Lithium-ion batteries (LIBs) play a pivotal role in various applications, including stationary energy storage systems and electric or hybrid vehicles. However, conventional LIBs are approaching their physical limits in terms of energy density and fast-charging capabilities [1,2]. In this context, ASSBs represent a promising alternative, offering the potential for significantly higher power and energy density while also addressing critical safety concerns. Despite their promise, ASSBs present numerous challenges that are the focus of ongoing research.

The solid-state nature of all ASSB cell components, combined with the volume changes of the active materials during (de-)lithiation, introduces complex interplays between electrochemical, transport and mechanical processes, which strongly affect the overall cell performance [ 3–5 ]. In LIBs, electrodes are typically designed as porous microstructures that allow the liquid electrolyte to infiltrate, ensuring significant wetting of the AM across all regions and enabling relatively short pathways for ion transport [ 6,7 ]. However, the scenario changes in ASSBs as the inorganic SE is already integrated into the electrode during fabrication. As a result, achieving a uniform distribution and full contact between AM and SE particles is not easy to achieve [ 8 ], leading to more complex microstructural challenges than in traditional LIBs.

In ASSBs, the SE, alongside the AMs, plays a critical role by providing chemical stability and an ionic conductivity exceeding several mS.cm−1 at room temperature, which is necessary to match the performance of conventional LIBs. Among a multitude of material classes of solid electrolytes, lithium thiophosphates demonstrate the highest conductivities, some of which exceed 20 mS.cm−1 [ 9,10 ]. Beyond their high conductivity, thiophosphate-based SEs stand out also due to their unique mechanical properties, especially their malleability caused by low Young’s moduli, which allows the electrodes to be densified at low temperatures without the need for energy-intensive sintering processes [ 11,12 ].

A number of research groups have investigated the microstructure of ASSB electrodes through modeling and charge transport measurements [ 13–21 ]. These studies have demonstrated a direct correlation between the microstructure architecture and the percolating behavior of SE, which is contingent on the active surface area available for Li-ion insertion. Therefore, the performance of ASSBs is significantly influenced by factors such as material composition [ 14,15 ], microstructural arrangement [ 17,21 ], particle size [ 16–20 ], and manufacturing conditions [ 13 ]. Among these studies, several of them have directly linked charge transport measurements of ASSB cathodes with detailed microstructural information obtained from tomography [ 18 ] or from manufacturing process simulation by our group [ 13 ].

For instance, Minnmann et al. [ 8 ] identified SE particle size as a critical parameter determining charge transport in 3D reconstruction of composite cathode microstructures obtained from Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM), accounting for tortuosity effects and structural inhomogeneities. Alabdali et al. from our group [ 13 ] simulated in 3D a slurry-based manufacturing process (wet processing) of ASSB composite cathodes, incorporating conventional manufacturing parameters, and demonstrated that the degree of compression applied during the cathode manufacturing significantly affects the ionic and the electronic charge transport in thiophosphate-based electrodes. Other studies have also linked in 3D the electrode performance with its composite microstructure. For example, Neumann et al. [ 18 ] combined theoretical and experimental approaches to identify the limiting factors for the electrochemical performance of β-LPS-based ASSBs using microcomputed tomography (micro-CT) images. The findings were that a reduced contact between the electrode layer and the current collector, along with delamination of the SE from the active particle surface, significantly influences cell performance. Another noteworthy study by Bielefeld et al. [ 17 ] examined the influence of lithium-ion kinetics, particle arrangement, and void distribution on the electrochemical performance of NMC622/Li₆PS₅Cl composite cathodes, employing stochastically generated cathode microstructures. Their study resulted in a proposed optimized microstructure aimed at improving performance. Nonetheless, key limitations of their study include the stochastic nature of the microstructure generation process and the absence of carbon and binder domains. While a stochastic microstructure generation does not allow the investigate the influence of manufacturing parameters, the lack of the consideration of carbon and binder does not allow to reflect real-world cathodes.

Here, we present, for the first time to our knowledge, a comprehensive computational modeling workflow that examines the influence of the degree of calendering on the final performance of slurry-based composite electrodes. This study uses NMC622/Li₆PS₅Cl-based cathode microstructures with the presence of carbon and binder, generated through conventional calendering during manufacturing process simulations. This computational workflow is able to correlate the manufacturing process, the composite cathode microstructure and the cell performance, as it combines Coarse-grained Molecular Dynamics (CGMD) for the manufacturing simulation of the slurry, drying and calendering with a 4D-resolved performance model describing electrochemistry and transport mechanisms. The three-dimensional spatial locations of AM, SE, and Carbon-Binder Domain (CBD) within the electrode, as predicted from CGMD simulations, are considered explicitly as separated phases, each of them with specific physical properties. Our electrochemical performance model permits the study of the impact of the calendering degree on ionic and electronic transport, the heterogeneities of electrochemical reactivity within the electrode volume and its overall electrochemical performance. These findings are intended to provide guidelines for optimizing ASSB composite cathode designs.

Our computational modeling workflow consists of two main parts. The first part is already published [ 13 ] and devoted to the generation of the electrode microstructures under different degrees of calendering using CGMD modeling technique. The second part is devoted to the simulation of the electrochemical behavior of the electrodes upon discharge by using the Finite Element Method (FEM).

The manufacturing process of NMC622 based electrodes was performed experimentally and reported by Alabdali et al. [ 13 ]. By using the obtained manufacturing properties, a predictive model was carried out by simulating in 3D a slurry-based manufacturing process of ASSBs composite electrodes using CGMD technique in LAMMPS [ 22 ] computational software. It involves three major steps in the electrode wet manufacturing process: the slurry preparation, the drying and the calendering as shown in Figure 1. These simulations account for the AM, the SE and the CBD but it does not distinguish explicitly between carbon and binder. The CGMD technique is based on applying force fields/contact forces representing the interaction between particles and their mechanical properties, and these force fields were parameterized to match the experimental properties.

From the slurry to the dry electrode, the CBD particles are shrinked to the diameter corresponding to the solid size to mimic the evaporation of the solvent and the calendering step was modeled by a plane moving downward at constant speed to compress the electrode while maintaining the bottom surface fixed. The readers can refer to our previous work for more details about the simulation of the slurry, drying and calendaring process [ 23–25 ].

Different microstructures were generated from our CGMD model as illustrated in Figure 2a, each one corresponding to a different calendering degree, i.e. a different percentage of reduction of the thickness due to the applied calendering pressure . The usability of this model is limited for calendering degrees under 35 %, as it was discussed in [ 13 ] because above 35 % a decrease in the electrical conductivity was observed due to the partial occupation of the volume of CBD particles by other materials due to high pressure. For the following, we will work with the microstructures presenting three different compression degrees (0 %, 20 %, 35 %), each one corresponding to a different formulation, different thickness and different porosity as displayed in Table S1. Thus, the effect of microstructural variability on the effective electrode properties (i.e. ionic tortuosity, active area and effective conductivities) is considered in this work.

The use of a meshing technique constitutes the first step for the importation of the electrode microstructures generated from the CGMD modeling workflow into our 4D-resolved electrochemistry simulator. The meshes have been generated with our in-house software INNOV [ 26,27 ], which relies on a voxelization technique to create multi-phase volumetric meshes for Finite Element Method (FEM) calculations. Meshed electrode microstructures for 0 %, 20 % and 35 % calendering degrees, which are referred to hereafter as Cal0%, Cal20% and Cal35% and for corresponding compositions, are provided in Figure 2b.

We then use our 3D-resolved performance model with a Li-foil for the anode, Li6PS5Cl for the separator and for the composite electrode generated by our manufacturing simulations, to evaluate how the differences in the calendering degree impact the electrochemical response. The electrochemical evaluation of the ASSB cell is conducted without the application of any external forces, with the calendering process applied exclusively before the cycling. This approach allows us to isolate and analyze the intrinsic effects of calendering on the cell performance. Commercial software COMSOL Multiphysics® [ 28 ] was used as our FEM calculation platform. All the calculations were performed in the Matrics platform (Université de Picardie Jules Verne) [ 29 ] using one node with 500 GB of RAM and 1 processor (Intel® manufacturing simulation developed using CGMD technique, (b) Composite electrode microstructures after the multi-phase meshing process using INNOV and (c, d, e, f) volume fractions of AM, SE, CBD and pores for each calendering degree respectively.

Xeon® CPU E5-2680 v4 @ 2.40GHz, 28 cores). The computational domain of our electrochemical model consists of four phases: AM, CBD, SE and current collector CC.

The first material domain is the AM which features ionic and electronic transport. The lithium transport within the AM particles has been solved using Fickian diffusion as given below: (1) (2) − δ ,  = 0 where Cs is the lithium concentration in AM particles, DAM is AM phase diffusivity and t is time. Electric potential (ϕs) in each of the AM, CBD and CC domains can be solved using Ohm’s law as follows: Here, δe,i is the effective electronic conductivity of the domain, where i represents AM,CBD and CC. Moreover, the electric potential (ϕSE) for ionic transport in the SE domain can be estimated using charge conservation as shown below: − δ  where, δ

is the effective ionic conductivity in the SE phase. In order to capture the single ion conductor characteristics of Li6PS5Cl, the transference number of lithium ions is set to tLi+ = 1. Therefore, the concentration of lithium ions in the SE phase of the composite cathode is considered to be constant due to the high cationic transference number that results in negligible concentration gradients in the SE. Butler−Volmer kinetics is used to describe the electrochemical reaction occurring at the active AM-SE contact and is expressed as follows: (3) (4) (5) =

−  =  −  − where is the exchange current density, F is the Faraday constant, R is the universal gas constant, T is temperature, and η is overpotential. The overpotential η is given by the following expression: Here,

is the equilibrium potential difference in NMC622 material. In this model and in contrast to our previous work in [ 30 ], we did not account for the volume change in AM during lithiation. As the formation of side products and the loss of contact area due to swelling and shrinking of the AM introduces significant uncertainties in the kinetic parameters, therefore we extract parameters from experiments in the pristine state. Assuming lack of porosity of CBD domain is a first approximation, as one knows that CBD can be porous [ 31 ]. All the parameters used in the modeling framework are listed in Table S4 of the Supporting Information.

We describe in this section the charge transport simulations carried out to correlate microstructure

with transport kinetics. The calculations to determine the effective conductivities (δ) and geometric tortuosity (τg) were performed employing the ConductoDict and DiffuDict modules of GeoDict 2023 (Math2Market) [ 32 ], using a standard desktop computer. δ and τg are two chosen parameters to provide a quantitative indication of the effect of calendering degree on the electrode’s electrochemical performance. They are simple observables defined to account for both ionic and electronic properties of the simulated uncalendered and calendered electrodes. The electronic effective conductivity δe was calculated by solving the Poisson equation in the simulation domain, applying a 1 V potential difference between opposite sides along the z direction (perpendicular to the calendering plane). Then, Ohm’s law was used to obtain the δe. The electronic conductivities of the AM and the CBD phases were set to 0.005 S m-1 and 15.93 S m-1 [ 33–35 ], respectively. The τg values were calculated from the determined effective diffusivity according to: τg = (6) where is the volume fraction occupied by the SE and is the effective diffusion coefficient for Li ions in the SE medium. is in turn calculated by solving Fick’s first law in the SE domain, with a concentration difference between the outer xy planes. is obtained from the overall diffusive flux as:

= × (7) Since τg is only a geometrical magnitude, it is independent of the values chosen for and the diffusion coefficient within the SE. The ionic effective conductivity δion can be determined according to the McMullin number [ 36 ] NM:

NM = = (8) with Dbulk and δbulk stand for the bulk electrolyte diffusivity and the bulk ionic conductivity, respectively. The Dbulk was set at 1 m2s-1 and δbulk was provided by the supplier and it is equal to 1.25 mScm-1. All of these input parameters were considered isotropic. Periodic boundary conditions were considered for the outer xz and yz planes.

Simulations were performed within the voltage range of 2.6 – 4.2 V vs. Li+/Li for different C-rates for each degree of calendering. The key findings from the analysis of the simulated discharge curves presented in Figure 3 are as follows. Firstly, the model accurately captures the loss of specific capacity while increasing the C-rate, i.e. the capacity drops from 188.28 mAh.g-1 at C/50 to 62.8 mAh.g-1 at C/5 for the Cal20% case. Furthermore, the specific capacity at a given C-rate is higher for the 35 % case than the 20 % and 0 % ones. This trend is similar to the one found for LIB cathodes by Liu et al. [ 34 ], who demonstrated through modeling that increased calendering reduces interfacial resistance between the CC and CBD, enhancing electronic conductivity and thus leading to better overall cell performance.

Another trend arising from Figure 3e is the difference of specific capacity between the calendering degrees cases tends to shrink by decreasing the C-rates. At low C-rates, the difference between the three cases is minor (Figure 3d). However, at high currents, the effect is relatively prominent (Figure 3a). This observation can be explained by the transition from a kinetically-limited regime at high C-rates to a thermodynamically-dominated regime at lower C-rates, which is a phenomenon well known in Li ASSBs cells [ 37 ] and also, reported by our group in LIBs modeling [ 38 ]. At high C-rates, kinetic factors, such as charge transport limitations, limited active surface area and polarization effects, dominate the electrochemical behavior of the electrode. The pronounced difference in performance between calendering degrees at these rates can be attributed to variations in tortuosity factor and the accessibility of charge transport pathways. This is in line with the findings of Minnmann et al. [ 8 ], who demonstrated by modeling ASSBs electrodes corresponding to different SE particle sizes, that high C-rate performance is constrained by kinetic limitations, including increased resistance in charge transport pathways and decreased interfacial contact between AM and SE. As a result, calendering plays a significant role in eliminating these kinetic bottlenecks. On the other hand, at lower C-rates, the electrode performance is more influenced by thermodynamic factors. The relatively small difference in specific capacity across calendering degrees at low C-rates suggests that kinetic limitations are less critical under these conditions. Instead, microstructural heterogeneities in the electrode become the dominant factor affecting performance.

Figure 4 presents the lithium concentration profiles for the cycled electrodes’ AM at C/50 discharge rate at different cell voltages: 3.9V, 3.65V, and 2.6V, corresponding to the beginning, middle, and end of discharge, respectively. Notably, the cathode with a higher degree of calendering exhibits a relatively uniform AM utilization across the entire composite cathode (Figure 4c). In contrast, the uncalendared electrode in Figure 4a displays localized lithiation, which is due to a reduced number of percolating pathways.

This observation is consistent with the calculated ion-flux distributions for Cal0%, Cal20%, and Cal35% at the end of discharge, as illustrated in Figure 5, which reveal more pronounced regions of high ionic current density. These results indicate that increased bottlenecks (i.e. localized regions where ion or electron movement is significantly restricted) impede ion flow in the uncalendered electrode. These heterogeneities, such as bottlenecks or reaction current localization, affect the overall efficiency of Li-ion (de)intercalation [ 39 ]. Overall, our findings clearly indicated that higher calendering degrees enhance cell performance, as they enable more homogeneous microstructure with improved percolating pathways.

To identify the underlying mechanisms behind the differences in discharge curves and microstructure, we analyzed the key electrochemical kinetics that govern the system. In particular, we focused on the average reaction overpotential on AM-SE reacting interface and the SE potential. The observed decrease in average reaction overpotential (Figure 6a) with increasing degrees of calendering can be attributed to the enhanced contact between the AM and SE particles. The high activation overpotential for the Cal0% electrode, as shown in Figure 6c, highlights the significant voltage loss required to drive the charge transfer process due to slow rection kinetics at the AM-SE interface, either from a high reaction energy barrier or low reaction area [ 39 ]. Cal0% exhibits a much higher activation overpotential ( ) compared to Cal20% and Cal35%, primarily due to the lower active area resulting from calendering. Figure 6d demonstrates that the active area becomes denser and forms more continuous AM-SE contact at higher degrees of calendering. This improvement is a result of the compression applied during the calendering process, which promotes more uniform contact and reduces interfacial resistance that affects reaction kinetics. A better contact reduces energy barriers for charge transfer, allowing for more efficient electrochemical reactions at the AMSE interface. In parallel, the reduction in electrolyte potential with increased calendaring (Figure 6b) is largely the result of decreased ionic resistance within the SE. As calendering improves the packing density of SE particles, the ionic percolation network becomes more continuous, facilitating the movement of ions through the SE phase. This improved ionic conduction within the solid-state matrix is critical for maintaining low overpotentials during discharge and ensuring efficient energy delivery from the cathode.

The enhanced interfacial contact and the improved ionic percolation were found to be the most significant contributors to the variations observed in the discharge profiles, their associated overpotentials, and overall electrochemical performance. A detailed investigation of these factors within the electrode microstructures, prior to cell integration, is provided in the subsequent sections.

To assess how the microstructure influences the kinetics of composite electrodes, we analyzed the interface area, a key descriptor that reflects the distribution of different phases. Specifically, the interface between AM and the SE, referred to as SAM-SE, is of particular importance as it is where lithium-ion transfer occurs. A large interface area is critical for minimizing charge transfer impedance [ 18 ].

As shown in Figure 7a, the specific surface area between AM and SE increases with higher degrees of calendering, with Cal35% exhibiting the largest contact area. Consequently, the pore-coverage of the AM decreases, as SAM-pores reduces from 0.02 m2g⁻¹ for Cal0% to 0.004 m2g⁻¹ for Cal35%, while SAM-SE increases from 0.01 to 0.019 m2g⁻¹. This increase in AM-SE contact is attributed to the pressure applied during the calendering process, which reduces voids between AM particles as already observed in the volume fraction diagram (Figure 2e), resulting in enhanced AM-SE connectivity. The specific surface area of the AM is measured at 0.16 m2g⁻¹ , and the fraction of AM surface covered by SE increases from approximately 10% at Cal0% to nearly 28% at Cal35%. Although, for Cal35%, around 6% of the AM surface is still in contact with pores, 24% with CBD and 42% with other AM particles. These findings suggest that maximizing SAM-SE and minimizing residual porosity are key to fabricating highly compact electrodes with minimal porosity, thereby optimizing the electrochemical performance of calendered electrodes. Which is in line with the findings of Bielefeld et al. [ 17 ], who demonstrated that a cone-like microstructure where the AM and the SE are arranged into conical formations in direct contact, exhibits higher values of active interface area between AM and SE compared to stochastically generated microstructures and experimental outcomes. This enhanced active interface area contributes in a higher amount of electrochemically accessible material which determines the achievable capacity [ 8,16,40 ], thereby improving the overall performance in ASSBs.

In addition, we performed charge transport simulations to assess geometrical descriptors, as described in section 2.3. to further elucidate the relationship between microstructure and transport processes. The geometric ionic tortuosity factor (τg) for the uncalendered microstructure, illustrated in Figure 8a, was approximately 10. This high value indicates a significant degree of complexity in the ionic transport pathways, primarily due to the inhomogeneous distribution of SE particles and the limited number of continuous ionic channels. Such a microstructure presents multiple bottlenecks for ion transport, resulting in a more tortuous path for ionic conduction [ 15,21,41 ], which ultimately impairs the overall ionic mobility and, consequently, the electrochemical performance of the electrode. As the degree of calendering increases, τg is reduced significantly, reaching a value of around 4 in the highly calendered electrodes. This marked decrease in tortuosity reflects the enhanced homogeneity of the SE particle distribution [ 8 ], as well as the creation of more continuous and accessible ionic pathways. These findings are consistent with the homogenized microstructure and lithiation observed in Figure 4, where the distribution of SE and AM particles becomes more uniform, leading to fewer localized bottlenecks in ion flux, as shown in the ion flux distribution in Figure 5.

Compared to the effective ionic conductivity, the effective electronic conductivity shows less dependence on the calendering degree with 0.24 mS cm-1 for the uncalendered electrode and 0.31 mS cm-1 for the Cal35% electrode, in Figure 8b. The observed increase in electronic conductivity with higher calendering degrees can be directly attributed to the improved contact area between the AM and CBD, as illustrated in Figure 7b. This enhancement in contact area facilitates more effective electronic percolation throughout the electrode, ensuring that electrons can traverse the electrode more efficiently. The improvement in microstructural connectivity, ionic and electronic, is essential for optimizing charge transport and thereby the overall performance of the battery system. Our results clearly demonstrate that the combination of poor ionic connectivity and reduced electronic percolation leads to heterogeneous lithiation, as only certain regions of the electrode experience sufficient ionic and electronic flux for full lithiation to occur. This highlights the critical role of microstructural optimization, specifically through calendering, in achieving uniform charge distribution and maximizing electrochemical efficiency.

In this study, we introduce a 4D-resolved computational workflow that, for the first time, simulates the electrochemical performance of ASSB composite electrode microstructures obtained by manufacturing simulations. The model uses a sulfide-type SE, NMC622 as AM, and a blend of carbon and binder.

Our analysis of the electrochemical performance showed that the surface contact area is a key geometric factor in the electrode microstructure. A larger contact area between the AM and SE, resulting from the calendering process, significantly reduces ion flux bottlenecks and minimizes localized ion concentrations. We also quantified the ionic geometrical tortuosity, as well as the electrode’s electronic conductivity, under different calendering conditions. These findings revealed that more compact electrode microstructures, achieved through higher degrees of calendering, shorten the pathways for charge transport, increase the number of conductive paths, and lead to more uniform lithiation throughout the cathode. The improvement of electrochemical performance with calendaring is, thereby, explained by the increasing number of percolating pathways resulted from larger the contact area between AM-SE and AMCBD. Additionally, the heterogeneities in the state of lithiation of AM and bottlenecks in the uncalendered electrode microstructure further confirm the benefits of calendering.

Overall, our results highlight that high calendering degrees are essential for optimizing the contact area between AM and SE, reducing ionic tortuosity, and improving cycling and rate performance of ASSB cells.

Despite the enhancements in overpotential and structural integrity due to calendering, the current method does not achieve the necessary C-rate performance and current density required for industrial applications, particularly under normal usage and fast charging conditions. Specifically, the capacity reaches a maximum of 200 mAh/g at a low C-rate of C/50 but declines significantly at higher C-rates, far below industrial standards. This poor performance can be attributed to the conventional calendering method employed, which involves uniaxial compression. The uniaxial press method compresses the electrode material in a single dimension, resulting in suboptimal tortuosity, even at low porosity levels. Unlike traditional liquid electrolyte batteries, ASSBs do not benefit from the liquid filling the pores, which can mitigate some of the effects of high tortuosity. Therefore, while uniaxial calendering contributes to some degree of improvement, it is evident that it cannot fully meet commercial performance levels. This gap underscores the need for alternative calendering techniques (e.g. isostatic calendering) or innovative electrode fabrication methods that can further optimize the internal structure of ASSB electrodes, ensuring efficient ion transport and meeting the rigorous demands of industrial applications.

Future work will incorporate the volume changes in AM during lithiation to capture the complex interactions between electrochemical and mechanical processes, which are crucial for the overall performance of solid-state batteries. Also, as this work utilized the conventional calendering technique which is uniaxial, our next study will involve the use of isostatic calendering technique to bridge the performance gap in ASSB manufacturing by further optimizing the internal structure of ASSB electrodes, ensuring efficient ion transport and meeting the rigorous demands of industrial applications.