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This chapter provides a broad overview of the various computational modeling techniques used to gain fundamental insights into coupled electrochemical processes that occur in battery materials at electronic-to-mesoscopic scales. Furthermore, representative successes of these techniques in modeling electrodes, electrolytes, and electrode-electrolyte interfaces are highlighted to establish the current state-of-the-art in the field.
Lead-acid batteries (LABs) play a pivotal role in the energy storage sector with applications spanning from starting-lighting-ignition batteries to grid energy storage. Passivation of lead negative electrodes by PbSO 4 particles is a fundamental mechanism limiting the performance of LAB. In this regard, an electrochemical model is developed that simulates the nucleation and growth (N&G) dynamics of PbSO 4 particles on a flat lead electrode, responsible for its passivation. The model considers the electrochemical reactions between lead electrode and sulfuric acid, N&G of PbSO 4 particles, passivation of the lead surface, and the ternary transport of PbSO 4 (aq), bisulfate, and protons in H 2 SO 4 electrolyte. The model is validated with a dataset of cyclic voltammetry (CV) responses collected at several scan rates and H 2 SO 4 concentrations. The model shows remarkable qualitative and quantitative agreement with the experimental data including CV peak features, discharge capacity, and particle size. The model was employed to explore key N&G quantities, such as supersaturation, nucleation rate, particle count, growth rate, particle size, and surface coverage, and to examine how their interactions influence electrode utilization. Parametric studies were also conducted to evaluate how scan rates and acid concentrations influence the previously mentioned N&G quantities and, subsequently, the utilization of the electrode.
Future long-duration missions will require a sustainable and efficient system capable of yielding a minimum of 75% O 2 recovery from metabolic CO 2 to achieve self-sufficiency for long space missions beyond Earth's low orbit. A Macro-fluidic Electrochemical Reactor (MFECR) development effort to electrochemically recover O 2 from CO 2 is underway at NASA Marshall Space Flight Center (MSFC) to increase current O 2 recovery efficiency and reduce air revitalization (AR) system complexity at the International Space Station (ISS) habitat and future long missions. The authors have developed and deployed a digital twin of an actual single cell of the MFECR via a comprehensive 3D multiphysics model that thoroughly replicates the exact configuration and fluid/material domains of the MFECR. This model's electrochemical physics consists of multicomponent-multiphase electrochemical-driven reactions leading to CO 2 conversion to C 2 H 4 and CO along with the formation of H 2 on the cathode in parallel with the generation of O 2 and H 2 O on the anode. This electrochemical model is coupled with all the physics phenomena involved in the process, including but not limited to fluid and non-ideal mass transfer of reactant and product species in free and porous media, convective/conduction/radiative heat transfer, and conduction of DC electrical current with Joule heating generation. The digital twin has proved to be an essential tool for performing different qualitative studies, including the effect of reducing the height (increasing the respect ratio) of the serpentine walls, leading to a further redesign of the EDU (the newly redesigned MFECR EDU has been fabricated and is expected to be used in future tests), the evaluation of setting different MFECRs connected in series, and the assessment of feeding air directly to the MFECR skipping the preceding metabolic CO 2 separation from air. The MFECR's test stand is fully automated and equipped with several inline measurements (flow, pressure, temperature, pH, component concentration) systems on all six MFECR's IO streams, allowing reliable experimental validation of the model, parametric determination of all electrochemical reactions, and process optimization.
The electrochemical nitrogen reduction reaction (NRR) is a promising route to enable carbon-free ammonia production. However, this reaction is limited by the poor activity and selectivity of current catalysts. The rational design of superior NRR electrocatalysts requires a detailed mechanistic understanding of current material limitations to inform how these might be overcome. The current understanding of how scaling limits NRR on metal catalysts is predicated on a simplified reaction pathway that considers only proton-coupled electron transfer (PCET) steps. Here, we apply grand-canonical density functional theory to investigate a more comprehensive NRR mechanism that includes both electrochemical and chemical steps on 30 metal surfaces in solvent under an applied potential. We applied ..phi..max, a grand-canonical adaptation of the Gmax thermodynamic descriptor, to evaluate trends in catalyst activity. This approach produces a ..phi..max "volcano" diagram for NRR activity scaling on metals that qualitatively differs from the scaling relations identified when only PCET steps are considered. NH3* desorption was found to limit the NRR activity for materials at the top of the volcano and truncate the volcano's peak at increasingly reducing potentials. These revised scaling relations may inform the rational design of superior NRR electrocatalysts. This approach is transferable to study other materials and reaction chemistries where both electrochemical and chemical steps are modeled under an applied potential.
Electrochemical reduction of CO 2 gas is a novel CO 2 utilization technique that has the potential to mitigate the global climate crisis caused by anthropogenic CO 2 emissions, and enable the large-scale storage of energy generated from renewable sources in the form of carbon-based chemicals and fuels. However, due to the complexity of the electrochemical reactions, the explicit first-principles models for CO2 reduction are not available yet, and there has been a limited effort to develop process modeling, optimization and control of CO 2 electrochemical reactors. To this end, a rotating cylinder electrode (RCE) reactor has been constructed at UCLA to understand the mass transfer and reaction kinetics effects separately on the productivity. In the RCE reactor, the applied potential strongly influences the reaction energetics and the electrode rotation speed affects the hydrodynamic boundary layer and modifies the film mass transfer coefficient, which involves convective and diffusive transport. Further, the present work aims to develop a multi-input multi-output (MIMO) control scheme for the RCE reactor that integrates techniques from artificial and recurrent neural network modeling, nonlinear optimization, and process controller design. Specifically, production rates of two products from the experimental reactor, ethylene and carbon monoxide, are controlled by manipulating two inputs, applied potential and catalyst rotation speed. Process dynamics and controllability are analyzed, a feedback control strategy is designed and the controllers are tuned accordingly. The experimental electrochemical cell is employed to gather data for process modeling and implement the multivariable control system. Finally, the experimental results are presented which demonstrate excellent closed-loop performance by the control system and regulation of the outputs at three different set-points including an economically-optimal set-point.
Electrochemical technologies have garnered intense interest in both academic research and industrial applications due to their potential to increase energy efficiency and reduce carbon footprint. However, electrochemical process fundamentals have been absent from the chemical process simulators available to millions of chemical engineers worldwide. To expedite process research and development of electrochemical technologies in the chemical industry, it is imperative that essential electrochemical process fundamentals be incorporated into process simulators to support modeling and simulation of electrochemical processes. Here, this study examines three process fundamentals key to the research and development of electrochemical processes: electrochemical reaction kinetics, electrolyte thermodynamics, and heat and mass transfer. It further illustrates application of these process fundamentals with a case study modeling an electrochemical process for the conversion of acrylonitrile to adiponitrile. The modeling example highlights the roles of applied voltage on reaction rates, and electron flow rates on the performance of electrochemical processes. It suggests that the applied voltage and electron flow rates are two unique concepts that should be included in simulators for electrochemical processes.
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The pH dependence of proton-coupled electron transfer (PCET) reactions, which are critical to many chemical and biological processes, is a powerful probe for elucidating their fundamental mechanisms. Herein, a general, multichannel kinetic model is introduced to describe the pH dependence of both homogeneous and electrochemical PCET reactions. According to this model, a weak pH dependence can arise from the competition among multiple sequential and concerted PCET channels involving different forms of the redox species, such as protonated and deprotonated forms, as well as different proton donors and acceptors. The contribution of each channel is influenced by the relative populations of the reactant species, which often depend strongly on pH, leading to complex pH dependence of PCET apparent rate constants. This model is used to explain the origins of the experimentally observed weak pH dependence of the electrochemical PCET apparent rate constant for a ruthenium-based water oxidation catalyst attached to a tin-doped In2O3 (ITO) surface. The weak pH dependence is found to arise from the intrinsic differences in the rate constants of participating channels and the dependence of their relative contributions on pH. This model predicts that the apparent maximum rate constant will become pH-independent at higher pH, which is confirmed by experimental measurements. Our analysis also suggests that the dominant channels are electron transfer at lower pH and sequential PCET via electron transfer followed by fast proton transfer at higher pH. Furthermore, this work highlights the importance of considering multiple competing channels simultaneously for PCET processes.
The expansion of renewable technologies and electrification of the transportation sector is driving increased demand for next-generation battery materials that provide higher power and energy density with superior cycling and calendar life stability. Silicon (Si) has a theoretical capacity nearly 10x that of graphite, and is therefore a promising anode material candidate to meet these rigorous performance demands. While leading Si anode battery demonstrations are approaching target metrics for cycle life, a series of complex and interrelated modes of reactivity lead to reduced calendar life and therefore challenge practical adoption of these materials. Deconvoluting the degradation processes that impact Si calendar life is critical to informing the rational and accelerated design of improved Si materials. In the present work, we employ novel sampling techniques and GC-MS-FID characterization to measure gas-phase composition during initial Si cycling, which we tie to selective mechanisms of Si passivation. We utilize a tiered analysis approach to identify and quantify the gas-phase reaction products associated with three advanced Si material candidates under practical operating conditions. Ex situ analysis of Si powders (pure chemical reactivity) is coupled with nondestructive in situ sampling of Si electrodes in a practical pouch-cell format (coupled chemical and electrochemical reactivity). We link the observed gas-phase species evolution to electrochemical behavior and measured calendar life of the three Si materials. Further, we evaluate the voltage-resolved evolution of gas-phase species for one such Si nanomaterial, where nonmonotonic gas generation implies competition between passivating reaction pathways. The measured gas-phase compositional data serves as a critical input for our advanced electrochemical SEI models to identify favorable vs unfavorable reaction pathways to stabilize Si. In addition to bolstering a fundamental understanding of Si reactivity, the present approach informs specific and quantifiable gas-phase metrics tied to calendar life improvements in Si, which can streamline and accelerate the process of next-generation material development.
Effective electrochemical CO 2 reduction to liquid fuels requires that the local catalytic environment facilitates the desired reactivity, yet a microscopic understanding of this environment is difficult to achieve from experiment alone. In this work, a 3D reaction-diffusion model was developed to explore the effects of electrode surface area and local geometry on the performance of a heterogeneous catalyst that performs a two-step CO 2 reduction cascade reaction to CO and then CH 3 OH under aqueous conditions. Kinetic parameters for the model were inspired by experimental results using a cobalt phthalocyanine (CoPc) catalyst. Three-dimensional architectures composed of arrays of square pillars with varying dimensions and either smooth or periodically modulated surfaces were tested, revealing the extent to which geometry modulates the performance of the cascade reactions. Although structural variations modulate local concentration gradients, we find that electrochemically active surface area predominantly governs the overall cascade reaction. Moreover, the results suggest that supersaturation of CO, with concentrations up to ten-fold higher than the equilibrium solubility limit, might be critical for more efficient conversion to CH 3 OH. For any given geometry, the spatially averaged ratio of [CO] to [CO 2 ] is dictated by the electrochemically active surface area and determines the yield of CH 3 OH. For a fixed surface area, geometries that spatially confine the electrolyte yield moderate local [CO] to [CO 2 ] ratios within small volumes. In contrast, less confining geometries result in a broader distribution of local ratios spread over larger volumes, with both configurations yielding the same spatially averaged [CO] to [CO 2 ] ratio. These insights provide valuable design principles—highlighting the critical importance of surface area and possibly CO supersaturation—for engineering advanced electrode architectures that leverage intermediate trapping and CO supersaturation to enhance overall performance in tandem CO 2 reduction systems.
Experimental validation of Finite Element Method (FEM) models varying electrochemical governing equations, inclusion of chemical reactions, and time on the resultant damage profile for two galvanic couples is explored. Two anode materials (Magnesium AZ31 and Carbon Steel) in contact with a cathode (Stainless Steel 304 L) were modeled in/exposed to NaCl (1 and 0.1 M respectively for the anode materials) for up to one week. The physics approach, inclusion of chemical reactions, and the boundary conditions required to accurately represent the damage profile in FEM models depended on the galvanic couple materials and, ultimately, the corrosion rate. For high rates of corrosion (i.e., magnesium anode), the Nernst-Planck equation with Electroneutrality was sufficient to describe the damage, while, for low rates of corrosion (i.e., carbon steel anode), the Laplace equation was sufficient. In all cases, the most complete governing equation (Nernst-Planck-Poisson Equation) was not necessary to accurately describe the damage. Precipitation reactions in solution also played a critical role in the predicted damage profile, especially for high corrosion rate systems. Finally, for short time periods (< 6 h), the choice of governing equations does not significantly influence damage profile results. Overall, the choice of physics to reduce error in simulations relies on the boundary conditions, geometry, conductivity of the solution, electrochemical potential differences, and time of exposure. The above results are discussed with regard to accuracy and computational savings.
The International Space Station (ISS) is presently equipped with an elaborate, heavy, and high-power consuming system that recovers approximately 50% of O 2 from metabolic CO 2 as part of the atmospheric revitalization (AR) at the ISS habitat. Future long-duration missions will require a sustainable and efficient system capable of yielding a minimum of 75% O 2 recovery to reach the self-sufficiency required for long space missions beyond earth’s low orbit. A Macrofluidic Electrochemical Reactor (MFECR) technology development effort is currently underway at NASA Marshall Space Flight Center (MSFC) to not only increase significantly current O 2 recovery efficiency, improving self-sufficiency on AR at the ISS habitat and future long missions, but also reduce the complexity of the system. The authors have developed and deployed a comprehensive 3D multiphysics model that thoroughly replicates the actual configuration and fluid/material domains of the MFECR. The coupled physics in this multiphysics model include multicomponent-multiphase electrochemical-driven reactions, non-ideal mass transport mechanism, free and porous flow, heat transfer, CO 2 solubility on alkaline electrolyte, water condensation on porous medium, and DC electrical current generation along with Joule heating effect. This model is aimed to conduct quantitive benchmark on three different MFECR’s layouts, one without serpentine paths (plain) and two with serpentines leading to four and twelve paths respectively. Once experimental data is generated via a test matrix of 200 tests, the model will be validated to conduct MFECR’s process optimization and revalidate the quantitive benchmark on three different MFECR’s layouts.
The microscopic mechanism of the alkali ion-electron recombination reaction at the three phase boundary zone formed by a porous metal electrode in the alkali vapor on the surface of an alkali beta'-alumina solid electrolyte (BASE) ceramic has been studied by comparison of the expected rates for the three simplest reaction mechanisms with known temperature dependent rate data; and the physical parameters of typical porous metal electrode/BASE/alkali metal vapor reaction zones. The three simplest reactions are tunneling of electrons from the alkali coated electrode to a surface bound alkali metal ion; emission of an electron from the electrode with subsequent capture by a surface bound alkali metal ion; and thermal emission of an alkali cation from the BASE and its capture on the porous metal electrode surface where it may recombine with an electron. Only the first reaction adequately accounts for both the high observed rate and its temperature dependence. New results include crude modeling of simple, one step, three phase, solid/solid/gas electrochemical reaction.
Commercialization of lithium-air batteries faces many challenges, such as electrolyte decomposition, short cycle life, low energy and power density, etc. However, commercialization of Li-O2 batteries for aeronautics is much more challenging due to additional safety constraints on cyclability and performance (high specific power and specific energy). For this presentation, we will discuss inter-related aspects of physics-based modeling of a pack: cell and battery model calibration. In addition, we will evaluate and present optimal battery designs for high discharge current density, high discharge time, and low battery mass using simulation-based optimization.The Finite Element Model (FEM) used to simulate a Li-O2 cell is based on the work of Bevara [1]. The different aspects of the model are based on: porous electrode theory and concentrated electrolyte theory; quantum tunneling model for the resistance of conformal layer of discharge product (Li2O2) [1]; Butler-Volmer kinetics for electrochemical reaction; Fick's diffusion for oxygen transport; and an oxygen dissolution model is applied at the air/electrolyte interface [2]. The electrolyte properties such as ion conductivity, ion diffusion, oxygen diffusion, and mass density of the electrolyte were taken from Molecular Dynamics (MD) simulations [3]; while the other model parameters, which includes mass of cell components, were calibrated to match experiments at high discharge current densities. The cell mass includes the anode, cathode, separator, electrolyte, and other components (such as current collector). This calibrated model is used to perform parametric studies on cathode thickness, porosity, tortuosity, carbon particle size, electrolyte transport and material properties, partial pressure of oxygen, discharge time, and discharge current density to study optimal designs for high specific power and energy. References:1. Bevara, V. & Andrei, P. (2014), J. Electrochem. Soc. 161 (14), A2068-A2079.2.Mehta, M. & Andrei, P. (2015), J. Power Sources. 286, 299-308.3.Liyana-Arachchi, T.; Haskins, J.; Burke, C.; Diederichsen, K.; McCloskey, B.; & Lawson, J. (2018), J. Phys. Chem. B. 122 (36), 8548 - 8559.4.Choi, W.; Kikumoto, H.; Choudhary, R. & Ooka, R. (2018), Applied Energy, 209, 306-321.
In this study, WPI and its partners sought to understand galvanic corrosion in Mg-Al friction stir weld (FSW) joints. Unlike fusion welds, FSW is done in the solid state. This limits (but does not eliminate) the formation of brittle Al-Mg intermetallics, resulting in better joint strength and corrosion resistance. This study aimed to understand corrosion behavior of Mg-Al FSW joints by using a Cahn-Hilliard phase field electrochemistry model based on the work of Pongsaksawad et al. Its context challenge problem was an ultra-light door designed by Magna with 6061-Al sheet outer and ZEK100-Mg sheet inner panels, joined by an adhesive and FSW. Unlike most FSW joints, which weld through the softer material into the harder one, the Al sheet’s hem joint around Mg required the FSW tool to through the harder Al into the softer Mg, which was itself a challenge. Despite this challenge, PNNL succeeded in consistently making very strong FSW lap joints, by using a triflute tool and power control. Characterization showed mostly separate Al and Mg regions in the weld, usually with a hook protruding from Al into Mg, which likely contributed to high joint strength. Nanohardness mapping showed higher hardness in thin Mg swirls into the Al nugget, likely due to the intermetallics. The study used the industry standard SAE J2334 Cyclic Corrosion Test (CCT) to simulate corrosion conditions over the life of a vehicle, as well as linear polarization testing and ASTM G71 pitting corrosion testing. Corrosion reactions were: H 2 O + ½O 2 + 2e - → 2OH - at the Al cathode, and either Mg → Mg 2+ + 2e - or Mg + 2OH - → Mg(OH) 2 + 2e - at the Mg anode, with electron transfer through the joint. Mass loss increased with Al section length, supporting the hypothesis that galvanic corrosion in Al-Mg joints is limited by the cathodic reaction. Both pitting corrosion (first anode reaction) and hydroxide film formation (second reaction) were observed. The J2334 CCT test method was slightly modified, adding a chromium solution cleaning step after each week of corrosion testing, in order to remove Mg oxides and hydroxides and accurately measure mass loss over time. That said, FSW joints treated in this way did not did not exhibit significant reduction in lap shear strength of the joints vs. newly welded samples which had not undergone corrosion. Corrosion appeared to consist mainly of pitting in Mg in a way which did not directly affect the bond between the materials where the joints failed. A Cahn-Hilliard phase field model coupled with electrical potential described the electronically mediated galvanic corrosion electrochemical reactions described above in the four-component Al-Mg-H 2 O-(H 2 O+½O 2 ) system. This 2-D model successfully predicted Mg(OH)₂ formation at the anode in some circumstances, and Mg pitting corrosion in others, and showed the correct electric field directions in both cases. The model predicted Mg pit corrosion depth within a factor of two of measured pits.
Solid oxide electrolysis cells (SOEC) have been receiving significant attention recently because of their high energy efficiency and fast hydrogen production. In this study a multi-physics model to simulate the SOEC performance and structural reliability of a state-of-the-art planar SOEC design was developed. The electrochemical reactions, fluid dynamics, species transport, electron transfer, and heat transfer were modeled in the commercial computational fluid dynamics (CFD) software STAR-CCM+. The thermomechanical analysis and the associated structural reliability evaluations were conducted using the commercial finite element analysis software ANSYS. The electrochemistry model was validated by using the experimentally obtained current-voltage (I-V) characteristics of the electrode-supported SOECs. The reliability analysis using a risk-of-rupture approach showed low failure probabilities under standard operating conditions considered in this study. For cells operated at voltages well above a thermoneutral voltage, the reliability evaluations indicated a potential risk of cell failure, but the damage was concentrated locally in specific areas of the cell which typically do not lead to total loss of cell function. The presented approach provides insights for evaluating representative cell and stack performances and structural reliability without intensive testing and for developing optimally performing and structurally reliable SOECs for efficient hydrogen generation.
Understanding the electrochemical properties of mineral–water interfaces tends to rely upon electrical double layer (EDL) models, but these models are based on the assumption that electrostatic equilibrium is constantly maintained. In reality, interfacial reactions, ion diffusion, and their electrochemical signatures are based in nonequilibrium conditions of locally or globally imbalanced electrical fields where current EDL models have limited purview. In this work, we performed molecular dynamics (MD) simulations of the orthoclase (001) surface in contact with a 1 M NaCl aqueous solution under various electric fields, to explore the interplay between EDL structure and dynamics when perturbed by electric fields of different direction and strength, by confinement, and by different distributions of structural surface charge. The simulations showed that confinement between two opposing (001) surfaces led to the development of an induced field when the applied field was perpendicular to the surfaces and, as a result, to ionic diffusion coefficients that were independent of electric field strength. In contrast, when the applied field was parallel to the surfaces, confinement resulted in ionic diffusion coefficients that were more strongly dependent on the magnitude of the electric field than in bulk water. Differences in the density and distribution of aluminol groups on the two surfaces had a significant impact on how the interfacial structure and dynamics varied in the presence of an electric field. Notably, these differences resulted in an electro-osmotic flow with opposite directions at the two surfaces under parallel applied electric field. Overall, the MD simulations highlighted the importance of considering atomic-level structure and heterogeneities when developing models of the electrochemical properties of mineral–water interfaces.