considered to take place in such a way that the liquid mercury comes out at several points (region B) from the inner core of the liquid mercury pool (drop) toward the electrode/solution interface; that is, the liquid mercury seems to be fed at region A (Figure 9A).44,45 The solution at the interface responds accordingly, and similarly to the liquid mercury, an incessant feeding of the electrolyte solution from the bulk at region A also takes place to minimize the total momentum at the electrode/solution

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Figure 9. Schematic representations of (A) the growth of microinstability at the mercury/solution interface and (B) an ECC with a voltammogram, and an HMDE surrounded (C) homogeneously and (D) inhomogeneously by the electrogenerated product (e.g., BTD•-). The various parts of the HMDE are typically shown in panel C, and the solvent dipole and electrolyte ions are omitted from panels C and D.

interface. Such a feeding of the solution at region A obviously makes several microinstability (convection) zones at the interface (region B). At a suitable condition, region B may aggregate together to result in a macroscopic instability at the interface. The diameter, density, amplitude toward the bulk, and the lifetime of region B entirely depend on several physico(electro)chemical parameters (see the Appendix). Specifically, the increase in the concentration of the electroactive species and the decrease in the concentration of the supporting electrolyte (in the conductivity of the solution) have been understood to show the same effect on the growth rate and the size of region B: They make the rate of region B faster (the number per unit area) and the size (diameter) smaller.45 Later, the Aogaki’s group successfully visualized the formation of the cellular convection zone52,53 accompanied by the polarographic streaming maximum at the mercury pool electrode/aqueous solution interfaces. A quantitative relationship between the streaming maxima current (jV) and various physico(electro)chemical parameters involved with the instability at the electrode/solution interface has also been established (see the Appendix). The current density (j) at the polarographic maximum region at a time t has been expressed as45

j ) jF + jV ) jF + ∆j(λ0)e(pt)

(1)

where jF is the current density before the perturbation, ∆j is the magnitude of the initial perturbation of current with an initial wave length of λ0, and p is a transient time constant. In fact, p

is related to a set of physico(electro)chemical parameters, including the slope of the ECC, the concentration overvoltage at a steady-state (E*), the steady-state concentration of redox species at the electrode surface (C*), the bulk concentration of the redox species, and so on (see the Appendix). From eq 1, it is clear that the initial perturbation (resulting in ∆j) at the electrode/solution interface is increased exponentially to become a macroscopic one at a particular condition. It has been shown that the value of p may be a real or imaginary number, and thus, p may be expressed as p ) (x or ix, where x is a real number and i ) x-1. If the value of x is real and negative, then jV f 0; so, j ) jF; that is, the interface becomes stable, whereas if the value of p is positive, then jV > 0, and obviously, j > jF, resulting in the maximum on the voltammogram. In contrast, if the imaginary part of p is nonzero (the exponential term in eq 1 can be expressed as eix ) cos x + i sin x), then the oscillatory mode adds to the above-mentioned instability at the electrode/solution interface,45 and thus, the system becomes very complicated with a self-insisting characteristic. Therefore, the magnitude and nature of p are the determining factor of the state (stability or instability) of the electrode/solution interface. Thus, we can understand that in the solution containing a higher concentration of the supporting electrolyte, a higher concentration of the redox species is required to observe the streaming maxima and vice versa. In this study, the necessity of the higher concentration of BTD (e.g., 20 mM) in EMIBF4 (6.4 M) to observe the streaming maxima (Figure 7) and the CVACO (Figures 2-6) is in agreement with the above-

Nonlinear Phenomena at Hg Electrode/RTIL Interface mentioned modern theory. Here, the cause of the localization of the streaming maxima at the rising part of the voltammogram (Figure 7) may be explained by considering the potential dependency of the p value. In fact, the values of E*, C*, and the slope of the ECC and so on in the whole potential range of the voltammogram, especially where the faradic process takes place (e.g., at points a1, a2, and a3 in Figure 9B), are not kept constant; that is, the magnitude of p varies with the potential axis of the voltammogram. In fact, Aogaki et al. have observed that the value of p, which has been calculated by putting the relevant parameters in the kinetic equation derived for the quantitative measurement of the polarographic maxima of the first kind (Appendix), is the highest at the potential of the maxima observed during the deposition of metals (lead and mercury).45 At this stage, although it is difficult to provide a quantitative measure of p, it may have a unique value at the potential of streaming maxima, and hence, region B may possess a longer lifetime and combine together, resulting in a macroscopic instability at the interface and the maxima on the voltammogram (Figure 7). As pointed out by Aogaki et al. in their theory, the oscillatory mode adds to the above-mentioned instability when the value of p becomes an imaginary number.44,45 Previously, we have visualized that the pink BTD•- species formed in the cathodic process of the CV of the BTD/BTD•- redox couple gathers at the neck portion of the HMDE in DMSO solution (Figure 9D) instead of the expected homogeneous diffusion of BTD•(Figure 9C).10 Moreover, the CVACO has been found to take place at a triggering potential (at ca. -1.2 V in the anodic cycle of the CVs, Figures 4 and 5) at which the concentration of BTD•- species at the bottom portion of the HMDE has been observed to be scarce.10 In fact, just before attaining the onset potential of the CVACO, the concentration of BTD•- species at the bottom portion of the HMDE (i.e., C* value) has been practically observed to be zero (Figure 9D).10 Such a situation at the HMDE surface may possibly result in the oscillatory current maxima. Thus, the observed CVACO can be generally considered as the polarographic maxima of the first kind with an oscillatory mode. In this context, the fact that no CVACO was observed at a faster potential scan rate (Figures 3 and 5) may be reasonably ascribed to the shorter time scale of the CV measurement, which results in the formation of a smaller amount of BTD•- species in the cathodic process, as well as the lesser degree of inhomogeneous diffusion of the BTD•- species at the neck portion of the HMDE. On the other hand, the oscillation observed in the i-t curves (Figure 6B) is comparable to the CVACO. In this case, the shift of current maxima to a larger t with increasing t0 (Figure 6B), which results in a larger amount of the BTD•- species at the HMDE surface, may be ascribed to the longer elapse of time required for the creation of an inhomogeneous distribution of BTD•- species at the HMDE (Figure 9D), which fulfils the threshold condition of the oscillation (described above). Conclusions The polarographic streaming maximum and the CVACO at the HMDE that are well-known to take place in the conventional molecular solvents (e.g., DMSO) containing the supporting electrolyte of an appropriate concentration were observed in EMIBF4 RTIL. These observations could be successfully explained on the basis of the modern concept of the polarographic maxima of the first kind: the observed maximum and CVACO result from an enhanced instability at the HMDE/ solution interfaces induced by the streaming of the HMDE

J. Phys. Chem. B, Vol. 111, No. 44, 2007 12855 surface, and the oscillating mode of the instability is observed as the CVACO. Acknowledgment. The present work was financially supported by Grant-in-Aids for Scientific Research on Priority Areas (No. 417), Scientific Research (No. 12875164), and Scientific Research (A) (No. 19206079) to T.O. from the Ministry of Education, Culture, Sports, Science and Technology, Japan and the VBL program at Tokyo Tech. M.M.I. gratefully acknowledges the Interdisciplinary Graduate School of Science and Engineering of Tokyo Tech for the Postdoctoral fellowship. Appendix The quantitative equation (two-dimensional) of the polarographic maxima of the first kind is as follows:45

λ(λ - 1)(Kx1 + λξ + 1)ξ2 {ηe(x1 + θξ - 1) + ηmθ(x1 + ξ - 1)}a2 + KHL′(x1 + θξ - 1) × {λ(x1 + ξ - 1) - (x1 + λξ - 1)} ) 0 (A1) where where E*, l, n, C*, C0, and D are the concentration

{

(nF)2DC0 nF exp E*(z) K) κRT RT H)

{

}

}

for z ) 0

(A2)

nF RT exp E* × slope of the ECC nFC0 RT for z ) 0 (A3)

L′ ) -

l2 dC* D dz z)0

( )

(A4)

θ)

µe µm

(A5)

ξ)

p k2l

(A6)

a ) kl λ)

µe (Schmidt number) D

(A7) (A8)

overvoltage at a steady-state, unit length, number of electron transfer at the interface, steady-state concentration at the electrode surface, bulk concentration, and diffusion coefficient of the active species, respectively. κ, ηe, and µe are the conductivity, viscosity, and kinematic viscosity (µe ) ηe/Fe, where Fe is the density of solution) of the solution. ηm and µm are the viscosity and kinematic viscosity (µm ) ηm/Fm, Fm is the density of mercury) of mercury. k, F, R, and T are the wave number of disturbance at the interface, Faraday constant, gas constant, and temperature, respectively. Obviously, eq A1 is a complicated one. By putting the values of all of the parameters into eq A1, the value of p (time constant) can be determined using the Newton-Laphson method. References and Notes (1) Fahidy, T. Z.; Gu, Z. H. In Modern Aspects of Electrochemistry; White, R. E., Bockris, J. O’M., Conway, B. E. Eds.; Plenum Press: New York, 1995; Vol. 27. (2) Wojtowitcz, J. In Modern Aspects of Electrochemistry; Bockris, J. O’M., Conway, B. E. Eds.; Plenum Press: New York, 1973; Vol. 8. (3) Pagitsas, M.; Sazou, D. J. Electroanal. Chem. 1999, 471, 132.

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