Effects of surface stress on lithium-ion diffusion kinetics in nanosphere electrodes of lithium-ion batteries

Recent Developments of Nanomaterials and Nanostructures for High‐Rate Lithium Ion Batteries

“…[93] In addition, Zhang et al conducted a research to study the effects of surface stress of spherical nanoparticles (2 nm) on the diffusion kinetics of lithium ions by a chemo-mechanical coupled model. [94] It was found that surface stress might result in capacitive behaviour of the electrode nanomaterials. [94] Recently, Ji et al studied the influence of anisotropic strain on the activation energy as well as diffusion of lithium ions in graphite anodes based on density functional theory combined with kinetic Monte Carlo method.…”

“…[94] It was found that surface stress might result in capacitive behaviour of the electrode nanomaterials. [94] Recently, Ji et al studied the influence of anisotropic strain on the activation energy as well as diffusion of lithium ions in graphite anodes based on density functional theory combined with kinetic Monte Carlo method. [95] The authors found that compressive/tensile strain perpendicular to the graphite surface could lead to an increase/a reduction in energy barrier.…”

Diffusion-induced stress in a functionally graded incompressible elastic sphere

“…For present purposes, we limit the analysis to charging a particle with a radial constant rate (similar to conditions used in [23,24]). It is worth noting that the proposed solutions can be generalized not only by including more general (and physical) boundary and initial conditions but also by including for example other geometries (cylindrical or hollow materials), plastic, viscous ( [28,60,61,62,63]), surface effects ( [11,64,65,66]) or concentration dependent coefficients [67].…”

“…can be written asC[m, n + 1] = C[m, n] − δ t 2 mδ R Jf [m, n] + J f [m, n](79)whilst initial and boundary conditions (10)-(13) can be written asC[m, 0] = C0 , 0 ≤ m ≤ M ; (80) Jf [0, n] = 0, 0 ≤ n ≤ N ; (81) Jf [M, n] = − J0 , 0 ≤ n ≤ N ; (82) Tr [M, n] = 0, 0 ≤ n ≤ N ; (83) ũ[0, n] = 0, 0 ≤ n ≤ N ;(84)respectively. By applying finite central, forward or backward (depending if it is computed at the inner or boundary of the domain) difference derivatives, at a fixed time step n, the evolution equation (79) can be solved by implementingC[m, n + 1] = C[m, n] − 1, n] , 0 < m < M − 1; (86) C[m, n + 1] = C[m, n] + δ t − 1, n] , m = M − 1; (87) C[m, n + 1] = C[m, n] + δ t δ R 2 m J0 + J0 + Jf [m − 1, n] , m = M,(88)by using(26) or(66) for the computations of the hydrostatic stress in Jf . SinceT r (R, t) = 2F(R, t),(89)by a backwards recursive method it holdsTr [m − 1, n] = Tr [m, n] − 2δ R F[m, n], 0 ≤ m ≤ M,(90)taking into account condition (83), while for the hoop stress it holds Tθ [m, n] = Tr [m, n] + H[m, n], 0 ≤ m ≤ M,…”

An Investigation of Surface Stress on the Fracture Mechanics Behavior of Classical and Phase-Separating Planar Electrodes

“…They concluded that when the effects of hydrostatic stress were taken into account, the phase transformation process occurred more rapidly. Zhang et al [35] investigated the effects of surface 5 stress, stress dependent chemical potential and stress mediated diffusivity on lithium diffusion kinetics. The results showed that with decreasing the particle size, less lithiation was attained inside the electrode in which the lithium ions were accumulated in the vicinity of surface region because of larger compressive stress caused by surface stress.…”