Grand Canonical Monte Carlo Study of Li Intercalation into Graphite

Abstract

A computational model is proposed to study lithium-graphite intercalation compounds in the framework of Monte Carlo simulations in the Gran Canonical Ensemble. The results suggest the existence of fractional stages between stages II and I, which are rarely found in most experimental electrochemical measurements. These fractional stages seem to be part of a more general intercalation mechanism suggested for other intercalation compounds. The thermodynamic information obtained from the simulations for these fractional states at room temperature is discussed in the context of experimental data. In addition, clear evidence was found for the existence of a new stage, supported by recent experimental measurements.

Transitions of lithium occupation in graphite: A physically informed model in the dilute lithium occupation limit supported by electrochemical and thermodynamic measurements

“…(10) We define the difference, D(x), between the modified and standard Langmuir isotherms as . (11) In terms of output, we verified that this approximation is equivalent to taking the two layer model with input parameters g = 0 and Δ = 0, as shown in supplemental Figure S3-S6. The utility of this approximation is based on the observation that the partial molar entropy, as a function of x, does not depend on α or β as shown in Figure 6d.…”

“…In addition to fundamental understanding, these phenomena are important for achieving a cell level picture for practical applications such as battery management and aging. In our recent and ongoing work, we described order disorder transitions, including the Stage I-Stage II transition, through Grand Canonical Monte Carlo simulations [1,[9][10][11]] and a two level, mean field approach [2,12] . This transition is responsible for the main step in voltage with respect to lithium occupation (state of charge) that occurs close to 50 % lithiation in graphite.…”

“…(b) Open circuit voltage (OCV) values obtained from the entropy profiling procedure. Inset shows the same profile over a narrower potential window.Entropy profiles, shown inFigure 2a, display a transition at approximately x = 0.5, which is the order/disorder transition associated with the Stage I -Stage II transformation[2,4,11,[25][26] .…”

Kinetic Monte Carlo applied to the electrochemical study of the Li-ion graphite system

“…On the other hand, other authors have examined the effect of morphology and structural properties of the electrodes [27,28] on the kinetics of this system. However, we have only found few articles presenting 0 i (or 0 j ) as a function of lithium occupation for Li-ion/graphite systems [14,26] While Grand Canonical Monte Carlo techniques have enabled calculation of the thermodynamic properties of the present system, like partial molar enthalpy and entropy [29,30], kMC has the advantage of considering also kinetic phenomena. In a previous work…”

Numerical simulations of cyclic voltammetry for lithium-ion intercalation in nanosized systems: finiteness of diffusion versus electrode kinetics

“…For example, we found in kinetic Monte Carlo (kMC) simulations of graphite nanoparticles that well resolved voltammetric features were obtained at sweep rates several orders of magnitude higher than those used in multi-particle experimental systems [17,18]. The model proposed in these articles was suitable for describing other relevant characteristics of Li-ion/graphite system like the criticality of phase transition [19][20][21][22], the intercalation in the equilibrium [23,24] and the influence on kinetics on Li intercalation [25].…”