Assessing Carbon-Based Anodes for Lithium-Ion Batteries: A Universal Description of Charge-Transfer Binding

Many key performance characteristics of carbon-based lithium-ion battery anodes are largely determined by the strength of binding between lithium (Li) and $s{p}^2$ carbon (C), which can vary significantly with subtle changes in substrate structure, chemistry, and morphology. Here, we use density functional theory calculations to investigate the interactions of Li with a wide variety of $s{p}^2$ C substrates, including pristine, defective, and strained graphene, planar C clusters, nanotubes, C edges, and multilayer stacks. In almost all cases, we find a universal linear relation between the Li-C binding energy and the work required to fill previously unoccupied electronic states within the substrate. This suggests that Li capacity is predominantly determined by two key factors—namely, intrinsic quantum capacitance limitations and the absolute placement of the Fermi level. This simple descriptor allows for straightforward prediction of the Li-C binding energy and related battery characteristics in candidate C materials based solely on the substrate electronic structure. It further suggests specific guidelines for designing more effective C-based anodes. The method should be broadly applicable to charge-transfer adsorption on planar substrates, and provides a phenomenological connection to established principles in supercapacitor and catalyst design.

Figure 1

(a) Band structure of graphene ($6\times 6$ cell) without (left) and with (right) Li. The Fermi level (blue line) is set to zero. (b) Charge density difference between Li-free and Li-adsorbed graphene for states above (left) and below (middle) the Dirac point, and for all states (right). Electron accumulation (depletion) upon Li adsorption (purple) is indicated by the yellow (blue) isosurface of ${10}^{-3}/{\mathrm{Bohr}}^3$. (c) Band structure of a ${\mathrm{DV}}_{\mathrm{t}5\mathrm{t}7}$ defect ($6\times 6$ cell) without (left) and with (right) Li.

Figure 2

Linear dependence of $\mathrm{\Delta }{ϵ}_{\mathrm{Li}-\mathrm{X}}$ on $W_{fil\mathrm{Li}ng}$ for (a) pristine graphene with different Li concentrations, (b) graphene under varying isotropic tensile strain, based on the percent increase in the lattice parameter, (c) defective graphene, where black circles represent adsorption directly at a defect site (Def), and blue triangles at an off-defect region (Off-def), (d) different-sized hexagonal graphene clusters with $N_{\mathrm{C}}$ C atoms and Li adsorption at the center, (e) CNTs of similar diameter (9.0–9.8 Å) but different chiralities ($\sim {\mathrm{LiC}}_{600}$), with top-right (bottom-left) points representing semiconducting (metallic) CNTs, and (f) all tested substrates. Red lines are linear fits; fitting parameters are given in [17].

Figure 3

(a) Band structure of graphene with dense Li concentration (${\mathrm{LiC}}_6$). (b) Concentration dependence of $\mathrm{\Delta }{ϵ}_{\mathrm{Li}-\text{graphene}}$, showing the breakdown of linear dependence at high Li loading. (c) Band structure of a GNR with Li adsorbed at an armchair (AC) edge (black/red are spin up/down). Insets for (a) and (c) show charge density contributions from the states marked by arrows. (d) $\mathrm{\Delta }{ϵ}_{\mathrm{Li}-\text{graphene}}$ as a function of separation between periodically stacked ${\mathrm{LiC}}_6$ layers, with the corresponding Li-induced electron accumulation shown (following Fig. 1 scheme). (e) Electrostatic potential ($-U$; minimum set to zero) normal to stacked ${\mathrm{LiC}}_6$ layers at the separations in (d), decreasing from top to bottom.