A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell

Abstract

a b s t r a c tWe formulate the continuum field equations and constitutive equations that govern deformation, stress, and electric current flow in a Li-ion half-cell. The model considers mass transport through the system, deformation and stress in the anode and cathode, electrostatic fields, as well as the electrochemical reactions at the electrode/electrolyte interfaces. It extends existing analyses by accounting for the effects of finite strains and plastic flow in the electrodes, and by exploring in detail the role of stress in the electrochemical reactions at the electrode-electrolyte interfaces. In particular, we find that that stress directly influences the rest potential at the interface, so that a term involving stress must be added to the Nernst equation if the stress in the solid is significant. The model is used to predict the variation of stress and electric potential in a model 1-D half-cell, consisting of a thin film of Si on a rigid substrate, a fluid electrolyte layer, and a solid Li cathode. The predicted cycles of stress and potential are shown to be in good agreement with experimental observations.

Mitigating mechanical failure of crystalline silicon electrodes for lithium batteries by morphological design

“…The concurrent processes of Li transport, phase transformation and elasto-plastic deformation in Si anodes have inspired numerous modeling works [19][20][21][22][23][24][25] . Several groups developed models to explain the anisometric volume expansion of c-Si nanowires upon lithiation 14,18,24 .…”

Variation of stress with charging rate due to strain-rate sensitivity of silicon electrodes of Li-ion batteries

“…Fortunately, this mechanical damage can be mitigated by nanostructuring the silicon anodes, as has been successfully demonstrated in nanowires [6,7], thin films [8][9][10][11][12], nanoporous structures [13,14], and hollow nanoparticles [15,16]. Specifically, recent experiments and theories indicate that one can prevent fracture by taking advantage of lithiation-induced plasticity [11,[17][18][19][20][21][22].…”

“…A number of studies have examined plastic deformation in Li x Si [5,12,18,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Sethuraman et al measured stresses during cycling of Li x Si electrodes, finding plastic flow, which results in dissipation of energy comparable to that of polarization losses [18].…”

Chemomechanics of ionically conductive ceramics for electrical energy conversion and storage

“…Sethuraman et al further suggested that device designs that minimized stress formation during cycling would have improved charge/discharge capacities. Building off of this work, Bower et al developed an extensive analytical model of a simple layered LIB based on the field equations for coupled stress, diffusion, electric fields, and electrochemical reactions [180]. The model was able to reproduce most features of the potential and stress cycles originally observed by Sethuraman et al quite successfully, confirming the energy dissipation resulting from stress-potential coupling.…”