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gations, respectively. The long CNT is blocked by residual catalyst, amorphous graphite Nanomaterials 2022, 12, 3528 and internal defects, while the ultra-short CNTs have a higher orifice density, shorter length and unobstructed channels. Here, the orifice density of a CNT can be defined as the number of openings per unit mass of CNTs. Furthermore, our previous work [42] indicated there can be another blockage by ion 8 of 13 aggregation when CNTs are soaked in salt solution. Shortening of the length of nano- tubes can effectively mitigate the blockage of filling ions as well. Figure 6. A schematic comparing the filling capacity of raw long CNTs and ultra-short CNTs. Figure 6. A schematic comparing the filling capacity of raw long CNTs and ultra-short CNTs. Furthermore, our previous work [42] indicated there can be another blockage by ion 3.3. Discussion of Filling Capacity of CNTs aggregation when CNTs are soaked in salt solution. Shortening of the length of nanotubes The ultra-short CNTs were less susceptible to blocking, resulting in higher can effectively mitigate the blockage of filling ions as well. ion-enrichment capacity. We can demonstrate that the ion-enrichment capacity of these u3l.3tr.aD-sihscourstsCioNnTofsFiisllsinagtisCfapcatocirtytohfrCoNugTsh simple mathematics. Let us assume that a CNT comprises concentric zigzag SWCNTs, that the distance between neighboring carbon The ultra-short CNTs were less susceptible to blocking, resulting in higher ion- atoms is 0.14 nm and that the interlayer spacing between the two nearest concentric enrichment capacity. We can demonstrate that the ion-enrichment capacity of these ultra- SWCNTs is 0.34 nm [53]. For a SWCNT of length l, the number of carbon atoms in short CNTs is satisfactory through simple mathematics. Let us assume that a CNT comprises SWCNT layer k is: concentric zigzag SWCNTs, that the distance between neighboring carbon atoms is 0.14 nm and that the interlayer spacing between the two nearest concentric SWCNTs is 0.34 nm [53]. nk=(l/0.14)×(1.33πdk /0.14 3) For a SWCNT of length l, the number of carbon atoms in SWCNT layer k is: where dk is the diameter of SWCNTs in layer k, determined by: (1) n = (l/0.14) × (1.33πd /0.14 kk √ 3) (1) (2) where dk is the diameter of SWCNTs in layer k, determined by: where d is the inner diameter of the CNT. Thus, the total number of carbon atoms in the d =d+0.68(k−1) k CNTs (n) is: where d is the inner diamente=r of th(le/C0N.1T4.)T×h(u1s.,3t3hπedtot/al0n.1u4mb3e)r of carbon atoms in t(h3e) N CNTs (n) is: k =1 N k √ dk = d+0.68(k−1) (2) where N is the total number of SWCNT layers. The mass of the CNT, M, should be: n = ∑(l/0.14) × (1.33πdk/0.14 3) (3) M=12n/NA (4) M = 12n/NA (4) k=1 where N is the total number of SWCNT layers. The mass of the CNT, M, should be: where NA is the Avogadro’s constant (6.02 × 1023/mol). If we assume that the space occupancy of the filling material inside the CNTs is η, the mass of the filling material, m, is: m= 0.25 × 10−21ηρπd2l (5) where ρ is the relative density of the filling material. From the above, we can determine the filling capacity for a specific filling material, γ: γ = m/M = 0.456ηρd2/(0.5dN + 0.17N(N + 1)) (0 ≤ η ≤ 1) (6) Thus, the ion-enrichment capacity of a filling material can be assessed conveniently using Equation (6). Figure 7 visualizes Equation (6) when we assume the ultra-short CNTs have a space occupancy of 0.2. The ion-enrichment capacity increases with the inner diameter of CNTs, while it decreases with the increase in the total number of layers. For example, for MWCNTs with an average inner diameter of 7 nm and an average layer number of 20, and assuming the filling material is crystalline KCl with a relative density of 1.98 and a space occupancy of 0.2 (this is just an assumption), the K-enrichment capacity of CNTs is 30.9 mg/g. If the average value of the layer number of MWCNTs, N, can be decreased to 3, the K-enrichment capacity of the CNTs increases to ~354 mg/g.PDF Image | Ion Enrichment inside Ultra-Short Carbon Nanotubes
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