(Keynote) Clustering, Oscillations and Chaos in Electrochemical Many Particle Systems with Coexisting States: From CO Oxidation on Pt to Insertion Batteries
Authors: Salman Munir , Krischer Katharina 
Published: July 2021

Bistability, i.e. the coexistence of different states at identical external parameters, is a frequently encountered phenomenon in electrode reactions. If the reactions occur on individual, i.e. spatially separated, catalytically active areas that are all electrically connected, each individual active area can be considered as a bistable component, and the entire ensemble of all active areas as a many particle system of such interconnected bistable components. Examples range from (micro-)electrode arrays, where each of a usually moderate number of individual electrodes constitutes the bistable components, to insertion battery cathodes, where each of the billions of nano-particulate storage particles can be considered a bistable component.
In this talk, we will demonstrate that despite of their completely different chemical nature, from a dynamic point of view, all these systems can be treated mathematically under a common framework. We will start by introducing the general mathematical description and compile key results that can be derived [1]: (1) All steady states are composed of one, two or three cluster states, i.e. each of the individual components takes on one of the three values which correspond to the three steady states of the individual bistable component at the corresponding common value of the external voltage. (2) Stable steady states possess at most one electrode on the intermediate, autocatalytic branch. As a consequence, the electrodes transition sequentially from one stable state to the other one as the current density is increased. This sequential activation is a generalization of the mosaic instability described in phase transition systems. (3) Ensembles of globally coupled bistable components might exhibit oscillations. We will derive necessary condition of when the many particle system might become oscillatory and illustrate this condition with an intuitive LC analogue.
In the second part of the talk we will apply our general theory to two prominent examples. We will start with the CO oxidation on an array of Pt micro-electrodes, where experiments showed collective oscillations [2,3]. For this system, the necessary condition for a Hopf bifurcation to occur translates to the condition that components in two different groups (or, equivalently two of the three steady states of the bistable elements) have different slopes in either of the two dependences: the change of the coverage with potential at constant CO coverage, or in the change of the current with CO coverage at constant potential. While the first derivative is always positive, the current increases with coverage in the active state (where the coverage is low), but decreases in the passive (CO covered state) or the intermediate states which possess relatively high coverages. The existence of stable oscillations is indeed also observed in simulations. Besides oscillations, this system shows also period doubling cascades and chaos.
Our second example involves Li insertion batteries. Here, the chemical potential of each storage nanoparticle exhibits a non-monotonic characteristic as a function of the degree of charging [4]. Hence, the two stable states of a bistable component can be identified with charged and discharged nanoparticle of the insertion material, and a battery under charging / discharging conditions can be classified as a bistable many component system. During charging / discharging with a constant current oscillations of the potential have been reported [5], whose origin has not yet unambiguously been identified. We present a simplified model of the dynamics of the Li ion batteries and again apply our criterion for a Hopf bifurcation to the model. In this case, the necessary condition is not fulfilled so that the origin of the observed oscillations remains in the dark.
[1] M. Salman, Chr. Bick and K. Krischer, Phys. Rev. Research 2, 043125 (2020)
[2] D. Alfonso Crespo-Yapur, Antoine Bonnefont, Rolf Schuster, Katharina Krischer, and Elena R. Savinova, ChemPhysChem 14, 1117 (2013).
[3] S. Bozdech, Y. Biecher, E. R. Savinova, R. Schuster, K. Krischer, and A. Bonnefont, Chaos 28, 045113 (2018).
[4] W. Dreyer, J. Jamnik, C. Guhlke, R. Huth, J. Moskon, M. Gaberscek, Nat Mater. 9, 448 (2010).
[5] D. Li, Y. Sun, Zh. Zang, L. Gu, Z. Chen, H. Zhou, Joule 2, 1265 (2018)