Electrochemical Oscillations Research Articles

The Studies of Spontaneous Potential Oscillation in a Galvanostatic Copper Electrodeposition and the Crystallographic Textures Thereof

This study reports the influence of the current density and the electrode rotating speed on spontaneous potential oscillation and crystallographic textures of the electrodeposited copper. The potential only spontaneously oscillated in the range of -0.44V ~ -0.49V with respect to saturated mercury-mercurous sulfate electrode (SMSE). This result implies that the electrochemical reduction of copper ions at the metal/solution interface is affected by those organic additives, and the electrochemical oscillation reaction depends on a specific potential range, which may relate with the adsorbed chemical species. In addition, the waveform of the potential oscillation is adjustable by the electrode rotating speed and the current density, and it affects the crystal structure and the surface microstructure of the deposited copper. The plated copper layers were characterized by FIB, FE-SEM, and HR-TEM, and we found a layered structure with a series of parallel twinned boundaries. Furthermore, the layered structure only formed with the specific waveform of the potential oscillation. The spontaneous potential oscillations observed in the copper deposition are explained according to the electrochemical studies and the corresponding microstructure analyses.

Synchronization of Current Oscillations in Dual-Anode Dissolution System in the Presence of a Common Cathode Electrode

The coupling behavior of multiple working electrodes with a reference and counter electrode has been explored in several different electrochemical systems [1, 2]. Many phenomena are known to exist at far-from-equilibrium conditions such as in-phase[3, 4], anti-phase[3], and out-of-phase[5] synchronization, clustering[6], and chimera states [7, 8]. Large majority of these studies was performed in the traditional ‘three-electrode’ configuration with reference, counter, and a multi-electrode array as a working electrode. The coupling among the working electrodes typically occurs through an external resistance interface [9] or through potential drops in the electrolyte [10]. In this contribution, we explore the nonlinear dynamics of oscillatory Ni dissolution in a dual anode system; instead of the traditional reference/counter electrodes, we apply a single nickel cathode. With increasing the cathode size we see a transition from desynchronized through partially synchronized to fully synchronized behavior of the current oscillations of the anodes. The experiments thus imply that changing the cathode size affects the coupling between the anodes. Similar transition was seen when the cathode size was kept constant, but the individual resistances attached to the anodes were varied. The synchronization transitions were interpreted by the charge transfer resistance of the cathode, which inherently couples the electrodes. Further experimentation has shown that similar transitions can be seen with other cathodes (e.g., Pt, glassy carbon, and tin). The experiments thus show that the nonlinear behavior of a complex cathode-anode cell can be greatly simplified when majority of the overpotential is due to driving the anodic reactions to a far-from equilibrium state, while the relatively simple cathode (with small overpotential and fast kinetics) acts as a coupling element between the anodes. Such simplification can be a useful tool for interpreting the complex kinetic behaviors of galvanic and electrolytic cells that have time-scale separations between the cathodic and anodic processes. 1. Kiss, I.Z. and J.L. Hudson, Phase synchronization of nonidentical chaotic electrochemical oscillators. PCCP, 2002. 4(12): p. 2638-2647. 2. Cruz, J.M., M. Rivera, and P. Parmananda, Experimental observation of different types of chaotic synchronization in an electrochemical cell. Physical Review E, 2007. 75(3): p. 035201. 3. Kiss, I.Z., Y. Zhai, and J.L. Hudson, Predicting mutual entrainment of oscillators with experiment-based phase models. Phys. Rev. Lett., 2005. 94(24): p. 248301. 4. Kiss, I.Z. and J.L. Hudson, Phase synchronization and suppression of chaos through intermittency in forcing of an electrochemical oscillator. Physical Review E, 2001. 64(4): p. 046215. 5. Kiss, I.Z., Q. Lv, and J.L. Hudson, Synchronization of non-phase-coherent chaotic electrochemical oscillations. Physical Review E, 2005. 71(3): p. 035201. 6. Wang, W., I.Z. Kiss, and J.L. Hudson, Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. Chaos, 2000. 10(1): p. 248-256. 7. Wickramasinghe, M. and I.Z. Kiss, Spatially organized dynamical states in chemical oscillator networks: Synchronization, dynamical differentiation, and chimera patterns. PloS one, 2013. 8(11): p. e80586. 8. Wickramasinghe, M. and I.Z. Kiss, Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions. PCCP, 2014. 16(34): p. 18360-18369. 9. Kiss, I.Z., W. Wang, and J.L. Hudson, Experiments on arrays of globally coupled periodic electrochemical oscillators. J. Phys. Chem. B, 1999. 103(51): p. 11433-11444. 10. Jain, S., et al., The effect of IR compensation on stationary and oscillatory patterns in dual-electrode metal dissolution systems. Electrochim. Acta, 2009. 55: p. 363-373.

Electrochemical Oscillation during H2O2 Reduction in Basic Solutions

A new type of electrochemical oscillation has been found to appear as a current oscillation in the H2O2-NaOH-Pt system. The oscillation, named oscillation I, appears within the potential region where an N-shaped negative differential resistance (N-NDR) is observed. The N-NDR is attributed to the formation of under-potential deposited hydrogen (upd-H) which suppresses the reduction of HO2 - produced from H2O2. Moreover, oscillation I also appears in the H2O2-H2SO4-Pt system when the salts such as Na2SO4 and K2SO4 are added to electrolytes, because the local pH at the electrode surface even in H2SO4 solutions becomes basic during the H2O2 reduction. Electrochemical impedance measurements indicate that oscillation I is classified into an NNDR oscillator, and also that the N-NDR plays a crucial role in the positive feedback loop in oscillation I. The surface concentration of HO2 - plays a role as the slow process in the negative feedback loop.

Transient chaotic behavior during simultaneous occurrence of two electrochemical oscillations

We have found that a chaotic oscillation transiently appears when two kinds of current oscillations, named oscillation A and oscillation α, occur simultaneously. Oscillations A and α appear during the reduction of H2O2 and S2O8 2− respectively on the Pt electrode. When the electrode potential is stepped from the rest potential to a potential where both the oscillations appear, a period-1 oscillation first appears, and then a period-doubling bifurcation cascade occurs. After that, the transient chaos appears, which is followed by a sequence of mixed-mode oscillations (MMOs). The appearance of the chaotic behavior and the MMOs can be explained on the basis of the reported mechanisms for oscillations A and α. Both the oscillations are caused by an N-shaped negative differential resistance (N-NDR) due to the formation of under-potential deposited H (upd-H), indicating that a positive feedback mechanism works during the simultaneous occurrence of oscillations A and α. On the other hand, negative feedback mechanisms for oscillations A and α include the surface concentration of H2O2 and S2O8 2−, respectively. We can, then, conclude that the combination of the positive feedback mechanism and the two negative feedback mechanisms of different time scales gives rise to the chaotic behavior and the MMOs, which has been verified by numerical simulations.

Periodicity hubs and spirals in an electrochemical oscillator

The control parameter space of lasers, electronic circuits, and biological oscillators was recently discovered to be riddled with remarkable points, called periodicity hubs, responsible for a wide-ranging self-organization of the systems. Although displaying features which resemble the organization seen in chemical models, periodicity hubs have not been detected in such models thus far. Here, we report numerical evidence that periodicity hubs and the infinite spirals of stable oscillations issuing from them exist profusely in an electrochemical oscillator model. For selected parameter ranges, we observe sequences of nonchaos-mediated mixed-mode oscillations. Chemical hubs open the possibility of studying experimentally the complex self-organization of stable oscillations and complicated phenomena of current interest. We report high-resolution stability diagrams providing reference charts to guide experimental work as well as stringent tests for the validity of the electrochemical oscillator model used.

The Effect of Nitrate on Salt Layers in Pitting Corrosion of 304L Stainless Steel

Current oscillations were observed during one-dimensional pitting corrosion of 304 L stainless steel in neutral 1 M NaCl solutions with varying NaNO3 concentrations. Synchrotron X-ray diffraction was used to identify the salt layer at the corrosion front. It was found that, although current oscillations were induced in solutions with higher concentrations of NaNO3, the salt species in the pit did not change and a nitrate-free salt was present in all solutions. At higher NaNO3 concentrations, a change of salt crystal morphology was detected. Electrochemical oscillations were seen to coincide with secondary pitting on the pit surface indicating that two corrosion regimes were operating in parallel. Synchrotron radiography was used on artificial pits to measure the change in corrosion front and material loss in situ. Before nitrate was added, the corrosion front showed non-uniform material loss across the interface when beneath the salt layer. Nitrate addition induced a local region of passivation that propagated across the pit surface. Surface roughness was quantified using R-values and seen to vary without a clear trend until passivation, after which it stayed constant. A mechanism is suggested in which partial passivation occurs in these systems, where passivated areas are undercut as the corrosion front moves, generating surges in current.

Shilnikov Homoclinic Bifurcation of Mixed-Mode Oscillations

The Koper model is a three-dimensional vector field that was developed to study complex electrochemical oscillations arising in a diffusion process. Koper and Gaspard described paradoxical dynamics in the model: they discovered complicated, chaotic behavior consistent with a homoclinic orbit of Shil'nikov type, but were unable to locate the orbit itself. The Koper model has since served as a prototype to study the emergence of mixed-mode oscillations (MMOs) in slow-fast systems, but only in this paper is the existence of these elusive homoclinic orbits established. They are found first in a larger family that has been used to study singular Hopf bifurcation in multiple time scale systems with two slow variables and one fast variable. A curve of parameters with homoclinic orbits in this larger family is obtained by continuation and shown to cross the submanifold of the Koper system. The strategy used to compute the homoclinic orbits is based upon systematic investigation of intersections of invariant manifolds in this system with multiple time scales. Both canards and folded nodes are multiple time scale phenomena encountered in the analysis. Suitably chosen cross-sections and return maps illustrate the complexity of the resulting MMOs and yield a modified geometric model from the one Shil'nikov used to study spiraling homoclinic bifurcations.

Tunable Electrochemical Oscillation and Regular 3D Nanopore Arrays of InP

Tunable potential oscillations are obtained by electrochemical etching of n-InP (100) in the 3 M NaCl solution using the chronoptentiometry with current ramp. The regular 3D nanopore arrays are formed with the change of the current density from 320 to 260 mA·cm−2 at the scan rate 0.72 - 0.80 mA·cm−2·s−1. The results showed that the current density ranges and scan rate have the effect on the E-t curves and the pore's morphology. The scan rate can regulate not only on the charge consumed per period but also on the amplitude of potential oscillation, and shown that the charge per period and the amplitude can be tuned when proper electrochemical parameters are selected. Furthermore, the pore's morphology will change from the regular structure to irregular with the increasing of the scan rate. In addition, the relation has also been discussed between the E-t curves and the pore's morphology.

Potentiostatic current and galvanostatic potential oscillations during electrodeposition of cadmium.

Cathodic current and potential oscillations were observed during electrodeposition of cadmium from a cyanide electrolyte on a vertical platinum electrode, in potentiostatic and galvanostatic experiments. Electrochemical impedance spectroscopy experiments revealed a region of negative real impedance in a range of non-zero frequencies, in the second descending branch with a positive slope of the N-shape current-potential curve. This kind of dynamical behaviour is characteristic of the HN-NDR oscillators (oscillators with the N-Shape current-potential curve and hidden negative differential resistance). The oscillations could be mainly attributed to the changes in the real active cathodic area, due to the adsorption of hydrogen molecules and their detachment from the surface. The instabilities of the electrochemical processes were characterized by time series, Fast Fourier Transforms and 2-D phase portraits showing quasi-periodic oscillations.

Self-organization of TiO2 Nanobamboos by Anodization with Deep Eutectic Solvent

We report an unconventional electrochemical spontaneous oscillation of current in Ti anodization by adding deep eutectic solvent (DES) of 2–10% to a fluoride-containing electrolyte; nanobamboos (NBs), i.e., nanotubes decorated with periodic exterior rings, were formed by the DES-assisted anodization. Spontaneous formation of NBs occurred upon application of a constant 20V voltage, together with a self-induced current oscillation that corresponds well to the NB structures. The initial voltage must be higher than a threshold of approximately 14V to induce the self-organization of the NBs. Once a dense layer of TiO2 is formed at 10V or lower, formation of the NBs is suppressed even when a higher voltage (above 15V) is applied. The NBs formed with the spontaneous current oscillation were densely packed (ca. 1.54×1010cm−2) with each NB possessing many rings spaced 20–35nm apart. The thickness of each ring was ca. 10nm. By increasing the DES concentration to 10 wt%, the diameter of the NBs increased from 45 to 110nm and their growth rate increased from 0.16 to 0.3μm/h. The spontaneous current oscillation we observed differs from the conventional electrochemical oscillation because (1) oscillation period is quite long (7min) and (2) the oscillation results in the periodic modulation of TiO2 NBs. The self-organized nanobaoboos were characterized for various anodization conditions, and a mechanism was proposed with the basis of the high conductivity and high viscosity of DES.

On the origin of damped electrochemical oscillations at silicon anodes (revisited).

Electrochemical oscillations accompanying the formation of anodic silica have been shown in the past to be correlated with rather abrupt changes in the mechanical stress state of the silica film, commonly associated with some kind of fracture or porosification of the oxide. To advance the understanding on the origin of such oscillations in fluoride-free electrolytes, we have revisited a seminal experiment reported by Lehmann almost two decades ago. We thereby demonstrate that the oscillations are not stress-induced, and do not originate from a morphological transformation of the oxide in the course of anodisation. Alternatively, the mechanical features accompanying the oscillations can be explained by a partial relaxation of the field-induced electrostrictive stress. Furthermore, our observations suggest that the oscillation mechanism more likely results from a periodic depolarisation of the anodic silica.

Electrochemical Oscillation during H2O2 Reduction in Basic Solutions

INTRODUCTIONChemical and electrochemical oscillations have been studied extensively because they are attractive phenomena from the viewpoint of dynamic self-organization of molecular systems.The H2O2 reduction at Pt electrodes in acidic solutions (H2O2 + 2H+ + 2e- → 2H2O) has a unique feature where various kinds of oscillations, named oscillations A, B, C, D, E, F and G, are observed, as we reported more than a decade ago. Oscillation A is observed in the potential region of formation of under-potential deposited H (upd-H), whereas oscillation B is observed in the region of hydrogen evolution reaction (HER) (see. Fig. 1b). Oscillations C and D are observed in the presence of a small amount of Cl- or Br-ions which adsorb on Pt surface. Oscillations E, F and G are observed when a single-crystal Pt(111) or Pt(100) electrodes are used.We have also reported that another oscillation, named oscillation H, appears under current controlled conditions in the presence of Na2SO4 or K2SO4 in the H2O2-H2SO4-Pt electrochemical system [1]. In the presence of the Na+ or K+ ions originating from the salts, the transport rate of H+ to the electrode surface by the electromigration decreases [2] and consequently the local pH at the electrode surface becomes basic during the reduction of H2O2. When the solution is basic, H2O2 dissociates to form HO2 - ion (H2O2 ⇌ HO2 - + H+) because H2O2 is a weak acid. The presence of HO2 -ion probably attributes to the appearance of oscillation H [1].Recently, we have found another current oscillation appears during the reduction of H2O2when the solution is basic. In this work, we studied the conditions for the appearance of the oscillation and the mechanism of the oscillation itself.RESULTS and DISCUSSIONFigure 1 shows the current (I) – potential (E) curves for a Pt-disc electrode in 0.14 M NaOH + 0.25 M H2O2 and 0.05 M H2SO4 + 0.25 M H2O2 with or without Na2SO4, measured under current controlled conditions. In the basic solution (Fig. 1a), the H2O2-reduction current started to flow at ca. 0.1 V vs. SHE. A current oscillation appeared at around -0.85 V. The HER occurred in the potential region below ca. -0.95 V.In the acidic solution without Na2SO4 (Fig. 1b), oscillations A and B appeared. However, in the presence of Na2SO4 (Fig. 1c), both oscillations A and B did not appear. The current oscillation did at around -0.85 V and the HER occurred in the potential region below ca. -0.95 V, similarly to the basic solution. This was because the local pH at the electrode surface was basic in the presence of Na+ ions. The waveform of the oscillation was periodic, as shown in Figure 2. The oscillation period was around 0.1 s and it increased as the potential decreased. Very similar behavior was observed by the addition of K2SO4.These results show that the current oscillation appeared during the H2O2 reduction when the solution was basic. That is, the current oscillation appeared during the electrochemical reduction of HO2 - ion (HO2 - + H2O + 2e- → 3OH-). It appeared in the potential region where a negative differential resistance (NDR) was formed. Therefore, the NDR played an important role for the appearance of the oscillation.This work is partially supported by the Research Institute for Science and Technology of Tokyo Denki University under Grants Q12E-02.REFERENCES[1] Y. Mukouyama, M. Hasegawa, S. Yamamoto, S, Nakanishi and H. Okamoto, ECS Trans., 58 (2013) in press.[2] Y. Mukouyama, M. Kikuchi and H. Okamoto, J. Electroanal. Chem., 617, 179 (2008).

Porosification of Silicon from the Viewpoint of Nonlinear Dynamics

Anodic dissolution of silicon in HF solutions leads to formation of porous silicon. Formation of a wide variety of porous structures has been reported. In the course of the studies, electrochemical oscillations have been found in silicon anodization. Because a symmetry breaking is necessary for the formation of porous silicon, such oscillatory phenomena have attracted keen attention for the understanding of porous silicon formation. Formation of macroporous silicon, whose pore diameter is several micrometers, has been explained based on the current burst model proposed by Föll and his colleagues. In the current burst model, macropore formation has been explained based on desynchronization of local oscillators on a silicon surface.Recent studies on nonlinear dynamics in electrochemistry have shown that spatiotemporal pattern formation is closely related to a negative differential resistance (NDR) observed in the current density vs. potential curve. However, NDRs have not been considered in porous silicon formation so far. We have focused our attention on the emergence of NDR in anodization of silicon, and have discussed the spatial pattern formation on silicon. Recently, we have found that a clear S-shaped NDR is observed after the correction of iR-drop in the electrolyte solution, when using an HF solution containing alcohol such as 2-propanol. In the S-shaped NDR region, an array of microgrooves is spontaneously formed on the silicon surface. Since an S-shaped NDR is induced by a positive feedback which is independent on electrode potential, while electrode potential plays a role of an negative feedback. In the present case, we think that the microgroove array is induced by Turing instability. According to earlier studies, the size of Turing patterns observed in electrochemical systems is on the scale of millimeters. Astonishingly, the size of the present Turing pattern is on the scale of micrometers. In the present paper, the reason why the characteristic size is so small will be discussed in detail. In addition to the Turing pattern formation, formation of other spatiotemporal patterns in silicon electrochemistry, which is difficult to be explained in the classical framework of spatiotemporal pattern formation in electrochemistry, will be discussed.

Construction of Arnold Tongue Structures for Coupled Periodic Oscillators

Arnold tongue structures generated due to the mutual entrainment of two periodic oscillators are studied experimentally and numerically. This mutual entrainment is provoked due to the mutual (bidirectional) coupling between the two oscillators. In experiments, this bidirectional coupling is achieved by immersing a couple of anodes (oscillators) in a common electrolytic solution. A voltage mismatch between these anodes renders the time period of the uncoupled electrochemical oscillators non-identical. Moreover, the coupling strength between the two oscillators is uniquely determined by the distance separating them. Systematically varying the distance between these two anodes as a function of their voltage mismatch, phase locked domains were located. Subsequently, Arnold tongue structures were constructed in the experiments. Numerical simulations, using a model for electrochemical corrosion, corroborate our experimental findings.

Rotational Waves in Rings of Electrochemical Oscillators

Chemical and biological systems exhibit network properties dependent upon the behavior of individual units and the interactions between units.[1] The presence or absence of interactions and the strength of the interactions determine the topology of the network and in turn the network properties. From a mathematical perspective, a variety of non-rotating and rotating waves can exist for a ring of locally coupled units[2] and the non-rotating solutions are the dominant outcome when coupling is the only mean of interactions regardless of the initial conditions.[3] Therefore, engineering is required to achieve solutions aside from the dominant non-rotating state. The formation of waves is examined in oscillatory nickel dissolution where units of individual oscillators interact through external resistance which controls the strength of interaction. An experimental technique using a locally coupled twenty nickel electrode ring is presented in which through a combination of temporary alterations in topology and the application of global feedback provides all possible rotational solutions. There are four rotational waves which can propagate about the ring and are distinguished by the velocity and the number of waves. The propagation rate is inversely proportional to the number of waves in the rotation (m) for all rotations. Solutions with no rotation have an m value of zero while rotational solutions are obtained for m=1,2,3,4. Larger m values (m ≥ 5) are shown to not be stable in the network. The results thus indicate that while network plasticity is thought to be significant in the operation of neural systems, it can also play a role in pattern selection of chemical systems.

Clustering in globally coupled oscillators near a Hopf bifurcation: theory and experiments.

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.

Stochastic Resonance in Electron Transfer Oscillations of Extended Viologen

Selective generation of only odd harmonics and the absence of even harmonics were never described for electrochemical oscillators though this phenomenon is known in special fields of physics and in biological systems. The heterogeneous electron transfer to the extended viologen with four repetitive viologen units yields electrochemical current oscillations. Small perturbation of the applied voltage by only a few millivolts sine wave results in current oscillations, which selectively enhance only the odd harmonic higher frequencies. The effect is explained in terms of the theory of stochastic resonance occurring in driven oscillating reactions. The described interplay of heterogeneous and homogeneous coupled electron transfers complies with the behavior of a nonlinear potential-symmetric system.

Electrochemical Oscillations during Reduction of Nitrate Ions on Cu and Ag

We have found that two types of oscillations, named oscillations I and II, occur during the electrochemical reduction of nitrate ions, not only on Cu, as has been reported in our earlier paper (ECS Transactions 50 (2013) 61), but also on Ag in acidic solutions, such as HNO3 solutions. As for the reduction on Cu, oscillation II also occurs in non-acidic solutions, e.g. KNO3 solutions with or without NaOH. The hydrogen bubbles produced by the water reduction evolve synchronously with oscillation II. The mechanism of oscillation II can be explained by a solution-stirring effect due to the bubble evolution. Furthermore, we have found that another oscillation, named oscillation III, appears for Cu in basic solutions, such as NaOH + KNO3 solutions, while hydrogen bubbles evolve constantly. The mechanism of oscillation III cannot be explained by the solution-stirring effect and it awaits further investigation.

New Electrochemical Oscillation Appeared in H2O2-H2SO4-Pt System by Addition of Na2SO4 and K2SO4

We have studied the H2O2 reduction on Pt in 0.10 M H2SO4 + 0.25 M H2O2 solutions and found that a new potential oscillation, named oscillation H, appears under current controlled conditions when Na2SO4 or K2SO4 is added to the solutions. The oscillation range is between ca. 0.1 and 0.6 V, where a negative differential resistance (NDR) is formed. Oscillation H, therefore, is classified into a hidden-NDR oscillator. We have also found that oxygen bubbles evolve constantly from the electrode surface during oscillation H and showed that the local pH at the electrode surface is basic due to the presence of the salts. Therefore, the oxygen bubbles are produced probably by the catalytic decomposition of HO2 - formed via the dissociation of H2O2 at the electrode surface.

Analogy between electrochemical oscillations and quantum physical processes

In (photo) electrochemical oscillations, the discretization of phase oscillators leads to a sequence of time dependent oscillator density functions which describe the passing of the oscillators through their minimum at each cycle. Two consecutive oscillator density functions are connected by a Markov process represented by a linear integral equation of second order which is homogeneous in the case of sustained oscillations. The kernel of the integral equation is a normalized Greens Function and represents the probability density for the periods of the oscillators. Both together, the oscillator density function and the two-dimensional probability density for the periods of the oscillators define a random walk. The relation of the model to the holographic principle is discussed briefly. Further, a detailed analysis of a kernel of the integral equation leads to a frequency distribution g for the period length. Additionally, it is possible to determine the energy E in dependence on the period length from the electrochemical process. The product g E shows qualitatively the same behaviour as the radiation of a black body, indicating that the discretization of phase oscillators, when represented by phase space analysis, show an analogy to quantum processes.