Universal Algorithm for Simulating and Evaluating Cyclic Voltammetry at Macroporous Electrodes by Considering Random Arrays of Microelectrodes

An algorithm for the simulation and evaluation of cyclic voltammetry (CV) at macroporous electrodes such as felts, foams, and layered structures is presented. By considering 1D, 2D, and 3D arrays of electrode sheets, cylindrical microelectrodes, hollow‐cylindrical microelectrodes, and hollowspherical microelectrodes the internal diffusion domains of the macroporous structures are approximated. A universal algorithm providing the timedependent surface concentrations of the electrochemically active species, required for simulating cyclic voltammetry responses of the individual planar, cylindrical, and spherical microelectrodes, is presented as well. An essential ingredient of the algorithm, which is based on Laplace integral transformation techniques, is the use of a modified Talbot contour for the inverse Laplace transformation. It is demonstrated that first‐order homogeneous chemical kinetics preceding and/or following the electrochemical reaction and electrochemically active species with non‐equal diffusion coefficients can be included in all diffusion models as well. The proposed theory is supported by experimental data acquired for a reference reaction, the oxidation of [Fe(CN)6]4− at platinum electrodes as well as for a technically relevant reaction, the oxidation of VO2+ at carbon felt electrodes. Based on our calculation strategy, we provide a powerful open source tool for simulating and evaluating CV data implemented into a Python graphical user interface (GUI)

Finite Heterogeneous Rate Constants for the Electrochemical Oxidation of VO2+ at Glassy Carbon Electrodes

The electrochemical oxidation of VO2+ at planar glassy carbon electrodes is investigated via stationary and rotating linear sweep voltammetry as well as via chronoamperometry. It is demonstrated that introducing finite kinetic rate constants into the Butler-Volmer equation captures the experimentally observed concentration dependence of the ordinate intercept in Koutecky-Levich plots that cannot be explained by using the classical model. This new concept leads to a three-term Koutecky-Levich equation considering mass transport limitations, Butler-Volmer kinetics, as well as finite heterogeneous kinetics simultaneously. Based on these findings it is pointed out that stationary linear sweep voltammetry followed by an irreversible Randles-Sevcik analysis is not sufficient for deducing the electrode kinetics of the VO2+-oxidation. In contrast, it is verified experimentally and theoretically that a Tafel analysis will still provide reasonable values of k(0) = 1.35 . 10(-5) cm/s and alpha = 0.38, respectively. Finally, it is shown that introducing the concept of finite heterogeneous kinetics into the theory of stationary linear sweep voltammetry also explains the failure of the irreversible Randles-Sevcik relation leading to an extension of the classical model and providing insight into the electrochemical oxidation reaction of VO2+

A simple and effective method for the accurate extraction of kinetic parameters using differential Tafel plots

The practice of estimating the transfer coefficient (α) and the exchange current (i0) by arbitrarily placing a straight line on Tafel plots has led to high variance in these parameters between different research groups. Generating Tafel plots by finding kinetic current, ik from the conventional mass transfer correction method does not guarantee an accurate estimation of the α and i0. This is because a substantial difference in values of α and i0 can arise from only minor deviations in the calculated values of ik. These minor deviations are often not easy to recognise in polarisation curves and Tafel plots. Recalling the IUPAC definition of α , the Tafel plots can be alternatively represented as differential Tafel plots (DTPs) by taking the first order differential of Tafel plots with respect to overpotential. Without further complex processing of the existing raw data, many crucial observations can be made from DTP which is otherwise very difficult to observe from Tafel plots. These for example include a) many perfectly looking experimental linear Tafel plots (R2 > 0.999) can give rise to incorrect kinetic parameters b) substantial differences in values of α and i0 can arise when the limiting current (iL) is just off by 5% while performing the mass transfer correction c) irrespective of the magnitude of the double layer charging current (ic), the Tafel plots can still get significantly skewed when the ratio of i0/ic is small. Hence, in order to determine accurate values of α and i0, we show how the DTP approach can be applied to experimental polarisation curves having well defined iL, poorly defined iL and no iL at all

examples of monometallic, homobimetallic and heterobimetallic complexes

Mononuclear PtII and the first dinuclear PtII complexes along with a cyclometalated heterobimetallic IrIII/PdII complex bearing mesoionic carbene donor ligands are presented starting from the same bis-triazolium salt. The mononuclear PtII complex possesses a free triazole moiety which is generated from the corresponding triazolium salt through an N-demethylation reaction, whereas the mononuclear IrIII complex features an unreacted triazolium unit

Theory and Experiment

Selective modification of the morphology and intrinsic electrocatalytic activity of porous electrodes is urgently required to improve the performance of vanadium redox flow batteries (VRFBs). For this purpose, electrospinning was exploited to prepare high‐performance nanofiber‐based composites. Blends of polyacrylonitrile, polyacrylic acid, and polyaniline with carbon black were electrospun into a 3D free‐standing nanofibrous web, which was utilized as a novel electrode. By extending the recent theory of cyclic voltammetry at porous electrodes to account for interfacial double‐layer capacities, nonlinear effects of ohmic resistances, and parasitic reactions, we could quantitatively investigate non‐faradaic as well as desired and undesired faradaic current contributions. Combination of experimental and theoretical studies allowed a unique quantitative assessment of the intrinsic catalytic activity of selected electrode materials concerning the VO2+/VO2+ redox reaction

Improvement of Oxygen-Depolarized Cathodes in Highly Alkaline Media by Electrospinning of Poly(vinylidene fluoride) Barrier Layers

Oxygen‐depolarized cathodes (ODC) were developed for chlor‐alkali electrolysis to replace the hydrogen evolution reaction (HER) by the oxygen reduction reaction (ORR) providing electrical energy savings up to 30 % under industrially relevant conditions. These electrodes consist of micro sized silver grains and polytetrafluoroethylene, forming a homogeneous electrode structure. In this work, we report on the modification of ODCs by implementing an electrospun layer of hydrophobic poly(vinylidene fluoride) (PVDF) into the ODC structure, leading to a significantly enhanced ORR performance. The modified electrodes are physically characterized by liquid flow porometry, contact angle measurements and scanning electron microscopy. Electrochemical characterization is performed by linear sweep voltammetry and chronopotentiometry. The overpotential for ORR at application near conditions could be reduced by up to 75 mV at 4 kA m−2 and 135 mV at a higher current density of 9.5 kA m−2. Consequently, we propose that modifying ODCs by electrospinning is an effective and cost‐efficient way to further reduce the energy demand of the ORR in highly alkaline media

Theorie der Zyklischen Voltammetrie an Makroporösen Elektroden

Investigating the electrokinetic performance of novel electrode materials by means of diffusional cyclic voltammetry has emerged to the standard approach in electrochemistry. The straightforward implementation of the method in a three-electrode compartment provides scientists with a feasible ex-situ technique for assessing reaction kinetics in terms of potential-dependent redox currents. Providing that well-defined diffusion conditions are complied, i.e. the experiments are conducted at planar electrodes in a semi-infinite diffusion domain, characteristic features such as the separation, symmetry and magnitude of the redox peaks can be related unambiguously to the electrode kinetics. However, as soon as non-planar electrodes or electrodes with finite diffusion domains are employed an equivocation between the measured redox peaks and the intrinsic electrode kinetics emerges. Consequently, a quantitative interpretation of cyclic voltammetry data becomes exceptionally arduous. In particular porous structures like felts and foams, predominantly utilized as electrode materials in the field of battery research, exhibit an intimidating ambiguity of the polarographic current signal. Therefore, the majority of experimentalists restrict themself to a qualitative interpretation of cyclic voltammetry data in terms of arbitrarily chosen onset-potentials. Scientists who are still targeting to quantify the electrode kinetics usually aim to exploit alternative techniques such as electrochemical impedance spectroscopy. However, from a theoretical perspective this approach is not capable of solving the dilemma either since the experiments are subjected to the same diffusion complication, examined with a different potential perturbation only. Consequently, developing a theory of cyclic voltammetry for porous electrodes is inevitable to permit a quantitative analysis of experimental results. This thesis consists of the cumulative work on the theory of cyclic voltammetry at macroporous electrodes with emphasis on felt-like structures. It is demonstrated that linking the high sensitivity of cyclic voltammetry with a sophisticated mathematical diffusion model allows for an electrochemical and morphological characterization of porous electrodes simultaneously, promoting the so-called „electrochemists spectroscopy “ to the next level. All theoretical concepts are supported by experimental data acquired for the electrochemical redox-reactions of vanadium(II)/ vanadium(III) and oxovanadium(IV)/ dioxovanadium(V), relevant in the field of vanadium redox-flow battery research. In a first approximation, porous electrodes are treated as random arrays of microelectrodes in a finite diffusion space with a statistically fluctuating size. A systematic investigation of simulated and experimentally acquired cyclic voltammetry data for both, porous and non-porous electrodes, draws an enlightening picture on the complex interplay of electrode porosity and reaction kinetics. With this knowledge, precise values for the heterogeneous rate constant of the oxovanadium(IV)/ dioxovanadium(V) redox reaction are obtained. These values usually scatter over orders of magnitude in the recent literature, most likely due to an inconsequent interpretation of data. In another study, a strategy for real-space simulation of cyclic voltammetry at carbon felt electrodes is presented. For this purpose, in-situ micro X-ray computed tomography is exploited to construct a template of the three-dimensional diffusion domain inside a porous electrode. This renders any statistical assumptions obsolete. To perform the simulations, two self-reliant computational methods, namely digital simulation and convolutive modeling, are combined. The resulting method offers significant advantages with respect to computation time, programming effort and mathematical complexity. Since effects of electrochemical double-layer charging, nonlinear contributions of ohmic resistances, coupled chemical reactions and limited electron transfer kinetics can be accounted for readily, the novel approach covers an extraordinarily wide range of electrochemical situations. The exceptional endowment of simulating polarographic experiments at porous electrodes was finally implemented into an open source program named „Polarographica “. This software provides the experimentalists community with a straightforward way of interpreting cyclic voltammetry data of porous electrodes in terms of a fitting routine. Since many other electroanalytical techniques are supported in the environment of Polarographica as well, it will eventually lead to a more decent interpretation of cyclic voltammetry data, based on mathematical models instead of ambiguous current peaks and arbitrarily chosen onset-potentials

Insights into the sodiation mechanism of hard carbon-like materials from electrochemical impedance spectroscopy

To render the sodium ion battery (SIB) competitive among other technologies, the processes behind sodium storage in hard carbon anodes must be understood. For this purpose, electrochemical impedance spectroscopy (EIS) is usually undervalued, since fitting the spectra with equivalent circuit models requires an a priori knowledge about the system at hand. The analysis of the distribution of relaxation times (DRT) is an alternative, which refrains from fitting arbitrarily nested equivalent circuits. In this paper, the sodiation and desodiation of a hard carbon anode is studied by EIS at different states of charge (SOC). By reconstructing the DRT function, highly resolved information on the number and relative contribution of individual electrochemical processes is derived. During the sloping part of the sodiation curve, mass transport is found to be the most dominant source of resistance but rapidly diminishes when the plateau phase is reached. An equivalent circuit model qualitatively reproducing the experimental data of the sloping region was built upon the DRT results, which is particularly useful for future EIS studies on hard carbon SIB anodes. More importantly, this work contributes to establish EIS as a practical tool to directly study electrode processes without the bias of a previously assumed model