Digital Techniques Assisted in Tailoring Electrode Structure to Optimize Electrode Kinetics

Digital Techniques Assisted in Tailoring Electrode Structure to Optimize Electrode Kinetics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Digital Techniques Assisted in Tailoring Electrode Structure to Optimize Electrode Kinetics Yubai Li, Heng Huang, Zhifu Zhou, WeiTao Wu, Lei Wei, Hu Chengzhi, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6035965/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Poor rate performance limits the application of high-areal-loading electrodes in energy storage, largely due to cathode microstructure. In this study, we integrated X-ray computed tomography (XCT) with digital technology to quantify the correlation between electrode structure and internal kinetic performance of lithium-ion electrodes. Results show that electrode structure intricately influences internal kinetics, thereby affecting rate capacity and nominal potential. Based on the parametric relationship between electrode structure and electrochemical-thermal properties, we explored the effects of structural regulation on electrode performance. Vertical channels significantly enhanced the rate capability and ohmic heating rate of small-particle electrodes, while solid-phase diffusion (SPD) dominated the discharge performance of large-particle electrodes, diminishing the impact of tortuosity strategies. Furthermore, electrodes with abundant SPD barriers exhibit unidirectional propagation of reaction fronts, resulting in a deeper SPD-limited region. This observation inspired the integration of two structural strategies that favor both mass transport and reaction penetration. Optimized electrode structures enhanced energy density at high rates and accommodated diverse particle sizes and thicknesses. Additionally, the coupling effect of the heat transfer environment on electrode performance was investigated. This study presents a novel paradigm for bottom-up electrode design using microstructure-resolved model, providing both microscopic mechanisms and quantitative insights for advanced battery development. Physical sciences/Engineering/Mechanical engineering Physical sciences/Engineering/Chemical engineering Lithium-ion batteries Microstructure-resolved model Structure regulation Rate capability Thermal behavior Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1 Introduction The fast-discharging capability of the cathode allows lithium-ion batteries (LIBs) to deliver significant power in a short time, which is crucial for the acceleration performance of electric vehicles (EVs) and the peak load regulation capacity of grid energy storage systems [ 1 ]. However, as the demand for higher energy density increases, increasing electrode thickness or reducing porosity has become a common principle for LIBs [ 2 , 3 ]. This hinders mass transport within the electrode, significantly shortening the operating time at high current densities [ 4 ]. Consequently, commercial electrodes have been designed with varying microstructures and component trade-offs to suit various application types, such as energy-type or power-type applications. This results in a compromise that fails to simultaneously meet the required energy and power densities for high-rate applications. Therefore, to further expand the market share, designing electrode structures that allow LIBs to perform effectively in diverse application scenarios is essential. This requires a microscale-based analysis of the relationship between electrochemical performance and three-dimensional (3D) electrode structure, ensuring the development of rational structure modification strategies. At higher current densities, internal mass diffusion becomes the primary factor limiting electrode performance [ 3 ]. The slow electrolyte phase diffusion (EPD) rate causes lithium ions (Li + ) to accumulate on the separator side and even leads to a concentration depletion near the current collector. The increasing concentration gradient across the thickness results in significant polarization overpotential, causing premature termination of operation. At its core, this issue can be mitigated by improving electrolyte performance, such as through the use of concentrated electrolytes [ 5 ] and the development of electrolyte additives [ 6 ]. The underlying principle is that these approaches increase salt diffusion rates and ion activity, thereby reducing concentration gradient across thickness. Additionally, low porosity in high areal loading electrodes creates a more tortuous Li + penetration network, leading to power loss and material waste near the current collector. Although tortuosity engineering methods, such as gradient porosity [ 7 ] and vertical channels [ 8 ], have received positive feedback, most studies focus on single electrode structures. This leaves the universality of tortuosity strategies and their underlying mechanisms largely unexplored. The diffusion kinetics that limit performance are also reflected in the solid-phase diffusion (SPD) within the active material (AM). Slow SPD causes the embedded lithium (Li) to accumulate on the surface of AM particles, forming a significantly large concentration gradient along the path. Additionally, a Li-rich active interface gradually inhibits charge transfer reactions, which results in slower lithiation rates [ 9 ]. This generates not only high concentration overpotential and interface activation overpotential at high rates, but also leads to underutilization of the material within the particles. In addition to material modification strategies like elemental concentration gradients [ 10 ] and doping [ 11 ], structural adjustments, such as reducing particle size, have been provided to be effective in enhancing the SPD rate. However, electrodes containing excessive amounts of small particles exhibit a larger specific surface area, which accelerate the side reaction rates and the development of local hotspots, compromising cycle durability and posing thermal risks [ 12 , 13 ]. For electrodes with larger particle sizes, aside from the detriments to SPD, the smaller interface areas also limit reaction rates. However, it is undeniable that their higher tap density and mechanical strength make them preferred in energy-oriented LIBs [ 14 ]. Selecting an appropriate particle size combination can mitigate many drawbacks, however, electrodes with different particle size distributions (PSDs) exhibit varying competitive kinetic behaviors at high rates, which complicates the limiting factors of electrode performance. Currently, optimizing electrode rate performance relies on experimental approaches, which fall short in providing monitoring of internal operational states during discharge processes and a physics-based understanding. Consequently, multiphysics field models based on porous theory have emerged as advantageous optimization tools and are widely applied [ 15 ]. Unfortunately, homogeneous theoretical approaches, such as treating electrodes as uniformly distributed spherical particles, overlook the effects of heterogeneous microstructures (e.g., point contacts, 3D morphological edges) on reaction nonuniformity [ 16 , 17 ]. This limitation prevents these models from achieving 3D heterogeneous structural optimization tasks. Nano X-ray computed tomography (nano-XCT) has emerged as a highly valuable 3D imaging technique, widely applied in the study of electrode materials [ 18 – 20 ]. For instance, Lu et al. [ 21 ] employed nano-XCT to observe, in situ, the structural changes of electrodes during the calendering process at the particle level, and used electrochemical models to elucidate the structure-performance relationship. However, the carbon and binder domains (CBD) in electrodes exhibit X-ray attenuation coefficients similar to air, posing a significant challenge for reconstructing the three-phase electrode structure containing AM, CBD, and pores. To address this, various mathematical algorithms have been developed to numerically add the CBD phase within the AM-pore region, substantially reducing both the difficulty and cost of such studies. Mistry et al. [ 22 , 23 ] developed a stochastic EIP generation algorithm based on the cohesive tendencies of CBD and AM, and the validated structural-electrode parameter relationships have been widely applied in numerical simulations of electrode operational characteristics [ 24 , 25 ]. Notably, most studies conduct electrochemical simulations by calculating the effective transport parameters of the 3D digital twin structure, which are then incorporated into the P2D model. Although this approach shortens simulation times, it neglects potential biases arising from the heterogeneous structure, which may lead to deviations in the dynamic evolution. Moreover, the investigation of rate capability on the cathode side is primarily established through coin cell experiments or numerical simulations in an isothermal environment. During practical high-rate operation, internal heat accumulation from electrode impedance in integrated modular batteries has been shown to significantly alter electrode kinetics [ 26 ], leading to notable performance discrepancies. Therefore, integrating 3D models of microscale structure and considering thermal coupling effects is crucial for providing precise guidance in electrode optimization processes. This study aims to obtain comparable electrode structures by combining nano-XCT scanning experiments with digital processing techniques. Subsequently, a validated numerical model is used to elucidate the relationship between the microstructure of the electrodes and the internal dynamics (such as mass transfer, reactions, and heat generation) in LIBs. The study investigates the parametric correlations between electrode structure, rate performance, areal loading, and heat generation rate, providing deeper insights into the development of power- and energy-dominant electrodes. Various electrode configurations are considered, with a focus on the coupled effects of particle size, CBD fraction, and electrode thickness on performance. The efficacy of a laser patterning strategy is then evaluated for electrodes with different particle sizes. Based on the observed phenomenon of the reaction front migration, a tortuosity and particle gradation electrode structure that favors kinetics is proposed and its structural advantages across multiple dimensions are assessed. Electrochemical-thermal modeling explores performance variations under different heat exchange conditions, enhancing the understanding of multiphysics coupling in the electrode structure optimization process. 2 Results and discussion 2.1 Structure parameters that control the rate capability of the electrode A comprehensive investigation of the microscopic-scale dynamic changes induced by different electrode structural configurations is crucial for optimizing electrode performance. To explore the effect of particle size on the electrode, two electrodes with significantly different particle size distributions (PSDs) were selected as the subjects of study. Their three-dimensional (3D) structures were reconstructed using nano-XCT (Zeiss Xradia Ultra 800) (Fig. S1 ). Due to the differing active material loadings, the active material architecture with a consistent volume fraction (54.17%) was iteratively generated by random insertion (Fig. S2a). In addition, we employed digital twins to deal with electrodes with different pore structures instead of dealing with the challenge of segmenting the inactive phase. Using pre-fabricated active materials as samples, a CBD addition program was applied via MATBOX to generate electrodes with varying CBD contents (Fig. S2b). MATBOX, developed by Usseglio-Viretta et al. [ 23 ], is a software for virtual electrode structure fabrication. The fabrication algorithm, which has undergone peer review and experimental validation, is widely used in electrode microstructure simulation studies. Detailed procedures for the nano-XCT experiments and virtual electrode fabrication are provided in the experimental section. It is important to note that the average diameter of cathode particles at both laboratory and industrial scales can vary significantly from 2 µm to 12 µm [ 27 , 28 ], and is primarily designed based on specific application requirements (power-oriented or energy-oriented). The large-particle and small-particle electrodes used in the model are derived from commercial lithium-ion battery cathodes. The PSD assessment results indicate that the large-particle electrode shows a bimodal distribution with a D 90 ~ 10 µm (Fig. 1 c), while the small-particle electrode exhibits a unimodal distribution with a D 90 ~ 5 µm (Fig. 1 d). The significantly different distribution characteristics and D 90 values allow these electrodes to serve as comparative subjects for investigating strategies to enhance the energy density of electrodes at high rates. Based on the prepared electrode structure, the material properties of the electrodes were calculated using direct numerical simulations (Supplementary Note 1), with the results shown in Figs. 1 e-f. When the active components of the electrode were fixed, a competitive relationship was observed between the CBD content (electron conduction) and porosity (ion diffusion). As the CBD content increased, the diffusion of mass within the electrode became more difficult, and the tortuosity of the pores exhibited an exponential growth trend (Fig. 1 e). Lu et al. [ 29 ] analyzed the relationship between electrode porosity and diffusion resistance using XCT and rolling equipment, showing a consistent trend. Notably, the results were significantly higher than those predicted by the Bruggeman empirical formula, which can be attributed to the assumptions regarding particle morphology and spatial distribution, as well as the neglect of CBD components [ 30 ]. Figure 1 f shows the dependence of the effective conductivity on the CBD content, with a similar trend to the variation of tortuosity, a result also captured by Ghadban et al. [ 31 ] through numerical simulations. However, slight differences were observed in the high CBD fraction due to the differing electrode skeleton components (96.5 wt.% vs. 94 wt.%). The larger specific surface area (α s ) of small particle electrodes, which accounts for the cohesive forces and adhesion energy between the slurry molecules, leads to more complex connection pathways for CBD molecules, thus forming more tortuous Li + diffusion paths (Fig. 1 e). In contrast, the smaller α s of larger particles allows CBD to more easily form electrical bridges (Fig. 1 f) [ 32 , 33 ] . In addition to their physical properties, the AM and porosity structure also govern the complex reaction and transport kinetics, leading to trade-offs in electrode performance. Therefore, the aforementioned digital twin electrode structure is utilized, and a model based on the 3D microstructure is employed to investigate the impact of particle size, porosity, and thickness on the electrochemical rate capability. Here, electrodes with different CBD fractions are used to reflect the real-world effect of porosity on electrode performance. Specifically, the 4 wt.% CBD fraction corresponds to a porosity of 37.83%, while the 12.5 wt.% CBD fraction corresponds to a porosity of 20.81% (Detailed model and electrode parameters are provided in Table S1 -2). For convenience, different parameters are combined with hyphens to denote specific electrodes. For instance, the 30 µm large particle (LP) electrode with a low CBD fraction (LC) is denoted as 30 µm-LP-LC, while the 80 µm small particle (SP) electrode with a high CBD fraction (HC) is denoted as 80 µm-SP-HC. The neglected structural parameters refer to all electrodes incorporating the parameter. The state of lithiation (SOL) and Li + concentration (C e ) distributions in electrodes with different design parameters under 3C are shown in Fig. 2 . At the particle level, comparing 30 µm-LP and 30 µm-SP, LP particles exhibit larger concentration gradients across core-surface spans due to the average 1.34 µm-longer Li diffusion paths (Figs. 2 a-b and 2 e-f). The average SOL at the particle level is quantified, and the colors are coded using the internal SOL gradient (ΔSOL = SOL max - SOL min ) to reflect the degree of concentration polarization within the particle. The results reveal linear correlations between particle SOL, ΔSOL, and particle size, with particles smaller than 2 µm in LP showing similar lithiation levels to SP. Gradually developing Li concentration gradients within electrodes directly contribute to capacity losses, this is reflected in SOL distributions at discharge completion (Figs. S3a-d). Compared to SP, concentration polarization within LP particles intensifies further before discharge completion. Additionally, significant unused material remains within SP due to lost active surface area (Figs. S3c-d). The D 90 particle selected from 30 µm-LD exhibits surface-concentrated Li layers and uniformly distributed Li cores (Figs. S4a-b). Rapid concentration changes are observed within the concentrated thin layers, while nearly no concentration gradient is evident within the cores, indicating restricted diffusion of embedded Li within particles. Quantitative analysis shows a 21.6% reduction in average Li insertion and a 16.2% decrease in the volume fraction of concentrated Li layers (determined by second-order SOL differentials) in LP due to a 1.8-fold increase in particle diameter. This suggests that reducing particle size significantly alleviates solid-phase diffusion (SPD) limitation, enabling electrodes to absorb more Li at the same reaction rate. Expanding to the electrode level, in the 30 µm-LC, electrolyte-phase diffusion (EPD) does not restrict electrode performance due to the weak Li + transport resistance (τ LP−LD ~ 2.31 vs. τ SP−LD ~ 2.34), exhibiting a uniform SOL gradient across thickness (Figs. 2 a and 2 e). For HC with the same CBD fraction, the larger surface area of SP creates a more tortuous pore network in 3D space (Fig. 1 f) [ 31 ]. Nonetheless, the shorter Li + transport distance results in a uniformly distributed C e across the electrode (Figs. 2 b and 1 f), thus minimizing the impact of EPD limitation (further theoretical elaboration will follow). This is evidenced in the SOL qualitative analysis, where SOL in HD remains linearly correlated with particle size. Furthermore, internal concentration gradients within HD particles continue to develop, further reducing material utilization at discharging completion (Figs. S3c-d). This underscores that, apart from particle size, the reaction surface area related to porosity also constitutes an impediment to rate capability. In thicker electrodes, the diffusion of Li + toward the current collector becomes more challenging, restricting more reaction regions to lower electrolyte salt concentrations. Additionally, increased AM raises the working current, exacerbating the burden of Li diffusion within particles and thereby disrupting the competitive balance between SPD and EPD. Comparing the 30 µm-LC and 80 µm-LC, the increased thickness leads to a slight Li + concentration near the separator (Figs. 2 c and 2 g), but this is insufficient for EPD to exert limiting effects, thus, SOL continues to strongly correlate with particle size. A quantitative study of the same D 90 particle reveals that increasing thickness has minimal impact on the average inserted Li amount and the thickness of the concentration layer (Figs. S4c-d). Despite a 0.38 µm decrease in the concentration layer, this results in a negligible difference of only 0.5% in average inserted Li amount due to similar constraints imposed by SPD. Furthermore, the SOL distribution at the end of discharge shows that the polarization level within LD particles is weakly affected by an increase in thickness (Figs. S3e and S5g). For the 80 µm-HC, increasing electrode thickness significantly imposes limitations due to EPD (Figs. 2 d and 2 h), reflected by higher SOL and greater ΔSOL near the separator. SOL is also found to strongly correlate with distance from the separator. Specifically, SP exhibits a narrow particle size distribution with minimal variation in SOL levels between particles. In contrast, LP shows a graded change in SOL and ΔSOL across the entire electrode thickness according to particle size, indicating that LP is influenced by slow SPD, consistent with the findings of Lu et al. [ 34 ] that larger particle sizes extend SPD-limited regions. From a reaction kinetics perspective, particle lithiation is driven by activation overpotential (η), related to equilibrium lithiation potential (V eq (SOL) = ϕ s - ϕ e - η, where ϕ s is solid-phase electron potential, and ϕ e is liquid-phase ion potential). Figs. S7a-d illustrate uniform activation overpotential η and heterogeneous V eq distribution on LP/SP electrodes, suggesting SOL gradients across electrode thickness are driven by e − or Li + transport polarization. Given the lumped porosity model, which neglects the CBD distribution effects on e − conduction pathways, almost no difference in solid-phase potential ϕ s is observed in the electrodes (Figs. S5e-f). Therefore, preferential lithiation near the separator is dependent on liquid-phase potential ϕ e . As a function of reaction current, Li + flux on the separator side further increases with higher areal loading. However, constrained by transport resistance, larger C e gradient develops across electrode thickness (Figs. 2 d and 2 h), leading to development of liquid-phase potential ϕ e gradients according to Ohm's law (Figs. S5g-h). Li + concentration polarization significantly reduces V eq level, enabling particles to react faster under the same activation overpotential. This also explains why the 30 µm-HD does not encounter SPD limitations (Figs. 2 c and 2 g). Additionally, SPD limitations within LP-HD dominate before discharge completion (Fig. S3f). However, due to higher tortuosity (τ LP−HD ~ 7.16 vs. τ SP−HD ~ 11.34), the Li + concentration near the 80 µm-SP-HD current collector is nearly depleted at 50% DOD, hindering particle utilization by the end of discharge (Fig. S3h). Figure 3 a illustrates the variation of electrode capacity with discharge rate. As the discharge rate increases, the electrode capacity exhibits a declining trend. At 3C, the effect of particle size on the electrode performance becomes significantly more pronounced than that of porosity, as reflected in the comparison of the 80 µm-HC electrode. Additionally, capacity data for similar electrodes are presented using symbols, with supporting dynamic voltage verification results at different discharge rates from Fig. S6a for cross-validation of different electrode structures. The consistent trend across the data confirms the feasibility of the model (Detailed validation can be seen at Fig. S6). Figures 3 b-c summarize structure-dependent electrode capacity and average potential at 3C. For specific capacity, the impact of thickness on electrode performance is minimal. Particle size once again highlights its dominant role over porosity in determining electrode capacity (Fig. 3 b), underscoring the competitive advantage of SPD. The average potential of the electrode reflects its power capability, and unlike the dependence of specific capacity on structure, the average potential is primarily governed by EPD, which is associated with porosity. This structural effect becomes more pronounced in thicker electrodes (Fig. 3 c), further emphasizing the importance of mitigating EPD in thicker electrodes. The electrochemical-thermal multi-physical interactions in electrodes generate unexplored relationships between structural characteristics and heat generation, with quantification results under isothermal conditions presented in Figs. 3 d-e. The heat sources during electrode operation can be categorized into reversible and irreversible heat. In numerous high-rate discharge scenarios, the irreversible heat, primarily consisting of ohmic heat and reaction heat, contributes most significantly to the total heat generation and thus receives considerable attention [ 25 , 26 ]. Therefore, this study focuses on the coupling relationship between structure and irreversible heat generation rate. As shown in Figs. 3 d-e, a larger electrode thickness corresponds to a higher operating current, which leads to an increase in the rates of ohmic or reaction heat. Moreover, EPD control the dominant type of heat generation. For instance, in the 30 µm electrode, the activation heat rate in the LC electrode is relatively higher, while ohmic heat dominates in the HC electrode (Fig. 3 d). The 80 µm electrode, with its more tortuous ion transport paths, leads to the activation heat in the LC electrode rising to the level of ohmic heat, whereas in the HC electrode, ohmic heat remains the absolute dominant factor (Fig. 3 e). With the growing demand for energy density in practical applications, thicker electrodes are being designed, which will continue to increase the CBD fraction and rolling density to improve both gravimetric and volumetric energy densities. The potential gradient across the electrode thickness leads to a higher ohmic heating rate and lower average potential for electrodes with lower porosity. These attenuation effects become increasingly unacceptable in thicker electrodes (Figs. 3 b-e). This undoubtedly results in energy loss and heat generation at high charge/discharge rates. Therefore, the subsequent work in this study will integrate the aforementioned knowledge to explore performance optimization strategies for thicker HC electrodes. 2.2 Enhancement mechanism of electrode performance by laser patterning Given the widespread application of laser patterning technology in improving thick electrode performance, this section simulates the 80 µm-HC with different PSDs to investigate the mechanisms of performance enhancement through tortuosity engineering. Dunlap et al. [ 35 ] used femtosecond pulsed lasers to fabricate patterned grooves in NMC622 electrodes. SEM characterization showed ablation holes at a 75° channel angle, attributed to the shape of the incident beam and the morphology of the particles. The maximum diameter of the channels (the separator side) was approximately 36 µm, with a depth of about 50% electrode thickness. To avoid significant material waste, this study employs a lattice laser patterning method that extracts a quarter-cone section from the pristine electrode on the separator side to obtain a representative patterned electrode (Figs. 4 a and 4 b). This technique has recently been applied to graphite anodes to enhance fast-charging capabilities [ 36 ], but the mechanism for improving the discharge performance of cathodes still requires detailed exploration. Due to the higher areal loading, the material loss caused by laser ablation in this work is slightly higher than the values reported by Dunlap et al. [ 35 ] (11.4 wt% for LP, 11.4 wt% for SP). Due to the symmetry of the actual structure centered around the introduced channels, a symmetric model approach is employed in this work. As outlined in Supplementary Note 3, the boundary condition treatment of the symmetric model does not introduce any additional impact on the electrode performance or the direction of the electric field propagation. Figures S7a and S7b show the physical parameters along the thickness direction of the (un)patterned electrodes. The introduced channel not only causes a loss of active material but also leads to a reduction in the active surface area (red dashed lines). However, the trade-off does not significantly change their specific surface area (Laser_SP ~ 0.89%, Laser_LP ~ 2.1%), which is consistent with observations from experimental measurements [ 35 ]. Additionally, the in-plane porosity (x-direction) and through-plane porosity (z-direction) near the separator increase in local regions, likely acting as intermediary storage stations for Li + diffusion deeper into the electrode. A further electrochemical simulation reveals the impact of structural changes on internal mass diffusion and reaction kinetics, as shown in Figs. 4 c-e. Compared to the pristine electrodes (Figs. 2 d and 2 h), Laser_LP and Laser_SP shorten the Li + transport distance through in-plane diffusion paths, highlighted by the direction of Li + streamlines. This provides the electrodes with a more homogeneous C e distribution across the thickness, and the mitigated ϕ e gradient extends the SPD-limited region in both electrodes. Additionally, the particle surfaces exposed by beam ablation reach lithiation saturation earlier and exhibit lower interfacial reaction currents, while the reaction rates in the other areas remain high (third column of Figs. 4 c-d). Uneven reaction flux causes uneven stress, leading to mechanical fracture of particles, especially larger ones, during long-term lithium insertion and extraction cycles [ 37 ]. Figure 4 e further quantifies the material distribution across the electrode thickness before and after patterning. Observing the trend of the scatter symbols, the patterned electrode alleviates the C e gradient across the electrode, resulting in 24.1% and 19.3% increases in C e on the current collector side for Laser_LP and Laser_SP, respectively. Nevertheless, due to the SPD limitation, the SOL distribution in Laser_LP does not significantly improve (top of Fig. 4 e, compared with Fig. 2 d), while the SOL distribution in Laser_SP becomes more uniform (bottom of Fig. 4 e, compared with Fig. 2 h). This phenomenon is more pronounced at 5C discharge rates where the Ce concentration gradient is more pronounced (Figs. S7c-d). The shaded areas in Fig. 4 e indicate lithium concentration variations within the electrode plane. LP shows nearly identical SOL distribution and in-plane variation at the electrode level before and after patterning, suggesting that tortuosity engineering to mitigate EPD limitations provides minimal improvement for LP performance. In contrast, because Laser_SP is primarily constrained by EPD, its SOL distribution is more uniform across the thickness (bottom of Fig. 4 e). Additionally, the SOL near the separator in Laser_SP is lower than in SP, extending the same in-plane SOL polarization level to a depth of 50 µm (shaded region), allowing the reaction front to penetrate deeper. The influence of electrode structure on heating is further investigated, as shown in Fig. 4 f. Compared to the pristine electrode, the patterned electrode significantly reduces the ohmic heating rate, with a greater improvement observed in SP. In contrast, the activation heat remains similar across electrodes, suggesting that the fractured particle surfaces and altered reaction pathways do not notably affect the rate of interfacial heating. Figures 4 g-j provide a visual representation of the heterogeneous distribution of heat generation rates across the electrodes. In the pristine electrode, liquid-phase ohmic heat (q e ) is primarily concentrated near the separator, where significant C e and ϕ e gradients exist. The greater pore tortuosity in SP results in intensified ohmic heat near the separator, while the smaller surface area and interface potential polarization contribute to a higher level of activation heat (q r ) on the LP electrode (Figs. 4 g-h). Heating behaviors in the patterned electrodes display distinct characteristics. The introduced channels alter the direction of ion diffusion, but the channel cross-sectional area gradually decreases, causing the ohmic heat in the patterned electrode to focus near the bottom of the channels (Supplementary Note 3). In contrast, activation heat levels in the structured electrode are similar to those in the pristine electrode, and the heating rate on fractured particles is significantly lower than on particle surfaces within the electrode interior. This indicates that structural modifications not only create asymmetric electrochemical-mechanical stress on the fractured particles (Figs. 4 c-d), but also lead to uneven thermal expansion due to the heterogeneous distribution of activation heat. The ohmic heat concentration zones shown in Figs. 4 i-j will accelerate this process, potentially causing particle fracture within the electrode during cycling. Thus, this highlights the need to consider tortuosity-based electrode strategies, similar to the patterning approach, to mitigate cycle life degradation caused by heterogeneous heating. Figure S8 summarizes the voltage curves of the (un)patterned LP/SP electrodes at different discharging rates. Due to the smaller applied current, the unmodified electrodes exhibit the same specific capacity at 0.2C (Figs. S8a-b). At 1C, Laser_LP shows a slight improvement in accessible capacity and average potential, while Laser_SP shows only an enhancement in the voltage plateau. As the discharge rate further increases to 3C, the capacity and power performance of the patterned electrodes improve significantly, with Laser_SP showing more pronounced performance gains due to the introduced channels. Additionally, laser patterning is essentially a subtractive manufacturing strategy, and the material waste during production should be considered when comparing its actual effectiveness. Therefore, the areal capacity vs. rate curves of the electrodes are plotted, as shown in Figs. S8c-d. When the discharge rates are below 3C, the disadvantage of wasted capacity in the modified electrodes is evident, although the patterned electrodes provide significant power enhancement at 3C. Fortunately, this drawback is well compensated for at higher rates, especially for Laser_SP, which achieves an 18.5% capacity gain and a 20.4% power gain at 5C. For LP, superior energy and power improvements are delayed until a discharge rate of 10C. At such high working currents, the fractured particles exposed to high reaction flux will exacerbate the dissolution of transition metals, leading to premature electrode failure [ 38 ]. The imbalance between SPD and EPD in the electrode also feeds back into the kinetic evolution of reaction processes, manifesting as a regular distribution of charge transfer current density (J ct ) during discharge. This can be reflected by the voxel distribution of local J ct and SOL at different discharge moments, as shown in Fig. 5 . The top region of the electrode (TOP) is defined as the area from 70 µm to 80 µm from the separator side, while the bottom region of the electrode (BOT) refers to the area within 0 to 10 µm near the current collector. A distance of 70 µm is sufficient to characterize the temporal lag of the reaction front propagation on the electrode. For the small particles of SP and Laser_SP, the electrode reaction is mainly controlled by EPD at the initial stage, thus, TOP acquires a larger reaction current and preferential lithiation. At the same time, the reaction participation in BOT is lower (Figs. 5 a-d, stage ①). From stage ① to ②, the reaction barrier at TOP continues to increase due to slow SPD [ 39 ], while the J ct gradually decreases and shifts to BOT. This migration of reaction current helps reduce concentration polarization within TOP particles. Subsequently, SPD and EPD reach a quasi-equilibrium state, with minimal changes in electrode reactions over time (from stage ② to ③). During this process, the concentration polarization of Li in the electrode continuously increases (the SOL voxel distribution broadens) until a lithiation saturation peak distribution (PD S ) appears at the TOP (Figs. 5 a and 5 c). The PD S peak indicates SPD-induced limitations, triggering the particle surface to close reaction sites and causing J ct to further decrease. Similarly, the reaction front shifts again to the BOT region until the end of discharge (Figs. 5 b and 5 d, stages ③ and ④). Fig. S9a visualizes the J ct at various stages of Laser_SP, clearly reflecting the propagation of the reaction front along the electrode thickness. Additionally, compared to SP, the J ct distribution in the local regions of Laser_SP is more concentrated, and the difference in J ct between TOP and BOT is smaller, indicating that the alleviation of Li + diffusion resistance makes the electrode reaction more uniform at the same time, facilitating more efficient material utilization. The reaction process in large-particle electrodes, however, displays distinct characteristics, as shown in Figs. 5 e-h. In both LP and Laser_LP, the phase of uniform J ct distribution observed in small-particle electrodes is absent. This difference arises from the dominant SPD limitation, which is also reflected in the broader SOL voxel distribution in large-particle electrodes (Figs. 5 e and 5 g). Beginning with stage ①, the SPD constraint continually drives reaction energy barriers across the particle surface, resulting in a sustained decrease in J ct in the TOP region. Although the reaction current propagation also exhibits lag, contrary to that in small-particle electrodes, the BOT region in large-particle electrodes reaches saturation by stage ③, reducing J ct at the particle surface and pushing the reaction front deeper into the electrode (Fig. S9b). Notably, compared to LP, Laser_LP maintains a higher J ct peak in the TOP region during stage ④, due to the cracked particle surface. The cracked surface accelerates the reaction rate, and the reduced ion diffusion distance alleviates the lag in the reaction current propagation, manifesting as broader PDS saturation peaks in the TOP and BOT regions (Figs. 5 g and 5 h), which mitigate concentration gradients within the large particles. Compared to the small-particle electrodes, both the J ct and SOL in large-particle electrodes exhibit broader voxel distributions, indicating stronger interfacial activation and concentration polarization due to the larger particle size. Fortunately, as the driving force behind the lithiation reaction, the spatial shuttling effect of J ct maximizes the utilization of electrode materials. Furthermore, the propagation of the reaction front within electrodes with different PSD distributions offers new insights into the design of electrodes for specific applications. 2.3 Particle Gradation Engineering The effectiveness of laser patterning, which varies with electrode PSD, is analyzed previously. Here, this knowledge is applied to design advanced electrode structures for maximizing performance. First, it is necessary to clarify the exact correlation between the PSD and electrode performance. Accordingly, pristine electrodes with bimodal particle size distributions of 25%, 50%, and 75% large particle fractions are generated (referred to as PXX% henceforth). The particles in the electrodes are assumed to be spherical, with sizes corresponding to the maximum SP and LP particle sizes (7 µm and 12.5 µm, Figs.S3b and S3d), which are typical in commercial electrodes. To ensure random particle distribution, a random packing model is developed using MATLAB, generating particle models with structural parameters identical to those reconstructed from XCT. Due to the various geometrical topologies of small and large particles, parameters such as tortuosity, conductivity, and specific surface area are calculated based on the distribution weights of different particle sizes. The SOL and C e distributions in the pristine electrodes at 3C and 50% DOD are shown in Figs. S10a-c. As the fraction of large particles increases from P25% to P75%, the SOL and the C e gradient on the electrode gradually decreases, and SPD limitations become more dominant. Quantitative SOL results across the plane are shown in Figs. 6 b-d, with the shaded area representing the in-plane Li concentration difference (SOL standard deviation). In regions of Li + accumulation near the separator, both SOL and concentration polarization are high. As the fraction of small particles decreases, the average SOL level in the deeper regions of the electrode increases, while the corresponding shaded area also grows, indicating that increasing large particles improves material utilization in the deeper regions but reduces overall material utilization efficiency. The simulation using the P2D model for P0% are shown in Fig. S11, voltage curve of the P2D model is slightly lower than that of the 3D particle model, with a more uniform SOL gradient across the thickness. This is because the P2D homogenization theory neglects the effects of 3D particle edges on Li + transport and weakens the face contact effects between particles and between particles and inactive components. To improve the utilization of electrode materials, it is proposed a tortuosity-graded particle electrode (TG) that combines laser perforation and particle size layering strategies. In TG, particles are arranged in a gradient, with smaller particles placed above larger ones, which is reported to be achieved through layer-by-layer coating before calendering [ 40 ]. In this study, the structure of the TG is simulated using a random filling program. According to theoretical derivations (details in Supplementary Note 2), the volume ratio, weight ratio, and thickness ratio of electrode layers with different particle sizes are the same. Therefore, different TGXX% samples (TGXX% denotes TG with a specific proportion of large particles) are obtained by applying constraints on thickness and volume ratios to achieve varying proportions of large particles. Additionally, to ensure a fair comparison of performance, the thickness of the TG is increased to maintain the same areal loading as that of the pristine electrode. Comparing Figs. 6 e-g, as the fraction of large particles increases, a trend of expanding lithiation saturation areas is noted, however, the C e and SOL gradients in TG are significantly smaller. The SOL across the plane (Figs. 6 b-d, red) shows the average SOL level in the small particle layer of TG is higher than that in the pristine electrode, with a larger lithiation saturation shaded area. To quantify the structural advantages of TG in transport kinetics, an assessment criterion for the SPD limitation depth is introduced. This requires a reference model in which the influence of Li + diffusion on electrode reactions is eliminated. Specifically, the tortuosity factor is the Bruggeman constant (~ -0.5), and the electrolyte cation transference number is maximized (~ 1) [ 41 ]. The in-plane SOL standard deviation comparison provides the electrode regions solely limited by SPD, with the calculation method illustrated in Fig. 6 a. Results of the SPD limitation depth are shown as arrows in Figs. 6 b-g, where blue color corresponds to the pristine electrode and red color corresponds to the TG electrode. For the pristine electrode, the SPD limitation depth increases with the fraction of large particles. However, P75% still exhibits EPD-limitation regions (Figs. 6 d and 6 g). In contrast, TG75% is entirely controlled by SPD (red arrows). The final discharge capacity differences are minimal, because both the pristine electrode and TG are predominantly limited by SPD at 3C. The significant difference is that fast ion channels in TG markedly enhance power performance, as indicated by the gray curves in Figs. 6 h-j. The improvement in the voltage-power plateau of the TG electrode arises from the alleviation of the Li + concentration gradient, as illustrated in Figs. S10d-e. This results in the Li + transport characteristics being maintained within the optimal concentration range (1.2 M), thereby mitigating the rise in the liquid-phase overpotential. Moreover, the alleviation of the ion concentration gradient significantly reduces the ohmic heating rate in the TG electrode, while the self-assembled structure of the particles enhances the heating rate of the activation energy (Figs. 6 h-j). The SPD-limited region for 80 µm electrodes is summarized in Fig. 7 a, where solid symbols represent results at the end of discharge (prematurely stopped). The SPD-limited region fraction in TG is consistently larger than in pristine electrodes, with the gap widening towards both ends of the PSD spectrum, which is centered at 50% LP (large particle fraction). This trend is also observed in 120 µm electrodes (Fig. 7 b), indicating that the mixed particle fraction of 25% or less is preferred. Additionally, at the same areal loading, TG electrodes with specific LP may suffer from the detrimental effects of increased thickness (Fig. 7 b). To understand the structural advantages of TG in promoting favorable reaction kinetics, the diffusion competition within the electrodes is characterized using the differential SOL at the particle level, comparing P50% and TG50%. Figures 7 c-d show the spatiotemporal evolution of ΔSOL in pristine electrodes at incremental DOD. In the early stages of discharge, most Li + current (J l ) is generated near the separator, creating a significant C e gradient (Figs. S10d-e), leading to a continuous rise in particle ΔSOL at this location (Fig. 7 c). At 0.15 DOD, SPD limitation begins to take effect, resulting in stratification of particle ΔSOL. This persists until 0.4 DOD, when particles near the separator reach a lithium saturation state first, and SPD limitation begins to dominate. Subsequently, ΔSOL near the separator decreases while ΔSOL in deeper particles increases, indicating the transfer of the reaction front. In the early stages of TG discharge, similar to pristine electrodes, the reaction front is concentrated near the separator, with small particle ΔSOL continuously rising (Fig. 7 d). However, starting at 0.5 DOD, small particles, rather than large ones, reach lithium saturation first and rapidly extend to the remaining small particle locations. The fast SPD and interfacial reaction kinetics significantly increase the volume fraction of the concentrated Li layer, raising the output voltage of TG electrodes by 3.4% compared to pristine electrodes at the same moment. Figures 7 e-f compare the rate performance of the two electrodes with different LP fractions. Even at very low current densities, significant capacity differences between electrodes with different LP fractions are observed. The effect of PSDs on the capacity of pristine electrodes is most pronounced at 14.2 mA·cm − 2 , where P100% exhibits a rated capacity of 61.7 mAh·g − 1 higher than P0% (Fig. 7 e). When the fraction of LP less than 25%, the ability of PSD to enhance high-rate performance is limited, even resulting in negative gains under extremely high discharge conditions, consistent with the analysis in Figs. 7 a-b. Additionally, the increase in specific surface area leads to faster side reaction rates, necessitating a trade-off in design to mitigate adverse effects on cycle performance. For TG electrodes, the maximum capacity difference related to PSD is larger ~ 73.1 mAh·g − 1 (Fig. 7 f). Compared to pristine electrodes (black symbols representing P0%), TG performance improvements are primarily observed at higher current densities. The capacity of TG0% (blue symbols) maintains a 13.7 mAh·g − 1 capacity advantage at 28.4 mA·cm − 2 . Wood et al. [ 42 ] also conducted combined experiments on electrodes with different PSDs and found a similar magnitude of capacity advantage for layered cathodes. Furthermore, the loss of active surface area caused by TG requires consideration, especially under SPD-limited conditions such as large-particle electrodes and low current densities. This is reflected in the average capacity loss of 1.9 mAh·g − 1 for TG100% compared to P100% across various rates (Fig. 7 f, gray symbols). Figures 7 g and 7 h compare the areal capacity of electrodes with varying LP fractions as thickness increases, providing insights into the performance trade-offs associated with thickness scaling in electrodes tailored for specific applications. For thicker pristine electrodes, configurations with different particle size ratios show a markedly enhanced capacity at low rates. However, at higher rates, the EPD limitations of thick electrodes become more pronounced, resulting in a rapid decline in area-specific capacity. The extent and rate of performance decay in thicker electrodes depend on the particle fraction configuration, which is differentiated by critical rate and critical capacity. When electrode thickness increases from 80 µm to 200 µm, the 25%LP configuration shows performance degradation when the C-rate exceeds 2.7, with an area capacity of 2.2 mAh·cm − 2 . In contrast, for the 75%LP electrode, the C-rate and capacity decrease to 2.5C and 1.7 mAh·cm − 2 , respectively. The structural advantages of the TG greatly increase the tolerability of the performance loss suffered by the thickness expansion (Fig. 7 h). For a 200 µm TG, the critical rate and capacity of the 25%LP configuration are 4.9C and 1.7 mAh·cm − 2 , and for the 75%LP configuration, they are 4.3C and 1.2 mAh·cm − 2 . On average, the TG increases the critical rate by about 43% and reduces critical capacity by roughly 26% compared to pristine electrodes. This suggests that thicker TG exhibit rate performance more comparable to that of thinner electrodes. 2.4 Electrode performance in non-isothermal heat transfer environments Due to the strong temperature dependence, heat transfer environments potentially affect the reactions and transport processes operating at the electrode base, leading to performance variations. Specifically, compared to non-isothermal environments, the heat generated by electrode impedance is entirely absorbed by the isothermal environment. This slows electrode reaction kinetics and transport kinetics, leading to a continued increase in overpotential resistance (Fig. 8 a). Therefore, to account for practical thermal benefits, a bidirectional coupling between the electrochemical field and the temperature field is established through temperature coefficients and the Arrhenius equation within electrochemical parameters (Fig. 8 h). This allows for estimating the overall electrode temperature rise using a lumped thermal model due to the small geometric Biot number [ 43 ]. A challenge in model validation is accurately detecting weak heat generation from single-layer cathodes in experiments, necessitating methods to examine electrode heat generation rates for comparing model predictions, as shown in Fig. S12. At 25°C and 1C, electrode heat generation rates range from 60 to 100 µW·mm − 3 , consistent with the magnitude reported by Yan et al. [ 44 ]. It should be noted that the study does not consider the effect of CBD on electrode interface reactions, which is reported as a significant factor influencing activation energy and total heat generation [ 45 ]. Additionally, structural and thermodynamic parameters of electrode materials, such as particle size, open-circuit potential, and entropy coefficient, also influence heat generation rate curves. The established electrochemical-thermal model is initially used to investigate the discharge voltage curves of the electrodes at different temperatures, as shown in Figs. 8 b and 8 i. When the temperature decreases from 25°C to -10°C, the TG electrode exhibits a lower capacity loss in an isothermal environment compared to the pristine electrode (54.9 mAh·g − 1 vs. 77.3 mAh·g − 1 ). However, under non-isothermal conditions, the TG electrode the TG electrode shows a higher capacity loss than the pristine electrode (30.4 mAh·g − 1 vs. 29.8 mAh·g − 1 ), and consistently demonstrates lower capacity across all temperatures (Fig. 8 i). Figures 8 c and 8 j analyze the differences described above from the perspective of electrode heat generation rates. In an isothermal environment, electrode heating is not influenced by self-heating, instead, the heat generation rate of the electrode solely originates from internal resistance (activation heat + ohmic heat). Compared to the TG electrode, the pristine electrode exhibits higher heat generation rates at all temperatures due to its larger ionic transport resistance and interfacial overpotential. However, energy losses are mainly due to voltage drop, causing the pristine electrode to reach the cutoff condition earlier (Fig. 8 c). When self-heating effects are considered, the performance of both TG and the pristine electrode significantly improves (Figs. 8 i-j), with the surprising result that the pristine electrode outperforms the TG electrode. This reflects the interaction between internal resistance and thermal gain. Figures 8 d and 8 k provide a macroscopic analysis of how heat exchange conditions impact the comparative performance of the two electrodes. In the isothermal environment, the SOL of the electrode is concentrated in the range 0–0.2 (Fig. 8 d). Compared to the pristine electrode, the SOL distribution of the TG during discharge is wider because more small particles are utilized, with higher intensities around 0.4 and 0.8 in the later stages of discharge (black markers and 3D visualization in Fig. 8 f). Additionally, the SOL distribution of the TG is observed to diverge at 0.2 DOD, which is due to the reaction front shifting to the large particle layer (Fig. 8 f). In the non-isothermal environment, the two electrodes exhibit similar and wider SOL distributions. The lag in the lithiation reaction of the large particles causes the SOL distribution of the TG to start bifurcating at 0.3 DOD (Fig. 8 k). In fact, the SPD influenced by the temperature rise makes the capacity more dependent on large particles, and the contact effect of small particles in the pristine electrode further improves the utilization of large particles (Fig. 8 m), resulting in the predominant capacity advantage of the pristine electrode. The preceding analysis confirms that electrolyte resistance is the dominant factor in electrode voltage loss (Figs. 6 h-j). Therefore, the changes in liquid-phase ohmic heat across the electrode thickness are analyzed on a global scale (Figs. 8 e and 8 l). In an isothermal environment, the high ionic diffusion resistance in the pristine electrode causes localized heating near the separator (Fig. 8 e and 3 D visualization in Fig. 8 f). In contrast, the TG electrode benefits from structural advantages, which result in a more uniform distribution of liquid-phase ohmic heat. In a non-isothermal environment, the increase in temperature significantly enhances the diffusion rate and conductivity of the liquid phase in both electrodes, contributing to more uniform heat during operation. Notably, the lower electrolyte resistance of the TG electrode generates a limited impact on enhancing the electrochemical performance. Finally, the output performance of the electrode voltage and capacity is evaluated using Ragone plots, as shown in Figs. 8 g and 8 n. Since power is positively correlated with discharge current, the energy density of the electrodes decreases with increasing power in both environments. It is noteworthy that a significant drop in energy density (red markers) is present at high power. It represents the maximum power the electrode can release before a rapid decline in specific energy. In the isothermal environment, this inflection point is located near 1C, and as the temperature decreases, the decline in specific energy becomes more pronounced (Fig. 8 g). The structural disadvantage of the pristine electrode is evident at 0°C, where it declines more at 1C compared to TG, whereas at 25°C, the critical discharge rate increases to 5C. In the non-isothermal scenario, an ‘energy cliff’ is observed only in the pristine electrode below 0°C (Fig. 8 n), and this inflection point increases from 1C in the isothermal environment to 12C. Additionally, almost no difference in output performance is observed between the two electrodes at room temperature, and the critical rate at low temperatures also increases to 12C. The Ragone plots in the non-isothermal environment characterize the significant performance differences of the electrodes under various heat transfer conditions, providing more realistic predictions for electrode structure design and battery management systems (BMS). 3 Conclusion This study combines nano-XCT and digital twin technologies to obtain different electrode structures, which are used to investigate the effects of electrode structure adjustment strategies through experimentally validated electrochemical models. The objective is to improve the trade-off between electrode energy and power at high current density. The quantitative relationship between the electrode's physical properties and structure preliminarily reveals the competition in internal mass transport. Increasing the CBD content enhances the electronic conductivity, but inevitably increases the ionic transport resistance. Predictions from the electrochemical model suggest that reducing particle size is an effective method for improving rate capacity. Increasing electrode thickness leads to limited electrolyte-phase diffusion, thereby reducing electrode capacity and increasing heat generation rate. Fortunately, this can be addressed by patterned channels. The use of small-particle electrodes improved material utilization near the current collector by 11.82% at 3C, and effectively reduced the ohmic heating rate under high-rate conditions. However, the slight performance improvement indicates that large-particle electrodes are less sensitive to bypass strategies, and patterned electrodes exhibit a disadvantage in terms of area-specific capacity loss under low operating rates. In electrodes with large particles, the insufficient development of liquid-phase potential gradients leads to the absence of an equilibrium stage in the reaction, resulting in a unidirectional reaction wave during discharge. Based on this insight, an electrode that synergistically combines tortuosity engineering and graded particle strategy (TG) has been proposed. The structure with favorable kinetics enables the TG to exhibit superior rate capability across different PSDs, allowing it to better accommodate the material structure and range of rates compared to pristine electrodes. It also demonstrates advantages over pristine electrodes in terms of areal capacity and overpotential loss, thus adapting to the material structure and rate range. The non-isothermal electrochemical-thermal model provides insights into the operating mechanisms of electrodes at the full battery scale. The self-heating effect enables the pristine electrode to utilize impedance dependent on EPD limitation, allowing its capacity performance at various temperatures to surpass that of the TG. The alleviated EPD limitation allows the TG to exhibit superior electrochemical performance at extreme rates in different heat transfer environments, with discharge rates corresponding to the ‘energy cliff’ being significantly higher than those of the pristine electrode. In summary, this study provides an in-depth analysis of the kinetic differences within the electrode, exploring strategies to optimize rate capability under different heat-exchange environments. These insights support the design of rapid discharge protocols and the development of more advanced electrode structures. 4 Experimental and modelling methods 4.1 X-ray computed tomography and 3D image analysis The commercial ternary electrode sheet comprises a Li[Ni 0.6 Mn 0.2 Co 0.2 ]O 2 cathode coating and an aluminum foil current collector, with an areal density of 21.6 mg·cm − 2 , and the cathode coating contains 96.5% active material. The electrode sheet is cut into approximately 0.5 mm pieces and fixed on the sample stage using epoxy resin. The Zeiss Xradia Ultra 800, with a spatial resolution of 126 nm, is chosen, and the target voltage is set to 40 kV with a target current of 30 mA. A total of 901 tomographic images are collected from 0° to 180° and with an exposure time of 18 s. The corrected aligned ray images are reconstructed using the filtered back projection algorithm [ 46 ], yielding an electrode pillar region of 64 × 64 µm. The scanned images are imported into Avizo for cropping, rotation, and position calibration; finally, a representative region of 40 µm 3 is extracted. This is followed by a region segmentation process. The reconstructed 3D structure is further characterized, and information is extracted at the particle and pore levels. TauFactor is then used to calculate the 2D projection flux simulation [ 47 ]. 4.2 Digital twin electrodes The scanned 2D grayscale images show clear details of particle edges (Fig. S1 a). However, the low X-ray absorption of CBD blurs the boundaries, making it difficult to distinguish them from pores. Therefore, this study segments only the particle phase, which is a common practice in nano-XCT imaging studies of LIB cathodes. For the particle phase, grayscale value variations spanning from particle to mixed phase (Fig. S1 b) are detected, with distinguishable grayscale value boundaries in the particle regions. The watershed algorithm and full width at half maxima method (FWHM) yield particles of similar average size and consistent particle boundary contours (Figs. S1c-d). This demonstrates the effectiveness of the segmentation based on the FWHM method. To obtain small-particle electrodes with the same volume fraction and different particle size distributions, previously scanned Li[Ni 0.5 Mn 0.2 Co 0.3 ]O 2 electrodes at the same resolution were used. As demonstrated in Fig. S2a, a dataset sampled from the CT particle is used. Based on the CT-reconstructed electrode structure, particles are randomly inserted into the electrode. It should be noted that Boolean operations are applied to the inserted particles to acquire non-overlapping particles. The iteration of the above steps continues until the particle volume fraction reaches the preset value of 54.17%. Due to the height range limitations of the nano-CT field of view (typically 65 µm), the acquisition of thick electrodes is achieved by vertical stitching, constrained by budget and time. Here, a more common numerical method is employed, i.e., doubling the electrode thickness by mirroring the filled electrode. This method, which treats the physical parameters and particle sizes of the electrode as in situ extensions, is widely used in electrode thickness studies [ 29 ]. Subsequently, CBD is virtually added to the two-phase electrode with the identical porosity. Due to the stirring and drying conditions, the evaporation rate of the slurry solvent causes local variations in CBD morphology, leading to tortuous Li + transport paths [ 48 ]. In this study, the MATBOX software developed by Mukherjee et al. [ 22 , 49 ] is used to add CBD to the electrode. The mode based on interface energy and the maximum shape factor forms bridges between particles to reduce electronic conduction limitations, as shown in the generated electrode structure in Fig. S2b. An adaptive mesh is applied to the three-phase electrode in Simpleware, followed by direct numerical simulation to calculate the conductivity and tortuosity parameters (Fig. 1 ). 4.3 Electrochemical and thermal coupling models based on 3D microstructure This study extends the Newman model [ 16 ] to the particle level to describe electrochemical reactions and mass transport. Solid-phase lithium transport within particles is described using Fick's law, while Li + movement in the electrolyte is driven by potential or concentration gradients (concentrated solution theory). The Butler-Volmer equation describes the charge transfer reactions at the particle/electrolyte interface, and the potential changes in the solid and liquid phases conform to Ohm's law. These governing equations are executed in COMSOL Multiphysics using multiple partial differential equations (PDEs). It is worth noting that the pores in the model include nanopores within the CBD, thus treated as a homogeneous mixture of CBD and pores using a lumped model. The coupling of the temperature field is deconstructed at the particle level based on the electrochemical-thermal coupling model developed by Gu and Wang [ 50 ]. Reversible and activation heat act as surface heat sources at the particle/electrolyte contact interface, while Ohmic heat is allocated to the heterogeneous phase. The evolution and feedback of electrode temperature are considered using a lumped thermal model. Detailed governing equations, boundary conditions, and parameters can be found in the Supplementary Information. Declarations Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 52106226, 52176058). 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J Electrochem Soc 147:2910 Additional Declarations There is NO Competing Interest. Supplementary Files supplementaryinformation.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6035965","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":422063739,"identity":"1bf23cc9-1fb2-4573-86eb-b9f86f7fae82","order_by":0,"name":"Yubai Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3UlEQVRIie3PQQsBQRTA8bepWYdhrk+KrzClpPgws5d1UlsuDqJNPQdx5lvwDZYtJ+6Kw7pwdlEusuTiYuaozL93mXq/egNgs/1g+QxAOlhibhgmqtPQE/YmFcHjgUw2vgGBFwFvNm1S4UgrA+LyajHo1px55FFHsQjEcKQ0h6VkusaMjJa0U/wAuNnO9YQzZHIZpgRPILFlQu7IZexQoGRsSHKEWCCHQCkjwtr12QSl4M4AVeRz7V+EiBf74NrrU/l8vNzujZIYjr8TgKz8eHLN+jM3MViy2Wy2v+4B2lxBl3PGXfEAAAAASUVORK5CYII=","orcid":"","institution":"Dalian University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Yubai","middleName":"","lastName":"Li","suffix":""},{"id":422063740,"identity":"f86f4a6c-658b-4858-8797-debed14dc407","order_by":1,"name":"Heng Huang","email":"","orcid":"","institution":"Dalian University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Heng","middleName":"","lastName":"Huang","suffix":""},{"id":422063741,"identity":"1a3dcfca-2701-4520-a5e3-4a07e5d5884a","order_by":2,"name":"Zhifu Zhou","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Zhifu","middleName":"","lastName":"Zhou","suffix":""},{"id":422063742,"identity":"4345fd4c-edbf-4491-9425-f9023afae318","order_by":3,"name":"WeiTao Wu","email":"","orcid":"","institution":"Nanjing University of Science and Technology, School of Mechanical Engineering","correspondingAuthor":false,"prefix":"","firstName":"WeiTao","middleName":"","lastName":"Wu","suffix":""},{"id":422063743,"identity":"0d8db732-69f0-4e34-bfd0-dfaf1ee0590e","order_by":4,"name":"Lei Wei","email":"","orcid":"","institution":"Southern University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"Wei","suffix":""},{"id":422063744,"identity":"56055cc4-aea8-4a5e-b2dc-259197fbdb63","order_by":5,"name":"Hu Chengzhi","email":"","orcid":"","institution":"Dalian University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Hu","middleName":"","lastName":"Chengzhi","suffix":""},{"id":422063745,"identity":"dec70986-a126-4c10-9483-52eb17ecb4f8","order_by":6,"name":"Jiaxuan Ma","email":"","orcid":"","institution":"Dalian University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Jiaxuan","middleName":"","lastName":"Ma","suffix":""},{"id":422063746,"identity":"4bbbe0e3-933a-4a23-9b4a-9bcfbc562d05","order_by":7,"name":"Linsong Gao","email":"","orcid":"","institution":"Xiangtan Universit","correspondingAuthor":false,"prefix":"","firstName":"Linsong","middleName":"","lastName":"Gao","suffix":""},{"id":422063747,"identity":"39c1e120-188b-42fb-a604-51b7df0fdf9f","order_by":8,"name":"Yang Li","email":"","orcid":"","institution":"Dalian University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Li","suffix":""},{"id":422063748,"identity":"2fb9bb9e-e419-4470-96a7-697e28917d83","order_by":9,"name":"Yongchen Song","email":"","orcid":"https://orcid.org/0000-0002-9864-8483","institution":"Dalian University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yongchen","middleName":"","lastName":"Song","suffix":""}],"badges":[],"createdAt":"2025-02-15 10:35:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6035965/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6035965/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":77604873,"identity":"a53ff858-96a8-4caf-a3f4-821ddb84b56c","added_by":"auto","created_at":"2025-03-03 13:33:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":430249,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSensitivity of electrode physical parameters to structure. (a) \u003c/strong\u003eXCT cross-sectional images of large particle electrodes and\u003cstrong\u003e(b)\u003c/strong\u003e small particle electrodes. The scale bar represents 5 mm.\u003cstrong\u003e \u003c/strong\u003eParticle size distribution statistics for\u003cstrong\u003e (c) \u003c/strong\u003elarge particle electrodes and\u003cstrong\u003e (d) \u003c/strong\u003esmall particle electrodes.\u003cstrong\u003e (e-f) \u003c/strong\u003eImpact of electrode structure on physical parameters:\u003cstrong\u003e(e) \u003c/strong\u003epore tortuosity,\u003cstrong\u003e (f) \u003c/strong\u003eeffective electrical conductivity of the electrode.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/af8bc0810cbcd101dc48cbd5.png"},{"id":77604876,"identity":"1e8153c9-9277-4cde-91eb-2948efac23e9","added_by":"auto","created_at":"2025-03-03 13:33:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1225149,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpatial distribution of SOL and C\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ee\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e under different electrode configurations at 3C. (a)\u003c/strong\u003e 30 mm-LP-LC, \u003cstrong\u003e(b)\u003c/strong\u003e 30 mm-LP-HC, \u003cstrong\u003e(c)\u003c/strong\u003e 80 mm-LP-LC, \u003cstrong\u003e(d) \u003c/strong\u003e80 mm-LP-HC, \u003cstrong\u003e(e)\u003c/strong\u003e 30 mm-SP-LC, \u003cstrong\u003e(f)\u003c/strong\u003e 30 mm-SP-HC, \u003cstrong\u003e(g)\u003c/strong\u003e 80 mm-SP-LC, \u003cstrong\u003e(h)\u003c/strong\u003e 80 mm-SP-HC. The results are derived from a 50% Depth of Discharge (DOD), and the insets display CT slice images with particle regions color-coded.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/440b3a1c589bfeaf89c0920d.png"},{"id":77604888,"identity":"779cd7d3-0a11-47c3-8903-1e494c2d8e91","added_by":"auto","created_at":"2025-03-03 13:33:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":650734,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eElectrochemical-thermal performance related to electrode structure.\u003c/strong\u003e \u003cstrong\u003e(a)\u003c/strong\u003e Relationship between electrode capacity and discharge rate, with symbols representing experimental results for electrodes with similar structures. \u003cstrong\u003e(b)\u003c/strong\u003e Specific capacity and \u003cstrong\u003e(c)\u003c/strong\u003e average potential for different electrode structures. Thermal generation rates for different electrode structures at \u003cstrong\u003e(d)\u003c/strong\u003e 30 mm and \u003cstrong\u003e(e)\u003c/strong\u003e80 mm. \u003cstrong\u003e(f)\u003c/strong\u003eQuantitative variation and \u003cstrong\u003e(g)\u003c/strong\u003eheterogeneity distribution in the activation heat generation rate of LC electrodes as a function of electrode thickness. \u003cstrong\u003e(h)\u003c/strong\u003e Quantitative variation and \u003cstrong\u003e(i)\u003c/strong\u003eheterogeneity distribution in the ohmic heat generation rate of HC electrodes as a function of electrode thickness.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/625fb7c432b9d54e13adc6c0.png"},{"id":77606546,"identity":"ed146655-5a42-454f-aad1-73c21312f3b0","added_by":"auto","created_at":"2025-03-03 13:41:36","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":3769276,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDischarge performance of laser-patterned electrodes. \u003c/strong\u003eSchematic of laser-patterned \u003cstrong\u003e(a)\u003c/strong\u003e LP and \u003cstrong\u003e(b)\u003c/strong\u003e SP. Distribution of mass and reaction flux in \u003cstrong\u003e(c) \u003c/strong\u003eLaser_LP and \u003cstrong\u003e(d)\u003c/strong\u003e Laser_SP at 3C and 50% DOD. \u003cstrong\u003e(e) \u003c/strong\u003eEvolution of mass along the thickness in electrodes at 3C and 50% DOD. \u003cstrong\u003e(f) \u003c/strong\u003eEvolution of heat generation rate of electrodes at 5C. Heat generation distribution in \u003cstrong\u003e(g) \u003c/strong\u003eLP, \u003cstrong\u003e(h)\u003c/strong\u003e SP, \u003cstrong\u003e(i)\u003c/strong\u003e Laser_LP and \u003cstrong\u003e(j)\u003c/strong\u003e Laser_SP at 5C and 40% DOD.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/10a2ea4efcad09fc3b3bceb0.png"},{"id":77604877,"identity":"dcb652c1-adcc-480c-be71-04e655a7e61f","added_by":"auto","created_at":"2025-03-03 13:33:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":498146,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDynamic evolution of reaction fronts at the electrode level. \u003c/strong\u003eAt 3C, the voxel distribution histograms of SOL and J\u003csub\u003ect\u003c/sub\u003e for the pristine SP electrode at the \u003cstrong\u003e(a)\u003c/strong\u003e TOP and \u003cstrong\u003e(b) \u003c/strong\u003eBOT. For the Laser_SP electrode, the voxel distribution histograms of SOL and J\u003csub\u003ect\u003c/sub\u003e at the \u003cstrong\u003e(c)\u003c/strong\u003e TOP and \u003cstrong\u003e(d)\u003c/strong\u003e BOT. For the pristine LP electrode, the voxel distribution histograms of SOL and J\u003csub\u003ect\u003c/sub\u003e at the \u003cstrong\u003e(e)\u003c/strong\u003e TOP and \u003cstrong\u003e(f)\u003c/strong\u003e BOT. For the Laser_LP electrode, the voxel distribution histograms of SOL and J\u003csub\u003ect\u003c/sub\u003e at the \u003cstrong\u003e(g)\u003c/strong\u003e TOP and \u003cstrong\u003e(h)\u003c/strong\u003e BOT. The voxel distribution of J\u003csub\u003ect\u003c/sub\u003e is represented by the left y-axis, and that of SOL is represented by the right y-axis.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/2de59ca3cd076364e1a93974.png"},{"id":77604874,"identity":"174af6bf-c566-42e3-9df1-4ad78594cd20","added_by":"auto","created_at":"2025-03-03 13:33:36","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":818947,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eElectrode performance with different PSD. (a) \u003c/strong\u003eApproach for calculating SPD limitation depth. At 3C and 50% DOD, in-plane SOL distribution along the thickness of different LP fraction electrodes: \u003cstrong\u003e(b)\u003c/strong\u003e 25%, \u003cstrong\u003e(c)\u003c/strong\u003e 50%, and \u003cstrong\u003e(d)\u003c/strong\u003e 75%. Distribution of SOL and C\u003csub\u003ee\u003c/sub\u003e in different LP fraction electrodes: \u003cstrong\u003e(e)\u003c/strong\u003e 25%,\u003cstrong\u003e (f)\u003c/strong\u003e 50%, and \u003cstrong\u003e(g)\u003c/strong\u003e 75%. Arrows indicate the depth of SPD limitation, with red representing TG and blue representing the pristine electrode. Decomposition of overpotential contributions during the discharge process for different LP fraction electrodes: \u003cstrong\u003e(h)\u003c/strong\u003e 25%, \u003cstrong\u003e(i)\u003c/strong\u003e 50%, and \u003cstrong\u003e(j)\u003c/strong\u003e 75%.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/cbe433ffb0389b46c2b8d6e3.png"},{"id":77604879,"identity":"72e98552-7ece-49ea-b58e-b50fe5dc4508","added_by":"auto","created_at":"2025-03-03 13:33:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1015046,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eElectrode performance with Different Structural Parameters.\u003c/strong\u003e At 3C and 50% DOD, the relationship between the LP fractions and the SPD-limited fraction in the electrodes with \u003cstrong\u003e(a)\u003c/strong\u003e80 mm and \u003cstrong\u003e(b)\u003c/strong\u003e120 mm thickness. Differential SOL at incremental DOD for\u003cstrong\u003e (c)\u003c/strong\u003e P50% and \u003cstrong\u003e(d)\u003c/strong\u003e TG50% particles. The effect of the LP fractions on the capacity of \u003cstrong\u003e(e)\u003c/strong\u003e pristine and \u003cstrong\u003e(f)\u003c/strong\u003e TG with 80 mm thickness. The effect of the LP fractions and discharging rate on the areal capacity of \u003cstrong\u003e(g)\u003c/strong\u003epristine and \u003cstrong\u003e(h)\u003c/strong\u003e TG at different electrode thicknesses.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/f8444bfa3d4faf82b2967b46.png"},{"id":77604881,"identity":"a7c14635-df37-48e5-9e43-c1e2f252cc1e","added_by":"auto","created_at":"2025-03-03 13:33:36","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":1507934,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eInfluence of heat transfer environment on electrode performance. \u003c/strong\u003eSchematic of multi-scale electrochemical thermal model of electrodes under \u003cstrong\u003e(a) \u003c/strong\u003eisothermal and \u003cstrong\u003e(h) \u003c/strong\u003enon-isothermal conditions. Effect of initial temperature on discharge voltage of electrodes (3C) under \u003cstrong\u003e(b) \u003c/strong\u003eisothermal and\u003cstrong\u003e (i) \u003c/strong\u003enon-isothermal conditions. At 0 °C and 3 C, Heat generation rates of electrodes in \u003cstrong\u003e(c)\u003c/strong\u003e isothermal and \u003cstrong\u003e(j)\u003c/strong\u003e non-isothermal environments. Incremental SOL of pristine electrode and TG under \u003cstrong\u003e(d) \u003c/strong\u003eisothermal and\u003cstrong\u003e (k)\u003c/strong\u003e non-isothermal conditions. Evolution of liquid-phase ohmic heat on electrode thickness in \u003cstrong\u003e(e)\u003c/strong\u003eisothermal and \u003cstrong\u003e(l) \u003c/strong\u003enon-isothermal environments. Distribution of SOL and ohmic heat on the electrode in \u003cstrong\u003e(f)\u003c/strong\u003e isothermal and \u003cstrong\u003e(m)\u003c/strong\u003e non-isothermal environments. The results for the isothermal environment are taken from 0.25 DOD, while the results for the non-isothermal are taken from 0.3 DOD. Ragone plots of electrodes at different temperatures under \u003cstrong\u003e(g) \u003c/strong\u003eisothermal and\u003cstrong\u003e (n) \u003c/strong\u003enon-isothermal conditions.\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/fc4f9a221431d99b74955277.png"},{"id":81173156,"identity":"6a620c82-d7bf-463a-81bb-5eebc60ccb31","added_by":"auto","created_at":"2025-04-23 05:43:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10319007,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/fccbc98e-5b78-4a0e-866f-84b3c5d957a8.pdf"},{"id":77604884,"identity":"3f580d20-a7e0-4baf-9f24-d9da919b19d2","added_by":"auto","created_at":"2025-03-03 13:33:36","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":16194890,"visible":true,"origin":"","legend":"","description":"","filename":"supplementaryinformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-6035965/v1/485817cf6b3fb493775d9a5d.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Digital Techniques Assisted in Tailoring Electrode Structure to Optimize Electrode Kinetics","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe fast-discharging capability of the cathode allows lithium-ion batteries (LIBs) to deliver significant power in a short time, which is crucial for the acceleration performance of electric vehicles (EVs) and the peak load regulation capacity of grid energy storage systems [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. However, as the demand for higher energy density increases, increasing electrode thickness or reducing porosity has become a common principle for LIBs [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. This hinders mass transport within the electrode, significantly shortening the operating time at high current densities [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Consequently, commercial electrodes have been designed with varying microstructures and component trade-offs to suit various application types, such as energy-type or power-type applications. This results in a compromise that fails to simultaneously meet the required energy and power densities for high-rate applications. Therefore, to further expand the market share, designing electrode structures that allow LIBs to perform effectively in diverse application scenarios is essential. This requires a microscale-based analysis of the relationship between electrochemical performance and three-dimensional (3D) electrode structure, ensuring the development of rational structure modification strategies.\u003c/p\u003e \u003cp\u003eAt higher current densities, internal mass diffusion becomes the primary factor limiting electrode performance [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The slow electrolyte phase diffusion (EPD) rate causes lithium ions (Li\u003csup\u003e+\u003c/sup\u003e) to accumulate on the separator side and even leads to a concentration depletion near the current collector. The increasing concentration gradient across the thickness results in significant polarization overpotential, causing premature termination of operation. At its core, this issue can be mitigated by improving electrolyte performance, such as through the use of concentrated electrolytes [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] and the development of electrolyte additives [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The underlying principle is that these approaches increase salt diffusion rates and ion activity, thereby reducing concentration gradient across thickness. Additionally, low porosity in high areal loading electrodes creates a more tortuous Li\u003csup\u003e+\u003c/sup\u003e penetration network, leading to power loss and material waste near the current collector. Although tortuosity engineering methods, such as gradient porosity [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] and vertical channels [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], have received positive feedback, most studies focus on single electrode structures. This leaves the universality of tortuosity strategies and their underlying mechanisms largely unexplored.\u003c/p\u003e \u003cp\u003eThe diffusion kinetics that limit performance are also reflected in the solid-phase diffusion (SPD) within the active material (AM). Slow SPD causes the embedded lithium (Li) to accumulate on the surface of AM particles, forming a significantly large concentration gradient along the path. Additionally, a Li-rich active interface gradually inhibits charge transfer reactions, which results in slower lithiation rates [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. This generates not only high concentration overpotential and interface activation overpotential at high rates, but also leads to underutilization of the material within the particles. In addition to material modification strategies like elemental concentration gradients [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] and doping [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], structural adjustments, such as reducing particle size, have been provided to be effective in enhancing the SPD rate. However, electrodes containing excessive amounts of small particles exhibit a larger specific surface area, which accelerate the side reaction rates and the development of local hotspots, compromising cycle durability and posing thermal risks [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. For electrodes with larger particle sizes, aside from the detriments to SPD, the smaller interface areas also limit reaction rates. However, it is undeniable that their higher tap density and mechanical strength make them preferred in energy-oriented LIBs [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Selecting an appropriate particle size combination can mitigate many drawbacks, however, electrodes with different particle size distributions (PSDs) exhibit varying competitive kinetic behaviors at high rates, which complicates the limiting factors of electrode performance.\u003c/p\u003e \u003cp\u003eCurrently, optimizing electrode rate performance relies on experimental approaches, which fall short in providing monitoring of internal operational states during discharge processes and a physics-based understanding. Consequently, multiphysics field models based on porous theory have emerged as advantageous optimization tools and are widely applied [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Unfortunately, homogeneous theoretical approaches, such as treating electrodes as uniformly distributed spherical particles, overlook the effects of heterogeneous microstructures (e.g., point contacts, 3D morphological edges) on reaction nonuniformity [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. This limitation prevents these models from achieving 3D heterogeneous structural optimization tasks. Nano X-ray computed tomography (nano-XCT) has emerged as a highly valuable 3D imaging technique, widely applied in the study of electrode materials [\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. For instance, Lu et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] employed nano-XCT to observe, in situ, the structural changes of electrodes during the calendering process at the particle level, and used electrochemical models to elucidate the structure-performance relationship. However, the carbon and binder domains (CBD) in electrodes exhibit X-ray attenuation coefficients similar to air, posing a significant challenge for reconstructing the three-phase electrode structure containing AM, CBD, and pores. To address this, various mathematical algorithms have been developed to numerically add the CBD phase within the AM-pore region, substantially reducing both the difficulty and cost of such studies. Mistry et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] developed a stochastic EIP generation algorithm based on the cohesive tendencies of CBD and AM, and the validated structural-electrode parameter relationships have been widely applied in numerical simulations of electrode operational characteristics [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Notably, most studies conduct electrochemical simulations by calculating the effective transport parameters of the 3D digital twin structure, which are then incorporated into the P2D model. Although this approach shortens simulation times, it neglects potential biases arising from the heterogeneous structure, which may lead to deviations in the dynamic evolution. Moreover, the investigation of rate capability on the cathode side is primarily established through coin cell experiments or numerical simulations in an isothermal environment. During practical high-rate operation, internal heat accumulation from electrode impedance in integrated modular batteries has been shown to significantly alter electrode kinetics [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], leading to notable performance discrepancies. Therefore, integrating 3D models of microscale structure and considering thermal coupling effects is crucial for providing precise guidance in electrode optimization processes.\u003c/p\u003e \u003cp\u003eThis study aims to obtain comparable electrode structures by combining nano-XCT scanning experiments with digital processing techniques. Subsequently, a validated numerical model is used to elucidate the relationship between the microstructure of the electrodes and the internal dynamics (such as mass transfer, reactions, and heat generation) in LIBs. The study investigates the parametric correlations between electrode structure, rate performance, areal loading, and heat generation rate, providing deeper insights into the development of power- and energy-dominant electrodes. Various electrode configurations are considered, with a focus on the coupled effects of particle size, CBD fraction, and electrode thickness on performance. The efficacy of a laser patterning strategy is then evaluated for electrodes with different particle sizes. Based on the observed phenomenon of the reaction front migration, a tortuosity and particle gradation electrode structure that favors kinetics is proposed and its structural advantages across multiple dimensions are assessed. Electrochemical-thermal modeling explores performance variations under different heat exchange conditions, enhancing the understanding of multiphysics coupling in the electrode structure optimization process.\u003c/p\u003e"},{"header":"2 Results and discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Structure parameters that control the rate capability of the electrode\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA comprehensive investigation of the microscopic-scale dynamic changes induced by different electrode structural configurations is crucial for optimizing electrode performance. To explore the effect of particle size on the electrode, two electrodes with significantly different particle size distributions (PSDs) were selected as the subjects of study. Their three-dimensional (3D) structures were reconstructed using nano-XCT (Zeiss Xradia Ultra 800) (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). Due to the differing active material loadings, the active material architecture with a consistent volume fraction (54.17%) was iteratively generated by random insertion (Fig. S2a). In addition, we employed digital twins to deal with electrodes with different pore structures instead of dealing with the challenge of segmenting the inactive phase. Using pre-fabricated active materials as samples, a CBD addition program was applied via MATBOX to generate electrodes with varying CBD contents (Fig. S2b). MATBOX, developed by Usseglio-Viretta et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], is a software for virtual electrode structure fabrication. The fabrication algorithm, which has undergone peer review and experimental validation, is widely used in electrode microstructure simulation studies. Detailed procedures for the nano-XCT experiments and virtual electrode fabrication are provided in the experimental section.\u003c/p\u003e \u003cp\u003eIt is important to note that the average diameter of cathode particles at both laboratory and industrial scales can vary significantly from 2 \u0026micro;m to 12 \u0026micro;m [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], and is primarily designed based on specific application requirements (power-oriented or energy-oriented). The large-particle and small-particle electrodes used in the model are derived from commercial lithium-ion battery cathodes. The PSD assessment results indicate that the large-particle electrode shows a bimodal distribution with a D\u003csub\u003e90\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;10 \u0026micro;m (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec), while the small-particle electrode exhibits a unimodal distribution with a D\u003csub\u003e90\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;5 \u0026micro;m (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed). The significantly different distribution characteristics and D\u003csub\u003e90\u003c/sub\u003e values allow these electrodes to serve as comparative subjects for investigating strategies to enhance the energy density of electrodes at high rates.\u003c/p\u003e \u003cp\u003eBased on the prepared electrode structure, the material properties of the electrodes were calculated using direct numerical simulations (Supplementary Note 1), with the results shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee-f. When the active components of the electrode were fixed, a competitive relationship was observed between the CBD content (electron conduction) and porosity (ion diffusion). As the CBD content increased, the diffusion of mass within the electrode became more difficult, and the tortuosity of the pores exhibited an exponential growth trend (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee). Lu et al. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] analyzed the relationship between electrode porosity and diffusion resistance using XCT and rolling equipment, showing a consistent trend. Notably, the results were significantly higher than those predicted by the Bruggeman empirical formula, which can be attributed to the assumptions regarding particle morphology and spatial distribution, as well as the neglect of CBD components [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef shows the dependence of the effective conductivity on the CBD content, with a similar trend to the variation of tortuosity, a result also captured by Ghadban et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] through numerical simulations. However, slight differences were observed in the high CBD fraction due to the differing electrode skeleton components (96.5 wt.% vs. 94 wt.%). The larger specific surface area (α\u003csub\u003es\u003c/sub\u003e) of small particle electrodes, which accounts for the cohesive forces and adhesion energy between the slurry molecules, leads to more complex connection pathways for CBD molecules, thus forming more tortuous Li\u003csup\u003e+\u003c/sup\u003e diffusion paths (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee). In contrast, the smaller α\u003csub\u003es\u003c/sub\u003e of larger particles allows CBD to more easily form electrical bridges (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef) [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] .\u003c/p\u003e \u003cp\u003eIn addition to their physical properties, the AM and porosity structure also govern the complex reaction and transport kinetics, leading to trade-offs in electrode performance. Therefore, the aforementioned digital twin electrode structure is utilized, and a model based on the 3D microstructure is employed to investigate the impact of particle size, porosity, and thickness on the electrochemical rate capability. Here, electrodes with different CBD fractions are used to reflect the real-world effect of porosity on electrode performance. Specifically, the 4 wt.% CBD fraction corresponds to a porosity of 37.83%, while the 12.5 wt.% CBD fraction corresponds to a porosity of 20.81% (Detailed model and electrode parameters are provided in Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e-2). For convenience, different parameters are combined with hyphens to denote specific electrodes. For instance, the 30 \u0026micro;m large particle (LP) electrode with a low CBD fraction (LC) is denoted as 30 \u0026micro;m-LP-LC, while the 80 \u0026micro;m small particle (SP) electrode with a high CBD fraction (HC) is denoted as 80 \u0026micro;m-SP-HC. The neglected structural parameters refer to all electrodes incorporating the parameter.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe state of lithiation (SOL) and Li\u003csup\u003e+\u003c/sup\u003e concentration (C\u003csub\u003ee\u003c/sub\u003e) distributions in electrodes with different design parameters under 3C are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. At the particle level, comparing 30 \u0026micro;m-LP and 30 \u0026micro;m-SP, LP particles exhibit larger concentration gradients across core-surface spans due to the average 1.34 \u0026micro;m-longer Li diffusion paths (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-b and\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee-f). The average SOL at the particle level is quantified, and the colors are coded using the internal SOL gradient (ΔSOL\u0026thinsp;=\u0026thinsp;SOL\u003csub\u003emax\u003c/sub\u003e - SOL\u003csub\u003emin\u003c/sub\u003e) to reflect the degree of concentration polarization within the particle. The results reveal linear correlations between particle SOL, ΔSOL, and particle size, with particles smaller than 2 \u0026micro;m in LP showing similar lithiation levels to SP. Gradually developing Li concentration gradients within electrodes directly contribute to capacity losses, this is reflected in SOL distributions at discharge completion (Figs. S3a-d). Compared to SP, concentration polarization within LP particles intensifies further before discharge completion. Additionally, significant unused material remains within SP due to lost active surface area (Figs. S3c-d). The D\u003csub\u003e90\u003c/sub\u003e particle selected from 30 \u0026micro;m-LD exhibits surface-concentrated Li layers and uniformly distributed Li cores (Figs. S4a-b). Rapid concentration changes are observed within the concentrated thin layers, while nearly no concentration gradient is evident within the cores, indicating restricted diffusion of embedded Li within particles. Quantitative analysis shows a 21.6% reduction in average Li insertion and a 16.2% decrease in the volume fraction of concentrated Li layers (determined by second-order SOL differentials) in LP due to a 1.8-fold increase in particle diameter. This suggests that reducing particle size significantly alleviates solid-phase diffusion (SPD) limitation, enabling electrodes to absorb more Li at the same reaction rate.\u003c/p\u003e \u003cp\u003eExpanding to the electrode level, in the 30 \u0026micro;m-LC, electrolyte-phase diffusion (EPD) does not restrict electrode performance due to the weak Li\u003csup\u003e+\u003c/sup\u003e transport resistance (τ\u003csub\u003eLP\u0026minus;LD\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;2.31 vs. τ\u003csub\u003eSP\u0026minus;LD\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;2.34), exhibiting a uniform SOL gradient across thickness (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee). For HC with the same CBD fraction, the larger surface area of SP creates a more tortuous pore network in 3D space (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Nonetheless, the shorter Li\u003csup\u003e+\u003c/sup\u003e transport distance results in a uniformly distributed C\u003csub\u003ee\u003c/sub\u003e across the electrode (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef), thus minimizing the impact of EPD limitation (further theoretical elaboration will follow). This is evidenced in the SOL qualitative analysis, where SOL in HD remains linearly correlated with particle size. Furthermore, internal concentration gradients within HD particles continue to develop, further reducing material utilization at discharging completion (Figs. S3c-d). This underscores that, apart from particle size, the reaction surface area related to porosity also constitutes an impediment to rate capability.\u003c/p\u003e \u003cp\u003eIn thicker electrodes, the diffusion of Li\u003csup\u003e+\u003c/sup\u003e toward the current collector becomes more challenging, restricting more reaction regions to lower electrolyte salt concentrations. Additionally, increased AM raises the working current, exacerbating the burden of Li diffusion within particles and thereby disrupting the competitive balance between SPD and EPD. Comparing the 30 \u0026micro;m-LC and 80 \u0026micro;m-LC, the increased thickness leads to a slight Li\u003csup\u003e+\u003c/sup\u003e concentration near the separator (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg), but this is insufficient for EPD to exert limiting effects, thus, SOL continues to strongly correlate with particle size. A quantitative study of the same D\u003csub\u003e90\u003c/sub\u003e particle reveals that increasing thickness has minimal impact on the average inserted Li amount and the thickness of the concentration layer (Figs. S4c-d). Despite a 0.38 \u0026micro;m decrease in the concentration layer, this results in a negligible difference of only 0.5% in average inserted Li amount due to similar constraints imposed by SPD. Furthermore, the SOL distribution at the end of discharge shows that the polarization level within LD particles is weakly affected by an increase in thickness (Figs. S3e and S5g).\u003c/p\u003e \u003cp\u003eFor the 80 \u0026micro;m-HC, increasing electrode thickness significantly imposes limitations due to EPD (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh), reflected by higher SOL and greater ΔSOL near the separator. SOL is also found to strongly correlate with distance from the separator. Specifically, SP exhibits a narrow particle size distribution with minimal variation in SOL levels between particles. In contrast, LP shows a graded change in SOL and ΔSOL across the entire electrode thickness according to particle size, indicating that LP is influenced by slow SPD, consistent with the findings of Lu et al. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] that larger particle sizes extend SPD-limited regions. From a reaction kinetics perspective, particle lithiation is driven by activation overpotential (η), related to equilibrium lithiation potential (V\u003csub\u003eeq\u003c/sub\u003e (SOL) = ϕ\u003csub\u003es\u003c/sub\u003e - ϕ\u003csub\u003ee\u003c/sub\u003e - η, where ϕ\u003csub\u003es\u003c/sub\u003e is solid-phase electron potential, and ϕ\u003csub\u003ee\u003c/sub\u003e is liquid-phase ion potential). Figs. S7a-d illustrate uniform activation overpotential η and heterogeneous V\u003csub\u003eeq\u003c/sub\u003e distribution on LP/SP electrodes, suggesting SOL gradients across electrode thickness are driven by e\u003csup\u003e\u0026minus;\u003c/sup\u003e or Li\u003csup\u003e+\u003c/sup\u003e transport polarization. Given the lumped porosity model, which neglects the CBD distribution effects on e\u003csup\u003e\u0026minus;\u003c/sup\u003e conduction pathways, almost no difference in solid-phase potential ϕ\u003csub\u003es\u003c/sub\u003e is observed in the electrodes (Figs. S5e-f). Therefore, preferential lithiation near the separator is dependent on liquid-phase potential ϕ\u003csub\u003ee\u003c/sub\u003e. As a function of reaction current, Li\u003csup\u003e+\u003c/sup\u003e flux on the separator side further increases with higher areal loading. However, constrained by transport resistance, larger C\u003csub\u003ee\u003c/sub\u003e gradient develops across electrode thickness (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh), leading to development of liquid-phase potential ϕ\u003csub\u003ee\u003c/sub\u003e gradients according to Ohm's law (Figs. S5g-h). Li\u003csup\u003e+\u003c/sup\u003e concentration polarization significantly reduces V\u003csub\u003eeq\u003c/sub\u003e level, enabling particles to react faster under the same activation overpotential. This also explains why the 30 \u0026micro;m-HD does not encounter SPD limitations (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg). Additionally, SPD limitations within LP-HD dominate before discharge completion (Fig. S3f). However, due to higher tortuosity (τ\u003csub\u003eLP\u0026minus;HD\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;7.16 vs. τ\u003csub\u003eSP\u0026minus;HD\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;11.34), the Li\u003csup\u003e+\u003c/sup\u003e concentration near the 80 \u0026micro;m-SP-HD current collector is nearly depleted at 50% DOD, hindering particle utilization by the end of discharge (Fig. S3h).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea illustrates the variation of electrode capacity with discharge rate. As the discharge rate increases, the electrode capacity exhibits a declining trend. At 3C, the effect of particle size on the electrode performance becomes significantly more pronounced than that of porosity, as reflected in the comparison of the 80 \u0026micro;m-HC electrode. Additionally, capacity data for similar electrodes are presented using symbols, with supporting dynamic voltage verification results at different discharge rates from Fig. S6a for cross-validation of different electrode structures. The consistent trend across the data confirms the feasibility of the model (Detailed validation can be seen at Fig. S6). Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb-c summarize structure-dependent electrode capacity and average potential at 3C. For specific capacity, the impact of thickness on electrode performance is minimal. Particle size once again highlights its dominant role over porosity in determining electrode capacity (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), underscoring the competitive advantage of SPD. The average potential of the electrode reflects its power capability, and unlike the dependence of specific capacity on structure, the average potential is primarily governed by EPD, which is associated with porosity. This structural effect becomes more pronounced in thicker electrodes (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec), further emphasizing the importance of mitigating EPD in thicker electrodes.\u003c/p\u003e \u003cp\u003eThe electrochemical-thermal multi-physical interactions in electrodes generate unexplored relationships between structural characteristics and heat generation, with quantification results under isothermal conditions presented in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed-e. The heat sources during electrode operation can be categorized into reversible and irreversible heat. In numerous high-rate discharge scenarios, the irreversible heat, primarily consisting of ohmic heat and reaction heat, contributes most significantly to the total heat generation and thus receives considerable attention [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Therefore, this study focuses on the coupling relationship between structure and irreversible heat generation rate. As shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed-e, a larger electrode thickness corresponds to a higher operating current, which leads to an increase in the rates of ohmic or reaction heat. Moreover, EPD control the dominant type of heat generation. For instance, in the 30 \u0026micro;m electrode, the activation heat rate in the LC electrode is relatively higher, while ohmic heat dominates in the HC electrode (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). The 80 \u0026micro;m electrode, with its more tortuous ion transport paths, leads to the activation heat in the LC electrode rising to the level of ohmic heat, whereas in the HC electrode, ohmic heat remains the absolute dominant factor (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee).\u003c/p\u003e \u003cp\u003eWith the growing demand for energy density in practical applications, thicker electrodes are being designed, which will continue to increase the CBD fraction and rolling density to improve both gravimetric and volumetric energy densities. The potential gradient across the electrode thickness leads to a higher ohmic heating rate and lower average potential for electrodes with lower porosity. These attenuation effects become increasingly unacceptable in thicker electrodes (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb-e). This undoubtedly results in energy loss and heat generation at high charge/discharge rates. Therefore, the subsequent work in this study will integrate the aforementioned knowledge to explore performance optimization strategies for thicker HC electrodes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Enhancement mechanism of electrode performance by laser patterning\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eGiven the widespread application of laser patterning technology in improving thick electrode performance, this section simulates the 80 \u0026micro;m-HC with different PSDs to investigate the mechanisms of performance enhancement through tortuosity engineering. Dunlap et al. [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] used femtosecond pulsed lasers to fabricate patterned grooves in NMC622 electrodes. SEM characterization showed ablation holes at a 75\u0026deg; channel angle, attributed to the shape of the incident beam and the morphology of the particles. The maximum diameter of the channels (the separator side) was approximately 36 \u0026micro;m, with a depth of about 50% electrode thickness. To avoid significant material waste, this study employs a lattice laser patterning method that extracts a quarter-cone section from the pristine electrode on the separator side to obtain a representative patterned electrode (Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). This technique has recently been applied to graphite anodes to enhance fast-charging capabilities [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], but the mechanism for improving the discharge performance of cathodes still requires detailed exploration. Due to the higher areal loading, the material loss caused by laser ablation in this work is slightly higher than the values reported by Dunlap et al. [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] (11.4 wt% for LP, 11.4 wt% for SP). Due to the symmetry of the actual structure centered around the introduced channels, a symmetric model approach is employed in this work. As outlined in Supplementary Note 3, the boundary condition treatment of the symmetric model does not introduce any additional impact on the electrode performance or the direction of the electric field propagation.\u003c/p\u003e \u003cp\u003eFigures S7a and S7b show the physical parameters along the thickness direction of the (un)patterned electrodes. The introduced channel not only causes a loss of active material but also leads to a reduction in the active surface area (red dashed lines). However, the trade-off does not significantly change their specific surface area (Laser_SP\u0026thinsp;~\u0026thinsp;0.89%, Laser_LP\u0026thinsp;~\u0026thinsp;2.1%), which is consistent with observations from experimental measurements [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Additionally, the in-plane porosity (x-direction) and through-plane porosity (z-direction) near the separator increase in local regions, likely acting as intermediary storage stations for Li\u003csup\u003e+\u003c/sup\u003e diffusion deeper into the electrode. A further electrochemical simulation reveals the impact of structural changes on internal mass diffusion and reaction kinetics, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec-e. Compared to the pristine electrodes (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh), Laser_LP and Laser_SP shorten the Li\u003csup\u003e+\u003c/sup\u003e transport distance through in-plane diffusion paths, highlighted by the direction of Li\u003csup\u003e+\u003c/sup\u003e streamlines. This provides the electrodes with a more homogeneous C\u003csub\u003ee\u003c/sub\u003e distribution across the thickness, and the mitigated ϕ\u003csub\u003ee\u003c/sub\u003e gradient extends the SPD-limited region in both electrodes. Additionally, the particle surfaces exposed by beam ablation reach lithiation saturation earlier and exhibit lower interfacial reaction currents, while the reaction rates in the other areas remain high (third column of Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec-d). Uneven reaction flux causes uneven stress, leading to mechanical fracture of particles, especially larger ones, during long-term lithium insertion and extraction cycles [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee further quantifies the material distribution across the electrode thickness before and after patterning. Observing the trend of the scatter symbols, the patterned electrode alleviates the C\u003csub\u003ee\u003c/sub\u003e gradient across the electrode, resulting in 24.1% and 19.3% increases in C\u003csub\u003ee\u003c/sub\u003e on the current collector side for Laser_LP and Laser_SP, respectively. Nevertheless, due to the SPD limitation, the SOL distribution in Laser_LP does not significantly improve (top of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee, compared with Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed), while the SOL distribution in Laser_SP becomes more uniform (bottom of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee, compared with Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh). This phenomenon is more pronounced at 5C discharge rates where the Ce concentration gradient is more pronounced (Figs. S7c-d). The shaded areas in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee indicate lithium concentration variations within the electrode plane. LP shows nearly identical SOL distribution and in-plane variation at the electrode level before and after patterning, suggesting that tortuosity engineering to mitigate EPD limitations provides minimal improvement for LP performance. In contrast, because Laser_SP is primarily constrained by EPD, its SOL distribution is more uniform across the thickness (bottom of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee). Additionally, the SOL near the separator in Laser_SP is lower than in SP, extending the same in-plane SOL polarization level to a depth of 50 \u0026micro;m (shaded region), allowing the reaction front to penetrate deeper.\u003c/p\u003e \u003cp\u003eThe influence of electrode structure on heating is further investigated, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef. Compared to the pristine electrode, the patterned electrode significantly reduces the ohmic heating rate, with a greater improvement observed in SP. In contrast, the activation heat remains similar across electrodes, suggesting that the fractured particle surfaces and altered reaction pathways do not notably affect the rate of interfacial heating. Figures\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eg-j provide a visual representation of the heterogeneous distribution of heat generation rates across the electrodes. In the pristine electrode, liquid-phase ohmic heat (q\u003csub\u003ee\u003c/sub\u003e) is primarily concentrated near the separator, where significant C\u003csub\u003ee\u003c/sub\u003e and ϕ\u003csub\u003ee\u003c/sub\u003e gradients exist. The greater pore tortuosity in SP results in intensified ohmic heat near the separator, while the smaller surface area and interface potential polarization contribute to a higher level of activation heat (q\u003csub\u003er\u003c/sub\u003e) on the LP electrode (Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eg-h). Heating behaviors in the patterned electrodes display distinct characteristics. The introduced channels alter the direction of ion diffusion, but the channel cross-sectional area gradually decreases, causing the ohmic heat in the patterned electrode to focus near the bottom of the channels (Supplementary Note 3). In contrast, activation heat levels in the structured electrode are similar to those in the pristine electrode, and the heating rate on fractured particles is significantly lower than on particle surfaces within the electrode interior. This indicates that structural modifications not only create asymmetric electrochemical-mechanical stress on the fractured particles (Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec-d), but also lead to uneven thermal expansion due to the heterogeneous distribution of activation heat. The ohmic heat concentration zones shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ei-j will accelerate this process, potentially causing particle fracture within the electrode during cycling. Thus, this highlights the need to consider tortuosity-based electrode strategies, similar to the patterning approach, to mitigate cycle life degradation caused by heterogeneous heating.\u003c/p\u003e \u003cp\u003eFigure S8 summarizes the voltage curves of the (un)patterned LP/SP electrodes at different discharging rates. Due to the smaller applied current, the unmodified electrodes exhibit the same specific capacity at 0.2C (Figs. S8a-b). At 1C, Laser_LP shows a slight improvement in accessible capacity and average potential, while Laser_SP shows only an enhancement in the voltage plateau. As the discharge rate further increases to 3C, the capacity and power performance of the patterned electrodes improve significantly, with Laser_SP showing more pronounced performance gains due to the introduced channels. Additionally, laser patterning is essentially a subtractive manufacturing strategy, and the material waste during production should be considered when comparing its actual effectiveness. Therefore, the areal capacity vs. rate curves of the electrodes are plotted, as shown in Figs. S8c-d. When the discharge rates are below 3C, the disadvantage of wasted capacity in the modified electrodes is evident, although the patterned electrodes provide significant power enhancement at 3C. Fortunately, this drawback is well compensated for at higher rates, especially for Laser_SP, which achieves an 18.5% capacity gain and a 20.4% power gain at 5C. For LP, superior energy and power improvements are delayed until a discharge rate of 10C. At such high working currents, the fractured particles exposed to high reaction flux will exacerbate the dissolution of transition metals, leading to premature electrode failure [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe imbalance between SPD and EPD in the electrode also feeds back into the kinetic evolution of reaction processes, manifesting as a regular distribution of charge transfer current density (J\u003csub\u003ect\u003c/sub\u003e) during discharge. This can be reflected by the voxel distribution of local J\u003csub\u003ect\u003c/sub\u003e and SOL at different discharge moments, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The top region of the electrode (TOP) is defined as the area from 70 \u0026micro;m to 80 \u0026micro;m from the separator side, while the bottom region of the electrode (BOT) refers to the area within 0 to 10 \u0026micro;m near the current collector. A distance of 70 \u0026micro;m is sufficient to characterize the temporal lag of the reaction front propagation on the electrode. For the small particles of SP and Laser_SP, the electrode reaction is mainly controlled by EPD at the initial stage, thus, TOP acquires a larger reaction current and preferential lithiation. At the same time, the reaction participation in BOT is lower (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea-d, stage ①). From stage ① to ②, the reaction barrier at TOP continues to increase due to slow SPD [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], while the J\u003csub\u003ect\u003c/sub\u003e gradually decreases and shifts to BOT. This migration of reaction current helps reduce concentration polarization within TOP particles. Subsequently, SPD and EPD reach a quasi-equilibrium state, with minimal changes in electrode reactions over time (from stage ② to ③). During this process, the concentration polarization of Li in the electrode continuously increases (the SOL voxel distribution broadens) until a lithiation saturation peak distribution (PD\u003csub\u003eS\u003c/sub\u003e) appears at the TOP (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec). The PD\u003csub\u003eS\u003c/sub\u003e peak indicates SPD-induced limitations, triggering the particle surface to close reaction sites and causing J\u003csub\u003ect\u003c/sub\u003e to further decrease. Similarly, the reaction front shifts again to the BOT region until the end of discharge (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed, stages ③ and ④). Fig. S9a visualizes the J\u003csub\u003ect\u003c/sub\u003e at various stages of Laser_SP, clearly reflecting the propagation of the reaction front along the electrode thickness. Additionally, compared to SP, the J\u003csub\u003ect\u003c/sub\u003e distribution in the local regions of Laser_SP is more concentrated, and the difference in J\u003csub\u003ect\u003c/sub\u003e between TOP and BOT is smaller, indicating that the alleviation of Li\u003csup\u003e+\u003c/sup\u003e diffusion resistance makes the electrode reaction more uniform at the same time, facilitating more efficient material utilization.\u003c/p\u003e \u003cp\u003eThe reaction process in large-particle electrodes, however, displays distinct characteristics, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee-h. In both LP and Laser_LP, the phase of uniform J\u003csub\u003ect\u003c/sub\u003e distribution observed in small-particle electrodes is absent. This difference arises from the dominant SPD limitation, which is also reflected in the broader SOL voxel distribution in large-particle electrodes (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eg). Beginning with stage ①, the SPD constraint continually drives reaction energy barriers across the particle surface, resulting in a sustained decrease in J\u003csub\u003ect\u003c/sub\u003e in the TOP region. Although the reaction current propagation also exhibits lag, contrary to that in small-particle electrodes, the BOT region in large-particle electrodes reaches saturation by stage ③, reducing J\u003csub\u003ect\u003c/sub\u003e at the particle surface and pushing the reaction front deeper into the electrode (Fig. S9b). Notably, compared to LP, Laser_LP maintains a higher J\u003csub\u003ect\u003c/sub\u003e peak in the TOP region during stage ④, due to the cracked particle surface. The cracked surface accelerates the reaction rate, and the reduced ion diffusion distance alleviates the lag in the reaction current propagation, manifesting as broader PDS saturation peaks in the TOP and BOT regions (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eg and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eh), which mitigate concentration gradients within the large particles. Compared to the small-particle electrodes, both the J\u003csub\u003ect\u003c/sub\u003e and SOL in large-particle electrodes exhibit broader voxel distributions, indicating stronger interfacial activation and concentration polarization due to the larger particle size. Fortunately, as the driving force behind the lithiation reaction, the spatial shuttling effect of J\u003csub\u003ect\u003c/sub\u003e maximizes the utilization of electrode materials. Furthermore, the propagation of the reaction front within electrodes with different PSD distributions offers new insights into the design of electrodes for specific applications.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Particle Gradation Engineering\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe effectiveness of laser patterning, which varies with electrode PSD, is analyzed previously. Here, this knowledge is applied to design advanced electrode structures for maximizing performance. First, it is necessary to clarify the exact correlation between the PSD and electrode performance. Accordingly, pristine electrodes with bimodal particle size distributions of 25%, 50%, and 75% large particle fractions are generated (referred to as PXX% henceforth). The particles in the electrodes are assumed to be spherical, with sizes corresponding to the maximum SP and LP particle sizes (7 \u0026micro;m and 12.5 \u0026micro;m, Figs.S3b and S3d), which are typical in commercial electrodes. To ensure random particle distribution, a random packing model is developed using MATLAB, generating particle models with structural parameters identical to those reconstructed from XCT. Due to the various geometrical topologies of small and large particles, parameters such as tortuosity, conductivity, and specific surface area are calculated based on the distribution weights of different particle sizes.\u003c/p\u003e \u003cp\u003eThe SOL and C\u003csub\u003ee\u003c/sub\u003e distributions in the pristine electrodes at 3C and 50% DOD are shown in Figs. S10a-c. As the fraction of large particles increases from P25% to P75%, the SOL and the C\u003csub\u003ee\u003c/sub\u003e gradient on the electrode gradually decreases, and SPD limitations become more dominant. Quantitative SOL results across the plane are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb-d, with the shaded area representing the in-plane Li concentration difference (SOL standard deviation). In regions of Li\u003csup\u003e+\u003c/sup\u003e accumulation near the separator, both SOL and concentration polarization are high. As the fraction of small particles decreases, the average SOL level in the deeper regions of the electrode increases, while the corresponding shaded area also grows, indicating that increasing large particles improves material utilization in the deeper regions but reduces overall material utilization efficiency. The simulation using the P2D model for P0% are shown in Fig. S11, voltage curve of the P2D model is slightly lower than that of the 3D particle model, with a more uniform SOL gradient across the thickness. This is because the P2D homogenization theory neglects the effects of 3D particle edges on Li\u003csup\u003e+\u003c/sup\u003e transport and weakens the face contact effects between particles and between particles and inactive components.\u003c/p\u003e \u003cp\u003eTo improve the utilization of electrode materials, it is proposed a tortuosity-graded particle electrode (TG) that combines laser perforation and particle size layering strategies. In TG, particles are arranged in a gradient, with smaller particles placed above larger ones, which is reported to be achieved through layer-by-layer coating before calendering [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. In this study, the structure of the TG is simulated using a random filling program. According to theoretical derivations (details in Supplementary Note 2), the volume ratio, weight ratio, and thickness ratio of electrode layers with different particle sizes are the same. Therefore, different TGXX% samples (TGXX% denotes TG with a specific proportion of large particles) are obtained by applying constraints on thickness and volume ratios to achieve varying proportions of large particles. Additionally, to ensure a fair comparison of performance, the thickness of the TG is increased to maintain the same areal loading as that of the pristine electrode.\u003c/p\u003e \u003cp\u003eComparing Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ee-g, as the fraction of large particles increases, a trend of expanding lithiation saturation areas is noted, however, the C\u003csub\u003ee\u003c/sub\u003e and SOL gradients in TG are significantly smaller. The SOL across the plane (Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb-d, red) shows the average SOL level in the small particle layer of TG is higher than that in the pristine electrode, with a larger lithiation saturation shaded area. To quantify the structural advantages of TG in transport kinetics, an assessment criterion for the SPD limitation depth is introduced. This requires a reference model in which the influence of Li\u003csup\u003e+\u003c/sup\u003e diffusion on electrode reactions is eliminated. Specifically, the tortuosity factor is the Bruggeman constant (~ -0.5), and the electrolyte cation transference number is maximized (~\u0026thinsp;1) [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The in-plane SOL standard deviation comparison provides the electrode regions solely limited by SPD, with the calculation method illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea. Results of the SPD limitation depth are shown as arrows in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb-g, where blue color corresponds to the pristine electrode and red color corresponds to the TG electrode.\u003c/p\u003e \u003cp\u003eFor the pristine electrode, the SPD limitation depth increases with the fraction of large particles. However, P75% still exhibits EPD-limitation regions (Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eg). In contrast, TG75% is entirely controlled by SPD (red arrows). The final discharge capacity differences are minimal, because both the pristine electrode and TG are predominantly limited by SPD at 3C. The significant difference is that fast ion channels in TG markedly enhance power performance, as indicated by the gray curves in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eh-j. The improvement in the voltage-power plateau of the TG electrode arises from the alleviation of the Li\u003csup\u003e+\u003c/sup\u003e concentration gradient, as illustrated in Figs. S10d-e. This results in the Li\u003csup\u003e+\u003c/sup\u003e transport characteristics being maintained within the optimal concentration range (1.2 M), thereby mitigating the rise in the liquid-phase overpotential. Moreover, the alleviation of the ion concentration gradient significantly reduces the ohmic heating rate in the TG electrode, while the self-assembled structure of the particles enhances the heating rate of the activation energy (Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eh-j).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe SPD-limited region for 80 \u0026micro;m electrodes is summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea, where solid symbols represent results at the end of discharge (prematurely stopped). The SPD-limited region fraction in TG is consistently larger than in pristine electrodes, with the gap widening towards both ends of the PSD spectrum, which is centered at 50% LP (large particle fraction). This trend is also observed in 120 \u0026micro;m electrodes (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb), indicating that the mixed particle fraction of 25% or less is preferred. Additionally, at the same areal loading, TG electrodes with specific LP may suffer from the detrimental effects of increased thickness (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb). To understand the structural advantages of TG in promoting favorable reaction kinetics, the diffusion competition within the electrodes is characterized using the differential SOL at the particle level, comparing P50% and TG50%. Figures\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec-d show the spatiotemporal evolution of ΔSOL in pristine electrodes at incremental DOD. In the early stages of discharge, most Li\u003csup\u003e+\u003c/sup\u003e current (J\u003csub\u003el\u003c/sub\u003e) is generated near the separator, creating a significant C\u003csub\u003ee\u003c/sub\u003e gradient (Figs. S10d-e), leading to a continuous rise in particle ΔSOL at this location (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec). At 0.15 DOD, SPD limitation begins to take effect, resulting in stratification of particle ΔSOL. This persists until 0.4 DOD, when particles near the separator reach a lithium saturation state first, and SPD limitation begins to dominate. Subsequently, ΔSOL near the separator decreases while ΔSOL in deeper particles increases, indicating the transfer of the reaction front. In the early stages of TG discharge, similar to pristine electrodes, the reaction front is concentrated near the separator, with small particle ΔSOL continuously rising (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ed). However, starting at 0.5 DOD, small particles, rather than large ones, reach lithium saturation first and rapidly extend to the remaining small particle locations. The fast SPD and interfacial reaction kinetics significantly increase the volume fraction of the concentrated Li layer, raising the output voltage of TG electrodes by 3.4% compared to pristine electrodes at the same moment.\u003c/p\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ee-f compare the rate performance of the two electrodes with different LP fractions. Even at very low current densities, significant capacity differences between electrodes with different LP fractions are observed. The effect of PSDs on the capacity of pristine electrodes is most pronounced at 14.2 mA\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, where P100% exhibits a rated capacity of 61.7 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e higher than P0% (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ee). When the fraction of LP less than 25%, the ability of PSD to enhance high-rate performance is limited, even resulting in negative gains under extremely high discharge conditions, consistent with the analysis in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea-b. Additionally, the increase in specific surface area leads to faster side reaction rates, necessitating a trade-off in design to mitigate adverse effects on cycle performance. For TG electrodes, the maximum capacity difference related to PSD is larger\u0026thinsp;~\u0026thinsp;73.1 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ef). Compared to pristine electrodes (black symbols representing P0%), TG performance improvements are primarily observed at higher current densities. The capacity of TG0% (blue symbols) maintains a 13.7 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e capacity advantage at 28.4 mA\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. Wood et al. [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e] also conducted combined experiments on electrodes with different PSDs and found a similar magnitude of capacity advantage for layered cathodes. Furthermore, the loss of active surface area caused by TG requires consideration, especially under SPD-limited conditions such as large-particle electrodes and low current densities. This is reflected in the average capacity loss of 1.9 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e for TG100% compared to P100% across various rates (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ef, gray symbols).\u003c/p\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eg and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eh compare the areal capacity of electrodes with varying LP fractions as thickness increases, providing insights into the performance trade-offs associated with thickness scaling in electrodes tailored for specific applications. For thicker pristine electrodes, configurations with different particle size ratios show a markedly enhanced capacity at low rates. However, at higher rates, the EPD limitations of thick electrodes become more pronounced, resulting in a rapid decline in area-specific capacity. The extent and rate of performance decay in thicker electrodes depend on the particle fraction configuration, which is differentiated by critical rate and critical capacity. When electrode thickness increases from 80 \u0026micro;m to 200 \u0026micro;m, the 25%LP configuration shows performance degradation when the C-rate exceeds 2.7, with an area capacity of 2.2 mAh\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. In contrast, for the 75%LP electrode, the C-rate and capacity decrease to 2.5C and 1.7 mAh\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, respectively. The structural advantages of the TG greatly increase the tolerability of the performance loss suffered by the thickness expansion (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eh). For a 200 \u0026micro;m TG, the critical rate and capacity of the 25%LP configuration are 4.9C and 1.7 mAh\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, and for the 75%LP configuration, they are 4.3C and 1.2 mAh\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. On average, the TG increases the critical rate by about 43% and reduces critical capacity by roughly 26% compared to pristine electrodes. This suggests that thicker TG exhibit rate performance more comparable to that of thinner electrodes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Electrode performance in non-isothermal heat transfer environments\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDue to the strong temperature dependence, heat transfer environments potentially affect the reactions and transport processes operating at the electrode base, leading to performance variations. Specifically, compared to non-isothermal environments, the heat generated by electrode impedance is entirely absorbed by the isothermal environment. This slows electrode reaction kinetics and transport kinetics, leading to a continued increase in overpotential resistance (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea). Therefore, to account for practical thermal benefits, a bidirectional coupling between the electrochemical field and the temperature field is established through temperature coefficients and the Arrhenius equation within electrochemical parameters (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eh). This allows for estimating the overall electrode temperature rise using a lumped thermal model due to the small geometric Biot number [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. A challenge in model validation is accurately detecting weak heat generation from single-layer cathodes in experiments, necessitating methods to examine electrode heat generation rates for comparing model predictions, as shown in Fig. S12. At 25\u0026deg;C and 1C, electrode heat generation rates range from 60 to 100 \u0026micro;W\u0026middot;mm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e, consistent with the magnitude reported by Yan et al. [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. It should be noted that the study does not consider the effect of CBD on electrode interface reactions, which is reported as a significant factor influencing activation energy and total heat generation [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Additionally, structural and thermodynamic parameters of electrode materials, such as particle size, open-circuit potential, and entropy coefficient, also influence heat generation rate curves.\u003c/p\u003e \u003cp\u003eThe established electrochemical-thermal model is initially used to investigate the discharge voltage curves of the electrodes at different temperatures, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ei. When the temperature decreases from 25\u0026deg;C to -10\u0026deg;C, the TG electrode exhibits a lower capacity loss in an isothermal environment compared to the pristine electrode (54.9 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e vs. 77.3 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e). However, under non-isothermal conditions, the TG electrode the TG electrode shows a higher capacity loss than the pristine electrode (30.4 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e vs. 29.8 mAh\u0026middot;g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), and consistently demonstrates lower capacity across all temperatures (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ei). Figures\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ej analyze the differences described above from the perspective of electrode heat generation rates. In an isothermal environment, electrode heating is not influenced by self-heating, instead, the heat generation rate of the electrode solely originates from internal resistance (activation heat\u0026thinsp;+\u0026thinsp;ohmic heat). Compared to the TG electrode, the pristine electrode exhibits higher heat generation rates at all temperatures due to its larger ionic transport resistance and interfacial overpotential. However, energy losses are mainly due to voltage drop, causing the pristine electrode to reach the cutoff condition earlier (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec). When self-heating effects are considered, the performance of both TG and the pristine electrode significantly improves (Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ei-j), with the surprising result that the pristine electrode outperforms the TG electrode. This reflects the interaction between internal resistance and thermal gain.\u003c/p\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ed and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ek provide a macroscopic analysis of how heat exchange conditions impact the comparative performance of the two electrodes. In the isothermal environment, the SOL of the electrode is concentrated in the range 0\u0026ndash;0.2 (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ed). Compared to the pristine electrode, the SOL distribution of the TG during discharge is wider because more small particles are utilized, with higher intensities around 0.4 and 0.8 in the later stages of discharge (black markers and 3D visualization in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ef). Additionally, the SOL distribution of the TG is observed to diverge at 0.2 DOD, which is due to the reaction front shifting to the large particle layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ef). In the non-isothermal environment, the two electrodes exhibit similar and wider SOL distributions. The lag in the lithiation reaction of the large particles causes the SOL distribution of the TG to start bifurcating at 0.3 DOD (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ek). In fact, the SPD influenced by the temperature rise makes the capacity more dependent on large particles, and the contact effect of small particles in the pristine electrode further improves the utilization of large particles (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003em), resulting in the predominant capacity advantage of the pristine electrode.\u003c/p\u003e \u003cp\u003eThe preceding analysis confirms that electrolyte resistance is the dominant factor in electrode voltage loss (Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eh-j). Therefore, the changes in liquid-phase ohmic heat across the electrode thickness are analyzed on a global scale (Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ee and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003el). In an isothermal environment, the high ionic diffusion resistance in the pristine electrode causes localized heating near the separator (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ee and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eD visualization in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ef). In contrast, the TG electrode benefits from structural advantages, which result in a more uniform distribution of liquid-phase ohmic heat. In a non-isothermal environment, the increase in temperature significantly enhances the diffusion rate and conductivity of the liquid phase in both electrodes, contributing to more uniform heat during operation. Notably, the lower electrolyte resistance of the TG electrode generates a limited impact on enhancing the electrochemical performance.\u003c/p\u003e \u003cp\u003eFinally, the output performance of the electrode voltage and capacity is evaluated using Ragone plots, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eg and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003en. Since power is positively correlated with discharge current, the energy density of the electrodes decreases with increasing power in both environments. It is noteworthy that a significant drop in energy density (red markers) is present at high power. It represents the maximum power the electrode can release before a rapid decline in specific energy. In the isothermal environment, this inflection point is located near 1C, and as the temperature decreases, the decline in specific energy becomes more pronounced (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eg). The structural disadvantage of the pristine electrode is evident at 0\u0026deg;C, where it declines more at 1C compared to TG, whereas at 25\u0026deg;C, the critical discharge rate increases to 5C. In the non-isothermal scenario, an \u0026lsquo;energy cliff\u0026rsquo; is observed only in the pristine electrode below 0\u0026deg;C (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003en), and this inflection point increases from 1C in the isothermal environment to 12C. Additionally, almost no difference in output performance is observed between the two electrodes at room temperature, and the critical rate at low temperatures also increases to 12C. The Ragone plots in the non-isothermal environment characterize the significant performance differences of the electrodes under various heat transfer conditions, providing more realistic predictions for electrode structure design and battery management systems (BMS).\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Conclusion","content":"\u003cp\u003eThis study combines nano-XCT and digital twin technologies to obtain different electrode structures, which are used to investigate the effects of electrode structure adjustment strategies through experimentally validated electrochemical models. The objective is to improve the trade-off between electrode energy and power at high current density. The quantitative relationship between the electrode's physical properties and structure preliminarily reveals the competition in internal mass transport. Increasing the CBD content enhances the electronic conductivity, but inevitably increases the ionic transport resistance. Predictions from the electrochemical model suggest that reducing particle size is an effective method for improving rate capacity. Increasing electrode thickness leads to limited electrolyte-phase diffusion, thereby reducing electrode capacity and increasing heat generation rate. Fortunately, this can be addressed by patterned channels. The use of small-particle electrodes improved material utilization near the current collector by 11.82% at 3C, and effectively reduced the ohmic heating rate under high-rate conditions. However, the slight performance improvement indicates that large-particle electrodes are less sensitive to bypass strategies, and patterned electrodes exhibit a disadvantage in terms of area-specific capacity loss under low operating rates.\u003c/p\u003e \u003cp\u003eIn electrodes with large particles, the insufficient development of liquid-phase potential gradients leads to the absence of an equilibrium stage in the reaction, resulting in a unidirectional reaction wave during discharge. Based on this insight, an electrode that synergistically combines tortuosity engineering and graded particle strategy (TG) has been proposed. The structure with favorable kinetics enables the TG to exhibit superior rate capability across different PSDs, allowing it to better accommodate the material structure and range of rates compared to pristine electrodes. It also demonstrates advantages over pristine electrodes in terms of areal capacity and overpotential loss, thus adapting to the material structure and rate range.\u003c/p\u003e \u003cp\u003eThe non-isothermal electrochemical-thermal model provides insights into the operating mechanisms of electrodes at the full battery scale. The self-heating effect enables the pristine electrode to utilize impedance dependent on EPD limitation, allowing its capacity performance at various temperatures to surpass that of the TG. The alleviated EPD limitation allows the TG to exhibit superior electrochemical performance at extreme rates in different heat transfer environments, with discharge rates corresponding to the \u0026lsquo;energy cliff\u0026rsquo; being significantly higher than those of the pristine electrode. In summary, this study provides an in-depth analysis of the kinetic differences within the electrode, exploring strategies to optimize rate capability under different heat-exchange environments. These insights support the design of rapid discharge protocols and the development of more advanced electrode structures.\u003c/p\u003e"},{"header":"4 Experimental and modelling methods","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.1 X-ray computed tomography and 3D image analysis\u003c/h2\u003e \u003cp\u003eThe commercial ternary electrode sheet comprises a Li[Ni\u003csub\u003e0.6\u003c/sub\u003eMn\u003csub\u003e0.2\u003c/sub\u003eCo\u003csub\u003e0.2\u003c/sub\u003e]O\u003csub\u003e2\u003c/sub\u003e cathode coating and an aluminum foil current collector, with an areal density of 21.6 mg\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, and the cathode coating contains 96.5% active material. The electrode sheet is cut into approximately 0.5 mm pieces and fixed on the sample stage using epoxy resin. The Zeiss Xradia Ultra 800, with a spatial resolution of 126 nm, is chosen, and the target voltage is set to 40 kV with a target current of 30 mA. A total of 901 tomographic images are collected from 0\u0026deg; to 180\u0026deg; and with an exposure time of 18 s. The corrected aligned ray images are reconstructed using the filtered back projection algorithm [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e], yielding an electrode pillar region of 64 \u0026times; 64 \u0026micro;m.\u003c/p\u003e \u003cp\u003eThe scanned images are imported into Avizo for cropping, rotation, and position calibration; finally, a representative region of 40 \u0026micro;m\u003csup\u003e3\u003c/sup\u003e is extracted. This is followed by a region segmentation process. The reconstructed 3D structure is further characterized, and information is extracted at the particle and pore levels. TauFactor is then used to calculate the 2D projection flux simulation [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Digital twin electrodes\u003c/h2\u003e \u003cp\u003eThe scanned 2D grayscale images show clear details of particle edges (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003ea). However, the low X-ray absorption of CBD blurs the boundaries, making it difficult to distinguish them from pores. Therefore, this study segments only the particle phase, which is a common practice in nano-XCT imaging studies of LIB cathodes. For the particle phase, grayscale value variations spanning from particle to mixed phase (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003eb) are detected, with distinguishable grayscale value boundaries in the particle regions. The watershed algorithm and full width at half maxima method (FWHM) yield particles of similar average size and consistent particle boundary contours (Figs. S1c-d). This demonstrates the effectiveness of the segmentation based on the FWHM method.\u003c/p\u003e \u003cp\u003eTo obtain small-particle electrodes with the same volume fraction and different particle size distributions, previously scanned Li[Ni\u003csub\u003e0.5\u003c/sub\u003eMn\u003csub\u003e0.2\u003c/sub\u003eCo\u003csub\u003e0.3\u003c/sub\u003e]O\u003csub\u003e2\u003c/sub\u003e electrodes at the same resolution were used. As demonstrated in Fig. S2a, a dataset sampled from the CT particle is used. Based on the CT-reconstructed electrode structure, particles are randomly inserted into the electrode. It should be noted that Boolean operations are applied to the inserted particles to acquire non-overlapping particles. The iteration of the above steps continues until the particle volume fraction reaches the preset value of 54.17%. Due to the height range limitations of the nano-CT field of view (typically 65 \u0026micro;m), the acquisition of thick electrodes is achieved by vertical stitching, constrained by budget and time. Here, a more common numerical method is employed, i.e., doubling the electrode thickness by mirroring the filled electrode. This method, which treats the physical parameters and particle sizes of the electrode as in situ extensions, is widely used in electrode thickness studies [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Subsequently, CBD is virtually added to the two-phase electrode with the identical porosity. Due to the stirring and drying conditions, the evaporation rate of the slurry solvent causes local variations in CBD morphology, leading to tortuous Li\u003csup\u003e+\u003c/sup\u003e transport paths [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. In this study, the MATBOX software developed by Mukherjee et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] is used to add CBD to the electrode. The mode based on interface energy and the maximum shape factor forms bridges between particles to reduce electronic conduction limitations, as shown in the generated electrode structure in Fig. S2b. An adaptive mesh is applied to the three-phase electrode in Simpleware, followed by direct numerical simulation to calculate the conductivity and tortuosity parameters (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Electrochemical and thermal coupling models based on 3D microstructure\u003c/h2\u003e \u003cp\u003eThis study extends the Newman model [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] to the particle level to describe electrochemical reactions and mass transport. Solid-phase lithium transport within particles is described using Fick's law, while Li\u003csup\u003e+\u003c/sup\u003e movement in the electrolyte is driven by potential or concentration gradients (concentrated solution theory). The Butler-Volmer equation describes the charge transfer reactions at the particle/electrolyte interface, and the potential changes in the solid and liquid phases conform to Ohm's law. These governing equations are executed in COMSOL Multiphysics using multiple partial differential equations (PDEs). It is worth noting that the pores in the model include nanopores within the CBD, thus treated as a homogeneous mixture of CBD and pores using a lumped model.\u003c/p\u003e \u003cp\u003eThe coupling of the temperature field is deconstructed at the particle level based on the electrochemical-thermal coupling model developed by Gu and Wang [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. Reversible and activation heat act as surface heat sources at the particle/electrolyte contact interface, while Ohmic heat is allocated to the heterogeneous phase. The evolution and feedback of electrode temperature are considered using a lumped thermal model. Detailed governing equations, boundary conditions, and parameters can be found in the Supplementary Information.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThis work is supported by the National Natural Science Foundation of China (Grant No. 52106226, 52176058).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKang K, Meng YS, Br\u0026eacute;ger J, Grey CP, Ceder G (2006) Electrodes with High Power and High Capacity for Rechargeable Lithium Batteries. Science 311:977\u0026ndash;980\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChoi JW, Aurbach D (2016) Promise and reality of post-lithium-ion batteries with high energy densities. 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J Electrochem Soc 147:2910\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Lithium-ion batteries, Microstructure-resolved model, Structure regulation, Rate capability, Thermal behavior","lastPublishedDoi":"10.21203/rs.3.rs-6035965/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6035965/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePoor rate performance limits the application of high-areal-loading electrodes in energy storage, largely due to cathode microstructure. In this study, we integrated X-ray computed tomography (XCT) with digital technology to quantify the correlation between electrode structure and internal kinetic performance of lithium-ion electrodes. Results show that electrode structure intricately influences internal kinetics, thereby affecting rate capacity and nominal potential. Based on the parametric relationship between electrode structure and electrochemical-thermal properties, we explored the effects of structural regulation on electrode performance. Vertical channels significantly enhanced the rate capability and ohmic heating rate of small-particle electrodes, while solid-phase diffusion (SPD) dominated the discharge performance of large-particle electrodes, diminishing the impact of tortuosity strategies. Furthermore, electrodes with abundant SPD barriers exhibit unidirectional propagation of reaction fronts, resulting in a deeper SPD-limited region. This observation inspired the integration of two structural strategies that favor both mass transport and reaction penetration. Optimized electrode structures enhanced energy density at high rates and accommodated diverse particle sizes and thicknesses. Additionally, the coupling effect of the heat transfer environment on electrode performance was investigated. This study presents a novel paradigm for bottom-up electrode design using microstructure-resolved model, providing both microscopic mechanisms and quantitative insights for advanced battery development.\u003c/p\u003e","manuscriptTitle":"Digital Techniques Assisted in Tailoring Electrode Structure to Optimize Electrode Kinetics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-03 13:33:31","doi":"10.21203/rs.3.rs-6035965/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a5cd64fd-d573-4bc1-8350-59b40355e50a","owner":[],"postedDate":"March 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":44988837,"name":"Physical sciences/Engineering/Mechanical engineering"},{"id":44988838,"name":"Physical sciences/Engineering/Chemical engineering"}],"tags":[],"updatedAt":"2025-04-23T05:35:15+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-03 13:33:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6035965","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6035965","identity":"rs-6035965","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}