As shown in Figure 1, the radial distribution functions (RDFs) of cations and oxygen atoms inside the five CNTs and bulk solution are calculated with the trajectory. We found that the radial distribution of O atoms around the two cations inside CNTs shows a maximum value and a minimum value, and they are both smaller than the radius of CNTs, which indicates that the coordination shells of two cations exist inside CNTs. The second peaks of RDFs are obviously weak in all cases, indicating that the second coordination shells of the cations may be unstable in all CNTs. At the same time, this phenomenon further confirms the rationality of all models.

To better study the detailed information of the coordination shell, the distances of the first maximum (r _max ) and minimum (r _min ) of cations and oxygen atoms inside the five CNTs and bulk solution are listed in Table 1. We observed that the r _max and r _min for Li⁺ were 2.0 and 2.6 Å inside CNTs, respectively, agreeing well with the corresponding bulk values observed in this work and the simulation results of others (Rasaiah et al., 2000; Zhou et al., 2002). The r _max and r _min values of 2.0 and 2.3 Å, respectively, were observed for confined Mg²⁺ inside all CNTs, which was similar to the findings of Pettitt and Rossky (1986). Table 1 also lists the coordination numbers (Nc) of water molecules around Li⁺ and Mg²⁺ in CNTs and the bulk solution. We found that the Nc of water molecules around Mg²⁺ remains 6.0 in all five CNTs and is consistent with its Nc in the bulk solution and the simulation results of other studies (Pettitt and Rossky, 1986; Rasaiah et al., 2000), which suggests that the Nc of water molecules around Mg²⁺ is not sensitive to the diameters of CNTs. Compared with the bulk solution, the Nc of water molecules around Li⁺ inside the CNTs with diameters of 1.28, 1.00, 0.87, and 0.73 nm has a different reduction, which is 3.7 inside 1.28 nm CNTs and 0.4 smaller than that of the bulk solution, while the other value is close to 3.0 in CNTs with diameters of 1.00, 0.87, and 0.73 nm, which is 1.1 smaller than the bulk counterpart. However, a different phenomenon occurs in the CNT with a diameter of 0.60 nm in which a complete first coordination shell is observed for Li⁺ compared to the 0.73, 0.87, and 1.00 nm CNTs, which indicates that the confinement effect of 0.60 nm CNT on Li⁺ is more obvious. In summary, the first coordination shell of Li⁺ is no longer complete in CNTs with diameters of 0.73, 0.87, and 1.00 nm, yet this case does not occur in the five CNTs for Mg²⁺. Furthermore, to clearly observe the first coordination shells of Li⁺ and Mg²⁺ in the five CNTs, the hydration structure of cations and the average bond lengths of cations and the O atoms of water molecules (Ow) in the bulk solution and CNTs are presented in Figure 2. The first coordination layer of Li⁺, constituted by four water molecules in the 0.60 nm CNT and the bulk solution and containing three water molecules and one Cl⁻ in the 0.73, 0.87, and 1.00 nm CNTs, was observed. These observations indicate that the 4-coordinated Li⁺ is more stable. Moreover, we determined that the average bond length between Li⁺ and Ow is 2.02 Å inside the CNT with a diameter 0.60 nm, and it is significantly longer by 0.11 Å than that in the bulk solution. This foundation indicates that the hydration layer of Li⁺ is looser in the 0.60 nm CNT. While the distances of Li⁺-Ow were similar in the 0.73, 0.87, and 1.00 nm CNTs, Cl⁻ may form the first coordination layer of Li⁺. Similar to the bulk solution, Li⁺ has four coordination with CNTs, and the reason for the difference in Nc is that Cl⁻ participates in the formation of the first coordination layer. We also observed that the bond length between Mg²⁺ and Ow in CNTs is nearly 3.0% larger than that in the bulk solution, which suggests that the first coordination layer of Mg²⁺ in the five CNTs is also looser than that in the bulk solution. Unlike Li⁺, Cl⁻ does not participate in the formation of the first coordination layer of Mg²⁺ in the bulk solution and CNTs.

To determine why Cl⁻ does not participate in the formation of the first coordination layer of Li⁺ in the 0.6 nm CNT, the simulation time of this system was extended by 400 ns under the same conditions. The distance between Li⁺ and Cl⁻ in the last 400 ns and the corresponding structure are shown in Supplementary Figure S2. Unexpectedly, the distance between Li⁺ and Cl⁻ was reduced to 2.29 Å at 341 ns, after which three water molecules occur around Li⁺, and Cl⁻ also participates in the formation of the first coordination layer, which is the same as in the 0.73, 0.87, and 1.00 nm CNTs. This phenomenon shows that the confinement effect of smaller CNTs makes the formation of contact ion pairs (CIPs) more difficult. Then, ab initio molecular dynamics (AIMD) simulations were performed using the CP2K program (Kuhne et al., 2020) to confirm the aforementioned results, and the simulation details are described in the Supplementary Simulation Methods Section. CNTs with diameters of 0.60, 0.73, and 1.28 nm were selected and studied. As shown in Supplementary Figure S3, the distance between Li⁺ and Cl⁻ is larger at 2.83–4.55 ps in the 0.60 nm CNT, which illustrates that Cl⁻ is insufficient to participate in the formation of the first coordination layer of Li⁺, and the distance decreases to 2.32 Å, manifesting the CIP of Li⁺ and Cl⁻ forms over the last time. These observations indicate that the formation of CIP between Li⁺ and Cl⁻ requires an intermediate [Li(H₂O)₄]⁺ in the 0.60 nm CNT. The distance between Li⁺ and Cl⁻ is directly reduced to 2.18 and 2.22 Å in a very short time in CNTs with diameters of 0.73 and 1.28 nm, and the coordination form of Li⁺ is [Li(H₂O)₃]⁺Cl⁻. From these results, we conclude that the required time for Cl⁻ to participate in the formation of the first coordination layer of Li⁺ is as follows: CNT (7, 7) > CNT (11, 11) > CNT (8,8), which is consistent with the previously presented trend for the Nc of water molecules around Li⁺ and demonstrates the consistency of MD and AIMD results.

Based on the electrostatic interaction between ions and water molecules, the water molecules around the ions show a certain orientation distribution. An orientation distribution function was proposed to characterize the orientation structure of water molecules around an ion by Zhou et al. (2002). It is defined as the distribution probability of the orientation angle between ions and water molecules. The orientation angle is presented in Figure 3A. The orientation distribution function of the water molecules around Li⁺ and Mg²⁺ inside the CNTs and bulk solution are shown in Figures 3B,C. The orientation of water molecules around Li⁺ is strongest in the bulk solution and CNTs with a diameter of 0.60 nm, yet the Li⁺ inside the CNTs with diameters of 1.28, 0.73, 1.00, and 0.87 nm takes third, fourth, fifth, and sixth place, respectively. For Mg²⁺, we observe that the maximum values of the distribution probability of the orientation angle in the CNTs with diameters of 0.60, 0.73, 0.87, 1.00, and 1.28 nm are 40.51, 28.27, 37.81, 41.23, and 60.73, respectively, and that in the bulk solution is 60.73, which are significantly larger than those of Li⁺ inside all CNTs. This indicates that the water molecules around Mg²⁺ are more ordered than those around Li⁺ under the confinement of CNTs. Moreover, their cosine values of the orientation angle present a maximum at −1, which shows the water molecules around ions approaching Li⁺ and Mg²⁺ with the O atoms and the H atoms away from the ions. The results show that the order degree of the water shell around the ions is proportional to the Nc of the water molecules around cations.

To further investigate the variation in shell order, we applied the hydration factor (F) parameter proposed by Zhou et al. (2002) and defined in Eq 2: F = N − 1 < cos ⁡ α < − 0.72 f i r s t s h e l l N a l l f i r s t s h e l l . (2)

F of Li⁺ (F_Li) and Mg²⁺ (F_Mg) inside the five CNTs and the bulk solution as a function of CNT diameter are shown in Figure 3D. We can observe two types of diameter dependences for F_Li. Inside the four CNTs with diameters of 0.73, 0.87, 1.00, and 1.28 nm, the F_Li values are 0.76, 0.75, 0.76, and 0.75, respectively, which are nearly the same compared to each other and all smaller than the bulk one by approximately 10.59% and 11.76%, which indicates that the shell order of Li⁺ is nearly identical inside these four CNTs. Both of these cases imply that the hydration of Li⁺ is nearly identical in these four CNTs, which is weaker than that of the bulk solution. However, we found that there is a considerable increase in F_Li occurring in the narrowest CNT with a diameter of 0.60 nm in Figure 3D, and it is nearly 4.7% larger than that in the bulk one. The Nc of Li⁺ inside this CNT is also nearly 4.7% compared with that of the bulk solution, which indicates that the hydration of Li⁺ inside this CNT may be similar to that in the bulk solution within 100 ns. In addition, we determined that F_Mg is nearly 0%, 0.3%, 0.2%, 0.2%, and 0% inside the five CNTs with diameters of 0.60, 0.73, 0.87, 1.00, and 1.28 nm, respectively, compared to that in the bulk solution, which implies that the hydration of Mg²⁺ inside all CNTs may be more similar to that in the bulk solution and is not sensitive to the diameter of the CNTs.

As shown in Figure 4, three pairwise interacting energies are divided. The binding of Li⁺ and Cl⁻ released approximately 86.00, 278.18, 274.91, 267.47, and 271.48 kJ/mol energy inside the five CNTs with diameters of 0.60, 0.73, 0.87, 1.00, and 1.28 nm, respectively. Meanwhile, at the interface between Li⁺ and Cl⁻, parts of the water were squeezed out, causing dehydration of Li⁺ and Cl⁻ (Li⁺−water term 46.45, 271.26, 259.18, 269.92, and 306.11 kJ/mol; Cl⁻−water term 57.53, 249.47, 234.85, 234.77, and 238.11 kJ/mol), which were partly compensated by the energy release due to Li⁺ and Cl^- interaction. From these data, we know that the interaction energy between Li⁺ and Cl⁻ inside the 0.60 nm CNT shows a maximum value. This observation indicates that the binding of Li⁺ and Cl⁻ in CNTs with a diameter of 0.60 nm is the most difficult, and the difficulty of dehydration of Li⁺ and Cl⁻ in CNTs with other sizes is nearly the same. Additionally, except for the 0.60 nm CNT case, the energy absorbed by the combination of Li⁺ and water molecules is slightly higher than that of the combination of Cl⁻ and water molecules in the CNTs with diameters of 0.73, 0.87, 1.00, and 1.28 nm, which indicates that Li⁺ coordinates with three water molecules [Li(H₂O)₃]⁺Cl⁻ in these four CNTs and is more stable than that in the 0.60 nm CNT. The same feature was observed for the confined Mg²⁺, and compared with the Li⁺ system, the required energy for dehydration between Mg²⁺ and Cl⁻ is much lower. This consistency indicates that the dehydration between Mg²⁺ and Cl⁻ is more difficult than that of Li⁺ and its water shell is harder inside the five CNTs. The released energies between Mg²⁺ and Cl⁻ in all CNTs are comparable, which suggests that the binding of Mg²⁺ and Cl⁻ is more stable in CNTs.

As shown in Figures 4C and D, the interaction energies between cations and Cl⁻ are computed during the last 50 ns simulation and includes the following: the electrostatic interaction, vdWs interaction, and total interaction between cations and Cl⁻. We determined that an average driving force of the binding process results from the strong electrostatic interaction between cations and Cl⁻, while the contribution of vdWs is nearly zero. This is caused by the strong electrostatic attraction between positive and negative ions. Consistent with the trend presented in Figure 4B, the interaction energy between Mg²⁺ and Cl⁻ in Figure 4D is comparable in all CNTs. However, the interaction energy between Li⁺ and Cl⁻ in the CNT with a diameter of 0.60 nm shows a different trend from that in the other CNTs in Figure 4C, which is caused by an obvious confined effect on Li⁺ in the 0.60 nm CNT. From an energy perspective, these observations suggest that the hydration of Li⁺ in CNTs with a diameter around 0.60 nm seems to be identical to that observed in the other CNTs.

To further explain the coordination situation of cations, the binding energies of Li⁺ and Mg²⁺ with the coordination molecules or ions are calculated by the quantum chemistry method in Figure 5. We determined that the binding energy of 3-coordinated Li⁺ with water molecules is more negative than that of 4-coordinated Li⁺ by −323.77 kJ/mol, which suggests that it is more stable than that of 4-coordinated Li⁺. This is consistent with the analysis results of the previous interaction energy between Li⁺ and Cl⁻. Moreover, the binding energy of 6-coordinated Mg²⁺ with water molecules is −1,446.75 kJ/mol and is the most stable combination mode in which the arrangement of the six water molecules around Mg²⁺ is relatively tight. This also indicates that the 6-coordinated water shell of Mg²⁺ is harder, and the interaction between Mg²⁺ and water molecules is easier than that of Li⁺. Therefore, the interaction between Mg²⁺ and Cl⁻ is weaker than that between Li⁺ and Cl⁻, which is consistent with the description in Figures 4C and D.

The weak interaction between CNTs and water molecules is shown in Figure 6 to illustrate the differences in the water shell inside the CNTs with diameters of 0.60, 0.73, and 1.28 nm and the different Nc of water molecules around Li⁺ (the details are described in the Supplementary Simulation Methods Section). The color-coding scheme is as follows: blue for attractive, red for repulsive, and green for intermediate interactions, which includes electrostatic and van der Waals interactions. First, the red patch is evenly distributed throughout the CNTs, which indicates that the CNT model is reasonable in this research. We determined that the presence of green patches between the CNTs and water molecules is widespread. In complexes with LiCl and H₂O in addition to the green patches, blue streaks are also observed, which are caused by hydrogen bonds among water molecules or halogen bonds between Cl⁻ and water molecules. For the LiCl solution inside the 0.60 nm CNT, we observed a smaller area of splattered green patches between the CNT and water molecules (Nw = 4) than in the case of the coordination of three water molecules, which suggests that the interaction between the CNT and water molecules in the [Li(H₂O)₄]⁺ form is weaker, and Cl⁻ has difficulty inserting into the first coordination layer of Li⁺ in the 0.60 nm CNT. When Cl⁻ participates in the first coordination layer of Li⁺, the area of green patches between CNTs and water molecules is larger and the interaction is stronger. The distribution of green patches between CNTs and water molecules in the 0.73 nm CNT is wider than that of the 0.60 nm CNT, which indicates that the interaction among water molecules around Li⁺ is weaker, and water molecules are more likely to be displaced by ions so that the CIP of Li⁺ and Cl⁻ is more easily formed in the 0.73 nm CNT. The same cases are analyzed in the 1.28 nm CNT as the 0.60 nm CNT, and the distribution of green patches between CNT and water molecules reaches its maximum when the CIP of Li⁺ and Cl⁻ is formed. However, due to the large number of water molecules contained in the 1.28 nm CNT, the hydrogen bond network between the water molecules is larger and the water molecules are more ordered, which results in insufficient stability in the formation of CIP in the CNT and is the same as the MD results.