Bruggeman's Exponents for Effective Thermal Conductivity of Lithium-Ion Battery Electrodes

Abstract

Simulations of lithium-ion battery cells are usually performed with volume averaging methods that employ effective transport properties. Bruggeman's model, which is widely used to determine these effective properties, is primarily based on the volume fraction of porous electrodes. It does not consider actual particle shape, size or the topology of constituent phases; these play a crucial role in determining effective transport. In this paper, a general derivation of the effective thermal conductivity of multiphase materials, which can be correlated with these factors, is derived using the volume averaging technique. Three-dimensional finite volume meshes of fully-resolved lithium-ion battery cathode microstructures are reconstructed from scanned images. Effective volume averaged thermal conductivity is then determined from numerical analysis of thermal transport on these meshes. It is shown that the Bruggeman model for effective thermal conductivity must be recalibrated to fit the effective thermal conductivity computed from these detailed simulations. The relevance of these results to effective transport properties typically employed in electrochemical simulations is presented. Commonly used theories for effective thermal transport in composites are evaluated for comparison. Furthermore, it is shown that Bruggeman's exponents yield an important quantitative measure, the connectivity, to characterize the physical path for transport through the underlying phases. The importance of lithium-ion batteries is now well recognized in light of the global energy crisis, global warming and the need for efficient and inexpensive energy storage options.1,2 Battery physics encompass thermodynamics, electrochemistry, material science, transport phenomena and solid mechanics, and span multiple length and time scales.3 Realistic modeling of batteries across these disparate physics and scales is critical for their effective and safe commercialization. 4 Research in lithium-ion batteries has been primarily driven by the need to develop cathode, anode and electrolyte materials that deliver high potential and capacity. 5,6 On the cell level, the battery consists of a porous composite anode and cathode filled with an electrolyte and separated by a separator. Typically, the thickness of such a sandwich is hundreds of microns, while lateral dimensions are of the order of centimeters. Lithium ions shuttle between cathode and anode during charge and discharge. Active cathode particles (for e.g. LiCoO 2 , LiMn 2 O 4 , LiFePO 4 ), which form the key constituent of batteries, are lithium insertion compounds and have high lithium ion conductivity. These active particles are spatially dispersed and held together by binder (such as polyvinylidene fluoride [PVDF]), while the electrolyte resides in the pores, wetting the active particles, and facilitating transport of lithium ions. The electronic conductivity of these active materials is generally low compared to lithium ion conductivity. Therefore additives like carbon particles are dispersed ...

Mesoscale Effective Property Simulations Incorporating Conductive Binder

“…The properties can be extracted from mesoscale simulation tools by considering a representative volume element (RVE) which contains a sufficient amount of composite material to be representative of the bulk electrode. 48,49 Despite the advancements in imaging, there has been noticeable difficulty in resolving the location of all phases within the mesostructure. Specifically, the inability to distinguish PVDF, carbon, and void from each other 23,50,51 when using X-ray tomography has resulted in the omission of the PVDF and carbon black phases in many of the modeling studies referenced above.…”

Fabrication of highly isotropic porous alumina refractory clinkers consisting of platelets using a gelatin-sol

“…Various equations and strategies for the evaluation of thermal conductivity in porous materials have been reported to date [32][33][34][35][36][37][38][39][40][41]. The raw material particles used in this study are high aspect ratio (AR) alumina platelets, so it is necessary to consider the anisotropy of the particles.…”

“…The raw material particles used in this study are high aspect ratio (AR) alumina platelets, so it is necessary to consider the anisotropy of the particles. Kanari's equation is a generalization of the Bruggeman equation to accommodate any particle shape, and can be expressed as follows [39][40][41]:…”

Untitled

“…For example, Doyle et al [18] used higher values of γ to better estimate the effective transport properties. Vadakkepatt et al [16] obtained different values of the Bruggeman's exponents for evaluation of effective thermal conductivity by using numerical simulation of fully resolved cathode microstructures of Li-ion battery.…”