Delithiation Process Research Articles

Application of Thin Film As Polymer Gel Electrolyte for 3D Li-Ion Battery

Three-dimensional materials can improve the performance of energy storage systems by providing large active surface. Thus, the research was focused on designing a full 3D battery based on electrodeposited Ni3Sn4 (Ni-Sn) anode and polymer gel electrolyte/separator that was coated via layer-by-layer (LbL) technique. Advantages of the LbL approach was appliance of polymer material onto a rough surface of 3D structured electrode material, and thickness control of the coated gel polymer electrolyte. The structure of deposited electrode material was confirmed by XRD. The thickness estimation of coated layers, and cross-section view of 3D battery were depicted via SEM. Electrochemical activity of Ni-Sn alloy with LbL coated gel electrolyte demonstrated redox couples for lithiation and delithiation processes. LbL technique proved that polymer can be coated uniformly onto 3D structure electrode and function as the electrolyte and separator.AcknowledgementThis research was supported by the research grants #091019CRP2114 “Three-dimensional all solid state rechargeable batteries” from Nazarbayev University.

Simulation-Based Analysis of Structural and Thermodynamic Aspects of the Electrochemical Lithiation of Silicon Nanoparticles

Lithium-ion batteries are among the most predominant energy storage systems for portable to stationary electronic devices. Lithium-ion batteries are indispensable to laptops, mobile phones, and electric vehicles due to their high energy/power density and long cycle life. Silicon has been intensively pursued as one of the most promising anode materials because of its high specific capacity (4200 mAh/g for Li22Si5), in comparison with the conventional graphite (372 mAh/g for LiC6), and its abundance. Despite its high capacity, silicon-based anode materials suffer from fast capacity loss caused by its large volume change (>300%), unstable solid electrolyte interphase and the physical disintegration, such as racking and crumbling, of the electrode structure during lithiation and delithiation processes. Therefore, there are various research activities to control the electrochemical performance of silicon anode materials. The engineering of silicon nanostructures proved to be an effective method for improving capacity and cycling stability, since nano-sized silicon can alleviate mechanical fractures during volume changes. In particular, silicon nanoparticles can be added into the void region in the polycrystalline graphite matrix, resulting in an effective increase in the overall energy density of the anode. In this work, we designed reasonable structural models of silicon nanoparticles in terms of particle size and lithiation ratio through Monte Carlo simulations, and we conducted a series of first-principle simulations to understand their intrinsic electrochemical properties. We reported the theoretical understandings of the detailed structural and thermodynamic mechanism of the actual lithiation process of silicon nanoparticle systems based on atomistic simulation approaches. We found that the rearrangement of the silicon bonding network is the key mechanism of the lithiation process, and that it is less frequently broken by lithiation in the smaller sizes of silicon nanoparticles. The decreased lithiation ability of the silicon nanoparticles results in the lithiation potential being significantly lower than that of crystalline silicon phases, which impedes the full usage of the theoretical maximum capacity. Thus, nanosized slicon could have a negative effect on performance if they become too fine-sized. These findings provide a detailed view of the electrochemical lithiation process of silicon nanoparticles and engineering guidelines for designing new silicon-based nanostructured materials for the anode of high capacity lithium ion batteries.

In Situ X-Ray Photoelectron Spectroscopy for All-Solid-State Batteries: Analysis of Lithiation and Delithiation Reactions of Silicon Thin-Film Electrode

Si is an attractive anode material for next-generation lithium batteries including all-solid-state batteries because it has a high theoretical capacity density (4200 mAh g-1). However, Si suffers from the irreversible capacity loss related to the severe volume expansion/shrinkage during the lithiation/delithiation processes. In liquid-type batteries, the main cause of the capacity loss is the continuous formation/decomposition of the solid electrolyte interphase (SEI) on the Si anodes [1]. However, the capacity loss of the Si anode is also regarded as a serious issue even in all-solid-state batteries without using electrolyte solution. Thus, a fundamental understanding of the lithiation/delithiation reactions of the Si anode is important to solve the problem. X-ray photoelectron spectroscopy (XPS) enables us to analyze the elemental composition, oxidation states, and electronic structure of the sample surface. In situelectrochemical XPS, which can measure the same position of a sample under the operational condition for batteries, allows a stepwise analysis of the reactions without interference from variation and inhomogeneity of samples [2]. Here, lithiation/delithiation reactions of an amorphous Si electrode in a thin-film cell is investigated by using an XPS apparatus equipped with an applying voltage system [3]. The amorphous Si with a thickness of about 100 nm is formed on the Li6.6La3Zr1.6Ta0. 4O12 (LLZT) sheet by radio-frequency magnetron sputtering, and the Cu is further coated on the sputtered Si layer by DC sputtering. During the Cu deposition, a stainless-steel stencil mask is used to yield an uncoated amorphous Si part with a diameter of about 2 mm as an analytical region for the XPS measurements. The Li metal layer is thermally deposited on the other side of LLZT. After the thin-film cell with the final structure of [Cu/Si(100 nm)/LLZT(500 µm)/Li metal(1.3 µm)] is connected to the sample holder in an Ar-filled glove box, it is transferred to the XPS apparatus by using a vacuum suitcase to prevent from exposing to open air. The cell is cycled between 0.01 and 1.2 V at 0.02C (1.245 µA) in UHV chamber of the XPS apparatus. The Si surface is observed by XPS before/after the lithiation/delithiation processes. The galvanostatic potential profiles show that the capacity for the first lithiation and delithiation processes is 3160 and 2977 mAh g-1, respectively. A broad Li 1s peak appears after the first lithiation process, confirming the Li insertion to the Si electrode. According to the peak fitting, the Li 1s peak is composed of lithium-silicide (LixSi), Li2O, and Li2CO3. The Li2O and Li2CO3 are possibly formed by the reaction of the lithium-silicide surface with a trace amount of residual gas from the vacuum chamber and LLZT. The Li2O and Li2CO3 contribute to the irreversible capacity loss because these components remain even after the subsequent delithiation process. In the Si 2p region, peaks originated from bulk Si (Si0) at 99.1 eV and Si suboxide (SiOx) at 101.9 eV are shifted to lower binding energy side. These peak shifts indicate the formation of lithium-silicide (LixSi) and lithium-silicate (Li4SiO4) due to the insertion of Li ions to each layer. Based on the calculation using the peak intensities and known physical parameters, it is proposed that the Si electrode has a surface structure of [Li2O (2.5 nm)/Li4SiO4 (0.9 nm)/LixSi] at this state. In addition, the composition of the LixSi is estimated to be Li3.27Si from the charge integration and the thickness of each layer. After the subsequent delithiation process, the Li4SiO4 peak remains in the same position. In contrast to the immobility of the Li4SiO4 peak, the LixSi peak is shifted back to the higher binding energy side, but it does not completely return to the original position of the Si0 peak. The composition of the lithium-silicide phase at this state is estimated to be Li0.14Si. Therefore, Li trapped in Li0.14Si and formation of Li4SiO4, Li2O, and Li2CO3 contribute to the irreversible capacity loss of the Si electrode.

Elucidating the Mechanism of Li Insertion into Fe1–xS/Carbon via In Operando Synchrotron Studies

The detailed understanding of kinetic and phase dynamics taking place in lithium-ion batteries (LIBs) is crucial for optimizing their properties. It was previously reported that Fe1-xS/C nanocomposites display a superior performance as anode materials in LIBs. However, the underlying lithium storage mechanism was not entirely understood during the 1st cycle. In this work, in operando synchrotron techniques are used to track lithium storage mechanisms during the 1st (de)-lithiation process in the Fe1-xS/C nanocomposite. The combination of in operando techniques enables the uncovering of the phase fraction alternations and crystal structural variations on different length-scales. Additionally, the investigation of kinetic processes, morphological changes, and internal resistance dynamics is discussed. These results reveal that the phase transition of Fe1-xS → Li2Fe1-xS2 → Fe0 + Li2S occurs during the 1st lithiation process. The redox reaction of Fe2+ + 2e- ⇌ Fe0 and the Fe K-edge X-ray absorption spectroscopy (XAS) transformation process are confirmed by in operando XAS. During the 1st de-lithiation process, Fe0 and Li2S convert to Li2-yFe1-xS2 and Li+ is extracted from Li2S to form Li2-yS. The phase transition from Li2S to Li2-yS is not detected in previous reports. After the 1st de-lithiation process, amorphous lithiated iron sulfide nanoparticles are embedded within the remaining Li2S matrix.

Multifunctional carbon-confined FeS nanoparticles for a self-supporting and high-capacity cathode in lithium ion battery

Seeking an advanced cathode is a key to develop lithium ion battery. Here, a self-supporting and high-capacity [email protected] cathode is prepared by the chemical etching, the electrodeposition of carbon precursor and the high temperature sulfidation. Owing to the confinement of carbon layer for particle growth and its excellent conductivity, the [email protected] nanocomposite is generated and shows an elevated electrochemical kinetic behavior compared to the bulk FeS. Besides, the carbon layer improves the volume effect during lithiation and delithiation process. Thus, the optimized electrode exhibits a high reversible discharge capacity of 2.58 mAh cm−2 at 0.2 mA cm−2 and a long cyclic stability (2.03 mAh cm−2 after 200 cycles at 0.8 mA cm−2).

Sustainable recycling of LiCoO2 cathode scrap on the basis of successive peroxymonosulfate activation and recovery of valuable metals

Increasing demand and waste of lithium-ion batteries (LIBs) has adversely affected resources and the environment. Multistage utilization of spent LIBs is essential to their sustainable development. Here, we propose a simple recycling method of LiCoO2 cathode scrap, based on the first use of the cathode scrap as a catalyst to degrade organic pollutants via peroxymonosulfate activation, and subsequent recovery of valuable metals from the used catalyst. Compared with pristine LiCoO2, the LiCoO2 cathode scrap exhibits excellent catalytic performance due to the active sites generated, such as the vacancy generation and electronic structure modulation by the degradation of LiCoO2 during the continuous lithiation and delithiation processes. The removal efficiency of cathode scrap to the o-phenylphenol exceeds 98% within 60 min, and the degradation efficiency is still above 95% after the 10th use because its unique sandwich and porous structure ensure the stability and recyclability. After multiple catalytic reactions, due to the generation of crack, the separation of the sandwich structure, and further degradation of active materials, the leaching efficiency of transition metals from the cathode scrap in deep eutectic solvent is promoted. 86% of lithium and 95% of cobalt are leached from the used catalyst respectively. This study provides a promising strategy for the sustainable development of LIBs and promotes the utilization of spent LIBs in multiaspect.

Atomic investigation on structural rearrangement of MoS2/graphene heterostructure upon electrochemical lithiation and delithiation

MoS2/graphene composite is a promising anode candidate with high rate capability and high capacity. In this work, first principles simulations are applied to study structural rearrangement of the MoS2/graphene heterointerface upon lithiation and delithiation. The atomic structures of MoS2/graphene after lithiation and delithiation processes indicates that the lithiated configuration cannot be restore to the original structure under delithiation. Both the length of Li–S bond and the distribution of Mo–Mo distance correspond to the permanent structural change of MoS2. The rearrangement in atomic configuration will influence the next lithiation process and result in irreversible lithium loss.

Electric field driven de-lithiation: A strategy towards comprehensive and efficient recycling of electrode materials from spent lithium ion batteries

Along with the rapidly growing market of lithium-ion batteries, exploration of efficient strategies to recycle the retired lithium-ion batteries has become an imminent issue. Herein, a green and comprehensive recycling method based on the direct current (DC) electric field driven de-lithiation is developed and the feasibility of the strategy is systematically investigated. The results demonstrate that during the recycling process, the lithium ions can be effectively recovered with simultaneous H2 production. Meanwhile, the de-lithiated electrode materials exhibit a remarkable electrocatalytic activity, which is proved to be related to their high specific surface area as well as their large amount of lattice oxygen. Based on the Daedalian combination of efficient lithium recycling and applications of the de-lithiated cathode materials for oxygen evolution reaction, this study provides an effective strategy for recycling and making maximum use of the spent lithium-ion battery electrode materials based on the DC electric field driven de-lithiation process.

Investigation of charge carrier dynamics in positive lithium-ion battery electrodes via optical in situ observation

We present optical in situ investigations of lithium-ion dynamics in lithium iron phosphate based positive electrodes. The change in reflectivity of these cathodes during charge and discharge is used to estimate apparent diffusion coefficients for the lithiation and delithiation process of the entire electrode. Thereby, a scaling analysis of the transport process is applied, which clearly reveals its diffusive character.Results are shown for cathodes, in which the common additive carbon as well as the conductive and electrochromic marker additives (indium tin oxide and antimony tin oxide) are used. The latter leads to a substantial increase of visibility of the optical effect in the cathodes while electric properties remain qualitatively unchanged.The procedure extends common characterization techniques of positive electrode materials via a novel and integral combination of electrical and optical measurements.

Evaluation of oxygen contribution on delithiation process of Li-rich layered 3d transition metal oxides

We investigated the oxygen contributions on delithiation process of different types of layered 3d transition metal oxides, Li2TiO3, Li2MnO3, and LiCoO2, using X-ray spectroscopies with the aid of density functional theory calculations. In delithiatied LiCoO2, electrons are extracted from highly hybridized Co 3d and O 2p orbitals without O2 loss. In Li2TiO3, the hybridized Ti 3d and O 2p orbitals at the valence band is mainly contributed by O 2p orbitals, and delithiated Li2TiO3 loses oxygen as the electrons are extracted. Li2MnO3 exhibits some hybridization. In delithiated Li2MnO3, a certain amount of oxygen is lost, but the large amount of oxidized O anions remains as peroxide and superoxide-like states, which would work as the redox active species. Therefore, the degree of hybridization between metal 3d and O 2p orbitals is a key factor to influence the stability of O anion redox during the oxidation process, which determines the electrode performance.

Halogen-Doping Effect on the Delithiation and Charge Transfer of (Li2S)10 Cluster.

Previous studies have suggested beneficial effects in lithium-sulfur batteries containing iodide in a sulfur-based cathode or as an electrolyte additive. These effects include preventing electrolyte degradation and improving the cycle stability of Li-S cells. However, little is known regarding the underlying reasons of such performance improvements. In this work, we present a theoretical study of the halogen-doping effect on the delithiation (charge) process on a (Li2S)10 model structure representing a potential final discharge product. It is revealed that the electron polaron is the dominant charge carrier during the charge process, and iodine is a facilitating agent for lithium detachment from the lithium sulfide cluster. However, the graphene support was found as potentially slowing down the ionic transport during the delithiation process due to charge transfer exerted by the support to the doped cluster that may retain the positive ions in the particle.

Simultaneous effect of particle size and location on stress development in the electrodes of lithium‐ion batteries

In this study, stress generation at the electrode in Li-ion batteries was studied using a two-dimensional cell-scale model that includes multiple active particles during galvanostatic discharge. Numerical simulations were performed using an electrochemical–mechanical coupled model to elucidate the simultaneous effects of particle size and location, lithium intercalation kinetics and binder constraints on the stress. The simulation results showed that when different sizes of particle are considered in the electrode, the small particles were discharged more than the large particles, resulting in higher level of stress in the smaller particles. In addition, the closer the particles were located to the separator, the larger the stresses that were developed in those particles. Therefore, a layered structure, where the particle size gradually increases as the distance from the particles to the separator decreases, can alleviate stress on the electrode. When binder constraints were considered for the electrode particles, the stress was increased at the anode and alleviated at the cathode upon discharge. This indicates that the effect of mechanical constraints on stress generation in the particles differs in the lithiation and delithiation process.

Theoretical Study of a New Porous 2D Silicon-Filled Composite Based on Graphene and Single-Walled Carbon Nanotubes for Lithium-Ion Batteries

The incorporation of Si16 nanoclusters into the pores of pillared graphene on the base of single-walled carbon nanotubes (SWCNTs) significantly improved its properties as anode material of Li-ion batteries. Quantum-chemical calculation of the silicon-filled pillared graphene efficiency found (I) the optimal mass fraction of silicon (Si)providing maximum anode capacity; (II) the optimal Li: C and Li: Si ratios, when a smaller number of C and Si atoms captured more amount of Li ions; and (III) the conditions of the most energetically favorable delithiation process. For 2D-pillared graphene with a sheet spacing of 2–3 nm and SWCNTs distance of ~5 nm the best silicon concentration in pores was ~13–18 wt.%. In this case the value of achieved capacity exceeded the graphite anode one by 400%. Increasing of silicon mass fraction to 35–44% or more leads to a decrease in the anode capacity and to a risk of pillared graphene destruction. It is predicted that this study will provide useful information for the design of hybrid silicon-carbon anodes for efficient next-generation Li-ion batteries.

Sequence-Defined Peptoids with -OH and -COOH GroupsAs Binders to Reduce Cracks of Si Nanoparticles of Lithium-Ion Batteries.

Silicone (Si) is one type of anode materials with intriguingly high theoretical capacity. However, the severe volume change associated with the repeated lithiation and delithiation processes hampers the mechanical/electrical integrity of Si anodes and hence reduces the battery's cycle‐life. To address this issue, sequence‐defined peptoids are designed and fabricated with two tailored functional groups, “—OH” and “—COOH”, as cross‐linkable polymeric binders for Si anodes of LIBs. Experimental results show that both the capacity and stability of such peptoids‐bound Si anodes can be significantly improved due to the decreased cracks of Si nanoparticles. Particularly, the 15‐mer peptoid binder in Si anode can result in a much higher reversible capacity (ca. 3110 mAh g−1) after 500 cycles at 1.0 A g−1 compared to other reported binders in literature. According to the density functional theory (DFT) calculations, it is the functional groups presented on the side chains of peptoids that facilitate the formation of Si−O binding efficiency and robustness, and then maintain the integrity of the Si anode. The sequence‐designed polymers can act as a new platform for understanding the interactions between binders and Si anode materials, and promote the realization of high‐performance batteries.

Thickness gradient promotes the performance of Si-based anode material for lithium-ion battery

The large volume change of the silicon (Si) during the lithiation and delithiation process has long been a problem impeding its application as one of the most promising anode materials for lithium-ion batteries (LIBs). In this paper, we proposed a conceptually new idea to address this problem simply by tapering the thickness of the electrode material film. The resulting thickness-gradient electrode exhibits considerable enhancement in the electrochemical performances including capacity, capacity retention, energy density, Coulombic efficiency, and rate capability in comparison to the traditional counterparts with uniform thickness. Such enhancement in the electrochemical performance can be attributed to the lessening of the stress concentration on the interface between the electrode film and the current collector upon the volume change of Si taking place in the lithiation and delithiation process. To make the best use of this strategy, the optimal design of the gradient thickness is proposed based on the theory of stress homogenization, followed by the experimental verification. The results of this paper provide a facile, cost-effective, and scalable way for enhancing the performance of Si-based anodes for LIBs. This strategy can be further extended to the other anode materials suffering the similar lithiation-induced volume change problem.

Boosting the performance of half/full lithium-ion batteries by designing smart architecture anode of SnS2 nanosheet coating on NiCo2S4 hollow spheres

An innovative and controlled strategy has been proposed to design tin disulfide (SnS2) nanosheet coating on nanostructure hollow sphere of ternary spinel sulfide (NiCo2S4) composites smart architecture as anodes (NiCo2S4/SnS2) for lithium-ion batteries (LIBs) by a facile template-free hydrothermal method. The NiCo2S4/SnS2 electrode showed good electrochemical performances, for instance, high reversible capacity (1260 mA h g−1@0.1 A g−1), favorable rate capability and good cycles stability (627 mA h g−1 @0.5 A g−1 after 300 cycles), which is ascribed to smart architecture hollow structure, good electrical conductivity and contribution of synergistic effect. The mechanism of lithiation and delithiation process in NiCo2S4/SnS2 composite electrodes was further shed light upon. Moreover, the advanced full batteries have been assembled by combing NiCo2S4/SnS2 anodes with commercial NMC111 cathodes, which presented good cycle stability and potential promising application. Our work provides novel way to design multifunction metal sulfides with desirable architecture and superior property in energy storage area.

Remaining Li-Content Dependent Structural Evolution during High Temperature Re-Heat Treatment of Quantitatively Delithiated Li-Rich Cathode Materials with Surface Defect-Spinel Phase.

Pre-extracting Li+ from Li-rich layered oxides by chemical method is considered to be a targeted strategy for improving this class of cathode material. Understanding the structural evolution of the delithiated material is very important because this is directly related to the preparation of electrochemical performance enhanced Li-rich material. Herein, we perform a high temperature reheat treatment on the quantitatively delithiated Li-rich materials with different amounts of surface defect-spinel phase and carefully investigate the structural evolution of these delithiated materials. It is found that the high temperature reheat treatment could cause the decomposition of the unstable surface defect-spinel structure, followed by the rearrangement of transition metal ions to form the thermodynamically stable phases, More importantly, we find that this process has high correlation with the remaining Li-content in the delithiated material. When the amount of extracted Li+ is relatively small (corresponding to the higher remaining Li-content), the surface defect-spinel phase could be dominantly decomposed into the LiMO2 (M = Ni, Co, and Mn) layered phase along with the significant improvement of electrochemical performance, and continuing to decrease remaining Li-content could lead to the emergence of M3O4-type spinel impurity embedding in the final product. However, when the extracted Li+ further achieves a certain amount, after the high temperature heat-treatment the Mn-rich Li2MnO3 phase (C2/m) could be separated from Ni-rich phases (including R3m, Fd3m, and Fm3m), thus resulting in a sharp deterioration of initial capacity and voltage. These findings suggest that reheating the delithiated Li-rich material to high temperature may be a simple and effective way to improve the predelithiation modification method, but first the amount of extracted Li+ should be carefully optimized during the delithiation process.

A carbon-doped anatase TiO2-Based flexible silicon anode with high-performance and stability for flexible lithium-ion battery

Flexible Si composite anodes consisting of mechanical anatase TiO2 robust buffer layer anchored on carbon cloth has been synthesized through the controllable in-situ sol-gel techniques. This novel TiO2 layers demonstrate the remarkable suppress ability to alleviate the silicon volume variation during the lithiation and delithiation process. As a result, the Si/TiO2-CC composite anodes exhibit the remarkable reversible areal capacity of 3.21 mA h/cm2 (1720 mA h/g of Si active particles) at the current density of 0.2 mA/cm2 and 1.82 mA h/cm2 (1380 mA h/g of Si active particles) at 3 mA/cm2, meanwhile, it can maintain the capacity retention of 94.5% after 100 cycles at 3 mA/cm2. Furthermore, an all-flexible battery based on Si/TiO2-CC anode and NCM811 cathode is also fabricated. The flexible battery shows excellent mechanical integrity and Si interface stability under continuous bending and twisting state, due to the “bridge” effect of TiO2 layer. Our work provides a new route to establish the silicon-based flexible anodes using high-modulus bonding materials to suppress silicon volume expansion.

Synthesis and research of MnO2–NiO composite as lithium-ion battery anode using spent Zn–Mn batteries as manganese source

In this work, we have successfully synthesized porous flower-like MnO2–NiO anode material for lithium ion batteries by facile hydrothermal method using the manganese source that is recovered from spent Zn–Mn batteries through hydrometallurgy recycling technology. Scanning electron microscopy (SEM) reveals that such an architecture provides short paths for lithium diffusion and large material/electrolyte contact area. The electrochemical measurements exhibit that the initial discharge capacity of MnO2–NiO composite is 2981 mAh·g−1 at a current density of 100 mA g−1 and retains at 502 mAh·g−1 after 100 cycles, much higher than that of pure MnO2. Even at a high current rate of 400 mA g−1, the specific capacity still remains at 297 mAh·g−1 after 50 cycles. The electrode exhibits excellent cycling performances and high capacity. Furthermore, the lithiation and delithiation processes of MnO2–NiO anode material have been studied in detail by X-ray diffraction characterization. We found that during the lithiation process, MnO2 reacts with lithium ions to form the intermediate product of Mn2O3, which is further reduced to Mn metal. NiO directly reacts with lithium ions to form Ni metal.

A Gaussian Process-Based Crack Pattern Modeling Approach for Battery Anode Materials Design

Abstract Silicon-based anodes are one of the promising candidates for the next generation high-power/energy density lithium ion batteries (LIBs). However, a major drawback limiting the practical application of the Si anode is that Si experiences a significant volume change during lithiation/delithiation, which induces high stresses causing degradation and pulverization of the anode. This study focuses on crack initiation within a Si anode during the delithiation process. A multi-physics-based finite element (FE) model is built to simulate the electrochemical process and crack generation during delithiation. On top of that, a Gaussian process (GP)-based surrogate model is developed to assist the exploration of the crack patterns within the anode design space. It is found that the thickness of the Si coating layer, TSi, the yield strength of the Si material, σFc, the cohesive strength between Si and the substrate, σFs, and the curvature of the substrate, ρ, have large impacts on the cracking behavior of Si. This coupled FE simulation-GP surrogate model framework is also applicable to other types of LIB electrodes and provides fundamental insights as building blocks to investigate more complex internal geometries.