Typical lithium-ion battery electrodes are porous composites comprised of active material, conductive additives, and polymeric binder, with liquid electrolyte filling the pores. The mesoscale morphology of these constituent phases has a significant impact on both electrochemical reactions and transport across the electrode, which can ultimately limit macroscale battery performance. We reconstruct published X-ray computed tomography (XCT) data from a NMC333 cathode to study mesoscale electrode behavior on an as-manufactured electrode geometry. We present and compare two distinct models that computationally generate a composite binder domain (CBD) phase that represents both the polymeric binder and conductive additives. We compare the effect of the resulting CBD morphologies on electrochemically active area, pore phase tortuosity, and effective electrical conductivity. Both dense and nanoporous CBD are considered, and we observe that acknowledging CBD nanoporosity significantly increases effective electrical conductivity by up to an order of magnitude. Properties are compared to published measurements as well as to approximate values often used in homogenized battery-scale models. All reconstructions exhibit less than 20% of the standard electrochemically active area approximation. Order of magnitude discrepancies are observed between two popular transport simulation numerical schemes (finite element method and finite volume method), highlighting the importance of careful numerical verification.

Lithium-ion battery electrodes are composed of active material particles, binder, and conductive additives that form an electrolytefilled porous particle composite. The mesoscale (particle-scale) interplay of electrochemistry, mechanical deformation, and transport through this tortuous multi-component network dictates the performance of a battery at the cell-level. Effective electrode properties connect mesoscale phenomena with computationally feasible battery-scale simulations. We utilize published tomography data to reconstruct a large subsection (1000+ particles) of an NMC333 cathode into a computational mesh and extract electrode-scale effective properties from finite element continuum-scale simulations. We present a novel method to preferentially place a composite binder phase throughout the mesostructure, a necessary approach due difficulty distinguishing between non-active phases in tomographic data. We compare stress generation and effective thermal, electrical, and ionic conductivities across several binder placement approaches. Isotropic lithiation-dependent mechanical swelling of the NMC particles and the consideration of strain-dependent composite binder conductivity significantly impact the resulting effective property trends and stresses generated. Our results suggest that composite binder location significantly affects mesoscale behavior, indicating that a binder coating on active particles is not sufficient and that more accurate approaches should be used when calculating effective properties that will inform battery-scale models in this inherently multi-scale battery simulation challenge.

Battery electrodes are composed of polydisperse particles and a porous, composite binder domain. These materials are arranged into a complex mesostructure whose morphology impacts both electrochemical performance and mechanical response. We present image-based, particle-resolved, mesoscale finite element model simulations of coupled electrochemical-mechanical performance on a representative NMC electrode domain. Beyond predicting macroscale quantities such as half-cell voltage and evolving electrical conductivity, studying behaviors on a per-particle and per-surface basis enables performance and material design insights previously unachievable. Voltage losses are primarily attributable to a complex interplay between interfacial charge transfer kinetics, lithium diffusion, and, locally, electrical conductivity. Mesoscale heterogeneities arise from particle polydispersity and lead to material underutilization at high current densities. Particle-particle contacts, however, reduce heterogeneities by enabling lithium diffusion between connected particle groups. While the porous composite binder domain (CBD) may have slower ionic transport and less available area for electrochemical reactions, its high electrical conductivity makes it the preferred reaction site late in electrode discharge. Mesoscale results are favorably compared to both experimental data and macrohomogeneous models. This work enables improvements in materials design by providing a tool for optimization of particle sizes, CBD morphology, and manufacturing conditions.

Macrohomogeneous battery models are widely used to predict battery performance, necessarily relying on effective electrode properties, such as specific surface area, tortuosity, and electrical conductivity. While these properties are typically estimated using ideal effective medium theories, in practice they exhibit highly non-ideal behaviors arising from their complex mesostructures. In this paper, we computationally reconstruct electrodes from X-ray computed tomography of 16 nickel–manganese–cobalt-oxide electrodes, manufactured using various material recipes and calendering pressures. Due to imaging limitations, a synthetic conductive binder domain (CBD) consisting of binder and conductive carbon is added to the reconstructions using a binder bridge algorithm. Reconstructed particle surface areas are significantly smaller than standard approximations predicted, as the majority of the particle surface area is covered by CBD, affecting electrochemical reaction availability. Finite element effective property simulations are performed on 320 large electrode subdomains to analyze trends and heterogeneity across the electrodes. Significant anisotropy of up to 27% in tortuosity and 47% in effective conductivity is observed. Electrical conductivity increases up to 7.5× with particle lithiation. We compare the results to traditional Bruggeman approximations and offer improved alternatives for use in cell-scale modeling, with Bruggeman exponents ranging from 1.62 to 1.72 rather than the theoretical value of 1.5. We also conclude that the CBD phase alone, rather than the entire solid phase, should be used to estimate effective electronic conductivity. This study provides insight into mesoscale transport phenomena and results in improved effective property approximations founded on realistic, image-based morphologies.

We compute the free energy minimizing structures of particle monolayers in the presence of enthalpic barriers of a finite height βV ext using classical density functional theory and Monte Carlo simulations. We show that a periodic square template with dimensions up to at least ten times the particle diameter disrupts the formation of the entropically favored hexagonally close-packed 2D lattice in favor of a square lattice. The results illustrate how graphoepitaxy can successfully order nanoparticulate films into desired patterns many times smaller than those of the prepatterned template. Recent work has shown that the symmetry of the assembled structure can be tuned by particle shape [4,5], polydispersity [6], anisotropic interactions [7,8], and the attachment of chemically active ligands [9,10]. It is even possible to use inverse methods of statistical mechanics to discover new forms of pairwise interactions that stabilize a desired structure [11][12][13][14]. In practice, particles often need to be directed externally to form the required lattices [15][16][17].The role of an external field in the assembly of particulate systems, however, is still incompletely understood.Here, we consider a model for the solution-based deposition and assembly of spherical particles onto a smooth, attractive surface with regularly spaced enthalpic barriers that represent, for example, prepatterned chemical or topographical features. Particles from a contacting fluid suspension can adsorb onto or desorb from the substrate, where they diffuse in the presence of the periodic barriers.As the liquid film dries, the equilibrium surface concentration increases until only a monolayer of deposited particles remains. For hard-sphere particles on a pattern-free substrate, a disordered liquid-like structure is favored for areal packing fractions  < 0.72.Above η = 0.72, a hexagonally close-packed (hcp) solid forms [18]. To successfully direct the particles into an alternative packing at Fig. 1: Monolayers assembled via deposition onto a substrate with repulsive barrier templates separated by a distance commensurate with the square lattice unit cell. The template in (a) trivially fixes each particle in its ideal location. The template in (b) uses sparser templating to direct assembly into the same structure.

Battery electrodes are composed of polydisperse particles and a porous, composite binder domain. These materials are arranged into a complex mesostructure whose morphology impacts both electrochemical performance and mechanical response. We present image-based, particle-resolved, mesoscale finite element model simulations of coupled electrochemical-mechanical performance on a representative NMC electrode domain. Beyond predicting macroscale quantities such as half-cell voltage and evolving electrical conductivity, studying behaviors on a per-particle and per-surface basis enables performance and material design insights previously unachievable. Voltage losses are primarily attributable to a complex interplay between interfacial charge transfer kinetics, lithium diffusion, and, locally, electrical conductivity. Mesoscale heterogeneities arise from particle polydispersity and lead to material underutilization at high current densities. Particle-particle contacts, however, reduce heterogeneities by enabling lithium diffusion between connected particle groups. While the porous composite binder domain (CBD) may have slower ionic transport and less available area for electrochemical reactions, its high electrical conductivity makes it the preferred reaction site late in electrode discharge. Mesoscale results are favorably compared to both experimental data and macrohomogeneous models. This work enables improvements in materials design by providing a tool for optimization of particle sizes, CBD morphology, and manufacturing conditions.

The combinations of particle aspect ratio and enthalpic-barrier templates that lead to translational and orientational ordering of monolayers of rectangular particles is determined using Monte Carlo simulations and density functional theory. For sufficiently high enthalpic barriers, we find that only specific combinations of particle sizes and template spacings lead to ordered arrays. The pattern multiplication factor provided by the template extends to approximately ten times the smallest dimension of the particle. Self-assembly processes, where particles organize into specific equilibrium structures dictated by their interparticle interactions and the thermodynamic conditions, have emerged as a promising tool for the manufacture of novel functional materials [1][2][3]. Recent studies have demonstrated how the form of the interparticle interactions, and hence the symmetry of the resulting assembled structures, can be influenced via particle shape [4][5][6][7], interaction anisotropy [8,9], particle polydispersity [10], solvent quality/composition [11], and the attachment of ligands to the particles [12,13]. Specific interactions that favor targeted structures can be designed directly using inverse methods of statistical mechanics [14][15][16][17]. The combination of interactions required for a specified structure is often complex and not well understood. In turn the particles that exhibit these interactions are generally not easily or inexpensively fabricated, which limits the usefulness of self-assembly for nanomanufacturing applications. The introduction of an external field (e.g., a chemically or topographically patterned substrate) that directs the assembly process obviates the need to engineer the interparticle interactions required to achieve a target structure. This so-called graphoepitaxial approach has proven successful for guiding the assembly of block-copolymers [18][19][20][21][22][23][24][25][26][27], and recently it has been shown to be effective

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