R García-García, RE García “Microstructural effects on the average properties in porous battery electrodes.” Journal of Power Sources, 309:11-19, 2016.

Abstract

A theoretical framework is formulated to analytically quantify the effects of the microstructure on the average properties of porous electrodes, including reactive area density and the through-thickness tortuosity as observed in experimentally-determined tomographic sections. The proposed formulation includes the microstructural non-idealities but also captures the well-known perfectly spherical limit. Results demonstrate that in the absence of any particle alignment, the through-thickness Bruggeman exponent α  , reaches an asymptotic value of α∼2/3 as the shape of the particles become increasingly prolate (needle- or fiber-like). In contrast, the Bruggeman exponent diverges as the shape of the particles become increasingly oblate, regardless of the degree of particle alignment. For aligned particles, tortuosity can be dramatically suppressed, e.g.  , α→1/10 for r_a→1/10 and MRD∼40. Particle size polydispersity impacts the porosity-tortuosity relation when the average particle size is comparable to the thickness of the electrode layers. Electrode reactivity density can be arbitrarily increased as the particles become increasingly oblate, but asymptotically reach a minimum value as the particles become increasingly prolate. In the limit of a porous electrode comprised of fiber-like particles, the area density decreases by 24%, with respect to a distribution of perfectly spherical particles.