## 3 Results and Discussion
### Lithiation
Some other cases of filling composite pores with silicon clusters are shown in Figure 3. There are atomic structures of model I with 18 Si16 clusters (Figure 3a), 36 Si16 clusters (Figure 3b), and 59 Si16 clusters (Figure 3c) obtained by numerical simulation of supercells lithiation. It is clearly seen that when the filling of pores with silicon reached maximum, the carbon frame was strongly deformed, but did not destruct. On the base of numerical simulation we can conclude that the maximum mass fraction of silicon has been reached. At the same time, the carbon frame seemed to \"compensate\" the dramatic increase in the volume of the anode material. A further increase in the mass fraction of silicon would inevitably lead to the destruction of the carbon frame and to an uncontrolled increase in the volume of the anode material. For the case (c) of Figure 3 the lithium ions covered only the surface of the silicon clusters. Clusters that fill all the pores of the carbon frame prevented intercalation of lithium ions. Figure 2: Lithiation of anode material on the example of model I with five Si16 clusters: (**a**) initial configuration; (**b**) result of numerical simulation. Detailed data on all numerical experiments for model I with different mass fractions of silicon are presented in Table 1 that shows the number of lithium ions and silicon atoms, Si16 clusters, the mass fraction of silicon, and such important parameters for the anode material as the ratio between lithium, carbon, and silicon atoms, as well as the capacity of the anode. The Li:C and Li:Si ratios show how lithium was distributed on the surfaces of the carbon frame pores and the silicon clusters. For model 1, the maximum number of lithium ions intercalated when the pores contain 5, 8, 11 silicon clusters. The coordination ratio was 1:2, i.e., every 2 carbon atoms imbibes 1 ion of lithium on average. As the mass fraction of silicon increases, this ratio changes for the worse. Two lithium ions can only bind to 5 carbon atoms, and in the case of a maximum concentration of silicon, they can bind only to 9 carbon atoms. A similar situation was observed for silicon. Maximum lithium adsorption, when each silicon atom imbibes 4 lithium ions, occurred only when amount of Si clusters was 5 and 8. In this case, the clusters had the largest surface for contact with lithium. As the mass fraction of silicon increased, the cluster structure was transformed and the surface in contact with lithium decreased. From Table 1 it is seen that at 13-20 wt.% each silicon atom imbibed 2 lithium ions, at 32.8 wt.%--only one lithium ion, and then less than one. Analyzing the simultaneous changes in the Li:C and Li:Si ratios with an increase in the mass fraction of silicon, we can already assume that composites with a silicon fraction of ~6-20 wt.% is the most effective. Note that the rest of the lithium ions, which are not adsorbed on either carbon or silicon, filled the free volume of pores. On the other hand, another important indicator of performance is capacity. As mentioned above, the anode capacity was calculated according to the Faraday principle. For example, for the case of 9.8 wt.% (1403.4 mAh:g\({}^{-1}\), model I), the capacity of Li-Si was ~2724.5 mAh:g\({}^{-1}\), but we had 9.8% of that capacity, that is, 267 mAh:g\({}^{-1}\). Pillared graphene contributed most of the capacity (~1136.4 mAh:g\({}^{-1}\)). It is known that the theoretical capacities of graphene and CNTs are the same and equal to 1116 mAh:g\({}^{-1}\)[52], respectively, pillared graphene of any form and topology must have the same capacity. In our work, we obtained a pure pillared graphene capacity of about 1136.4 mAh:g\({}^{-1}\) (1.88% error with a theoretical capacity). Numerical experiments found that for the model I the biggest capacity values were reached at 9.8-13 wt.% of silicon, and maximum capacity equaled to 1507.7 mAh:g\({}^{-1}\) (Table 1). The smallest capacity value of 922.4 mAh:g\({}^{-1}\) was found in the case of the maximum concentration of silicon--44.5 wt.%.