Porous Electrode Model Research Articles

THEORETICAL BASICS OF MONITORING THE CONDITION OF THE ELECTRODES OF CHEMICAL CURRENT SOURCES BY THE METHOD OF ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY

On the basis of the conducted critical review of modern physical models of the porous electrode, it сan be stated that under the conditions of non-uniform mass transfer taking into account the depth of the electrode, it is possible not only to develop new porous electrodes for a certain application, but also to control the state of electrochemical systems as a whole using the non-destructive method of electrochemical impedance spectroscopy. The presence of a macroscopic model of porous electrode allows one to use the integration of parameters over the surface of the electrode and obtain the average values of current, resistance and capacity within the electrode using the method of averaging in the volume ele­ment within the electrode, where porosity is the volume fraction of the void within the element, which is filled with electrolyte solution. This is the theoretical basis for using electrochemical impedance spectroscopy to assess the state of electrodes in electrochemical current sources. To take into account the influence of the aqueous electrolyte, it is possible to use a model taking into account the area of the effective wetted surface, which makes it possib­le to relate the wetting of the electrode pores with the electrolyte solution to the change in electrical conductivity and polarization of the electrode surface. In this case, when usingelectrochemical impedance spectroscopy, it is possible to obtain information about the following changes in primary current sources: 1– the effect of temperature, which leads to a decrease in the areas of the electrode wetted by the electrolyte, which affect the value of the capacity of the DEL, 2 – chemical processes that lead to the destruction of hydrophilic pores and pores with hydrophilic-hydrophobic walls, an increase in the hydrophobic component on the surface of the electrode, 3 – mechanical destruction of the electrodes. The use of models that take into account the geometry of pores makes it possible to obtain correct data for the analysis of the porous surface in the presence of an electrolyte and in cases of gas phase adsorption in presence of closed pores, as well as to use the value of the capacity on the surface of electrodes to assess the state of their performance.

Superior Rate Capability of Small Regenerated Graphite Particles Induced by Homogeneously Distributed Current Density Derived from Cracks and Intrinsic Defects.

As spent batteries can be considered as alternative raw sources of electrode materials; the development of regeneration techniques for spent graphite becomes key to realizing economic and environmental sustainability. Herein, the reutilization of small spent graphite particles is domonstrateddue to their special structural characteristics, which may directly contribute to the improvement of lithiation kinetics and high-rate charging during long-term cycling. Such intrinsic defects and external cracked channels may be introduced by the aging of intrinsic bulk structure and exfoliation of surface structure. On account of these potential advantages, a carbonized polypyrrole layer on sieved small graphite particles is developed to obtain superior rate performance. The coated amorphous/graphitic layer could repair the exposed edge and basal plane, and significantly facilitate Li ion diffusion during fast charging. Moreover, the enhanced performance may favor the improved homogeneity of current density distribution during fast charging, which is confirmed by a porous electrode model. The regenerated graphite with a disorder/order coating layer could effectively regulate the Li+ transport channel, exhibiting a high specific capacity at high-rate charging (102.7 mAh g-1 at 4 C after 500 cycles) without severe Li plating. This work provides an opportunity to utilize spent graphite in fast-charging batteries.

Porosity and tortuosity: Keys for accurate modeling of porous electrodes in supercapacitors

Modeling of porous electrodes in supercapacitors (SCs) is rather important for both characterizing and improving the charging/discharging process of SCs, but the current models fail to balance accuracy, flexibility, and detail characterization of the electrode structure, especially the porosity and tortuosity. In this work, we develop a porous tortuous electrode (PTE) model consisting of a stack of multiple parallel plate capacitors with adjustable structural parameters for accurate modeling of SCs. By solving the equivalent circuit of the PTE model, the influence of the electrode structures on electric capacity and relaxation time are characterized with experimental validation, signifying the keys for accurate modeling of SCs as tortuosity and porosity and offering a general formula for describing the relaxation time of SCs. Based on the adjustable parameters in the PTE model, the spatial heterogeneity of the electrodes enables more intricate electrode structure designs. The PTE model facilitates various electrode designs and provides insight into the charging and discharging kinetics of porous electrodes.

Coupling covariance matrix adaptation with continuum modeling for determination of kinetic parameters associated with electrochemical CO2 reduction

Coupling covariance matrix adaptation with continuum modeling for determination of kinetic parameters associated with electrochemical CO2 reduction

Effect of porous nature of anode on the performance of the soluble lead redox flow battery: A modeling and simulation study

A novel hybrid model consisting of two models, (1) a freshly developed porous electrode model and (2) a planar electrode model, is proposed for the soluble lead redox flow battery (SLRFB). The model accounts for simultaneous variations in ionic concentrations and potential fields in the electrolyte. It also accounts for variations in porosity, conductivity, and specific surface area at the porous anode due to the deposition/dissolution of the solids. The developed model is consistent with the solid′s deposition/dissolution mechanism. Hence, the choice of the model among the two for the simulation of a particular charge or discharge cycle follows naturally. Predictions of the model are validated using experimental data available in the literature. The model predictions suggest that the porous nature of the anode not only controls almost every feature of the battery characteristics but also governs the overall cycle life of the battery. Based on the insights developed using the model predictions, a necessary condition is derived for the battery operating procedure to achieve longer cycle life.

π Learning: A Performance‐Informed Framework for Microstructural Electrode Design

AbstractDesigning high‐performance porous electrodes is the key to next‐generation electrochemical energy devices. Current machine‐learning‐based electrode design strategies are mainly orientated toward physical properties; however, the electrochemical performance is the ultimate design objective. Performance‐orientated electrode design is challenging because the current data driven approaches do not accurately extract high‐dimensional features in complex multiphase microstructures. Herein, this work reports a novel performance‐informed deep learning framework, termed π learning, which enables performance‐informed microstructure generation, toward overall performance prediction of candidate electrodes by adding most relevant physical features into the learning process. This is achieved by integrating physics‐informed generative adversarial neural networks (GANs) with convolutional neural networks (CNNs) and with advanced multi‐physics, multi‐scale modeling of 3D porous electrodes. This work demonstrates the advantages of π learning by employing two popular design philosophies: forward and inverse designs, for the design of solid oxide fuel cells electrodes. π learning thus has the potential to unlock performance‐driven learning in the design of next generation porous electrodes for advanced electrochemical energy devices such as fuel cells and batteries.

Dynamic Multi-Dimensional Numerical Transport Study of Lithium-Ion Battery Active Material Microstructures for Automotive Applications

In support of GM’s traction battery efforts, we derived and implemented a method to describe the electrochemical performance of a battery cell considering the nuances of the electrode microstructure at the anode and the cathode and the corresponding impact on the electrochemical transport in the solid and liquid phases. To assess the capability of the method, we compared model results from the microstructure framework with the commonly used continuum-level porous electrode model, commonly referred to as the pseudo-2-dimensional model, or the Newman Model. The microstructure modeling framework was applied to simulate the electrochemical and transport processes within the battery cell to predict the concentration gradients, local state-of-charge distributions, reaction distributions, and the overall terminal voltage of the system. In this report, we provide a commentary on the validity and practicality of the microstructure approach to drive battery cell design.

Uneven phosphoric acid interfaces with enhanced electrochemical performance for high-temperature polymer electrolyte fuel cells.

Ultrahigh mass transport resistance and excessive coverage of the active sites introduced by phosphoric acid (PA) are among the major obstacles that limit the performance of high-temperature polymer fuel cells, especially compared to their low-temperature counterparts. Here, an alternative strategy of electrode design with fibrous networks is developed to optimize the redistribution of acid within the electrode. Via structural tailoring with varied electrospinning parameters, uneven migration of PA with dispersed droplets is observed, subverting the immersion model of conventional porous electrode. Combining with experimental and calculation results, the microscaled uneven PA interfaces could not only provide extra diffusion pathways for oxygen but also minimize the thickness of PA layers. This electrode architecture demonstrates enhanced electrochemical performance of oxygen reduction within the PA phase, resulting in a 28% enhancement of the maximum power density for the optimally designed electrode as cathode compared to that of a conventional one.

Electrochemical impedance simulation of porous electrodes with variously shaped pores using 3-dimensional finite element method

Porous electrodes are widely used in many applications, such as enzyme electrodes, energy devices, and electrosynthesis. However, evaluation of porous electrodes using electrochemical impedance spectroscopy, one of the most promising methods for determining electrochemically relevant structural information, is challenging. Thus, in this study, impedance spectra were simulated using a three-dimensional, finite element method-based model for porous electrodes. The shape of the electrode pore was varied, and the effect on the resulting impedance spectrum was analyzed. The results indicated that for certain pore shapes, such as wide and shallow cylinders, a three-dimensional model was required to obtain accurate results. However, for narrow and deep cylindrical pores, a classical one-dimensional approximation was sufficiently accurate, and a 45º inclined line was observed in the impedance spectra with high frequencies, even when a three-dimensional model was employed. Moreover, wide and shallow or narrowing pores result in a higher inclination angle, whereas widening or branching pores result in a lower inclination angle. These features were also observed when charge transfer and diffusion processes were considered in terms of a mediator-type enzyme electrode reaction.

Electrochemical Performance of LBO-coated Ni-rich NCM Cathode Material: Experimental and Numerical Approaches

Ni-rich NCM-based cathode materials have garnered significant research interest for the development of high-performance lithium-ion batteries (LIBs) owing to their high energy capacity and low cost. However, they undergo several electrochemical degradation reactions that deteriorate the cathode performance. To alleviate the deterioration of the cathode, researchers have adopted surface coating materials, especially Li3BO3 (LBO), which demonstrates a superior modification effect, for Ni-rich NCM. Here, we investigate the electrochemical characteristics of an LBO-coated Ni-rich NCM cathode via experimental and numerical approaches. The cathode is synthesized through a wet chemical deposition method, and electrochemical measurements are conducted using coin half-cells. To further understand the effect of coating layer on the electrochemical performance, we developed an electrode coating model with modifying the porous electrode model. The model employs an impurity layer (Li2CO3 and LiOH), a protective layer (LiF), and a coating layer (LBO) to predict the discharge performance of LIBs. The validation results of the model are consistent with the experimental results. Electrochemical prediction results demonstrate that the LBO-coated Ni-rich NCM cathode would increase the discharge capacity.

Title: Static Cell and Porous Electrode Model for Cycling Behavior of Aqueous Organic Redox Active Materials

Aqueous Organic Redox Flow Batteries (AORBs) have shown growing potential as a stationary energy storage technology for regulating intermittent renewable sources. For long charge/discharge duration systems, the capital cost of a redox flow battery asymptotically approaches the cost of the electroactive material.[i] Therefore, for commercialization of this technology, proper evaluation of the redox active electrolytes is needed. The capacity retention over time and over cycling is one of the most vital criteria for evaluation. For very stable electrolytes with fade rates less than about 10% per year, disentangling cycle-denominated and time-denominated fade can be very difficult for flow batteries due to longer cycle time and noise due to pumping and splashing. Thus, we have used a sealed, static, non-flow cell to achieve capacity measurements with greater cycling frequency and reduced noise, as shown in Figure 1. To isolate decomposition from crossover through the membrane or apparent capacity fade due to changes in the resistance of the cell, we use volumetrically unbalanced, compositionally symmetric cells with potentiostatic cycling.[iii] For proper capacity fade rate evaluation, material properties of the electrode and electrolyte should be considered when setting up cycling protocols because the amount of accessed charge depends on these properties. Thus, simulations from porous electrode models that consider these material properties can inform appropriate cycling conditions.Using Newman’s porous electrode theory[iv] to model our static cell, we have simulated the spatial distribution of ions and potentials over time in response to time-varying applied potentials. From the transient behavior, we simulated the potentiostatic cycling of these cells. The simulations show how the physics inside porous electrodes and cycling performance depend on material properties. For example, the diffusivities can affect the spatial distributions of ions across a porous electrode, as shown in Figure 2 (left), as well as the minimum acceptable time for cycling and the accessed capacity for given cycling parameters, as shown in Figure 2 (right). Using the same porous electrode model for simulations, we aim to show differences between apparent and real capacity fade. [i] F. R. Brushett, M. J. Aziz, and K. E. Rodby. ACS Energy Lett. 2020, 5, 879−884 [ii] D. G. Kwabi, Y. Ji, and M. J. Aziz. C hem. Rev. 2020, 120, 14, 6467–6489 [iii] M.A. Goulet and M. J. Aziz, “Flow Battery Molecular Reactant Stability Determined by Symmetric Cell Cycling Methods”. Journal of The Electrochemical Society, 165 (7) A1466-A1477 (2018) [iv] J. Newman and C. W. Tobias, J. Electrochem. Soc., 1962, 109, 1183 Figure 1

Dynamic Multi-Dimensional Numerical Transport Study of Lithium-Ion Battery Active Material Microstructures for Automotive Applications

Conventional porous electrode battery modeling for a variety of applications makes assumptions to reduce the complexity of the simulation where tradeoffs between computational complexity and electrode detail can be realized without significantly impacting the accuracy of the results. The most common porous electrode battery model is the pseudo-two-dimensional (P2D) model as popularized by Newman and colleagues. These porous electrode battery models typically focus on simulating gradients in two dimensions; the primary dimension through the thickness of the battery cell electrodes and separators, and the secondary dimension in the radial direction of spherical active material particles. The particles are distributed throughout what is assumed to be a homogeneous porous electrode domain. Typically, uniformity in particle size, porosity, and tortuosity is assumed.In this work, the development of a three-dimensional microstructure (3DMS) lithium-ion battery model will be presented. With the increase in computational resources available in academia and industry, simulation of the microstructure in 3D is possible. Active material domains of both the anode and cathode can be generated stochastically to create microstructures representing the electrodes, with voids surrounding the particle representing the electrolyte. A comparison between the P2D and 3DMS models with sensitivity analysis focused on items that can be probed with microstructure simulations will be discussed and similarities and/or differences in charge/discharge characteristics, overpotentials, and concentration profiles will be presented. The findings from this work will provide a path to simulate at the microstructure level, drive electrode design, and translate the effects of heterogeneity into a homogenous porous electrode model.

Classification of spatio‐temporal patterns in charging and discharging of Li‐ion batteries

AbstractWe classify the dynamic patterns that emerge in charging or discharging of Li‐ion batteries, under galvanostatic conditions, using simulations of the two‐phase one‐dimensional (1D) porous electrode model. This work examines the effect of the exchange current function, R0(X), which expresses the nature of kinetics. This extends our previous study with R0 = 1 where the same pattern emerges in charging or discharging, whether as a homogeneous or a step‐wise process made of multiple symmetry breaking events. With commonly‐used asymmetric R0(X), the emerging patterns may be one of the two above or as fronts that follow single SB event and the lithiation/delithiation behaviors are different. These effects are clear when parameters are uniform; nonuniformity leads to noise that mask the behavior. The full four‐variable model exhibits SB, even in absence of noise, since the liquid potential gradient () works like a perturbation. This similarity allows us to derive approximations to the full model behavior.

Porous Electrode Modeling and its Applications to Li‐Ion Batteries

AbstractBattery modeling has become increasingly important with the intensive development of Li‐ion batteries (LIBs). The porous electrode model, relating battery performances to the internal physical and (electro)chemical processes, is one of the most adopted models in scientific research and engineering fields. Since Newman and coworkers’ first implementation in the 1990s, the porous electrode model has kept its general form. Soon after that, many publications have focused on the applications to LIBs. In this review, the applications of the porous electrode model to LIBs are systematically summarized and discussed. With this model, various internal battery properties have been studied, such as Li+ concentration and electric potential in the electrolyte and electrodes, reaction rate distribution, overpotential, and impedance. When coupled with thermal, mechanical, and aging models, the porous electrode model can simulate the temperature and stress distribution inside batteries and predict degradation during battery operation. With the help of state observers, the porous electrode model can monitor various battery states in real‐time for battery management systems. Even though the porous electrode models have multiple advantages, some challenges and limitations still have to be addressed. The present review also gives suggestions to overcome these limitations in future research.

Maximizing Energy Efficiency of Porous Electrodes Via Topology Optimization

Conventional porous electrodes normally consist of homogeneous, unorganized collections of small-scale particles that offer little opportunity in terms of designing higher performance electrochemical devices. Indeed, simply increasing the surface area to maximize activity is usually detrimental to electrochemical transport because of increased tortuosity. Luckily, modern advanced and additive manufacturing methods present an opportunity for porous electrode structures that span length scales. In this presentation, we consider topology optimization as a tool to inform the design of porous electrodes. We introduce an optimization framework for a generic porous electrode model and apply it to two applications: an electrode driving a steady Faradaic reaction, and a transiently operated electrode in a supercapacitor. In each case, computationally designed electrodes that maximize energy efficiency are shown to outperform monolithic, homogeneous electrodes. For low effective ionic conductivity materials, the optimized designs exhibit hierarchical features with macropores that facilitate ionic transport.

Computational Modeling of Electrochemomechanics of High-Capacity Composite Electrodes in Li-Ion Batteries

Abstract Mechanical failure and its interference with electrochemistry are a roadblock in deploying high-capacity electrodes for Li-ion batteries. Computational prediction of the electrochemomechanical behavior of high-capacity composite electrodes is a significant challenge because of (i) complex interplay between mechanics and electrochemistry in the form of stress-regulated Li transport and interfacial charge transfer, (ii) thermodynamic solution non-ideality, (iii) nonlinear deformation kinematics and material inelasticity, and (iv) evolving material properties over the state of charge. We develop a computational framework that integrates the electrochemical response of batteries modulated by large deformation, mechanical stresses, and dynamic material properties. We use silicon as a model system and construct a microstructurally resolved porous composite electrode model. The model concerns the effect of large deformation of silicon on charge conduction and electrochemical response of the composite electrode, impact of mechanical stress on Li transport and interfacial charge transfer, and asymmetric charging/discharging kinetics. The study captures the rate-dependent, coupled electrochemomechanical behavior of high-capacity composite electrodes that agrees well with experimental results.

Computationally Efficient Quasi-3D Model of a Secondary Electrode Particle for Enhanced Prediction Capability of the Porous Electrode Model

Models of Li-ion batteries addressing a particular scale—from atomistic to continuum—have reached a certain level of maturity. Meanwhile, consistent multi-scale modelling approaches are still in their infancy despite their large potential to boost the accuracy and prediction capability of Li-ion battery models. As an answer to this challenge, the paper presents an advanced quasi-3D model of the active electrode material that tackles one of the main deficiencies of the porous-electrode theory (PET) based models which arises from a poor representation of the electrode topology. It is hypothesised that there exists a quasi-3D modelling representation of the active electrode material that adequately virtually replicates intra primary particle Li-distribution and features significantly shorter computational times compared to models featuring a fully 3D meshed electrode topology, which enables its full integration into the porous electrode model. An advanced quasi-3D model is constructed by the integration of the concentration and the chemical potential in each primary particle across its volume and by the introduction of the permeability parameter at the interfaces. Besides compatibility with PET and acceptable computational times, the model also exhibits results that are in good agreement with measured lithium concentration profiles inside secondary particles published in literature.

High power density & energy density Li-ion battery with aluminum foam enhanced electrode: Fabrication and simulation

Compared with aluminum foil (Al foil), the three-dimensional (3D) aluminum foam (Al foam) has the characteristics of 3D interconnected metal wires and through-hole structure with high specific surface area, which exhibits great potential for application in high-power energy storage devices. In this work, 3D Al foam-based and Al foil-based cathode sheets were fabricated and assembled into pouch cells. In-situ XRD was employed to analyze the electrochemical reaction behavior of the two types of porous electrodes. The 3D Al foam-based cathode demonstrated faster electron transfer and lithium-ion diffusion as compared to the Al foil-based electrode, which is helpful for a uniform electrochemical reaction and decreases the electrochemical polarization. Electrochemical simulations and porous electrode models were built to understand these phenomena. The Al foam-based LiFePO4 batteries exhibit much better power and energy performance than Al foil-based LiFePO4 battery. The power density of the Al foam pouch cells is 7.0–7.7 kW/L when the energy density is 230–367 Wh/L, which is the highest power and energy density among reported Al foam-based devices. The new findings open up opportunities for the development of high-power and high-energy-density commercial batteries.

Insights into the Role of Silicon and Graphite in the Electrochemical Performance of Silicon/Graphite Blended Electrodes with a Multi-Material Porous Electrode Model

Silicon/graphite blended electrodes are promising candidates to replace graphite in lithium ion batteries, benefiting from the high capacity of silicon and the good structural stability of carbon. Models have proven essential to understand and optimise batteries with new materials. However, most previous models treat silicon/graphite blends as a single “lumped” material, offering limited understanding of the behaviors of the individual materials and thus limited design capability. Here, we present a multi-material model for silicon/graphite electrodes with detailed descriptions of the contributions of the individual active materials. The model shows that silicon introduces voltage hysteresis to silicon/graphite electrodes and consequently a “plateau shift” during delithiation of the electrodes. There will also be competition between the silicon and graphite lithiation reactions depending on silicon/graphite ratio. A dimensionless competing factor is derived to quantify the competition between the two active materials. This is demonstrated to be a useful indicator for active operating regions for each material and we demonstrate how it can be used to design cycling protocols for mitigating electrode degradation. The multi-material electrode model can be readily implemented into full-cell models and coupled with other physics to guide further development of lithium ion batteries with silicon-based electrodes.

A novel methodology to estimate the state-of-health and remaining-useful-life of a Li-ion battery using discrete Fourier transformation

In this work, a multiphysics-based modeling approach is followed, which helps to diagnose the state-of-health (SoH) of the battery by using the discrete Fourier transform (DFT) analysis. The experimentally validated electrochemical model is considered based on the pseudo-2-Dimensional (P2D) porous electrode model. A constant current with a small perturbation (sinusoidal) on it is applied to the cell for testing purposes. The cell testing pulses of different frequencies are applied to the cell, and output responses are measured for the same. The change in battery output voltage response is observed with the contributing factors (SEI layer resistance, active material volume fraction reduction of anode) in the electrochemical model to observe the change in battery output voltage response. The spectrum analysis of the output voltage response is carried out to show the effect of aging on the battery using the DFT algorithm. Mathematical relationships between signal power and cell degrading parameters are formulated. Finally, a methodology is developed based on the obtained signal power values and the cell degrading factors, which concludes the present SoH of the cell and helps to give remarks to the remaining-useful-life (RUL) of the cell.