Activation energy is a well-known empirical parameter in chemical kinetics that characterizes the dependence of the chemical rate coefficients on the temperature and provides information to compare the intrinsic activity of the catalysts. However, the determination and interpretation of the apparent activation energy in multistep reactions is not an easy task. For this purpose, the concept of degree of rate control is convenient, which comprises a mathematical approach for analyzing reaction mechanisms and chemical kinetics. Although this concept has been used in catalysis, it has not yet been applied in electrocatalytic systems, whose ability to control the potential across the solid/liquid interface is the main difference with heterogenous catalysis, and the electrical current is commonly used as a measure of the reaction rate. Herein we use the definition of 'degree of rate control for elementary step' to address some of the drawbacks that frequently arise with interpreting apparent activation energy as a measure of intrinsic electrocatalytic activity of electrode. For this, an electrokinetic model Langmuir-Hinshelwood-like is used for making numerical experiments and verifying the proposed ideas. The results show that to improve the catalytic activity of an electrode material, it must act upon the reaction steps with the highest normalized absolute values of degree of rate control. On the other hand, experiments at different applied voltages showed that if the electroactive surface poisoning process take place, changes in can not be used to compare the catalytic activity of the electrodes. Finally, the importance of making measurements at steady-state to avoid large errors in the calculations of apparent activation energy is also discussed.
In this work, the effect of temperature on the electro-oxidation of formic acid on platinum was modeled and numerically investigated. Numerical simulations were carried out using an electrokinetic model recently validated through voltammetric and galvanostatic experiments. We show that the intrinsic electrocatalytic activity of the working electrode for the overall electrochemical reaction can hardly be interpreted from the apparent activation energy due to the complexity of the reaction scheme. A detailed analysis is possible through the estimation of the activation energies determined from the individual rate coefficients. By doing so, we observed that the direct pathway, with an activation energy of 91 kJ mol–1 at 0.40 V and 72 kJ mol–1 at 0.80 V, is the energetically easiest pathway for the formation of CO2 in the proposed reaction scheme. Regarding the self-organized potential oscillations under the galvanostatic regime, our model was able to reproduce experimentally observed results including the phenomena of temperature compensation and overcompensation. Importantly, we have introduced a formalism to classify the elementary steps that contribute to the increase and decrease of the oscillatory frequency in electrochemical systems. Our results shed light on the understanding of the temperature dependence of complex electrocatalytic reactions, and the developed methodology was proven to be robust and of general applicability.
In this perspective we proposed a workflow for the construction of micro-kinetic models that consists of at least four stages, starting with information gathering that allows proposing possible reaction mechanisms....
A methodology to determine how the variation in a kinetic parameter affects the global kinetic response of an electrochemical reaction is proposed. The so-called sensitivity analysis is applied to quantify the contribution of single reaction steps of an electrocatalytic system under an oscillatory regime using microkinetic analysis.
The development of electrocatalysts with high activity at low overpotentials for the methanol electro-oxidation reaction is one of the challenges to overcome toward the wider applicability of this alcohol in energy conversion systems. Many works in the last decades have contributed with mechanistic studies on this reaction. Nevertheless, the reaction scheme is intricate, which makes it difficult to correlate with the kinetic response in electrochemical experiments. In this paper, we propose a microkinetic model for the methanol electro-oxidation reaction on polycrystalline platinum. The model was built on relevant mechanistic aspects available in the literature and formulated based on the mean-field approach. The kinetic parameters were determined by optimization, and the validation was performed through comparison with distinct experimental data obtained by cyclic voltammetry, chronoamperometry, and also oscillatory time-series recorded under galvanostatic conditions. The resulting model was able to successfully simulate the nonlinear dynamics observed in galvanostatic experiments, including the chaotic behavior, as well as a reasonable voltammetric profile with the same set of electrokinetic parameters. The sensitivity analysis of the kinetic parameters showed that the electro-oxidation pathway through the formic acid intermediate is not significant under these experimental conditions and that the OHad and COad species are mainly involved in the origin of the oscillations, while species that affect the rate of formation/consumption of the latter causes the mixed-mode oscillations. The microkinetic approach used in this study can be extrapolated to other electrocatalytic reactions, allowing the complementarity between laboratory experiments and computational simulations.
Devido ao aumento das emissões de dióxido de carbono na atmosfera, problemas ambientais como o efeito estufa se intensificaram, sendo a provável causa do aumento na temperatura da Terra. Dentre as estratégias propostas para solucionar este problema, destaca-se a redução eletroquímica de CO2, uma vez que as emissões podem ser mitigadas e produtos de valor agregado podem ser obtidos. Neste trabalho, materiais formados pela combinação de ferro, nitrogênio e carbono, em diferentes proporções, foram estudados como eletrocatalisadores para a Reação de Redução de CO2 (CO2RR) para CO. A atividade e seletividade foram avaliadas por Espectrometria de Massas Diferencial Eletroquímica (DEMS) e por cromatografia gasosa.Os resultados mostraram que o aumento na quantidade de ferro leva à formação de partículas de ferro metálico e de Fe3O4, que catalisam a Reação de Evolução de Hidrogênio (HER), inibindo a CO 2 RR. Notou-se, entretanto, que estas partículas podem ser removidas sem danificar os sítios ativos para a CO2RR mediante lavagem em meio ácido (materiais denotados com H + ) ou por meio de ciclos de potencial, disponibilizando, assim, os sítios ativos. Foi observado que a formação e crescimento de partículas metálicas podem ser mitigados aumentando-se a quantidade de nitrogênio nos materiais. Os resultados de cromatografia gasosa mostraram que, em potenciais mais positivos, a produção de CO é governada pela quantidade de sítios ativos FeN4 e, assim, a maior eficiência faradaica foi apresentada pelo material Fe5N7,5C87,5H + (alto conteúdo de FeN4), atingindo 98% a -0,7 V (vs. RHE). Em potenciais mais negativos, os sítios formados por carbono dopado com nitrogênio passam a ter alta contribuição para a CO2RR e o material Fe1N7C93 (alto teor de N-C) apresentou a maior eficiência faradaica, com um valor de 78% a -0,9 V (vs. RHE).Palavras chave: Reação de redução de CO2; dióxido de carbono; CO; materiais tipo Fe-N-C; carbono dopado com nitrogênio; DEMS.
Kinetic modeling of electro-catalytic reactions based on micro-kinetic approaches allows at obtaining information on reaction mechanisms and determine how some parameters, such as rate coefficients, are affected by the conditions under which the catalyst operates.1 Unlike a kinetic model, which only considers the overall reaction rate, micro-kinetic modeling provides access to fundamental information of elementary reaction steps. In this sense, we present a micro-kinetic model linked to a proposed reaction mechanism for the formic acid electro-oxidation reaction (FAEOR) on platinum. The model was tested by numerical simulations under voltammetric and oscillatory regimes.2 We formulated the micro-kinetic model using the following workflow stages: i) Gathering information from literature, including spectroscopy and computational chemistry studies; ii) Mechanism proposal and model description that consists of a set of ordinary differential equations involving charge and mass balances on the electrocatalytic surface; iii) Numerical resolution of the model using a set of test parameters; iv) Comparison with different sets of experiments including cyclic voltammetry and potential oscillations under the galvanostatic regime. The initial electrokinetic parameters, associated with the rate coefficients, were adjusted and re-evaluated by an iterative procedure to improve the description of the experimental observations. The type of electrochemical experiments performed in the micro-kinetic model is fundamental to the success of validation. Under oscillatory conditions, galvanostatic experiments are an excellent complement to other electrodynamic techniques because the rate of several processes that are happening in the electrode-solution interface can be associated with oscillatory features such as frequency, amplitude, and oscillation format.3 Thus, the self-organized mode offers a sensitive tool to evaluate the proposed reaction mechanism. In this work, we studied the oscillatory characteristics in the electrochemical response of the FAEOR to determine the rate coefficients as a function of the electrode potential. The consistency of the numerical solution of our model (Figure 1), namely frequency and amplitude of the potential oscillations, with the experimental response makes our proposal a plausible possibility for the FAEOR, providing evidence to the clarification of this controversial process through a micro-kinetic approach. References (1) Campbell, C. T. Micro- and Macro-Kinetics: Their Relationship in Heterogeneous Catalysis. Top. Catal. 1994, 1 (3–4), 353–366. https://doi.org/10.1007/BF01492288. (2) Calderón-Cárdenas, A.; Hartl, F. W.; Gallas, J. A. C.; Varela, H. Modeling the Triple-Path Electro-Oxidation of Formic Acid on Platinum: Cyclic Voltammetry and Oscillations. Catal. Today 2021, 359, 90–98. https://doi.org/10.1016/j.cattod.2019.04.054. (3) Machado, E. G.; Varela, H. Kinetic Instabilities in Electrocatalysis. Encyclopedia of Interfacial Chemistry; Elsevier, 2018; pp 701–718. https://doi.org/10.1016/B978-0-12-409547-2.13369-4. Figure 1
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