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J. Phys. Chem. 1996, 100, 714-717
Dissipation Structure of Electrochemical Hydrodynamic Convection S. Nakabayashi,*,†,‡ M. Yanagida,‡ and K. Uosaki‡ PRESTO, Research DeVelopment Corporation of Japan, and Physical Chemistry Laboratory, Department of Chemistry, Faculty of Science, Hokkaido UniVersity, Sapporo 060, Japan ReceiVed: May 2, 1995; In Final Form: September 30, 1995X
A very curious hydrodynamic pattern appears in copper sulfate electrolyte solution between two parallel copper electrodes. The potential of the lower electrode is more negative than that of the upper electrode. The vertical cross sectional view of the convection pattern is observed by a Michelson laser interferometer. The convective flow divides the space of the fluid into roll cells similar to those of Rayleigh-Benard convection. The time evolution of the convection pattern is observed simultaneously with the electrochemical response.
Introduction The spatial and temporal patterns created in dissipating energy in nonlinear systems are very interesting.1,2 Dissipation structures are commonly observed in chemical,2-4 biological,5-7 and physical systems.1,8,9 Among them, Rayleigh-Benard convection1,9,13 is one of the most famous systems. The system was investigated by Lorentz9 using the Galerkin method or the spectral method and reduced the governing equations to a set of simple nonlinear differential equations. In this article, we present a curious hydrodynamic pattern similar to the RayleighBenard convection that is observed in a copper sulfate electrolyte solution between two parallel copper electrodes, which are placed normal to the gravitational direction. A bias potential is applied to make the potential of the lower electrode more negative than that of the upper electrode. In this situation, electrodissolution and deposition of copper proceed on the upper and the lower electrodes, respectively. The concentration of electrolyte, i.e., the density of the fluid near the upper electrode, becomes higher than that near the lower electrode. This makes the electrolyte hydrodynamically unstable, and steady convection occurs. The convection forms a pattern in the fluid when dissipating the electrochemical energy. The electrochemical convection is controlled by adjusting the electrode potential, and the motion of the electrolyte can be monitored spontaneously by the current passing through an electrolysis cell.
Figure 1. Optical arrangement of the Michelson laser interferometer and the electrochemical cell.
Experimental Section The configuration of the electrochemical cell is shown on the lower right of Figure 1. Copper wire, whose diameter is ca. 0.8 mm, was used as the electrodes. The electrolysis was conducted between identical electrodes. The electrodes were placed between an AR-coated quartz window and a mirror. The thickness of the electrolyte is ca. 1.5 mm. The diameter of the window and the mirror is 20 mm. The electrolyte solution used was an aqueous solution containing 0.1 M CuSO4 and 0.2 M Na2SO4. The electrochemical conditions were controlled by using a potentiogalvanostat, Hokuto Denko HA-151. The current and the potential were recorded on an X-Y recorder. In the potential and current step experiments, a function generator, * Author to whom correspondence should be addressed at Hokkaido University. † PRESTO. ‡ Hokkaido University. X Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-0714$12.00/0
Figure 2. Typical relationship between the current and the potential of the electrochemical convection cell. The potential is represented as the upper electrode potential with respect to the one of the lower electrode.
HP 3314A, was used combined with the potentiogalvanostat. The transient signal was recorded on an HP 54601A oscilloscope. The optical arrangement of the Michelson laser interferometer10,11 is shown in Figure 1. The coherent emission of 514.5 nm from an Ar+ laser was divided into two beams by a polarizing beam splitter. One of them, passing through the electrolyte solution between the two electrodes, was reflected by the sample mirror. The other beam was reflected by the reference mirror, and the two reflected beams were again © 1996 American Chemical Society
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Figure 3. Vertical cross sectional view of the concentration of copper sulfate obtained by the laser interferometer. The two electrodes are copper wire with a 0.8 mm diameter. The potential is +0.7 V in part a and -0.7 V in part b. The vertical and horizontal sizes of each interferogram are 1.7 mm and 2 mm, respectively.
Figure 4. Time evolution of the current and the interferogram by the positive potential step from 0 V to 0.2 V. The vertical and horizontal sizes of each picture are 1.7 mm and 2.0 mm, respectively.
combined at the polarizing beam splitter. The interferogram was projected on the screen and recorded by a video camera. This setup achieved a vertical cross sectional view of the spatial distribution of the refractive index in the electrolyte solution.
Because the refractive index of the aqueous solution containing Cu2+ is proportional to the concentration up to 1.2 M, the fringes in the interferogram are considered as the contour lines of the concentration. The concentration gap between the fringes was
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Figure 5. Relationship between the starting point of the convection, i.e., the time for the current minimum, te, and the final potential of the potential step.
0.01 M. The vertical and horizontal size of the interferogram was ca. 1.7 mm × 2 mm. Results and Discussion Figure 2 shows a typical relationship between the current and the potential applied between the two parallel electrodes whose gap is about 1 mm. The potential represented is the difference between the upper electrode potential, E1, and the lower electrode potential, E2; i.e., E ) E1 - E2. The potential is linearly varied as a function of time at the rate of 2 mV/s. In the positive potential region, the electrodissolution proceeds at the upper electrode and the electrodeposition at the lower
Nakabayashi et al. electrode. The observed current increases with the potential. In the negative potential region, the reverse reactions take place, i.e., the electrodissolution at the lower electrode and the electrodeposition at the upper electrode. Again, the observed current increases with the potential. The saturation current at positive potentials is two times larger than that at negative potential. The vertical cross sectional views of the fluid obtained by laser interferometry are shown in Figure 3. The potential is +0.7 V for Figure 3a and -0.7 V for part b. Figure 3a demonstrates that when E1 > E2, the spatial distribution of the copper sulfate is governed by convection and that the flow in the fluid is packed periodically along the electrodes. The distance between the upward and downward flow is ca. 1 mm. When E1 < E2, Figure 3b shows that the fringes are settled parallel to the electrode surface. In this situation, the concentration changes as a function of the vertical coordinate and the mass transfer proceeds by pure diffusion. Thus, the asymmetry of the current obtained in Figure 2 is caused by the convective motion of the fluid, which occurs only in the positive potential region. The time evolution of the flow and the current is observed by the potential step from 0 V to (0.2 V. For the negative potential step, the current decays monotonously12 and the fringes in the interferogram grow along the electrode surface. The current is governed by the diffusion when the potential is stepped to the negative direction. However, the responses to the positive potential step are completely different. The time evolution of the current and the fringes is shown in Figure 4. The decay of
Figure 6. Time evolution of the potential and the interferogram by the current step from 0 A to 1.0 mA. The vertical and horizontal sizes of each picture are 1.7 mm and 2.0 mm, respectively.
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Figure 8. Relationship between the starting point of the convection, i.e., the time for the potential maximum, tc, and the final current of the current step.
Figure 7. Potential transience as a function of the final current of the current step. The final currents are 1.0, 0.85, 0.75, 0.65, and 0.50 mA from part a to part e, respectively.
the current has a dip and a bump at 8 and 16 s, respectively. As shown in Figure 4a, the fringes grow along the electrode surface before the time of the dip. After the current passes the dip, the fringes are deformed as shown by Figure 4b. The deformation of the fringes gradually changes from that in part b to that in part c, and finally the stationary convection pattern like that in Figure 3a is obtained. Until passing the current dip, although the fluid is hydrodynamically unstable, the fluid remains stationary. At the time for the dip, the hydrodynamic convection starts, and after that, the current increases by the convective mass transport. To clarify the starting time for the convection, the time course of the current is measured as a function of the final potential of the potential step. The time on the current dip, te, decreases as the final potential of the positive step increases, as shown in Figure 5. Because the current increases as the potential is made positive, the density inversion is quickly reached in the more positive potential region; therefore, the dip appears quickly as the potential becomes positive. The relationship between the electrode potential and the patterns of the convection is further examined under the current control conditions. When the current is stepped from 0 to 1.0 mA, where the electrodissolution proceeds at the upper electrode and the electrodeposition at the lower electrode, the time course of the potential is shown in Figure 6. The transients show oscillatory behavior. The potential profile is completely different from the one in the opposite current direction, where the diffusion-controlled profile is obtained.12,14 The interferogram (Figure 6a and b) shows that the fluid remains stationary till the maximum of the potential, and after that, the convective motion starts. When the oscillations disappear, the stationary convection pattern is obtained as Figure 6c. The time course of the potential varies as a function of the current, as shown in Figure 7. The currents for the step
electrolysis are 1.0, 0.85, 0.75, 0.65, and 0.50 mA for curves a-e, respectively. As the current increases, the amplitude of the potential oscillations becomes large. The time on the potential maximum, tc, is plotted as a function of the current in Figure 8. Under the large current, the hydrodynamic convection starts quickly, which is qualitatively identical with Figure 5. Concluding Remarks The flow in the electrolyte solution between the two electrodes forms a spatial pattern, which is driven by the hydrodynamic instability caused by the proceeding of the electrochemical reaction in the gravitational field. The transient experiment shows that the time course of the motion of the electrolyte forms the oscillatory electrochemical behaviors under the potential- and current-controlled conditions. The motion of the fluid and the electrochemical response would be reduced into the combination of the hydrodynamic and the electrochemical equations.15 A detailed study is under way in this laboratory. References and Notes (1) Normand, C.; Pomeau, Y.; Velarde, M. G. ReV. Mod. Phys. 1977, 49, 581. (2) Scott, S. K. Chemical Chaos; Clarendon Press: Oxford, U.K., 1991. (3) Nakabayashi, S.; Kira, A. J. Phys. Chem. 1992, 96, 1021. (4) Nakabayashi, S.; Uosaki, K. Chem. Phys. Lett. 1994, 217, 163. (5) Matumoto, G.; Aihara, K.; Ichikawa, M.; Tasaki, A. J. Theor. Neurobiol. 1984, 3, 1. (6) Aihara, K.; Matumoto, G.; Ikegaya, Y. J. Theor. Biol. 1984, 109, 249. (7) Chialov, D. R.; Gilmour, R. F.; Jalife, J. Nature 1990, 343, 653. (8) Sano, M.; Stato, K.; Nasuno, S.; Kokubo, H. Phys. ReV. A 1992, 46, 3540. (9) Lorenz, E. N. J. Atmos. Sci. 1963, 20, 130. (10) Muller, R. H. In AdVances in Electrochemistry and Electrochemical Engineering Delahay, P., Tobias, C., Eds.; John Wiley & Sons: New York, 1973; Vol. 9, p 281. (11) Born, M.; Wolf, E. Principle of Optics; Pergamon Press: Oxford, U.K., 1975. (12) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; Wiley: New York, 1980. (13) Landau, L. D.; Lifshitz, E. M. Fluid Mechanics; Pergamon Press: New York, 1970. (14) Plonski, I. H. J. Electrochem. Soc. 1970, 117, 1048. (15) Bruinsma, R.; Alexander, S. J. Chem. Phys. 1990, 92, 3074.
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