Electrochemical computational determination

The use of impedance electrochemical techniques to study corrosion mechanisms and to determine corrosion rates is an emerging technology. Elec trode impedance measurements have not been widely used, largely because of the sophisticated electrical equipment required to make these measurements. Recent advantages in micro-elec tronics and computers has moved this technique almost overnight from being an academic experimental investigation of the concept itself to one of shelf-item commercial hardware and computer software, available to industrial corrosion laboratories. 

This capacity limit for a given cell size has been determined as a result of computer simulation by GP Battery Technologies, as referenced from J. Fan and D. Magnuson, in Rechargeable Lithium Batteries K.M. Abraham, E.S. Takeuchi, M. Doyle eds., PV 2000-21, the Electrochemical Proceedings Series, Pennington, NJ (2000). 

To summarize the impedance discussion so far an electrochemical cell is constructed, and its impedance Z determined as a function of frequency. From these impedance values, the real and imaginary impedances, Z and Z", respectively, are computed and hence a Nyquist plot is drawn. 

What is next Several examples were given of modem experimental electrochemical techniques used to characterize electrode-electrolyte interactions. However, we did not mention theoretical methods used for the same purpose. Computer simulations of the dynamic processes occurring in the double layer are found abundantly in the literature of electrochemistry. Examples of topics explored in this area are investigation of lateral adsorbate-adsorbate interactions by the formulation of lattice-gas models and their solution by analytical and numerical techniques (Monte Carlo simulations) [Fig. 6.107(a)] determination of potential-energy curves for metal-ion and lateral-lateral interaction by quantum-chemical studies [Fig. 6.107(b)] and calculation of the electrostatic field and potential drop across an electric double layer by molecular dynamic simulations [Fig. 6.107(c)]. 

Modern DFT has become a powerful tool to understand, predict, and discover electrochemical catalysts with improved ORR activity and stability. Computational free energy reaction diagrams provide insight into the potential-determining elementary reaction step of the ORR as a function of atomistic descriptors (surface-related properties) of the catalyst material. DFT-based volcano relations have been established pointing to improved catalyst systems. 

Finite difference — Finite difference is an iterative numerical procedure that has been used to quantify current-voltage-time relationships for numerous electrochemical systems whose analyses have resisted analytic solution [i]. There are two generic classes of finite difference analysis 1. explicit finite difference (EFD), where a new set of parameters at t + At is computed based on the known values of the relevant parameters at t and 2. implicit finite difference (IFD), where a new set of parameters at t + At is computed based on the known values of the relevant parameters at t and on the yet-to-be-determined values at t + At. EFD is simple to encode and adequate for the solution of many problems of interest. IFD is somewhat more complicated to encode but the resulting codes are dramatically more efficient and more accurate - IFD is particularly applicable to the solution of stiff problems which involve a wide dynamic range of space scales and/or time scales. 

Fourier transformation — In common with many other technologies, electrochemical instruments nowadays produce data in the form of a time series - a large array of numbers equally spaced in time. As an alternative to inspecting the data - usually electric current in electrochemical applications - in its raw time-series form, an alternative is to determine the amplitudes of the sinusoidal frequencies present in the signal. Fourier transformation is the procedure by which the time series is analyzed into its component frequencies. This task is delegated to a computer, usually through a fast Fourier transform or FFT program. 

Another key computational advance in electrochemistry has been the development of convenient programs for simulating voltanunetric responses. Such programs, which can be run on conventional personal computers, allow for determination of fundamental electrochemical parameters and reaction rates for coupled chemical reactions. Because of the prevalence of cyclic voltammetry, the majority of such applications are performed using DigiSim, which calculates... 

To determine the type of the chemical reaction involved and the sequence of chemical and electrochemical processes and finally to determine the value of the rate constant, it is necessary to record the waves of the substance C at various concentrations of B at a given temperature. For the computation of rate constant it is moreover necessary to know the value of the equilibrium constant K determined by an independent experiment. 

The equilibrium constant iTj can be determined using electrochemical techniques (Valenta, 1960) for the computation of the hypothetical diffusion current an estimate of the diffusion coefficient is necessary and a two-electron process is assumed. 

Standard electrode potential data are available for an enormous number of halfreactions. Many have been determined directly from electrochemical measurements. Others have been computed from equilibrium studies of oxidation/reduction systems and from thermochemical data associated with such reactions. Table 18-1 contains standard electrode potential data for several half-reactions that we will be considering in the pages that follow. A more extensive listing is found in Appendix 5. ... 

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