In the rapidly advancing field of electric vehicles, the performance of lithium-ion batteries (LIBs) is critically dependent on achieving high-speed charging and high-power output [1–4]. As these capabilities become increasingly essential, the optimization of electrode microstructure has emerged as a pivotal area of research [5–8]. While previous studies have extensively investigated compositional factors such as binder formulation, conductive additive content, and the intrinsic properties of active materials [9–13], the influence of active material particle size distribution within the electrode—beyond the characteristics of the constituent powder—remains relatively less explored.

Prior research has largely focused on the individual effects of either small or large active material particles [14–16]. In general, small particles offer a high surface area, which facilitates rapid lithium-ion diffusion and reduces overpotential; however, they are susceptible to detrimental side reactions and structural instability [17–19]. In contrast, large particles provide enhanced structural integrity and enable higher packing densities but exhibit sluggish kinetics [19,20]. To mitigate these inherent trade-offs, we propose an electrode design strategy based on a bimodal particle size distribution, achieved by precisely mixing large (~10 μm) and small (~4 μm) LiNi_0.8Co_0.15Mn_0.05O₂ (NCM) particles prior to electrode fabrication. This study emphasizes the critical importance of active material spatial arrangement at the electrode level as a tool for optimizing electrode microstructure. By systematically designing the mixing ratio of large and small particles, we investigate how the resulting particle spatial distribution influences key electrochemical performance metrics, including charge transfer resistance, electrochemically active surface area (ECSA), rate capability, and long-term cycling stability. Ultimately, this research positions bimodal particle engineering as a practical and scalable methodology for tailoring electrode architecture, providing valuable insights into the fundamental relationship between microstructure and electrochemical performance in the context of developing high-performance LIBs for fast charging and high-power applications.

The samples were prepared using Ni_0.8Co_0.15Mn_0.05(OH)₂ precursors with two distinct particle sizes, approximately 10 μm (large) and 4 μm (small), synthesized via the traditional co-precipitation method [21,22]. The precursor was thoroughly mixed with LiOH∙H₂O at a molar ratio of 1:1.03. This mixture was initially ground in a mortar and subsequently homogenized using a planetary centrifugal mixer (AR-100, THINKY Corp.) for 10 min [23]. The resulting mixture was calcined in a tube furnace (SH-FU-50STG-WG, SH Scientific) under a continuous flow of O₂ gas maintained at 0.6 L min^–1 using a mass flow controller (MF-200 CV, MFC Flow). The heat treatment involved a two-step profile: heating at 500°C for 5 h, followed by heating at 750°C for 10 h, with a controlled ramping rate of 2°C min^–1 between steps [24]. Slurries for electrode fabrication were prepared with a composition of 85 wt % active material (NCM), 7.5 wt% conductive additives (Super P carbon black and KS-6 graphite), and 7.5 wt% polyvinylidene fluoride binder.

Particle size and morphology were examined with a scanning electron microscope (SEM; VEGA3, Tescan), and the particle size distribution in each sample was measured through Image J software. An X-ray diffractometer (XRD; Rigaku D/Max-2500/PC) was used to study the crystallinity and crystal structure of two synthesized NCM with Cu K_α radiation from 10 to 140° at a scan rate of 1 used to study the crystallinity a min^–1. The Brunauer‒Emmett‒Teller (BET) surface area was determined from the analysis of nitrogen (N₂) adsorption/desorption isotherms obtained by a BELSORP MINI II (BEL Japan) instrument. The Barrett‒Joyner‒Halenda (BJH) method was used to analyze specific surface area, total pore volume, and BJH diameter of NCM. To determine the tap density, a sample of approximately 2 g of each powder was loaded into a 10 mL graduated cylinder. The cylinder was manually tapped for 10 min to achieve a stable, compacted volume. The tap density was subsequently calculated from the initial mass and the final measured volume.

Five distinct slurry formulations were prepared: one containing only large particles, one containing only small particles, and three incorporating mixtures of large and small particles at weight ratios of 3:1, 1:1, and 1:3. Following the powder mixing step, N-methyl-2-pyrrolidone (anhydrous, 99.5%, Sigma-Aldrich) was introduced to the blended powder and dispersed using an ultrasonic mixer for 10 min. The resulting homogeneous paste was subsequently coated onto aluminum foil utilizing an automatic mini coater. The fabricated electrode was then dried in a vacuum oven at 120°C for 12 h. Post-drying, the electrode was calendered to a thickness of 20 μm using a roll press and then precisely cut into circular discs with a punching tool. The active material loading density on the electrode was determined to be approximately 4 mg cm^‒2. CR2032-type coin cells were assembled within an argon-filled glove box. Each cell comprised an NCM cathode, a lithium metal anode, a separator, and an electrolyte. The electrolyte consisted of a 3:4:3 volumetric ratio of ethylene carbonate, dimethyl carbonate, and diethyl carbonate, containing 1.16 M LiPF₆.

The assembled half-cells were cycled for long-term test and rate performance test using battery cyclers (WBCS3000, WonATech Co., Ltd.) within the potential range of 2.7–4.3 V versus Li⁺/Li at 25°C (1C = 200 mA h g^‒1). For the cyclic voltammetry (CV) test and electrochemical impedance spectroscopy (EIS) analysis, a ZIVE BP2A electrochemical analysis was performed under a perturbation amplitude of 10 mV in the range of 0.001 Hz–10 kHz. Direct current (DC)-superimposed electrochemical impedance spectroscopy (DCSI-EIS) measurements were carried out during a constant current discharge process at 0.1C, within the voltage window of 4.2–3.6 V. Specific states of charge (SoC) were targeted by stopping the discharge at various voltages. At each voltage plateau, DCSI-EIS was measured by superimposing a small sinusoidal AC voltage (10 mV) on a series of stepwise DC currents (±100 μA range) using a ZIVE BP2A electrochemical workstation (WonATech Co., Ltd.). The resulting impedance spectra were fitted to extract charge transfer resistance (R_ct) at each DC level.

Monodisperse NCM precursor particles with distinct large and small sizes were synthesized using the coprecipitation method. Following synthesis, these precursors were subjected to calcination at an optimized temperature to obtain the final NCM materials. SEM images (Figs. S1A,B) demonstrate the successful synthesis of uniform NCM particles with both large and small morphologies. Analysis of particle size distribution (Figs. S1C,D) revealed narrow distributions, yielding average diameters of 10.5 μm and 4.4 μm for the large and small particles, respectively, thereby confirming a high degree of monodispersity in both samples. The phase formation and crystallinity of the calcined NCM powders were subsequently investigated by XRD analysis (Fig. S2A,B) and Rietveld refinement (Fig. S2C,D). Detailed Rietveld refinement results are summarized in Table S1. The XRD patterns for both samples exhibited well-defined diffraction peaks characteristic of a layered structure, notably indicated by the clear separation and intensity of the (003) and (104) reflections. The intensity ratio of the (003) to (104) peaks, a widely accepted metric for evaluating cation ordering and the integrity of the layered structure in NCM materials [25–28], further corroborated that both sets of particles formed highly crystalline layered oxides under the employed calcination conditions.

To systematically investigate the effect of particle size distribution on electrode structure and performance, electrodes were fabricated using monodisperse large particles (M1), monodisperse small particles (M5), and bimodal systems comprising mixtures of these two sizes at various ratios: M2 (large:small = 3:1), M3 (1:1), and M4 (1:3). A schematic illustration of the electrode structures, comparing particle arrangements in monodisperse and bimodal configurations, is presented in Fig. 1A. Hereafter, the powders with these compositions are referred to as M1‒M5 powders, and the corresponding battery electrodes fabricated from them as M1‒M5 electrodes. SEM analysis was employed to examine the morphology and particle distribution of the M1‒M5 powders (Fig. 1B). As the proportion of small particles increased from the monodisperse large particles (M1) to the monodisperse small particles (M5), the SEM images display the changing particle size composition and arrangement within the powder mixtures. To further characterize the intrinsic properties of the powders, the BET analysis was conducted. The specific surface area and total pore volume values were found to be comparable across all powder compositions (Table S1). Nitrogen physisorption isotherms (Fig. S3A) and corresponding BJH pore size distribution curves (Fig. S3B) further confirmed similar mesoporous characteristics among the powders, irrespective of the particle size ratio. These powder characterization results indicate that the intrinsic properties of the particles themselves, such as surface area and porosity, are largely similar across the different compositions. This suggests that any observed differences in electrochemical performance are more likely attributable to structural variations introduced during electrode fabrication and architecture rather than inherent differences in the primary particle characteristics. This conclusion is further supported by cross-sectional SEM images of the fabricated electrodes (Fig. 1C). Specifically, the monodisperse large particle electrode (M1) exhibits a densely packed structure after calendaring, which may facilitate electronic conductivity but consequently results in low porosity, potentially limiting ion diffusion. On the contrary, the monodisperse small particle electrode (M5) displays excessive inter-particle spacing, which is likely to increase R_ct [29,30]. In contrast to both monomodal designs, the bimodal M2 electrode achieves a more optimized architecture. To validate this observation quantitatively, we performed tap density measurements (Table S3). The results demonstrate that the bimodal M2 powder possesses the highest tap density (2.51 g mL^–1), significantly greater than that of the M1 (2.15 g mL^–1) and M5 (1.82 g mL^–1) powders. The superior packing of M2 is also evidenced by its minimal tapped volume (Fig. S4). These findings confirmed that a bimodal particle distribution is critical for engineering a compact electrode microstructure with high packing density. Therefore, these structural observations highlight the critical importance of optimizing particle size distribution during electrode fabrication to achieve a balance between compaction and porosity, which is essential for designing high-performance electrodes. To quantitatively evaluate how these structural differences resulting from varying particle size distributions translate into electrode-level electrochemical performance, a comprehensive series of electrochemical analyses was performed.

Based on the prior morphological analysis, wherein similar surface areas were observed across all powder samples, electrochemical behavior primarily dictated by intrinsic particle properties would theoretically yield minimal variation in initial capacities. However, the rate performance results (Fig. 2A) reveal significant variations in initial capacities among the electrodes as a function of C-rate. This observation strongly suggests that electrode-level architecture exerts a more dominant influence on electrochemical performance than intrinsic particle properties alone. For instance, the M1 electrode appears to benefit from enhanced electron transport due to its dense packing; however, this dense structure concurrently limits ion mobility, presumably due to lower porosity. Conversely, the M5 electrode exhibits diminished rate performance, which is hypothesized to stem from excessive interparticle spacing leading to increased internal resistance. In contrast, the M2 electrode demonstrates superior rate performance and stability, which is attributed to achieving an optimal balance between porosity and interparticle connectivity. These findings are further corroborated by the long-term cycling results (Fig. 2B). The M2 electrode consistently exhibits the highest initial capacity and retention among all samples, reinforcing the notion that an optimal balance between interparticle contact and porosity is crucial [31,32]. EIS measurements (Fig. 2C) further support this trend, with the M2 electrode displaying the lowest R_ct. Analysis of the voltage profiles (Fig. 2D) also indicates minimal capacity decay for the M2 electrode throughout cycling, reflecting enhanced electrochemical reversibility. The first-cycle differential capacity (dQ/dV) curves (Fig. 2E) reveal that the M5 electrode exhibits slower initial electrochemical kinetics compared to both the M1 and M2 electrodes. This sluggish kinetic behavior in M5 is likely attributable to its excessively small particle size, which is hypothesized to result in poor interparticle connectivity and consequently increased resistance. In contrast, the reduced polarization observed for the M2 electrode is attributed to its improved interparticle connectivity and well-balanced microstructure. The prominent redox peak observed near 4.2 V in the CV profiles (Fig. 2F) corresponds to the H2–H3 phase transition. This transition is associated with a substantial contraction of the c-axis lattice parameter and irreversible lattice oxygen redox reaction, both of which are known to induce structural degradation and particle cracking [22,27]. As the scan rate was increased from 0.1 mV s^–1 to 0.5 mV s^–1, the peak-to-peak voltage separation (ΔE_p) for M1 and M5 increased to 41.7 mV and 35.6 mV, respectively—values significantly larger than the 20.9 mV observed for M2. This indicates a greater overpotential at higher scan rates for M1 and M5. Notably, the H2–H3 transition peak for M5 is more pronounced and exhibits a more substantial shift to higher potentials as the scan rate increases, suggesting aggravated structural instability under fast-cycling conditions. In contrast, M2 exhibited a minimal ΔE_p and stable peak behavior, demonstrating the effective suppression of the deleterious H2–H3 transition and enhanced kinetic reversibility. Collectively, these results highlight the critical role of electrode porosity and microstructural optimization in dictating overall electrochemical performance, particularly rate capability and long-term stability.

To quantitatively investigate the evolution of ECSA under operational conditions, DCSI-EIS measurements were conducted. This approach was adapted from a recent study [33] that established an in situ methodology to track R_ct as a function of superimposed DC (I_DC), based on the modified Butler‒Volmer equation. This method enables the estimation of relative changes in ECSA by analyzing the curvature of R_ct – I_DC profiles. Fig. 3A shows the potential–SoC profile, with the SoC points at which DCSI-EIS measurements (colored points). At each selected SoC, EIS was conducted under a series of incremental DC bias currents, as shown in the DC profile (Fig. 3B). This configuration introduces controlled perturbations to the equilibrium condition, thereby inducing variations in the local surface concentration gradients of Li⁺ ions and modulating the effective exchange current density (j₀). Given that j₀ is inversely proportional to R_ct and scales with ECSA, the resulting R_ct – I_DC profiles provide a sensitive indicator of interfacial area dynamics. The fundamental relationship between R_ct and ECSA is given by the following equation:

where R is the gas constant, T is temperature, z is the number of electrons, F is Faraday’s constant, and A is ECSA. Under fixed temperature, electrolyte composition, and SoC, variations in R_ct are primarily attributed to changes in ECSA. To extract these relative changes, the R_ct – I_DC data were fitted using a modified Butler–Volmer equation incorporating a dimensionless ECSA variation parameter L:

Here, A₀ is the initial surface area (estimated from baseline EIS), α the charge-transfer coefficient, and η the overpotential. As shown in Fig. 3C, the M2 electrode demonstrates Gaussian-like R_ct – I_DC profiles across a range of SoC levels. In systems characterized by low ECSA, these profiles exhibit more pronounced curvature, which is indicative of enhanced sensitivity of R_ct to surface concentration gradients. Fig. S5 illustrates that the M1 and M5 electrodes display the steepest curvature in their respective R_ct – I_DC responses. In contrast, the M2 electrode presents the most linear and shallow curvature, suggesting a more stable and extended ECSA. Collectively, this comparative analysis (Fig. 3D) strongly supports the conclusion that optimal structural connectivity and porosity are critical determinants of stable electrochemical interface formation.

Fig. 4A presents cross-sectional SEM images, with particle boundaries delineated, revealing distinct morphological differences among the M1, M2, and M5 electrodes. These images visualize variations in particle packing density and inter-particle connectivity. Notably, the M2 electrode exhibits a more interconnected and moderately porous microstructure. This structure is highly favorable for establishing continuous charge transport pathways, a critical factor for efficient high-rate electrochemical operation [34,35]. This structural balance is considered essential for facilitating high-rate electrochemical performance. Consistent with these microstructural observations, the M2 electrode demonstrates superior cycling stability under high-rate conditions (Fig. 4B), further underscoring the benefits of its optimized architecture. To quantitatively evaluate the rate-dependent performance, Peukert’s constant (k) was determined from the rate-capability data. Originally formulated to describe capacity degradation with increasing discharge rates, Peukert’s law has been adapted for LIBs to capture kinetic limitations under high current density [36,37], which is defined as:

where C is the discharge capacity at current I, C₀ is the reference capacity at I₀, and k is the Peukert’s constant. A k-value approaching 1 indicates minimal polarization and efficient charge-transfer kinetics, desirable characteristics for high-rate performance. The extracted k-values for each electrode are presented in Figs. 4C–E. The M2 electrode exhibits the lowest k-value, closely approaching 1.0. This low k-value signifies minimal capacity degradation at high discharge rates and indicates enhanced transport properties within the electrode. In contrast, the M1 electrode shows a higher k-value than M2, which is likely attributable to its limited porosity, observed in the SEM images, which hinders ionic diffusion despite its relatively dense packing. The M5 electrode also displays the highest k-value. This higher k-value is attributed to excessive porosity and poor inter-particle connectivity, structural features that collectively contribute to increased internal resistance. These findings demonstrate the critical role of optimized electrode microstructure, achieved through careful control of particle connectivity and porosity (as exemplified by the M2 electrode design), in enabling high-rate operation of LIBs.

This study demonstrates that optimizing particle size distribution through the implementation of a bimodal system is paramount to enhancing the performance of LIBs. While investigations into monodisperse systems (M1 and M5) reveal inherent trade-offs between compaction density and porosity, the judiciously designed M2 bimodal system successfully yields a well-balanced electrode microstructure. This optimized structure features improved interparticle connectivity and precisely controlled porosity, addressing the limitations observed in monodisperse configurations. Consequently, the M2 electrode exhibits superior electrochemical performance across a spectrum of critical metrics, including enhanced capacity retention, improved rate capability, reduced interfacial resistance, and robust ECSA stability. In-depth DCSI-EIS analysis further corroborates these findings by confirming the sustained stability of the ECSA within the M2 electrode, thereby effectively mitigating resistive losses throughout prolonged cycling. Furthermore, analysis of Peukert’s constant emphasizes the exceptional capacity retention capability of the M2 electrode, particularly under high-rate discharge conditions. These results highlight the critical importance of deliberate particle arrangement at the electrode level and propose a practical and effective methodology for performance enhancement through the strategic utilization of powder-level bimodal systems. Our findings suggest that neither excessive compaction nor high porosity, when considered in isolation, is sufficient to achieve optimal LIB performance. Instead, a finely tuned bimodal particle size distribution presents a viable and practical approach to simultaneously improve fast-charging capabilities and ensure long-term cycling stability. By systematically investigating the intricate relationship between particle size distribution and electrochemical properties, this study provides valuable insights into the rational design and optimization of cathode microstructure, paving the way for the development of next-generation LIBs.