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Tracking variabilities in the simulation of Lithium Ion Battery electrode fabrication and its impact on
electrochemical performance
Alexis Rucci, Alain Ngandjong, Emiliano Primo, Mariem Maiza, Alejandro A.
Franco
To cite this version:
Alexis Rucci, Alain Ngandjong, Emiliano Primo, Mariem Maiza, Alejandro A. Franco. Track- ing variabilities in the simulation of Lithium Ion Battery electrode fabrication and its im- pact on electrochemical performance. Electrochimica Acta, Elsevier, 2019, 312, pp.168-178.
�10.1016/j.electacta.2019.04.110�. �hal-03105053�
1
Tracking Variabilities in the Simulation of Lithium Ion Battery Electrode Fabrication And Its Impact On
Electrochemical Performance
Alexis Rucci,1,2§ Alain C. Ngandjong,1,2§ Emiliano N. Primo, 1,2§ Mariem Maiza1,2 and Alejandro A. Franco1,2,3,4,*
1 Laboratoire de Réactivité et Chimie des Solides (LRCS), UMR CNRS 7314, Université de Picardie Jules Verne, HUB de l’Energie, 15 rue Baudelocque, 80039 Amiens, France.
2 Réseau sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, HUB de l’Energie, 15 rue Baudelocque, 80039 Amiens, France
3 ALISTORE-European Research Institute, FR CNRS 3104, HUB de l’Energie, 15 rue Baudelocque, 80039 Amiens, France.
4 Institut Universitaire de France, 103 boulevard Saint Michel, 75005 Paris, France.
§All these authors have equally contributed.
*corresponding author: [email protected]
2 Abstract
In this paper we report a comprehensive analysis and tracking of the variabilities associated to multiscale simulations coupling a Coarse Gained Molecular Dynamics (CGMD) model of Lithium Ion Battery electrodes fabrication with a 3D-resolved performance model at the cell scale. We quantify the impact on the final electrode structure of the initial conditions in the CGMD simulations in terms of initial random distribution in the slurry of the active material and carbon binder domain particles (CBD). This study is carried out with a batch of simulations at different slurry active material/CBD compositions. Results show that for each electrode composition there is a statistical dispersion in the predicted cell performance curves, in agreement with in house experimental results. Furthermore, in house experiments revealed a different correlation regime depending on the C-rate at which the cathode is operating. The proposed methodology and findings allows us to pave the way towards the design of reliable approaches to control the variables correlations in the multiscale modeling of electrodes fabrication and its impact on LIB performance.
Keywords
Multiscale simulation, electrochemical performance, NMC cathodes, uncertainty tracking, coarse- grained molecular dynamics
3 1. Introduction
Climate change, fossil fuels limitations and the exponential deployment of nomad technologies are driving a paradigm shift in the way the human civilization transforms and store energy. Because of their high energy density and long service life, Lithium Ion Batteries (LIB) play an important role in such a transformation.
Practical properties of LIB, namely their energy density, recharge time, durability and safety depends, among others, on the negative and positive electrode mesostructure (i.e. at the scales of 0.1 – 50 µm). The latter is characterized by the spatial location of the active material (AM) particles, carbon additive aggregates and binder constituting the composite electrode, which is strongly determined by the fabrication process parameters.[1–4] State-of-the-art mathematical modeling plays an important role in the understanding of the operation principles of composite electrodes. Many of the reported LIB models so far have attempted to track the impact of the electrode mesostructure on the cell response, following 1D, P2D or even 3D-resolved approaches, for different active material chemistries such as graphite, LiFePO4, LiCoO2 and LiNixMnyCozO2
.[5–7]
Even if performance models have already been successfully applied in a variety of studies, including cell design,[8,9] it is important to emphasize that a lack of precise knowledge of the model parameters can lead to a significant reduction of their prediction capability.[10]
Experimental measurements [11] and microscopic simulations [12] have demonstrated that the effective diffusivity and conductivity of the electrodes can deviate significantly from their homogenized approximations, underscoring the need for higher fidelity models to address this discrepancy. Similarly, the electrochemical reaction rate at the active material/electrolyte interface has been found to vary significantly with the local mesostructure.[13]
4 Therefore, it is clear that the development of an appropriate mesostructural picture for the electrodes is crucial for the correct analysis and evaluation of the influence of the electrode materials on the overall cell performance. In particular, this is urgently needed if one desires to boost the penetration of new high energy density chemistries in current LIB, such as silicon and Li-rich materials.[14] Significant efforts have been carried out in the recent years regarding this as the improvement in imaging techniques (such as FIB-SEM, micro and nano-CT) allows reconstructing the real composite electrode microstructures and injecting them into cell performance models. However, there are some limitations at the time of considering the simulation geometry, mainly because of the significant differences in the length scales together with the sensibility of the cell performance with the quality of segmentation and image resolution, being necessary to simplify some features of the composite electrode.[15,16] On the other hand, in silico generated structures are also an alternative technique for the development of the mesostructure full picture. Coming from averaged properties of electrode samples, as pore size distribution, particle size distribution, etc., active material elements are located randomly in a volume. Regarding CBD consideration, most of the current models use simplified approaches, such as considering only the active material phase or by a random distribution as a continuum media over the active material particles.[7,17–21]
The understanding of the fundamentals of the electrodes morphogenesis (self-organization) along the fabrication process is another way to rationalize the electrode mesostructure. The subjacent challenge links to the rheology of the slurries which depends on the chemistry of the mixed materials. This chemistry governs the interplays between attractive van der Waals forces, repulsive and attractive electrostatic forces, steric interactions, hydrodynamic interactions and Brownian forces among the suspension particles. In a previous paper [22] we have presented a
5 first version of a multiscale modeling platform allowing to link the simulation of the fabrication process with the evaluation of the cell performance, showing the importance of particle assembly during battery electrode fabrication and studying its effect on battery performance. Such a platform combines Coarse Grained Molecular Dynamics (CGMD) with a 3D-resolved performance model.
In that work we showed the effect in the discharging process due to changes of electrode formulation, exploring three cases: 85-15, 90-10 and 95-5 mass ratios of AM and carbon−binder domains (CBD). That work constituted the first step towards a most evolved simulation platform able to predict the fabrication/performance link for LIB. Still, an exhaustive optimization is needed, including the identification, quantification and tracking of the involved uncertainties in all the steps of the associated simulation workflow.
In general, computational models involve a list of parameters capturing geometrical or electrochemical properties, such as porosity, particle size distribution, conductivities, diffusion coefficients, etc. All of them are estimated by computational techniques or experimental measurements with their associated uncertainties.[4,23] The complexity of the problem increases if we consider multiscale models. In a multiscale study, small variabilities in one scale can result in very significant changes in another one. In view of this, it is of crucial importance to implement a simulation strategy to quantify and analyze the uncertainties in the computational workflow for the consolidation and reliable utilization of the multiscale modelling platform.[24,25]
In this work we track and carry out a comprehensive analysis of the uncertainties in the multiscale simulation of the LIB positive electrode fabrication process and its impact on the electrochemical performance at the cell scale. As our multiscale framework combines discrete and continuum simulations, it is important to investigate how electrode configuration variability (coming from slurry equilibration and subsequent evaporation through CGMD simulations)
6 propagates because the 3D-resolved performance model outcome depends on the location of the particles. The goal is focused in the quantification of the influence of random variabilities of the active material distribution during the simulation of the fabrication process and how this effect is propagated towards the final cell performance. For this purpose, correlations were made between several parameters and the electrochemical output of the cathodes. This methodology was compared with experimental results carried out in similar conditions, for obtaining common points and further insights to be taken into account by our platform.
2. Simulation methodology
2.1. Coarse-Grained Molecular Dynamics
As we pointed out in one of our previous publication [22] Molecular Dynamics (MD) is a relevant technique to simulate electrode self-organization along the fabrication process, from its inherent discrete character. Nevertheless, the computational cost would be too high if all the electrode components (AM, carbon black, binder and solvent) are explicitly considered in a MD model. For example, binder and solvent molecules are less than 1 nm, carbon back size is 50-100 nm, and the diameter of active material particles is 1-15 µm. Considering only carbon black and active material particles in the model, it is estimated that at least 106 particles would be needed to simulate an electrode with thickness ~50 µm. This would require at least one month of computing time for one simulation. To minimize the computational cost, each AM particle is represented with a sphere with a Gaussian size distribution and the mixture of solvent, binder and carbon are reduced into a micrometric sized CBD particle (fist panel of Figure 1), rendering a Coarse-Grained (CG) model.
7
[Please add here Figure 1]
In order to study the impact of the variability in the electrode structure on the electrochemical performance at the cell level, ten different initial configurations were generated by changing only the random seed number for each of the three compositions of AM and CBD, namely 85-15, 90-10 and 95-5 mass ratios. For the three compositions, the same amount of AM particles was used and, for meeting the required mass fractions, different amounts for CBD beads were added.
[Please add here Figure 2]
The equilibration is driven by interaction potentials between the particles in the system.
The two interaction potentials, Lennard-Jones potential shifted (LJ/SF) and Granular Hertzian potential which are implemented in the last version of LAMMPS simulation package [26] are used to describe the solid and solvent behavior respectively. During evaporation, the CBD particles are allowed to shrink in size with a consequent modification in their interaction potential that encourages CBD to adsorb more strongly on AM. The size of CBD particles before and after the evaporation have been parametrized for this system to reproduce experimental properties such as viscosity of the slurry and the mechanical properties of the composite electrode.[27] Figure 2 displays representative structures for the electrodes at the three compositions (all of them are presented in Figure S1 in the Supplementary Information).
The CGMD simulation of the complete slurry/electrode fabrication procedure is as follows:
(1) For each of the ten structures and for each composition, particles are randomly generated using different random seed numbers in a relatively large box size (Lx = 900 µm, Ly =
8 900 µm, Lz =3600 µm), ensuring the overlapping between particles. Motion of the particles with initial velocities that correspond to the temperature of 300 K;
(2) NPT simulation is performed at 1 bar pressure and 300 K. The elongated box starts adjusting its size to reach the set up pressure. After 8 x107 time steps, an equilibrated structure is reached representing a well-mixed slurry;
(3) Change the diameter of CBD particles from liquid to solid value, which allows the simulation box to shrink. This process mimics the drying of the slurry when the solvent evaporates.
An equilibrated structure representing the dry electrode is generated.
2.2. Continuum modeling
The 3D electrode structures obtained by CGMD were exported into a stereo lithography mesh using the freeware Blender.[28] Then all these structures were imported into COMSOL™
Multiphysics 5.3. [29]
The governing equations constitute an extension of the original 1D model proposed by Newman and co-workers.[30–32] The model consists on a set of equations describing the mass and charge transport both in the solid part and in the electrolyte. The main difference between the pseudo-2D model and a 3D one lies in the fact that in an averaged approach the flux between the solid-electrolyte interfaces is represented by a source term. However, in a 3D-resolved model, each phase is assigned to a specific voxel, whereby the de-/intercalation process at the active material- electrolyte is modeled as an interfacial flux.[33–35] The exchange current between both phases is described by the Butler-Volmer equation. At the cathode current collector, no-flux boundary conditions were considered. The mathematical equations in the model capturing the relevant physics for the calculation of the electrochemical performance are summarized in Table 1 and a
9 scheme of the system is presented in Figure 3. The values of each parameter are listed in Table S1, in the Supplementary Information.
[Please add here Figure 3]
Unlike the implicit consideration in the classical pseudo-2D models, our framework considers AM particles that are isolated from other particles but electronically connected by conductive carbon as in real LIB composite electrodes. In our continuum MD simulation, CBD particles are explicitly considered, although they require a tremendous computational effort due to their small size and great number particles (top panel of Figure 1). In the discrete electrochemical calculation (bottom panel of Figure 1), the condition of explicitly calculating the electronic conduction through the actual CBD particles is relaxed. Instead, all the volume surrounding the AM is effectively divided into domains of ionic and electronic conductivity based on inputs from the CGMD model considering an independent volume fraction for void and CBD, respectively. In this case, we implemented a hybrid approach using a mesostructured resolved model for the AM/electrolyte interface and an averaged model with effective parameters for the CBD/electrolyte interface (the equations for this interface can be found in Table 1). [22]
Table 1. Flow equations and boundary conditions for the different domains in the 3D simulation model and the geometrical definitions. Nomenclature can be found in the Supplementary Information.
Lithium foil electrode Lithium foil current
𝐼𝑎𝑝𝑝 = 𝐹𝜀𝑠𝑘𝐿𝑖0𝐶𝑒1−𝛽𝐿𝑖[𝑒𝑥𝑝 ((1−𝛽𝑅𝑇𝐿𝑖)𝐹(𝐿𝑖−𝑒))
− 𝑒𝑥𝑝 (−𝛽𝑅𝑇𝐿𝑖𝐹(𝐿𝑖−𝑒))]
Electrolyte-lithium foil
boundary conditions 𝐷𝑐𝑒𝑓𝑓𝛻𝐶𝑒 = −𝐼𝑎𝑝𝑝(1 − 𝑡+0) 𝐹
𝑒 = 0 Active material
10
Material balance 𝜕𝐶𝑠
𝜕𝑡 = −𝛻(−𝐷 𝛻𝐶𝑠) Butler-Volmer equation
𝐽𝐿𝑖 = 𝑖0[𝑒𝑥𝑝((1−𝛽)𝐹𝑅𝑇 )−𝑒𝑥𝑝(−𝛽𝐹 𝑅𝑇)] 𝑖0 = 𝑖00𝐶𝑒𝛼𝐶𝑠𝛼(𝐶𝑠𝑚𝑎𝑥− 𝐶𝑠) 1−𝛼
= 𝑠−𝑒− 𝑈 Particle-electrolyte
boundary conditions 𝐷𝜕𝐶𝑠
𝜕𝑟 = −𝐽𝐿𝑖 𝐹 Particle-current collector
boundary condition 𝜎𝑒𝑓𝑓𝛻𝑠 = 𝐽𝑐𝑒𝑙𝑙
= 𝑠−𝑒− 𝑈 Electrolyte
Material Balance 𝜕(𝜀𝑖𝐶𝑒)
𝜕𝑡 = −𝛻 (−𝐷𝑒𝑒𝑓𝑓𝛻𝐶𝑒+𝑡+0𝐽𝑒 𝐹 ) 𝐷𝑒𝑒𝑓𝑓 = 𝐷𝑒𝜀𝑖𝑝
Charge Balance 𝛻 ∙ 𝐽𝑒 = 0
𝐽𝑒 = −𝑘𝑒𝛻𝑒 − 𝑘𝐷𝛻𝑙𝑛 𝑐𝑒
𝑘𝐷 =2𝑅𝑇𝑘𝑒𝑒𝑓𝑓
𝐹 (𝑡+0 − 1) (1 +𝑑 𝑙𝑛 𝑓± 𝑑 𝑙𝑛 𝐶𝑒) 𝑘𝑒𝑒𝑓𝑓 = 𝑘𝑒𝜀𝑖𝑝
Electrolyte-current colector boundary conditions
𝐷𝑒𝑒𝑓𝑓𝛻𝐶𝑒=0
𝛻𝑒 = 0 Carbon and binder domains
Charge balance 𝛻 ∙ 𝐽𝑠 = 0
𝐽𝑠 = 𝜎𝑒𝑓𝑓𝛻𝑠 𝜎𝑒𝑓𝑓 = 𝜎𝜀𝐶𝐵𝐷 Geometrical definitions
11 Volume definitions 𝑉𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 = 𝑉𝐴𝑀+ 𝑉𝐶𝐵𝐷+ 𝑉𝑝𝑜𝑟𝑒𝑠
𝑉𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 = 𝑉𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒− 𝑉𝐴𝑀 = 𝑉𝐶𝐵𝐷+ 𝑉𝑝𝑜𝑟𝑒𝑠 Fraction of CBD
𝜀𝐶𝐵𝐷 = 𝑉𝐶𝐵𝐷 𝑉𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 Fraction of electrolyte
𝜀𝑒 = 𝑉𝑝𝑜𝑟𝑒𝑠 𝑉𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒
12 3. Experimental
3.1 Materials and chemicals
LiNi1/3Mn1/3Co1/3O2 (NMC) was supplied from Umicore. TIMCAL Super C65 was from IMERYS. Solef® Polyvinylidene fluoride (PVdF) was purchased from Solvay and N- methylpyrrolidone (NMP), from BASF. LP30 electrolyte, consisting in 1 M LiPF6 salt in EC:DMC (1:1 vol.%), was from Solvionic. All other reagents were battery-grade and were used without further purification.
3.2 Slurry preparation and electrochemical measurements
The slurry was made by mixing NMC and C65 powders with a pre-dissolved PVdF 6.5 wt% solution, prepared in NMP. Extra NMP was added until reaching the desired solid-to-liquid mass ratio (see Table 2). The mixture was performed in a Dispermat CV3-PLUS high-shear mixer for 2 h in a water-bath cooled recipient at 25 ºC. The slurry was coated over a 22 m thick Aluminum current collector using a comma-coater prototype-grade machine. The electrodes were calendared to match the porosities resulting from the simulations.
All electrochemical tests were performed in 2035 coin cells assembled in a dry room (H2O
<15 ppm). NMC cathodes were punched into 13 mm electrodes and were assembled into the coin cells using Celgard 2500 as separator and Li metal foil as counter-electrode. The charge-discharge experiments were performed with a BCS-805 battery cycler (BioLogic, Seyssinet-Pariset, France).
Table 2. Slurries properties
Electrode NMC wt% C65 wt% PVdF wt% Solid-to-
Liquid ratio
Slurry density/g cm-3
NMC85 85 9 6 46% 1.55 0.05
NMC90 90 6 4 55% 1.73 0.05
13
NMC95 95 3 2 67% 2.11 0.06
4. Results and Discussion 4.1. CGMD Simulations
[Please add here Figure 4]
For each composition, all the initial conditions in the fabrication process remains the same, changing only the initial random seed for generating the slurries. This change will give in each simulation a different location for the AM and CBD particles, resulting in a slightly change in the box dimensions. Table S2 (in Supplementary Information) presents, for each simulation, the volume of the equilibrated simulations box and its average. As the relative quantity of CBD increases, so does the size of the simulation box given that the amount of AM particles is constant for the three compositions.
[Please add here Figure 5]
The electrodes’ final state was further characterized in terms of its porosity and density of active material, as shown in panels A and B of Figure 4 respectively. The porosity increases with the proportion of AM, which comes from the different packing densities at each composition. By increasing the amount of smaller size CBD when going from 95-5 to 85-15, the particles accommodate in a more compact way. As expected, the AM density follows the order 95-5 > 90- 10 > 85-15: lower quantities of CBD render in smaller simulation box volumes. It can be seen that for each AM-CBD proportion both observables vary within a certain range. For understanding the origin of this variation, panels C and D of Figure 4 display the correlation plots between the porosity/density of AM and the corresponding volume of the simulation box for each equilibrated
14 structure. In all cases the coefficients show an excellent correlation between both variables indicating that the origin of the variance is due to the different arrangements of the AM and CBD particles in the equilibrated electrode state, which consequently affects the final volume of the simulation box.
Once obtained the equilibrated electrode mesostructures, the electrochemical simulation of the cathodes performance was carried out. For importing the electrodes morphology into COMSOL™ Multiphysics software to solve the Newman model’s equations, a previous meshing step is required for defining surfaces, interfaces and AM particles’ positions. Therefore, the meshing could add some additional uncertainty factor to the simulation as a coarsening of the structure may affect the resolution of the electrode. In order to avoid this, simulations for different mesh sizes were made. An example of this study is shown in Figure 5 for the 85-15 composition.
It is important to remark that as the mesh becomes finer, the computational cost increases significantly, from few hours for coarser mesh to about 3 days for a fine mesh, using an Intel® Core™ i7-6700 CPU @ 3.4 GHz with 32 GB of RAM. As we can see, for normal and fine meshes there are no significant changes in the final cell performances. In this work, for all the simulations a normal mesh was considered, with minimum and maximum mesh lengths of 1.1 µm and 6.2 µm respectively in order to achieve a compromise between the resolution of the electrode and the computational simulation time. An average amount of 11×104, 10×104 and 9×104 mesh elements were reached for the compositions 85-15, 90-10 and 95-5 respectively with the considered mesh size. The discharge profiles in Figure 5 show an inflection point at the end of discharge, rather than a smooth potential fall. This behavior is due to the reduced number of points used in the open- circuit voltage (OCV) mathematical expression for a high gradient region, from which it comes the observed behavior in the performance simulations (Figure S2).
15
[Please add here Figure 6]
Figure 6 A depicts the discharge profiles at C rate for the three studied compositions: 85- 15, 90-10 and 95-5 rates of AM-CBD. Shaded areas around the mean specific capacity represent the standard deviation intervals. Once the final equilibrated electrodes were obtained, each generated electrode had different particle spatial arrangement, with characteristic effective geometrical properties (such as porosity, thickness, etc.). Considering the used mathematical model showed in Table 1, the solid phase lithium concentration (and, in consequence, the exchange current and electric potential) depends on the AM spatial distribution, thus the electrochemical response will reflect all these differences as a statistical dispersion. The simulation box in each case implemented in COMSOL was bigger than the simulation box used for the CGMD simulations with the purpose to include the whole AM particles, preserving the trend observed in Figure 4 C. Simulation box volumes were compared with the obtained specific capacity (Figure 6 B). In this analysis, it was observed that specific capacity increased with the increasing box volume and, in consequence, with the increasing porosity or decreasing density. For each composition, the ratio between AM/CBD remained constant, whereby as the porosity/simulation box volume increases, the transport limitation diminishes resulting in a higher specific capacity at the end of discharge taking into account the high C-rate regime in which we are performing the simulations.[15,36,37] The results here presented are quite interesting, as uncertainty quantification coming from purely stochastic origin is rarely accounted in simulation studies.[2,5] It is also interesting to note how the sensitivity of the specific capacity towards the simulation box volume (and consequently, to the porosity and density of AM) is different depending on the composition of the cathode.
16 4.2. Experimental results
[Please add here Figure 7]
[Please add here Figure 8]
Figure 7 depicts the SEM cross-sectional images of the experimental NMC 85-15 (A), 90- 10 (B) and 95-5 (C) cathodes. The size of CBD phase surrounding the NMC particles decrease from A to C, as expected, but a careful inspection of the images reveals that for low NMC content the distribution of CBD is less homogeneous. One of the main reasons behind this is that the higher the amount of C65 conductive additive the higher the viscosity of the slurry (Figure S4 in Supplementary Information). High values of viscosity make less efficient the process of mixing of the solid materials with the binder solution and the coating of the resulting slurry at the current collector.[38]
[Please add here Figure 9]
In a similar way to the study performed for the simulated electrodes, Figure 8 A and B presents the porosity and density of AM (respectively) for the ten different performed electrochemical test for each composition. As stated in section 3.2 the thicknesses of the electrodes were adjusted through calendaring for matching the porosity values obtained through the CGMD simulation. The increase of NMC amount through the reduction of CBD within the slurry leads to the increase of the density of active material (Figure 8 B). Unlike the simulation results in Figure 4 C and D, the plots from panels C and D of Figure 8 evidence that no obvious correlation can be found between both of the variables and the electrode volume (all the correlation coefficients are lower than 0.5 in all cases). In the simulations, the mass of NMC is constant throughout all the 30
17 structures, while in the experimental results this variable changes slightly from one electrode to the other (in the three compositions) due to unavoidable heterogeneities during the coating and calendering process. If the porosity and density are plotted against both the electrode volume and the AM mass loading (panels A and B of Figure 9, respectively) an excellent correlation can be found between the variables (in the Supplementary Information there is a section explaining the calculation of correlation coefficients for two and three variable sets). In the case of the porosity, in the three compositions, it increases with higher electrode volume and lower AM mass loading, while the density logically increases in the other sense.
[Please add here Figure 10]
The average charge-discharge curves for the different NMC-C-PVdF compositions are presented in Figure 10 A. The galvanostatic experiments were performed at C rate, which corresponds to currents of 3.0, 4.5 and 6.8 mA cm-2 for NMC 85%, 90% and 95% respectively.
The same trend can be seen as in the case of simulations, i.e. when reducing the amount of CBD (and increasing therefore NMC) there is a decrease in the specific capacity. Nonetheless, a careful comparison reveals differences in terms of the absolute values of specific capacities, potential plateaus and shape of the curves. Average specific capacities for experimental NMC cathodes are (131 5), (119 6) and (75 7) mAh g-1 whereas for the simulated they are (126 5), (94 2) and (71 3) mAh g-1. While all the simulated curves have an initial potential of 4.5 V, the experimental ones show initial potentials equal to (4.2 0.1), (4.11 0.07) and (3.9 0.1) V for NMC 85%, 90% and 95% respectively. Furthermore, the shape of the curves looks less plateau- like and displays a sharper decrease in potential as discharge proceeds, especially in high NMC content conditions. These differences are linked with the general assumptions made in our 3D-
18 resolved performance model, namely, potential independent solid-state diffusion coefficient, simplified micro/mesoporosity effects (i.e. porosity is only considered as a volume fraction occupied by the electrolyte or CBD within the void of AM particles) [39] and the consideration of a single OCV curve for all the compositions.[6,22,40–42] In addition, as CBD phase is not explicitly imported in the electrochemical model there is no effect accounted for the heterogeneous distribution of the conductive carbon phase. This is of paramount importance specially in NMC 90% and 95% electrodes, in which the difference in shape and global specific capacity is the greatest with the simulated curve. The model limitations hereby described will be overcome in a future version of our multiscale computational platform, where we will consider explicitly the CBD location within the performance simulator.
All of these comes from the fact that at high C-rate the limited Li+ diffusion kinetics in the electrolyte (relative to the one of Li+ reduction in the NMC particles) leads to a depletion of Li+ at the former causing a significant overpotential. In this regime, rate performance is controlled by Li+ diffusion resistance within the electrolyte in the porous electrode structure.[36,43–46] The discharge profiles performed at C/10 rate (depicted in Figure S6, in the Supplementary Information) show almost identical specific capacity and a reduced standard deviation for the three essayed cathode compositions. For all the above, at this C-rate, small changes of the porosity/density/morphology of the electrodes originate major differences in the electrochemical output.
[Please add here Figure 11]
Figure 10 B displays the 2D correlation plot between the capacity and the electrode volume and AM mass loading. As we showed in Figure 9, the experimental results are a function also of
19 the AM mass loading therefore the correlation must be done against two variables sets. Taking into account that for obtaining the specific capacity we divide the capacity by the mass of AM and we remove its dependency with this extensive variable, the capacity is more suited for the analysis we want to perform. For illustrative purposes, the reader is referred to Figure S7 to verify the specific capacity correlation plot. In the case of capacity, the correspondence is lower than in the case of the simulated results and, interestingly, the correlation is the lowest for the NMC 95%
electrode. On the contrary, the magnitude of the correlation coefficients for the capacity of the three different AM-CBD compositions at C/5 and C/10 rate (Figure 11 A and B) is higher as the rate increases and in the latter, all the values are above 0.9. Therefore, the correspondence of the three variable sets increases by decreasing the C-rate. This rate-dependent correlation is related to the regimes in which thermodynamic and kinetic factors play a major role.[47] At low C-rates, the correlation is with thermodynamic effects entirely depending on the nature of the AM and CBD.[48] In this sense, as both of them do not change it is expected that the variability comes from the small changes in the mass of AM and the electrode volume from one experiment to the other. At high C-rates, kinetic effects are the relevant factors and are related to electrode processing dispersion leading to variations in the AM/CBD content heterogeneities or grain/pore size distribution in the electrodes. This variability is expected to depend on polarization resistances, effective solid or electrolyte phase conductivities, amongst others.[47] It is not surprising then that for NMC 95% at C rate, the lowest correlation between the two variable sets is found: kinetic control in the variability should be more important for the electrodes with the lowest amount of conducting CBD.
Battery production is characterized by a highly complex process chain and a large number of interactions between individual process steps, i.e., variation of a single process parameter can
20 cause a variety of other parameters to change.[49–51] Each step of fabrication can affect it its own way to the same system property, with whom the whole collection of them will define a single electrode state which will give a unique electrochemical response. An excellent discussion around this issue has been made recently by Thomitzek et al.[49]
The above discussion is in good agreement with the previous differences we found between the simulated and experimental curves. Kinetic effects have great impact in high C-rate regime, which in time produces a change in the variability dependence of the experimental results. In the simulated electrochemical performance, this variability can still be explained by electrode volume changes as the kinetic effects are not fully accounted in our model. As a final remark, we would like to stress that current available 3D electrode micro/mesostructure generators (such as GEODICT® [52]) rely on random location algorithm for placing the particles and performance models using the resulting electrode micro/mesostrucures consider AM and CBD as a single phase.[6] In our multiscale computational framework combining CGMD and 3D-resolved model, the final electrode mesostructure depends on the physics of interaction between the particles and adjustable parameters for each process during the fabrication (drying time, calendaring, etc.). As we demonstrated, electrochemical response is sensitive to the localization of the particles and therefore the position of them must be determined by the nature of the material and the slurry preparation conditions.
5. Conclusions
In the present work, a variability analysis was carried on in order to study the influence on the electrochemical response of the spatial distribution of AM for equilibrated electrodes after the simulation of their fabrication process using a CGMD model. Several samples of NMC electrodes
21 were generated for three AM/CBD ratios, i.e. 85-15, 90-10 and 95-5, and their electrochemical performance was evaluated during the discharge process at C rate using a 3D-resolved Newman performance model. Considering the same initial conditions both for fabrication simulation and cell performance modeling in each composition, significant discrepancies for each generated electrode were observed in the galvanostatic discharge profiles. Changes in the spatial arrangement of the AM and CBD are generated merely due to the different random seeds used for origination such structures, deriving in slightly different structures with distinctive properties such as porosity, density and volume. An excellent correlation was found between the observed electrochemical performance differences and the volume of each final equilibrated state. From the experimental point of view, the galvanostatic profiles presented an expected dispersion, which correlated both with the variability in the electrode volume and the AM mass loading at low C-rates. At high C- rate regime the correlation coefficients magnitude was lower as the main cause in the variability is related to AM/CBD heterogeneities and grain/pore size distribution.
The results obtained were also useful for setting the limitations of our multiscale computational workflow combining CGMD and continuum simulations, in order to take them into account in a future version of it. Nevertheless, and considering the level of approximations we made in the 3D-resolved electrochemical model, the trends and overall specific capacity values between simulated and experimental results are very good.
Conflict of interest
The authors declare no conflict of interests.
Acknowledgements
22 The authors deeply acknowledge Dr. Mathieu Morcrette and Sebastien Cavalaglio (LRCS) for helpful discussions. The authors acknowledge the European Union’s Horizon 2020 research and innovation programme for the funding support through the European Research Council (grant agreement 772873, “ARTISTIC” project) and for the funding support of A.R. postdoctoral position through the project POROUS4APP (grant agreement 686163). A.R. acknowledges Universidad Nacional del Sur, Argentina, for the leave in his teaching position. A.A.F. acknowledges Institut Universitaire de France for the support. The CGMD results presented here were obtained using the dedicated ARTISTIC project computational resources installed within the MatriCS platform at the Université de Picardie-Jules Verne. The authors thankfully acknowledge Umicore for providing the NMC active material for the experiments performed in this work. A.A.F.
acknowledges SAFT Batteries and FEDER for the partial funding support of Mariem Maiza’s PhD thesis.
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27 Figure 1. Overall computational workflow of the electrode manufacturing
simulation/electrochemical performance calculation
28 Figure 2. Representative equilibrated electrode structures for the three different AM-CBD compositions.
Figure 3. Scheme of the cell arrangement used for the 3D-Newman electrochemical performance simulation. Symbols are the same as in Table 1.
29 Figure 4. Top row: electrode porosity (A) and AM density (B) for three different compositions (85-15, 90-10, and 95-5). For each composition ten simulations were performed. Bottom row:
correlation plots between the porosity (C) and AM density (D) and the MD simulation box volume.
The correlation coefficients for each variable and composition are informed next to each linear fit (for further information regarding the calculation of the coefficients, see the Supplementary Information). Square, triangle and circle represent respectively the 85-15, 90-10 and 95-5 compositions.
30 Figure 5. Cell voltage vs. specific capacity calculated for the 85-15 composition. In this study four different volumetric mesh resolutions were considered and are shown in the upper part of the figure.
Figure 6. (A) Simulated average discharge profiles at C rate for 85-15 (green), 90-10 (blue) and 95-5 (red) electrodes. The shaded area represents the standard deviation of each average curve.
The raw profiles can be found in Figure S3. (B) Correlations between the COMSOL™ simulation box volume and the specific capacities obtained for each simulation at the end of discharge. The numbers next to each fit represent the correlation coefficients (for further information regarding the calculation of the coefficients, see the Supplementary Information).
31 Figure 7. Representative SEM cross-sectional images for NMC-C-PVdF cathodes: 85-9-6 (A), 90- 6-4 (B) and 95-3-2 (C).
Figure 8. Top row: porosity (A) and density of NMC particles (B) as a function of the number of experiments carried out through the three NMC/CBD compositions. Bottom row: correlation plots between the porosity (C) and AM density (D) and the electrode volume (coming from each average thickness). The correlation coefficients for each variable and composition are informed next to each liner fit (for further information regarding the calculation of the coefficients, see the Supplementary Information). Square, triangle and circle represent respectively the 85-15, 90-10 and 95-5 compositions.
32 Figure 9. 2D correlation plots for porosity (A) and density of NMC (B) as a function of the AM mass loading and electrode volume. Each set of values for the three compositions has its color scale displayed at the right part of the heat maps. The multiple correlation coefficients are displayed next to each surface (for further information regarding the calculation of the coefficients, see the Supplementary Information).
Figure 10. (A) Average discharge galvanostatic profile at C rate for NMC 85 (green), 90 (blue) and 95 (red) electrodes. The shaded area represents the standard deviation interval of each average curve. The raw profiles can be found in Figure S5. (B) 2D correlation plots for the capacity at C rate as a function of the AM mass loading and electrode volume. Each set of values for the three compositions has its color scale displayed at the right part of the heat maps. The multiple correlation coefficients are displayed next to each surface (for further information regarding the calculation of the coefficients, see the Supplementary Information).
33 Figure 11. 2D correlation plots for the capacity at C/5 (A) and C/10 (B) rates as a function of the AM mass loading and electrode volume. Each set of values for the three compositions has its color scale displayed at the right part of the heat maps. The multiple correlation coefficients are displayed next to each surface (for further information regarding the calculation of the coefficients, see the Supplementary Information).
34 Graphical Abstract
