Additions and Corrections
8616 The Journal of Physical Chemistry, Vol. 96,No. 21, 1992
occur between electrochemical oscillators and that many of the phenomena common to coupled systems can be produced in the two systems which were investigated. We have found transitions to chaos and to higher order chaos, phase-locking, extinction of oscillations, and the production of oscillations through coupling of two steady currents. Electrochemical oscillators have produced a rich variety of dynamic phenomena in uncoupled systems. It is likely that coupled electrochemical oscillators can be used for detailed tweparameter bifurcation studies. For direct comparisons of experimental results to analyses, one of the two parameters should be the coupling strength. In the case of the two disk electrodes in the second study described in this paper, the gap width between the electrodes might have served as this parameter. Unfortunately, however, the range of gap widths over which each electrode oscillated independently was very small, so all the results presented in this paper were obtained with a single gap width of 4 mm. The disk which rotated, of course, could produce oscillations for any arbitrary gap width; however, the nonrotating disk, since its flow was produced by the rotating one, oscillated only for certain gap widths. Changing the gap width thus changed not only the coupling strength, it also changed significantly the basic dynamics of the individual oscillators. The rotation of both of the disks would alleviate this deficiency since both would then produce oscillations for arbitrary gap widths. The mechanism of the coupling is certainly complicated and was not investigated in detail in this study. Two contributors to the coupling are the ohmic drop in the electrolyte and the transport of products or intermediates among the electrodes. The electrolyte concentration was 1 .Oand 1.6 M in the two sets of experiments, respectively. Although the ohmic drop may be small, it may be large enough to produce significant coupling effects. Transport of species may also play an important role. The changed electrolyte concentration can alter the potentials at which oscillations occur. For example, in the cobalt system, a decrease of the concentration of hydrochloric acid shifts the oscillating regime in the anodic direction and a decrease of the concentration of chromic acid causes a slight shift of the oscillating regime in the
cathodic direction. This shift follows rules which point to pitting corrosion (Hudson et al., 1988). In addition, diffusion and migration of charged species contribute to changes of concentrations near the electrodes. It is likely, in fact, that some combination of ohmic drop and transport leads to the coupling. Steady and oscillating currents give rise to potential gradients in the electrolyte between the two electrodes which will be balanced by the migration of ions; this is the concept of coupling through local current which was forwarded by Franck and Meunier (1953)to explain traveling excitations on passive iron waves and the coupling of oscillating Co wires.
Acknowledgment. This work was supported in part by the North Atlantic Treaty Organization, the National Science Foundation, the Center for Innovative Technology (Commonwealth of Virginia), and the Alexander von Humboldt Stiftung. Registry No. Co, 7440-48-4; HCI, 7647-01-0; CrO,, 1333-82-0; chromic acid, 7738-94-5.
References Bell, J. C. The Dynamics at Cobalt Electrodes in Chromic Acid El%trolytes. Ph.D. Dissertation, University of Virginia, 1991. Franck, U. F.; Meunier, L. Gekoppelte periodische Elektrodenvorgange. Z . Naturforsch. 1953, 86, 396-406. Hudson, J. L.; Bell, Joseph C.; Jaeger, Nils I. Potentiostatic Current Oscillations of Cobalt Electrodes in Hydrochloric Acid/Chromic Acid Electrolytes. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 1383-1 387. Lehmkuhl, G. D.; Hudson, J. L. Flow and Mass Transfer mear an Enclosed Rotating Disk: Experiment. Chem. Eng. Sci. 1971, 26, 1592-1600. Schlichting, H. Boundary Layer Theory; McGraw-Hill: New York, 1960. Wang, Y.; Hudson, J. L. Experiments on Interacting Electrochemical Oscillators. J . Phys. Chem., preceding paper in this issue.
ADDITIONS AND CORRECTIONS 1992, Volume 96 I. Rosenberg,* J. R. Brock,* and A. HeUer*: Collection Optics of T i 0 2 Photocatalyst on Hollow Glass Microbeads Floating on Oil Slicks. Page 3423. In the Introduction, first paragraph, the third sentence should read correctly as follows: ...the hole oxidizes absorbed water to OH radicals and protons; ....
