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The research program is aimed at exploring theoretical and experimental techniques for decoding complexity in electrochemical systems.

A simplified electrochemical reaction-diffusion model system was investigated:

C de/dt = (V-e)/R – nFk(e)c (1)

dc/dt = [-2 k(e) c  + 2D(c0-c)/a ] /a (2)

Equations (1) and (2) describe the charge and mass balances, respectively, for a reduction reaction. The essential variables are the electrode potential e and near-surface concentration of the electroactive species, c. C is double layer capacitance, A is the surface area of electrode, F is Faradaic constant, n is the number of electrons in the reaction, V is circuit potential, R is series resistance, a is Nernst diffusion layer thickness, and D and c0 are the diffusion constant and the bulk concentration of the electroactive species, respectively. k(e) is the potential dependent rate constant.

Although equations 1-2 constitute a relatively simple set of equations, analytical solutions are difficult to obtain because of the highly nonlinear dependence of rate constant k on potential. In collaborations with Prof. Gregory Yablonsky at Parks College of Engineering (Saint Louis University), we are investigating the importance of thermodynamic reciprocal trajectories for the description of the dynamics of the system. The method predicts that carefully chosen anodic and cathodic current transients will have a constant ratio equal to the reaction quotient at the open circuit electrochemical reaction system. We confirmed the presence of such trajectories in both numerical simulations with the model system (equations 1-2) and in experiments with a rotating disk-electrode setup with the ferrocyanide/ferricyanide charge transfer process.  These results will provide a way of predicting kinetic trajectories (e.g., charge/discharge of batteries) based on carefully chosen (reciprocal) kinetic trajectories and the equilibrium constant.

As an alternative approach to modeling, we have been developing methodologies to obtain null clines of electrochemical systems from direct measurements. Null clines in electrochemical systems are typically obtained from ordinary differential equations; for example the e nullcline is the functional form of setting the right hand side of equation 1 to zero. When time scale separation exists between the system variables, the dynamical evolution of system can be predicted using null cline information.

With graduate students Michael Hankins and Timea Nagy we have shown that null clines can be obtained with concurrent control perturbations of circuit potential and electrode rotation rate. Numerical simulations indicate that the method outlined in the proposal is capable of providing the null cline points for a variety of electrochemical systems including In(III) reduction, uniform corrosion of Fe, and, (with partial success) H₂ oxidation. The numerical simulations also indicate that the null-cline information can effectively predict  system’s dynamics and thus holds promise for alternative modeling routes to traditional kinetics/mass transfer based approaches. Our efforts should now focus on experimental implementation of the techniques; a major challenge is the concurrent measurement of essential chemical species during the oscillatory system and the control of circuit potential and surface concentrations. Michael Hankins will be presenting a poster about the results at the 45th American Chemical Society Midwest Regional Meeting.

Graduate student Mahesh Wickramasinghe has been exploring the dynamical features of generalized cathode-anode (such as the electrochemical water-gas shift reaction) systems with the simplifying concept of cathode half cell acting as a Faradayic resistance. It was shown that as the surface area of the cathode half-cell increases the  Faradayic resistance exhibits a  maximum and thus nontrivial nonlinear effects such as cell instabilities, oscillations, and synchronization patterns can occur with the single or multiparticle anode system. Graduate student Mahesh Wickaramasinghe is in his 4^rd year now; he has published three publications (two of them with the support of the Grant). These studies will be essential components for his research proposal and dissertation thesis in the Interdisciplinary and Applied Science graduate program of Saint Louis University.

The Petroleum Research Fund has been a valuable promoter of my academic activity. Preliminary results generated from the Fund was used in an awarded NSF CAREER grant “Emergent reactive properties of far-from-equilibrium electrochemical systems”. Stimulating collaboration developed with Prof. Gregory Yablonsky at Parks College of Engineering at Saint Louis University; Prof. Yablonsky is an expert in ‘traditional’ kinetic modeling of chemical systems. Our discussions on decoding chemical complexity are ongoing and will result in future grant submissions. I was invited to give a talk Electrochemical Society meeting in Vancouver and at the Annual Seminars and International Workshops on Mathematics in Chemical Kinetics and Engineering (MaCKiE) about the results obtained with the grant activity.