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Magnetic field effect on electrochemical oscillations during iron dissolution
Electrochemistry Communications 5 (2003) 321–324 www.elsevier.com/locate/elecom
Magnetic field effect on electrochemical oscillations during iron dissolution Qing-Kai Yu a, Yasuyuki Miyakita a, Seiichiro Nakabayashi a, Ryo Baba b
b,*
a Department of Chemistry, Faculty of Science, Saitama University, Saitama, 338-8570, Japan Department of Marine System Engineering, Tokyo University of Mercantile Marine, Etchu-jima, Tokyo, 135-8533, Japan
Received 4 February 2003; received in revised form 6 March 2003; accepted 6 March 2003
Abstract A fairly low magnetic field of ca. 30 mT was found to affect the period and the amplitude of the self-sustained current oscillation of an iron electrode. This was observed much distinctively when the direction of the applied field was normal to the electrode surface, i.e., non-magnetohydrodynamic (MHD) configuration. The Flade potential of the iron electrode was not affected by the magnetic field intensity of up to 4 T. The observed magnetic field effect was attributed to the depression of the natural convection in the vicinity of the electrode surface which was caused by the two local paramagnetic body forces, the magnetic field gradient force and/or the concentration gradient force. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Electrochemical oscillation; Iron electrode; Magnetic field; Oxide film; Natural convection
1. Introduction Non-linearity is one of the most important concepts in many fields of modern science growing in the last decade [1]. In particular, the external forcing to autonomous oscillating systems has been attractive in the basic science and technology [2], and also seems substantial for a future understanding of the biological and physiological systems [3,4]. Perturbation on electrochemical parameters in time has been widely employed as a common method in the forced non-linear electrochemical systems as well [5–7]. The magnetic field, for example, is known to influence electrochemical systems via the magnetohydrodynamic (MHD) force [8,9] and/or the two paramagnetic body forces, the field gradient force and the concentration gradient force [8–15]. These forces can modify the mass transport in the system. In addition, the thermodynamic stability of those compounds involved in the system, as well as the reaction
*
Corresponding author. Tel.: +81-3-5245-7469; fax: +81-3-52457434. E-mail address: [email protected] (R. Baba).
intermediates, and the electrochemical kinetics may both be affected by the high magnetic field [16,17]. In the present paper, weak but uniform magnetic fields were applied to the self-sustained current oscillation of iron electrodes. And this non-linear electrochemical system was studied in terms of the magnetic control of the dynamic behavior during its formation and reduction cycles of insulating oxide films at the electrode surface. The mechanism of the observed magnetic field effect was also discussed.
2. Experimental The iron disk electrode of 2 mm in diameter was made from an iron rod (Nilaco, 99.9%) and embedded in a Teflon holder. Before each experiment, the electrode was carefully polished with a fine emery paper and was rinsed by distilled water. A platinum wire (0.8 mm thick and 400 mm long) was used as the counter electrode. The electrode potential was measured with respect to SCE. The electrolyte solution containing 1:0 mol dm3 H2 SO4 was prepared with GC grade reagents (Wako Pure Chemicals) and Milli-Q water. All experiments
1388-2481/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S1388-2481(03)00057-2
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Q.-K. Yu et al. / Electrochemistry Communications 5 (2003) 321–324
were conducted at room temperature. The electrochemical measurements were carried out by a potentio/ galvanostat (HA-151, Hokuto Denko) and a function generator (HB-111, Hokuto Denko, or 3314A, Hewlett Packard). The signals from the potentio/galvanostat were fed to a digital recorder (8841 Memory Hicorder, Hioki). The electrochemical cell was set in order that the surface of the working disk electrode, facing downward, was located at the center of a handmade solenoid magnet 25 cm across. And the magnetic field was applied parallel or normal to the surface of the disk electrode by changing the geometry of the magnet. The Flade potential of the iron electrode was measured by the chronopotentiometric method [18] with the electrochemical cell placed at the magnetic center in the vertical bore 40 cm across of a super-conducting magnet (TM4V40, Toshiba). The magnetic field intensity was monitored by a gaussmeter (421, Lake Shore).
3. Results and discussion The current–potential (I–E) curve of the iron disk electrode in 1:0 mol dm3 H2 SO4 aqueous solution was shown in Fig. 1. As seen in the figure, the polarization behavior can be roughly divided into four regions: active, pre-passive, oscillatory and passive regions, respectively [7]. In the active region, the iron dissolving current was observed, while in the passive region, the electrode surface was covered with iron oxide and no current was obtained. In the pre-passive region, the electrode surface is covered with a salt film, which makes the observed limiting current decreased [7,19]. The electrode potential where the transition from the passive state back to the active state occurs under an open-circuit condition is called Flade potential [7,16–20].
Fig. 1. I–E polarization curve of an iron disk electrode in 1:0 mol dm3 H2 SO4 . Scan rate was 10 mV s1 .
Around the Flade potential, potentiostatic current oscillations take place due to the bistability of the iron electrode surface [19]. This potential range in the present system was approximately from +275 to +295 mV vs. SCE in the absence of magnetic field. A typical current oscillation at +290 mV is presented in Fig. 2. This figure also shows the behaviors under the magnetic field of 33.7 mT from t ¼ 120 to 240 s. The response time of the magnetic field was well within several seconds after switching on and off the solenoid employed. As shown in Fig. 2(a), both amplitude and time period of the current pulses were gradually changed when the magnetic field normal to the electrode surface ðB? Þ was ON, and quickly returned to their original levels when the field was OFF. The observed transience of the oscillation behavior was much slower than the intrinsic response of the magnet. Under the parallel magnetic field of the same intensity, on the other hand, i.e., B== ¼ 33:7 mT, any significant effect was not observed as shown in Fig. 2(b). When B? was 33.7 mT, the period of the oscillation was extended from ca. 6.5 to 11 s, and thus increased by ca. 65%. The prolonged time period under a magnetic field ðTM Þ was found to increase as the intensity of the applied magnetic field was raised. As seen in Fig. 3, the ratio of the increment in the period ðDT ¼ TM T0 Þ to the intrinsic period under zero field ðT0 Þ appeared proportional to the square-root or to the cubic-root of the magnetic flux density B. Whereas, it seems not conclusive yet, as Fahidy discussed on the statistical indeterminacy of the magnetic field effect on electrolytic mass transport, especially in such small ranges of B [21]. The period of this self-sustained current oscillation, however, would depend either on the thermodynamic stability of the surface oxide or on the mass transport of ions towards the electrode surface [19]. Pourbaix diagram is known to show how local pH and electrode potential govern the thermodynamic stability of metal oxides [20]. Since iron oxide ðc-Fe2 O3 Þ has a large magnetic susceptibility, v ¼ 4:2 105 m3 mol1 , the iron electrode might have gained additional internal energy upon its magnetization when an external magnetic field was applied. Then, in order to estimate the thermodynamic stability of iron oxide films under high magnetic fields, the time course of the open-circuit potential of the oxide-covered iron electrode dipped in the sulfuric acid solution was measured. This Flade potential measurement was repeated in the bore of a superconducting magnet with and without the magnetic field exerting normal to the electrode surface. Fig. 4 shows the time courses of the open-circuit potential captured by a pretriggered digital recorder with and without the field of 4 T. The curves appear exactly identical between the two cases, showing that the magnetic field did not give any influence on the Flade potential and, thus, on the thermodynamic stability of the iron oxide film.
Q.-K. Yu et al. / Electrochemistry Communications 5 (2003) 321–324
323
Fig. 2. (a) Time course of the oscillating current response with and without a magnetic field (33.7 mT, from 120 to 240 s). The field was applied normal to the electrode surface. Plot of the time period T for the corresponding current pulses is also shown below. (b) The same as (a) but the magnetic field was parallel to the electrode surface. The electrode potential was kept at +290 mV vs. SCE for both cases.
Fig. 3. Plot of DT =T0 vs. magnetic flux density B. DT is the change in the oscillation period under the magnetic field, i.e., TM T0 , where T0 and TM are the period in the absence and in the presence of the magnetic field, respectively. The electrode potential was kept at +290 mV vs. SCE.
The electrochemical equilibrium for the iron oxide is shown below: Fe2 O3 þ 6Hþ þ 2e () 2Fe2þ þ 3H2 O The magnetic energy Gm ðJ mol1 Þ can be written as vB2 =2l0 [22], where v is the magnetic susceptibility ðm3 mol1 Þ of iron oxide, B is the magnetic flux density ðkg A1 s2 Þ, and l0 is the magnetic permeability of the vacuum ð4p 107 N A2 Þ. As the magnetic energy of the iron oxide is much greater than that of the solution under the same field, then the equilibrium potential Eeq [V vs. SCE] of the reaction above is given as follows, based on the thermodynamic consideration [23]: Eeq ¼ 0:5 0:18pH 0:06 logðaFeð2þÞ Þ 8:7 105 B2 ; where aFeð2þÞ is the activity of Fe2þ . This suggests that the contribution of the magnetic field of 4 T is expected
Fig. 4. Time course of the open-circuit potential of an iron electrode under the magnetic field of 0 and 4 T. The electrode was anodically polarized in advance at +1.0 V vs. SCE for 10 min. Data were taken with a digital recorder pretriggered at 0 V vs. SCE, which gives the triggered point of t ¼ 0.
to be about 1.5 mV, which is consistent with the result of Fig. 4. Taking into account the dependence of local pH on the stability of iron oxide, the effect of mass transport of proton at the electrode surface was studied by using an iron rotating disk electrode (RDE). The result showed that the period of the self-sustained oscillation decreased as the rotation speed increased to make the mass transport towards the electrode surface enhanced. In consequence, the extension of the period under magnetic fields as shown in Fig. 2(a) suggests that the applied magnetic field depressed the mass transport. Recently, Leventis et al. [11–13] and Hinds et al. [14], independently of one another, derived two forces that can act on the media containing paramagnetic species. The one is the magnetic field gradient force FrB that is
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Q.-K. Yu et al. / Electrochemistry Communications 5 (2003) 321–324
proportional to CBgradB, where C is the concentration of the paramagnetic species, and the other is the concentration gradient force FrC that is proportional to B2 gradC and works whenever the field gradient is uniform or not. These paramagnetic body forces can both affect the liquid motion at the electrode surface and thus the external field can suppress the natural convective flow driven by the local density gradient in the solution under the gravity. When the field gradients are fairly large, for example at ferromagnetic microelectrodes with radii ranging from one to several hundred micrometers, FrB is the major force to confine electrogenerated paramagnetic species in the field gradients surrounding the electrodes, as reported by White et al. [8–10]. In the present study using a millimeter-sized iron disk electrode, both FrB and FrC act on the solution containing the paramagnetic Fe3þ and the diamagnetic Fe2þ ions that are emitted during the current oscillation. The spatiotemporal profile of the distribution of these ions in the close vicinity of the electrode is quite critical to the observed electrochemical oscillations, though itÕs timeand space-evolution is not fully elucidated yet. Hence, it still seems unclear, or rather not straightforward, which force, FrB or FrC , is the major to reduce the natural convection at the iron electrode in all phases during the current oscillations. The suppression of the natural convection can be demonstrated by the chronoamperometric experiments. Time course of the current response under the magnetic field normal to the electrode surface was measured with the electrode potential stepped from the rest potential to +200 mV vs. SCE, a pre-passive potential in the present system. The current once jumped up and then unevenly settled in several seconds down to a certain stationary level ðIM Þ, as typically depicted in the inset of Fig. 5. This behavior cannot be described by the simple Cottrell equation for one-dimensional diffusion because the diffusion constant was varied between the salt film and the solution [7,19]. The difference in the limiting currents thus obtained with and without the magnetic field, i.e.,
Fig. 5. Normalized change in the limiting current vs. magnetic flux density B. IM and I0 are the limiting currents under a given magnetic field and without the field, respectively.
I0 IM , was normalized against I0 , and was plotted in Fig. 5 as a function of the applied magnetic field. Although the data is slightly ambiguous in the smaller range of B, it is still obvious that the limiting current decreases as the magnetic field is increased. This also indicates that the natural convection is depressed by the magnetic field that was applied normal to the electrode surface. The potentiostatic current oscillation during the electrochemical iron dissolution was influenced by the weak external magnetic field through a hydrodynamic mechanism, and was not affected by the thermodynamic effect of the field. The magnetic enlargement of the oscillation period was induced by the suppression of the convective mass transport, which was consistent with the RDE experiments.
Acknowledgements This work was partly supported by the ‘‘Research for the Future (RFTF)’’ program sponsored by Japan Society for the Promotion of Science.
References [1] G. Nicolis, Introduction to Nonlinear Science, Cambridge University Press, Cambridge, 1995. [2] S.K. Scott, Chemical Chaos, Oxford Science Publications, London, 1991. [3] U.F. Franck, Prog. Biophys. Chem. 6 (1956) 171. [4] U.F. Franck, Angew. Chem. 17 (1978) 1. [5] A. Karantonis, M. Pagitsas, D. Sazou, Chaos 3 (1993) 243. [6] V.S. Varma, P.K. Upadhyay, J. Electroanal. Chem. 271 (1989) 345. [7] M. Pagitsas, D. Sazou, A. Karantonis, C. Georgolios, J. Electroanal. Chem. 327 (1992) 93. [8] M.D. Pullins, K.M. Grant, H.S. White, J. Phys. Chem. B 105 (2001) 8989. [9] S.R. Ragsdale, K.M. Grant, H.S. White, J. Am. Chem. Soc. 120 (1998) 13461. [10] K.M. Grant, J.W. Hemmert, H.S. White, Electrochem. Commun. 1 (1999) 319. [11] N. Leventis, X. Gao, J. Phys. Chem. 103 (1999) 5832. [12] N. Leventis, X. Gao, Anal. Chem. 73 (2001) 3981. [13] N. Leventis, X. Gao, J. Am. Chem. Soc. 124 (2002) 1079. [14] G. Hinds, J.M.D. Coey, M.E.G. Lyons, Electrochem. Commun. 3 (2001) 215. [15] M. Waskaas, Y.I. Kharkats, J. Phys. Chem. B 103 (1999) 4876. [16] T. Fahidy, J. Appl. Electrochem. 13 (1983) 553. [17] R.A. Tacken, L.J. Janssen, J. Appl. Electrochem. 25 (1995) 1. [18] A.J. Bard, L.R. Faulkner, Electrochemical Methods, Wiley, NY, 1980. [19] J.L. Hudson, T.T. Tsotsis, Chem. Eng. Sci. 44 (1994) 1493. [20] D.A. Jones, Principles and Prevention of Corrosion, MacMillan, NY, 1992. [21] T.Z. Fahidy, Electrochim. Acta 35 (1990) 929. [22] T. Kimura, Jpn. J. Appl. Phys. 40 (2001) 6818. [23] K.J. Vetter, Electrochemical Kinetics, Academic Press, NY, 1967.
Magnetic field effect on electrochemical oscillations during iron dissolution Qing-Kai Yu a, Yasuyuki Miyakita a, Seiichiro Nakabayashi a, Ryo Baba b
b,*
a Department of Chemistry, Faculty of Science, Saitama University, Saitama, 338-8570, Japan Department of Marine System Engineering, Tokyo University of Mercantile Marine, Etchu-jima, Tokyo, 135-8533, Japan
Received 4 February 2003; received in revised form 6 March 2003; accepted 6 March 2003
Abstract A fairly low magnetic field of ca. 30 mT was found to affect the period and the amplitude of the self-sustained current oscillation of an iron electrode. This was observed much distinctively when the direction of the applied field was normal to the electrode surface, i.e., non-magnetohydrodynamic (MHD) configuration. The Flade potential of the iron electrode was not affected by the magnetic field intensity of up to 4 T. The observed magnetic field effect was attributed to the depression of the natural convection in the vicinity of the electrode surface which was caused by the two local paramagnetic body forces, the magnetic field gradient force and/or the concentration gradient force. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Electrochemical oscillation; Iron electrode; Magnetic field; Oxide film; Natural convection
1. Introduction Non-linearity is one of the most important concepts in many fields of modern science growing in the last decade [1]. In particular, the external forcing to autonomous oscillating systems has been attractive in the basic science and technology [2], and also seems substantial for a future understanding of the biological and physiological systems [3,4]. Perturbation on electrochemical parameters in time has been widely employed as a common method in the forced non-linear electrochemical systems as well [5–7]. The magnetic field, for example, is known to influence electrochemical systems via the magnetohydrodynamic (MHD) force [8,9] and/or the two paramagnetic body forces, the field gradient force and the concentration gradient force [8–15]. These forces can modify the mass transport in the system. In addition, the thermodynamic stability of those compounds involved in the system, as well as the reaction
*
Corresponding author. Tel.: +81-3-5245-7469; fax: +81-3-52457434. E-mail address: [email protected] (R. Baba).
intermediates, and the electrochemical kinetics may both be affected by the high magnetic field [16,17]. In the present paper, weak but uniform magnetic fields were applied to the self-sustained current oscillation of iron electrodes. And this non-linear electrochemical system was studied in terms of the magnetic control of the dynamic behavior during its formation and reduction cycles of insulating oxide films at the electrode surface. The mechanism of the observed magnetic field effect was also discussed.
2. Experimental The iron disk electrode of 2 mm in diameter was made from an iron rod (Nilaco, 99.9%) and embedded in a Teflon holder. Before each experiment, the electrode was carefully polished with a fine emery paper and was rinsed by distilled water. A platinum wire (0.8 mm thick and 400 mm long) was used as the counter electrode. The electrode potential was measured with respect to SCE. The electrolyte solution containing 1:0 mol dm3 H2 SO4 was prepared with GC grade reagents (Wako Pure Chemicals) and Milli-Q water. All experiments
1388-2481/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S1388-2481(03)00057-2
322
Q.-K. Yu et al. / Electrochemistry Communications 5 (2003) 321–324
were conducted at room temperature. The electrochemical measurements were carried out by a potentio/ galvanostat (HA-151, Hokuto Denko) and a function generator (HB-111, Hokuto Denko, or 3314A, Hewlett Packard). The signals from the potentio/galvanostat were fed to a digital recorder (8841 Memory Hicorder, Hioki). The electrochemical cell was set in order that the surface of the working disk electrode, facing downward, was located at the center of a handmade solenoid magnet 25 cm across. And the magnetic field was applied parallel or normal to the surface of the disk electrode by changing the geometry of the magnet. The Flade potential of the iron electrode was measured by the chronopotentiometric method [18] with the electrochemical cell placed at the magnetic center in the vertical bore 40 cm across of a super-conducting magnet (TM4V40, Toshiba). The magnetic field intensity was monitored by a gaussmeter (421, Lake Shore).
3. Results and discussion The current–potential (I–E) curve of the iron disk electrode in 1:0 mol dm3 H2 SO4 aqueous solution was shown in Fig. 1. As seen in the figure, the polarization behavior can be roughly divided into four regions: active, pre-passive, oscillatory and passive regions, respectively [7]. In the active region, the iron dissolving current was observed, while in the passive region, the electrode surface was covered with iron oxide and no current was obtained. In the pre-passive region, the electrode surface is covered with a salt film, which makes the observed limiting current decreased [7,19]. The electrode potential where the transition from the passive state back to the active state occurs under an open-circuit condition is called Flade potential [7,16–20].
Fig. 1. I–E polarization curve of an iron disk electrode in 1:0 mol dm3 H2 SO4 . Scan rate was 10 mV s1 .
Around the Flade potential, potentiostatic current oscillations take place due to the bistability of the iron electrode surface [19]. This potential range in the present system was approximately from +275 to +295 mV vs. SCE in the absence of magnetic field. A typical current oscillation at +290 mV is presented in Fig. 2. This figure also shows the behaviors under the magnetic field of 33.7 mT from t ¼ 120 to 240 s. The response time of the magnetic field was well within several seconds after switching on and off the solenoid employed. As shown in Fig. 2(a), both amplitude and time period of the current pulses were gradually changed when the magnetic field normal to the electrode surface ðB? Þ was ON, and quickly returned to their original levels when the field was OFF. The observed transience of the oscillation behavior was much slower than the intrinsic response of the magnet. Under the parallel magnetic field of the same intensity, on the other hand, i.e., B== ¼ 33:7 mT, any significant effect was not observed as shown in Fig. 2(b). When B? was 33.7 mT, the period of the oscillation was extended from ca. 6.5 to 11 s, and thus increased by ca. 65%. The prolonged time period under a magnetic field ðTM Þ was found to increase as the intensity of the applied magnetic field was raised. As seen in Fig. 3, the ratio of the increment in the period ðDT ¼ TM T0 Þ to the intrinsic period under zero field ðT0 Þ appeared proportional to the square-root or to the cubic-root of the magnetic flux density B. Whereas, it seems not conclusive yet, as Fahidy discussed on the statistical indeterminacy of the magnetic field effect on electrolytic mass transport, especially in such small ranges of B [21]. The period of this self-sustained current oscillation, however, would depend either on the thermodynamic stability of the surface oxide or on the mass transport of ions towards the electrode surface [19]. Pourbaix diagram is known to show how local pH and electrode potential govern the thermodynamic stability of metal oxides [20]. Since iron oxide ðc-Fe2 O3 Þ has a large magnetic susceptibility, v ¼ 4:2 105 m3 mol1 , the iron electrode might have gained additional internal energy upon its magnetization when an external magnetic field was applied. Then, in order to estimate the thermodynamic stability of iron oxide films under high magnetic fields, the time course of the open-circuit potential of the oxide-covered iron electrode dipped in the sulfuric acid solution was measured. This Flade potential measurement was repeated in the bore of a superconducting magnet with and without the magnetic field exerting normal to the electrode surface. Fig. 4 shows the time courses of the open-circuit potential captured by a pretriggered digital recorder with and without the field of 4 T. The curves appear exactly identical between the two cases, showing that the magnetic field did not give any influence on the Flade potential and, thus, on the thermodynamic stability of the iron oxide film.
Q.-K. Yu et al. / Electrochemistry Communications 5 (2003) 321–324
323
Fig. 2. (a) Time course of the oscillating current response with and without a magnetic field (33.7 mT, from 120 to 240 s). The field was applied normal to the electrode surface. Plot of the time period T for the corresponding current pulses is also shown below. (b) The same as (a) but the magnetic field was parallel to the electrode surface. The electrode potential was kept at +290 mV vs. SCE for both cases.
Fig. 3. Plot of DT =T0 vs. magnetic flux density B. DT is the change in the oscillation period under the magnetic field, i.e., TM T0 , where T0 and TM are the period in the absence and in the presence of the magnetic field, respectively. The electrode potential was kept at +290 mV vs. SCE.
The electrochemical equilibrium for the iron oxide is shown below: Fe2 O3 þ 6Hþ þ 2e () 2Fe2þ þ 3H2 O The magnetic energy Gm ðJ mol1 Þ can be written as vB2 =2l0 [22], where v is the magnetic susceptibility ðm3 mol1 Þ of iron oxide, B is the magnetic flux density ðkg A1 s2 Þ, and l0 is the magnetic permeability of the vacuum ð4p 107 N A2 Þ. As the magnetic energy of the iron oxide is much greater than that of the solution under the same field, then the equilibrium potential Eeq [V vs. SCE] of the reaction above is given as follows, based on the thermodynamic consideration [23]: Eeq ¼ 0:5 0:18pH 0:06 logðaFeð2þÞ Þ 8:7 105 B2 ; where aFeð2þÞ is the activity of Fe2þ . This suggests that the contribution of the magnetic field of 4 T is expected
Fig. 4. Time course of the open-circuit potential of an iron electrode under the magnetic field of 0 and 4 T. The electrode was anodically polarized in advance at +1.0 V vs. SCE for 10 min. Data were taken with a digital recorder pretriggered at 0 V vs. SCE, which gives the triggered point of t ¼ 0.
to be about 1.5 mV, which is consistent with the result of Fig. 4. Taking into account the dependence of local pH on the stability of iron oxide, the effect of mass transport of proton at the electrode surface was studied by using an iron rotating disk electrode (RDE). The result showed that the period of the self-sustained oscillation decreased as the rotation speed increased to make the mass transport towards the electrode surface enhanced. In consequence, the extension of the period under magnetic fields as shown in Fig. 2(a) suggests that the applied magnetic field depressed the mass transport. Recently, Leventis et al. [11–13] and Hinds et al. [14], independently of one another, derived two forces that can act on the media containing paramagnetic species. The one is the magnetic field gradient force FrB that is
324
Q.-K. Yu et al. / Electrochemistry Communications 5 (2003) 321–324
proportional to CBgradB, where C is the concentration of the paramagnetic species, and the other is the concentration gradient force FrC that is proportional to B2 gradC and works whenever the field gradient is uniform or not. These paramagnetic body forces can both affect the liquid motion at the electrode surface and thus the external field can suppress the natural convective flow driven by the local density gradient in the solution under the gravity. When the field gradients are fairly large, for example at ferromagnetic microelectrodes with radii ranging from one to several hundred micrometers, FrB is the major force to confine electrogenerated paramagnetic species in the field gradients surrounding the electrodes, as reported by White et al. [8–10]. In the present study using a millimeter-sized iron disk electrode, both FrB and FrC act on the solution containing the paramagnetic Fe3þ and the diamagnetic Fe2þ ions that are emitted during the current oscillation. The spatiotemporal profile of the distribution of these ions in the close vicinity of the electrode is quite critical to the observed electrochemical oscillations, though itÕs timeand space-evolution is not fully elucidated yet. Hence, it still seems unclear, or rather not straightforward, which force, FrB or FrC , is the major to reduce the natural convection at the iron electrode in all phases during the current oscillations. The suppression of the natural convection can be demonstrated by the chronoamperometric experiments. Time course of the current response under the magnetic field normal to the electrode surface was measured with the electrode potential stepped from the rest potential to +200 mV vs. SCE, a pre-passive potential in the present system. The current once jumped up and then unevenly settled in several seconds down to a certain stationary level ðIM Þ, as typically depicted in the inset of Fig. 5. This behavior cannot be described by the simple Cottrell equation for one-dimensional diffusion because the diffusion constant was varied between the salt film and the solution [7,19]. The difference in the limiting currents thus obtained with and without the magnetic field, i.e.,
Fig. 5. Normalized change in the limiting current vs. magnetic flux density B. IM and I0 are the limiting currents under a given magnetic field and without the field, respectively.
I0 IM , was normalized against I0 , and was plotted in Fig. 5 as a function of the applied magnetic field. Although the data is slightly ambiguous in the smaller range of B, it is still obvious that the limiting current decreases as the magnetic field is increased. This also indicates that the natural convection is depressed by the magnetic field that was applied normal to the electrode surface. The potentiostatic current oscillation during the electrochemical iron dissolution was influenced by the weak external magnetic field through a hydrodynamic mechanism, and was not affected by the thermodynamic effect of the field. The magnetic enlargement of the oscillation period was induced by the suppression of the convective mass transport, which was consistent with the RDE experiments.
Acknowledgements This work was partly supported by the ‘‘Research for the Future (RFTF)’’ program sponsored by Japan Society for the Promotion of Science.
References [1] G. Nicolis, Introduction to Nonlinear Science, Cambridge University Press, Cambridge, 1995. [2] S.K. Scott, Chemical Chaos, Oxford Science Publications, London, 1991. [3] U.F. Franck, Prog. Biophys. Chem. 6 (1956) 171. [4] U.F. Franck, Angew. Chem. 17 (1978) 1. [5] A. Karantonis, M. Pagitsas, D. Sazou, Chaos 3 (1993) 243. [6] V.S. Varma, P.K. Upadhyay, J. Electroanal. Chem. 271 (1989) 345. [7] M. Pagitsas, D. Sazou, A. Karantonis, C. Georgolios, J. Electroanal. Chem. 327 (1992) 93. [8] M.D. Pullins, K.M. Grant, H.S. White, J. Phys. Chem. B 105 (2001) 8989. [9] S.R. Ragsdale, K.M. Grant, H.S. White, J. Am. Chem. Soc. 120 (1998) 13461. [10] K.M. Grant, J.W. Hemmert, H.S. White, Electrochem. Commun. 1 (1999) 319. [11] N. Leventis, X. Gao, J. Phys. Chem. 103 (1999) 5832. [12] N. Leventis, X. Gao, Anal. Chem. 73 (2001) 3981. [13] N. Leventis, X. Gao, J. Am. Chem. Soc. 124 (2002) 1079. [14] G. Hinds, J.M.D. Coey, M.E.G. Lyons, Electrochem. Commun. 3 (2001) 215. [15] M. Waskaas, Y.I. Kharkats, J. Phys. Chem. B 103 (1999) 4876. [16] T. Fahidy, J. Appl. Electrochem. 13 (1983) 553. [17] R.A. Tacken, L.J. Janssen, J. Appl. Electrochem. 25 (1995) 1. [18] A.J. Bard, L.R. Faulkner, Electrochemical Methods, Wiley, NY, 1980. [19] J.L. Hudson, T.T. Tsotsis, Chem. Eng. Sci. 44 (1994) 1493. [20] D.A. Jones, Principles and Prevention of Corrosion, MacMillan, NY, 1992. [21] T.Z. Fahidy, Electrochim. Acta 35 (1990) 929. [22] T. Kimura, Jpn. J. Appl. Phys. 40 (2001) 6818. [23] K.J. Vetter, Electrochemical Kinetics, Academic Press, NY, 1967.