Electrovariable nanoplasmonics: general discussion

Toward Optimal Performance and In‐Depth Understanding of Spinel Li4Ti5O12 Electrodes through Phase Field Modeling

“…A different, physics-based alternative to the empirical Butler-Volmer equation is provided by quantum mechanical theories of electron transfer [59] , such as the Marcus-Hush-Chidsey model (MHC) [60] which predicts an electron-transfer reaction-limited current that cannot be exceeded even at high over-potential [61] (opposite to BV theory, which predicts faster kinetics at higher overpotential). A generalized theory of mixed ion-electron transfer in solids [62] , combining MHC kinetics with nonequilibrium thermodynamics [18] , predict an approximately linear decrease in exchange current vs concentration, I 0 ~ 1-c, for mixed ion-electron transfer into a solid intercalation material, consistent with experimental measurement of I 0 (c) in LFP [30] , which can explain the linearly decreasing capacity at low rates. A preliminary result from implementing the generalized MHC theory in our LTO phase-field model is presented in Supporting Information B, which indeed shows a steeper decline in the voltage curve, closer to the experimental data.…”

“…Recently, the concentration evolution of individual LFP nanoparticles has been observed in operando during cycling under realistic conditions by scanning tunneling x-ray microscopy (STXM), which paves the way for unprecedented validation and application of phase-field models at the nanoscale [29] . The local exchange current density versus concentration was extracted from a massive dataset of STXM movies, and its behavior in the spinodal region, coupled with direct observations of phase separation, confirmed the theory that phase separation is suppressed by auto-inhibition during insertion and enhanced by auto-catalysis during extraction [30] . With advances in 3D simulations of LFP nanoparticles [20b, 21b] , a comprehensive picture of the lithium intercalation is emerging.…”

“…, which assumes one excluded site for the transition state during lithium insertion, leads to an asymmetric exchange current versus concentration, peaking at low concentrations, which has recently been validated by local measurements of the intercalation rate in LFP nanoparticles [29] . As a result, the insertion reaction is auto-inhibitory (and the extraction reaction is auto-catalytic) across the spinodal region, which leads to suppression of phase separation during insertion (and enhancement during extraction), as predicted theoretically [23,30] and later confirmed by in operando imaging of nanoparticle concentration profiles [29] . The effective overpotential !""…”

“…One reason may be the breakdown of the standard assumption of spherical symmetry, which promotes shrinking-core phase separation within each active particle. In the case of LFP, the canonical two-phase material, it is well established that the initial shrinking core model [56] cannot capture various surface phenomena predicted by phase-field models that relaxed this assumption [18][19][20][21] , such as the electroautocatalytic control of phase separation by surface reaction kinetics [23,30] , which was later verified experimentally [24] with definitive proof by in operando imaging of nanoparticles [29] . It is also important to note that a 1D phase field model of LFP nanoparticles [57] similar to our LTO model, which allowed for surface nucleation and departures from shrinking core morphologies, such as radial spinodal decomposition and annual stripes, also produced flat voltage profiles resembling ours for LTO and failed to capture the observed rate-dependent phase behaviour in LFP.…”

“…It is also important to note that a 1D phase field model of LFP nanoparticles [57] similar to our LTO model, which allowed for surface nucleation and departures from shrinking core morphologies, such as radial spinodal decomposition and annual stripes, also produced flat voltage profiles resembling ours for LTO and failed to capture the observed rate-dependent phase behaviour in LFP. Let us briefly discuss how departures from spherical symmetry that allow for electro-autocatalytic control of phase separation [30] may help explain varying voltage profiles in LTO. As discussed earlier, DFT results indicate that the phase interfaces are stabilized by mixed 8a/16c Li site occupation that resemble solid solution conditions on top of the nanoscale two phase separation, explaining the fast Li-ion mobility and phase-interface stabilization in LTO.…”