The decrease of the distance for six lithium atoms is due to the smallness of the cross section of the CNT. Hence, the stabilization of the four lithium model originates more significantly in the Li-Li interaction compared to other models. On the other hand, the Li-CNT distance is the longest for four lithium atoms. Therefore, we consider that Li-Li interaction is important for N Li ⩾ 4 for the (12,0) SWCNT. In contrast, for four lithium model, Li-Li distances are very close to the value of the bulk structure and the Li-Li interaction is expected to stabilize these lithium atoms. Hence, a repulsive force between lithium atoms is expected for this short distance. Particularly, for the insertion of six lithium atoms, Li-Li distances are about 2.9 Å, which is shorter than that of the bulk lithium structure (3.48 Å). 6, the Li-Li distance becomes short as the number of lithium atoms increases. This feature is explained from the viewpoint of the Li-Li distance. The adsorption energy of four lithium atoms is the largest (−1.13 eV) in this result, and the six lithium structure is strongly destabilized from the four lithium structure. 7, the adsorption energy of lithium atoms is shown as a function of the number of lithium atoms, which is defined in Eq. Hence, the inside adsorption is favored due to the difference of the charge transfer, which originates in the curved structure of the CNT wall. 4, since the positive kinetic energy regions associated with Li and C atoms are separate for both inside and outside adsorptions, we have confirmed that covalent property is weak and an ionic property is seen for the Li-C bond by our kinetic energy density. For a bond with ionic property, we see two separate positive kinetic energy regions associated with two atoms. This feature can be seen between carbon atoms in panel (b). 13,22,23 The positive kinetic energy region extends between atoms if the bond between the atoms has covalent property. It has been shown that this quantity classifies whether a bond has covalent property. Panels (a) and (b) show the results for the same planes in Fig. The definition of the kinetic energy density is given in Eq. 4, we show the zero kinetic energy density surface. This is due to the difference of the distance from the lithium atom as explained above. However, one outstanding feature of the inside adsorption is the larger density increase around carbon atoms in next hexagonal rings as seen in panel (a). For example, the electron density decreases behind the lithium atom, and the density increases between Li and C atoms and around C atoms. We can see some common properties for both distribution patterns. 3, electrons around lithium atoms move to the regions around carbons for both cases. The circles in panels (a) and (c) mean the cross section of our CNT model. Panel (b) (panel (d)) shows the plane including the Li, C(2), and C(3) atoms (Li, C(1), and C(4)), where these carbon atoms are the nearest from the Li atom. Panels (a) and (c) show the plane perpendicular to the axis. Panels (a) and (b) are the results of the lithium adsorption on the inside of the CNT, while panels (c) and (d) are those for the outside adsorption. $\rho (\vec$ ρ ( r ⃗ ) X is the electron density of a system, X. In their results, the density of lithium storage only in the interior of the (12,0) zigzag SWCNT was shown as LiC 6 by ab intio quantum chemical calculations. 12 They argued that the inner surface of CNTs can provide available site for the bare lithium ions. 11,12 It was proposed that the electrolyte molecules and the solvated lithium ions are eliminated by screen materials or defects on the end of CNTs and only bare lithium ions are stored in interior of the CNTs after the desolvation of the solvated lithium ions. Recently, some ideas using steric effects are proposed to improve the reversible capacity of lithium ions. In other words, electrolyte molecules and lithium ions solvated with the electrolyte molecules can freely enter into the interior of CNTs, and this inner surface of the CNTs does not provide available site for lithium ion storage, since the inner surface is similar to the basal plane of the graphite in the electrolyte. Second, lithium (not necessarily ions) stored in the interior of CNTs through open ends of CNTs is not suitable for lithium ion battery as reversible resources. One is that the direct diffusion through the sidewalls of pristine CNTs is difficult for lithium ions. It was reported that the reversible capacity is independent of whether the ends of single wall CNTs (SWCNTs) are open, though the amount of lithium storage is increased due to the diffusion into the inside of CNTs.
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