Homogenization Study of the Effects of Cycling on the Electronic Conductivity of Commercial Lithium-Ion Battery Cathodes

Abstract

State-of-the-art image acquisition, image analysis, and modern homogenization theory are used to study the effects of cycling on commercial lithium-ion battery cathodes' ability to conduct electronic current. This framework allows for a rigorous computation of an effective, or macroscale, electronic conductivity given an arbitrarily complicated three-dimensional microstructure comprised of three different material phases, i.e., active material, binder (polymer mixed with conductive carbon black), and electrolyte. The approach explicitly takes into account the geometry and is thus a vast improvement over the commonly used Bruggeman approximation. We apply our framework to two different types of lithium-ion battery cathodes before and after cycling. This leads us to predict an appreciable decrease in the effective electronic conductivity as a direct result of cycling. In addition, we present an ad-hoc "neighbor counting" methodology which meaningfully quantifies the effect of binder detaching from the surface of the active material due to the internal mechanical stresses experienced under operating conditions, thereby supporting the results of the homogenization calculations. ■ INTRODUCTIONA significant research effort is currently focused on the development of lithium-ion batteries for use in a variety of areas, e.g., the automotive industry and consumer electronics, because they exhibit several desirable qualities including no memory effects, little self-discharge, and a comparably high energy density. Many previous studies have considered how to model the electrochemical processes occurring within such cells, with the aim of informing the optimal design. The majority of these studies have been (at least partially) based on the seminal works of Newman et al. 6−9 Providing an exhaustive list, or even summary, of the extant work on lithium-ion batteries would be almost impossible. Instead, we point the interested reader toward one of the many books now available on the physical chemistry of electrochemical systems including lithium-ion batteries 24 . Of particular interest is modeling that allows for optimization of energy density, charge/discharge rates, safety, and cycling life. This contribution will focus on the latter, specifically the loss of efficacy of the electron transport in the electrode as it ages.Lithium-ion batteries are comprised of four key constituents: (i) the anode (the negative electrode during discharge); (ii) the cathode (the positive electrode during discharge); (iii) the electrolyte; and (iv) a porous separator that ensures unhindered passage of electrolyte (ionic current) while electronically isolating the two electrodes ( Figure 1). This assembly is sandwiched between two metallic current collectors, that connect to the external circuit, where energy is injected or removed from the system.During operation, which can only be maintained when both the ionic and the electronic charges are transported between the two electrodes ensuring overall charge neutrality, the chemical potential differe...

Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

“…This accounts for the reduction in the diffusive fluxes due to the obstacles provided by the intermingled phase, in this case the coffee grains. This permeability factor can either be computed via a homogenization calculation 34 or can be estimated using the Bruggemann approximation, which asserts that B = ε 3=2 l . 35 Unfortunately, neither D l nor D eff have been experimentally characterized.…”

“…When the coffee mass is altered, the only parameter that needs to be altered is the bed depth, L. We continue to operate under the assumption that the bed has a fixed volume fraction of coffee grounds, and hence the depth of the bed is directly proportional to the coffee dose (see Equation 25 and the Supplemental Information). When the pump overpressure (P tot ) is increased, the Darcy flux (q) is increased in direct proportion, 34 whereas the shot time is decreased in an inverse proportional manner (Equation 26 and the Supplemental Information). We monitor EY (the mass fraction of grains that are dissolved), enabling the isolation of both coffee mass and overpressure.…”

Causes of binder damage in porous battery electrodes and strategies to prevent it

“…The complexity of the geometry, consisting of a long thin polymer binder slab into which very large numbers of growing and shrinking microscopic electrode particles are embedded, renders direct solution of (1)- (8) intractable. This motivated us, in [9], to apply an upscaling procedure (also referred to as 'homogenization') that yields effective medium equations for the 'average' deformations on macroscopic lengthscales.…”

Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation

“…The original PET formulation has also been generalised by posing the problem, on both macro-and micro-scales, in higher numbers of dimensions. This enables the effects of electrode particle shape to be investigated, and also spatially inhomogeneities in electrode discharge that could arise, for example, from non-uniform heating or the positioning of the electrode tabs, see [15,19].…”