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Generalized Homogenization Theory and its Application to Porous Rechargeable Lithium-ion Batteries
A thermodynamically consistent coarsed-grained phase field model was developed to find the conditions under which a heterogeneous porous electrode can be treated as homogeneous in the description of Lithium-ions in rechargeable batteries. Four regimes of behavior under which the transport phenomena can be homogenized to describe porous LIBs were identied: regime (a), where the model is inaccurate, for physically accessible particle packings of aspect ratios smaller than c/a = 0.5 and electrode porosities between 0.34 to 0.45; regime (b), where the model is valid, for particles of aspect ratios greater than c/a = 0.7 and electrode porosities greater than 0.35; regime (c), where the model is valid, but the microstructures are physically inaccessible, and correspond to particles with aspect ratios greater than c/a = 0.7 and electrode porosities smaller than 0.34; and regime (d), where the model is invalid and the porous microstructures are physically inaccessible, and correspond to particles with aspect ratios smaller than c/a = 1 and electrode porosities smaller than 0.34.
The developed formulation was applied to the graphite | LixNi1/3Mn1/3Co1/3O2 system to analyze the effect of microstructure and coarsed-grained long-range chemomechanical effects on the electrochemical behavior. Specically, quantiable lithium distribution populations in the cathode, as a result of long range interactions of the diffuse interface, charge effects and mechanical stresses were identified: i) diffusion limited population due to negligible composition gradients, ii) stress-induced population as a result of chemically induced stresses, and iii) lithiation-induced population, as a consequence of the electrochemical potential gradients.