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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Molecular-Level Understanding of Structures and Dynamics of Imidazolium-Based Ionic Liquids around Single-Walled Carbon Nanotubes: Different Effects between Alkyl Chains of Cations and Nanotube Diameters Kuilin Peng, Xueping Wang, Qin Huang, Zhen Yang, Yunzhi Li, and Xiangshu Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03299 • Publication Date (Web): 14 Jul 2019 Downloaded from pubs.acs.org on July 18, 2019

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The Journal of Physical Chemistry

Molecular-level

Understanding

of

Structures

and

Dynamics

of

Imidazolium-Based Ionic Liquids around Single-Walled Carbon Nanotubes: Different Effects between Alkyl Chains of Cations and Nanotube Diameters

Kuilin Peng,1 Xueping Wang,1 Qin Huang,1 Zhen Yang,*,1 Yunzhi Li,*,2 Xiangshu Chen,*,1

1Institute

of Advanced Materials (IAM), State-Province Joint Engineering Laboratory of Zeolite

Membrane Materials, College of Chemistry and Chemical Engineering, Jiangxi Normal University, Nanchang 330022, People’s Republic of China

2School

of Chemistry and Chemical Engineering, Linyi University, Linyi, 276000,

Republic of China

ACS Paragon Plus Environment

People's

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Here we have performed a series of molecular dynamics simulations to investigate the solvation structures and dynamics of imidazolium-based ionic liquids (i.e., [Emim][BF4] and [Bmim][BF4]) around single-walled carbon nanotubes (CNTs) with two different diameters. We make an effort to address the effects of both the alkyl chains of cations and the CNT diameters on the interfacial properties as well as the reasons behind these effects. Our simulation results demonstrate that increasing the CNT diameter can lead to a larger interaction between the ions and the CNTs so that more cations and anions tend to aggregate around the larger CNT, while the alkyl chain is found to have a negligible effect on the relevant structures in the first solvation shell. Meanwhile, the imidazolium rings of cations prefer to be almost parallel to the CNT surface, and the preference can be further enhanced by the larger CNT diameter and the longer alkyl chain. On the other hand, either increasing the CNT diameter or the alkyl chain length can result in slower rotational motions of cations around the CNT but the latter have a more considerable effect, which is significantly different from their effects on the solvation structures. In addition, the anions have the same dependence of their rotational motions around the CNTs on the


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alkyl chain length as the cations. Our simulation analysis further reveals that the same dependence results from that the alkyl chains of cations can affect the hydrogen bonds between cations and anions, so that they have an indirect and considerable influence on the rotational motions of anions.

1. INTRODUCTION In the past decades, carbon nanotubes (CNTs) have always been a research hotspot in the scientific community due to their remarkable optical, mechanical, thermal, and electrical properties.1–5 Nevertheless, both the practical preparation and application of CNTs are mainly hindered by their low dissolving capacity in water and organic solvents because of the strong van der Waals attractions between them and their hydrophobic nature.6,7 Recently, many experimental investigations have demonstrated that ionic liquids (ILs), especially the imidazolium-based ILs, are able to replace those traditional solvents for making stable dispersions of various CNTs and metal nanoparticles without any other stabilizing agents.8–14 Therefore, it is possible to synthesize a variety of highly functionalized ILs suitable for the preparation and application of CNTs by modifying either the anion or the cation since their combinations are extremely large.15–17 However, the interaction mechanism and the relevant interfacial properties between the imidazolium-based ILs and the CNTs are still unclear up to now, which are extremely crucial to make a further progress in the CNT dispersions, to facilitate the possible application of individual CNTs, and to



accelerate the synthesis of CNT-based functional materials. Experimentally, a large number of efforts have been made to explore the interaction mechanism between the imidazolium-based ILs and the CNTs.6,8,18–25 A major opinion speculated from various experimental observations is that the π-π stacking interaction between the imidazolium cations and the CNTs should be responsible for the stable dispersion of CNTs in imidazolium-based ILs.8,22–24 On the contrary, both Raman and IR evidences of Li and co-workers6 indicated that the imidazolium-based ILs interact with the CNTs through the weak van der Waals interaction other than the π-π stacking. What’s more, Ding and Su18 attributed the primary interaction to a kind of static-assisted C–H-π hydrogen bond (HB) between the imidazolium rings of cations and the CNTs. More recently, Wojslawski et al.25 performed a detailed analysis of their adsorption data to reveal that the adsorption mechanism of ILs on the CNTs is complex, including the dominating π-π stacking with the indispensable van der Waals and electrostatic interactions. Above all, the debates from different experimental observations about the interaction mechanism between the imidazolium-based ILs and the CNTs may result from the situation that these experimental results originated from various investigated systems with different cations and anions in ILs and different CNT diameters. Furthermore, these collective experiments are unable to provide a direct observation on the corresponding microscopic interface properties.26,27 Therefore, it is still critical to provide a molecular-level understanding of the relevant interaction mechanism and interfacial properties.


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As a powerful analysis tool, molecular dynamics (MD) simulation can provide a direct and deep insight into both the interaction mechanism and the relevant interfacial properties between the imidazolium-based ILs and the CNTs at a molecular level.26,28–35 For example, Shim and Kim33 used MD simulations to demonstrate for the first time that both the [Emim]+ cations and the [BF4]– anions always display a smeared-out, cylindrical multi-shell density distributions around all CNTs with different diameters, and the imidazolium rings of [Emim]+ cations in the first solvation shell prefer to be parallel to the CNT surfaces due to the π-π stacking interactions between them. Subsequently, the other orientation pattern was further found from the MD simulation of Huo and Liu,26 where the imidazolium rings of [Bmim]+ cations next to the first solvation shell are perpendicular to the CNT(6,6) surface with their butyl chains appearing in the first solvation shell. In addition, Fedorov and co-workers34 compared three imidazolium-based ILs on the non-charged, positive, and negative CNT(6,6) surfaces, respectively. They found that the imidazolium rings of cations always tend to lay parallel to both the non-charged and negative CNT surfaces irrespective of the alkyl chain length. However, the alkyl chain length has a considerably influence on the orientation of imidazolium rings on the positive CNT surface, where the [Emim]+ cations are preferentially perpendicular to the surface, and the [Bmim]+ cations have both perpendicular and parallel orientations, and the [Omim]+ cations tend to be parallel to the surface. More recently, Noh and Jung36 further used equilibrium and non-equilibrium MD simulations to reveal that the rearrangement of the ionic layer structure on the electrode surface has a



considerable influence on the charging dynamics of the IL-based electric double layer capacitor. Despite the progress in the interaction mechanism and the structural orientations from previous experiments and simulations, few detailed studies were reported about the corresponding dynamics and HB properties of imidazolium-based ILs around the CNTs. To shed light on above issues, a series of MD simulations have been carried out here to explore the effects of both the alkyl chains of cations and the CNT diameters on the structures and dynamics of imidazolium-based ILs around the CNTs. Detailed solvation structures, structural orientations, rotational motions, interaction energies, and HBs of cations and anions in the first solvation shell of the CNTs have been provided and discussed. Different effects of both the alkyl chains of cations and the CNT diameters on the relevant structures and dynamics have been revealed for the first time in this work. The paper is organized as follows: the MD simulation details are present in Section 2. Then, the simulation results and discussion are shown in Section 3. Finally, we offer a few general conclusions in Section 4.

2. MD SIMULATION DETAILS In this work, two different imidazolium-based ILs of [Emim][BF4] and [Bmim][BF4] were considered and modeled by an all-atom force field proposed by Chaban et al.37 Based on the force field of Wang and co-workers,38 all atomic charges were scaled by 0.80 for the [Emim][BF4] IL and 0.84 for the [Bmim][BF4] IL in the


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version of Chaban et al.,37 to better reproduce the experimental properties including densities, heats of vaporization, diffusion coefficients, ionic conductivities, and shear viscosities. Meanwhile, two different armchair-type CNTs (4,4) and (12,12) were also considered here, with the diameters of 5.42 and 16.27 Å, respectively. During all MD simulations, the CNTs were always fixed and rigid with a C-C bond length of 1.42 Å so that the repeating unit length is 2.46 Å in the axial direction (i.e., z direction). Herein, all CNT length was always kept at 56.57 Å, corresponding to 23 times of 2.46 Å to meet the periodic boundary condition. Namely, the C atoms at the CNT edges were not saturated by the hydrogen atom since the periodic boundary condition was used for all three directions in this work. Each C atom in CNTs was treated as an uncharged particle interacting through the Lennard-Jones (L-J) potential, which has been extensively applied to describe the CNT properties.39–41 All L-J parameters and partial atomic charges of [Bmim][BF4], [Emim][BF4], and CNT used were summarized in Table S1 of the Supporting Information. Then, the mixed L-J parameters were derived by the Lorentz-Berthelot combining rule, i.e., σ ij =

1 (σ i + σ j ) and ε ij = ε iε j . In 2

addition, the cutoff distance of nonbonded interactions was always set to 15 Å, and the long-range electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method.42 All the simulation systems in this work were listed in Table S2 and the corresponding snapshots after equilibration are shown in Figure S1 of the Supporting Information. For each simulation system, an NPT MD of 10 ns was first carried out for equilibration, and then the next NPT MD was of 50 ns was performed for data



analysis with the trajectories stored every 100 fs. During all MD simulations, Newton’s equations of motion was integrated by using the Beeman algorithm with a time a time step of 1.0 fs. Meanwhile, both the temperature and pressure were controlled by using the Berendsen algorithm with the coupling times of 0.4 and 2.0 ps, respectively. Furthermore, it should be emphasized that the isobaric condition was controlled by only changing the x and y dimensions of the simulation cell. In addition, another NPT MD simulation of 100 ps following the above final configuration was performed to calculate the continuous HB dynamics. The trajectories were stored every 5 fs instead of 100 fs, which is short enough to accurately calculate continuous HB dynamics. All MD simulations in this work were performed by using the modified Tinker 7.0 code.43

3. RESULTS AND DISCUSSION Figure 1a and b shows the cylindrical radial distribution functions (RDFs) g (r ) of the [Emim]+ and the [Bmim]+ cations as well as the [BF4]– anion around the CNTs with different diameters, where the positions of two cations are represented by the geometric centers of their imidazolium rings and that of an anion is represented by its B atom, respectively. The cylindrical RDF is around the CNT axis (i.e., the z direction) and defined as the ratio of the local density ρ (r ) within a cylindrical shell at radial position r to the corresponding bulk density ρ bulk , i.e., g (r ) = ρ (r ) ρ bulk . We can see clearly from Figure 1a that the first maximum peaks of both cations around the


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larger CNT(12,12) are obviously higher than the counterparts around the smaller CNT(4,4), which can be well supported by the larger interaction energies between the imidazolium rings and the larger CNT as shown in Figure 1c. Similar phenomena can be observed for the anions in Figure 1b and e. These results indicate that both cations and anions tend to aggregate around the larger CNT due to the larger interactions between them. Figure 1 c-e present that the average interaction energies per segment arise from the imidazolium rings and alkyl chains of cations, and the anions in the first solvation shell with the CNT, respectively. Based on the corresponding RDF curves, the first solvation shell should be defined by the distance between the CNT surface (i.e., the radial distance of g (r ) = 0 ) and the first minimum valley. Herein, the radial positions of the first minimum valleys for the imidazolium cations and the anions are 9.2 and 8.8 Å around the CNT(4,4) while those are 14.7 and 14.2 Å around the CNT(12,12), respectively. It should be noted that each average interaction energy is taken over all tagged ions in the first solvation shell at all different equilibrium configurations. Furthermore, the effective interaction energies between the cations (or anions) and the CNT are only calculated through the Lennard-Jones potential in terms of the empirical force field used in this work. In addition, the comparisons in Figure 1 show that the first maximum peaks of cations are also considerable higher than those of anions around the same CNTs since the interaction energies between the imidazolium rings and the CNTs are twice more than those between the anions and the CNTs due to the presence of π-π stacking interactions, as shown in previous experimental22–24,44 and theoretical26,33–35 studies.



Furthermore, the following orientational distributions in Figure 2 also show that the imidazolium rings of cations tend to be parallel to the CNT surface. Such parallel orientation of the imidazolium rings on the CNT surface is an obvious characteristic for the presence of π-π stacking between them, as shown in previous MD simulations.33 Meanwhile, Figure 1a shows that both kinds of cations almost display the same structures in the first solvation shell around the CNTs but some minor differences in the second solvation shell. Therefore, the alkyl chains of cations have a negligible effect on the structure of cations in the first solvation shell around the CNTs since the dominating interactions between the cations and the CNTs arise from the imidazolium rings in the first solvation shell (see Figure 1c and d). However, the cations in the second solvation shell have no π-π stacking interaction with the CNTs so that the imidazolium rings are not a dominating factor. As shown in Figure S2 of the Supporting Information, the average interactions per ethyl chain of [Emim]+ cation with the CNTs are almost the same as those per imidazolium ring of [Emim]+ cation while those per butyl chain of [Bmim]+ cation with the CNTs are about three times larger than those those per imidazolium ring of [Bmim]+ cation in the second solvation shell. Therefore, longer alkyl chains can provide more contribution to the whole attractive interactions between the cations and the CNTs, leading to more [Bmim]+ cations gathering in the second solvation shell (see Figure 1a). On the contrary, the AFM observations of Li et al.45 showed that the alkyl chain length has an obvious effect on the solvation structure of imidazolium-based ILs on the Au(111) surface through comparison between [Bmim]FAP, and [Hmim]FAP ILs. They found


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that the [Hmim]+ is more strongly structured than [Bmim]+ due to the solvophobic interaction from the longer alkyl chains. Besides the different alkyl chain length, the contrary conclusion of Li and Atkin45 may result from different surfaces in our simulation since the Au(111) surface have no π-π stacking interaction with the imidazolium rings of cations but a stronger van der Waals interaction with the alkyl chains of cations. Next, Figure 2 presents the orientational distributions of the [Emim]+ and the [Bmim]+ cations in the first solvation shell of CNTs. As shown in Figure 2a, we define two vectors r1 and r2 for the CNT where the vector r1 is the CNT axis (i.e., the z direction) and the vector r2 is the radial direction of CNT across the geometric center of imidazolium ring. Meanwhile, the orientation of a cation is defined by its normal vector r3. Then, the orientation of a cation on CNT surface can be determined by the combination of the angle α between r1 and r3 and the angle β between r2 and r3. We can see from Figure 2b and c that all angle α distributions have a quite high and narrow peak around 90° while all angle β distributions show two big peaks located at about 15° and 165° respectively regardless of the alkyl chain length and the CNT diameter. Such angle distributions of α and β can clearly indicate that the imidazolium rings of cations are almost parallel to the CNT surface. Similar orientational phenomena have been observed for other imidazolium-based ILs near the CNTs and the graphenes.33,34,46–51 Moreover, the density functional calculations of Ghatee and Moosavi51 have further revealed that the hydrophobic imidazolium-based ILs with the [BF6]– anions rather than the hydrophilic ones with the Cl– anions tend to



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take a parallel orientation with the circumcoronene surface. This is because the hydrophobic ILs interact stronger with the circumcoronene than the hydrophilic ILs due to less anion-cation charge transfer and more charge modification on the circumcoronene in the case of hydrophobic ILs. In addition, the three peaks in both the α and β curves of the [Bmim]+ cations around both CNTs and the [Emim]+ cations around the CNT(12,12), are higher than that of the [Emim]+ cations around the CNT(4,4), showing that the orientational preference of cations can be further enhanced by the larger CNT and the longer alkyl chain. Beside the solvation structures, the rotational dynamics of cations and anions is another important characteristic at the interface, which can be calculated by the rotational time correlation function TCF Cr (t ) 52,53

Cr (t ) =

1 Ni

Ni

∑ u (t )u (0) j =1

j

j

(1)

where N i is the total number of ions (the cations or the anions) in the first solvation shell at time 0 and the u j (t ) is the unit vector of jth ion at time t. The angular bracket means that the ensemble averaging is taken over all tagged ions at different reference initial times. Herein, the normal vector r3 of the imidazolium ring and the vector r4 from the B atom to one F atom are used to represent the orientations of cations and anions, respectively. The detailed comparisons in Figure 3 show that the rotational TCF curves of both the [Emim]+ and the [Bmim]+ cations around the larger CNT(12,12) decay much slower than the counterparts around the smaller CNT(4,4), suggesting that the larger CNT can lead to a slower rotational motion of cations.


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Meanwhile, the [Bmim]+ cations rotate more slowly than the [Emim]+ cations when they are around the same CNTs. More importantly, the [Bmim]+ cations around the smaller CNT(4,4) also have a slower rotational motion than the [Emim]+ cations around the larger CNT(12,12), indicating that the alkyl chains of cations have a more considerable influence on their rotational motions on the CNT surface compared to the CNT diameter. Accordingly, the rotational relaxation time τ r can be obtained by fitting these rotational TCF curves in terms of a three weighted exponential function.53

As

shown

[Bmim]+/CNT(12,12)

in >

Table

1,

the

[Bmim]+/CNT(4,4)

order >

of

these

τr

values

[Emim]+/CNT(12,12)

is >

[Emim]+/CNT(4,4). In fact, the considerable interactions between the longer alkyl chains and the CNTs can provide a stronger anchoring effect on the imidazolium rings of cations to stick firmly to the CNT surface, as shown in Figure 1d. Additionally, it should be noted that such considerable effect of the alkyl chains on the rotational motions is significantly different from their negligible effect on the solvation structures (see Figure 1a). On the other hand, we can find that all rotational TCF curves of anions decay much faster than those of cations, indicating that the anions rotate much faster than the cations in the first solvation shell of CNTs due to the smaller interactions with the CNTs and their symmetry structure. Similar results have been observed for various ILs in the bulk phase and at the interface.54–56 To our surprise, however, the anions around the CNTs have the same dependence of rotational motions on the alkyl chain length and the CNT diameter as the cations. Actually, the rotational motions of cations



or anions is a local dynamics behavior. The previous simulation studies have revealed that the rotational motions of cations or anions in the bulk ILs are determined by their local and directional HBs rather than the whole electrostatic interactions,56–58 where stronger HBs can provide more restriction on their rotational motions. This is because the rotational motions of ions only require the rearrangements of their neighboring hydrogen bonds, as shown in the previous MD simulations.56–58 Therefore, the same order of the rotational motions between cations and anions may be attributed to that the alkyl chains of cations affect the HBs between cations and anions and then have an indirect influence on the anions. To confirm our deduction above, the HBs between cations and anions in the first solvation shell of CNTs is characterized through the corresponding continuous and intermittent HB TCFs of S HB (t ) and C HB (t ) , where the relaxation times of τ SHB and τ CHB can be also calculated through the same three weighted exponential function.39,59–61 Furthermore, the larger values of τ SHB and τ CHB mean the larger HB strength. Based on the geometric criteria defined from our previous simulation,55 the HB formation (C—H…F) between the imidazolium rings of cations and the anions is R HF < 3.5 Å and θ CHF > 135°. Then, the comparisons from Figure 4 demonstrate that either increasing the CNT diameter or the alkyl chain length can result in a slower decay for both the S HB (t ) and C HB (t ) curves in the first solvation shell and the HB TCFs of [Bmim]+ cations around the smaller CNT(4,4) also have a slower decay than the [Emim]+ cations around the larger CNT(12,12), suggesting that both the larger CNT diameter and the longer alkyl chain can result in the enhanced HBs between


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cations and anions in the first solvation shell of CNTs but the latter has more effect. More importantly, we can find clearly from Table 1 that the order of the HB strength is well consistent with those of the rotational motions of both cations and anions, which confirms our deduction above. Our simulation results further confirmed that the rotational motions of anions around the CNTs are still determined by the relevant HBs, as shown those in the bulk ILs.56–58

4. CONCLUSIONS In this work, a series of MD simulations have been carried out to systematically explore the structure and the dynamics properties of two kinds of imidazolium-based ILs (i.e., [Emim][BF4] and the [Bmim][BF4]) around two CNTs (4,4) and (12,12), respectively. Our simulation results show that the alkyl chain has a negligible effect on the structures of cations in the first solvation shell around the CNTs while the CNT diameter has an obvious effect on the relevant solvation structures. Meanwhile, the imidazolium rings of cations prefer to be almost parallel to the surface of the CNTs, and both the larger CNT and the longer alkyl chain can further enhance the preference. On the other hand, the alkyl chains of cations are found to have a more considerable influence on the their rotational motions on the CNT surface compared to the CNT diameter, which is significantly different from the comparison results in the solvation structures. More interestingly, the anions around the CNTs display the same dependence of their rotational motions on the alkyl chain length and the CNT



diameter as the cations, although the anions have no the side alkyl chain. The identical order in their rotational motions can be attributed to the HBs between cations and anions around the CNTs. This is because the alkyl chains of cations affect the HBs between cations and anions so that they have an indirect influence on the rotaional motions of anions. Our simulation results clearly reveal that both the CNT diameter and the alkyl chain length can result in the enhanced HBs between cations and anions in the first solvation shell of CNTs but the latter has more effect. Therefore, our simulation results in this work provide a molecular-level understanding of the key role of the alkyl chain of cation and the CNT diameter to determining the unique interfacial properties of imidazolium-based ILs around the CNTs, which is of importance for the stabilization mechanism of the CNT dispersing in the imidazolium-based ILs.

ASSOCIATED CONTENT Supporting Information 1. Details of force field and simulation systems；2. Typical equilibrium snapshots; 3. Average interaction per segment in the second solvation shell.

AUTHOR INFORMATION Corresponding Author


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*E-mail: [email protected] (Z.Y.) *E-mail: [email protected] (Y.Z.L.) *E-mail: [email protected] (X.S.C.)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 21463011 and 21863005), Natural Science Foundation of Jiangxi Province (No. 20171BAB203012), Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) under Grant No.U1501501, the Sponsored Program for Cultivating Youths of Outstanding Ability in Jiangxi Normal University.

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Page 26 of 33

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Table 1. Rotational relaxation time and structural relaxation time τ C

HB

τ r (ps) of cations and anions, average lifetime τ SHB (ps) (ps) of the HBs between the cations and the anions in the first

solvation shell around the CNTs.

system

τ r (cation)

τ r (anion)

τ SHB

τ CHB

[Emim][BF4] /CNT(4,4)

747.3

19.6

5.71

155.76

[Bmim][BF4] /CNT(4,4)

1871.0

22.2

7.08

497.58

[Emim][BF4]/CNT(12,12)

1299.8

20.1

6.24

238.94

[Bmim][BF4]/CNT(12,12)

2828.5

22.5

7.94

736.52


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Figure Captions Figure 1. Cylindrical RDFs of (a) the cations and (b) the anions around the CNTs, as well as average interaction energies per segment in the first solvation shell with the CNTs: (c) the imidazolium rings of cations, (d) the alkyl chains of cations, and (e) the anions, as shown in the middle

schematic

illustration.

The

[Emim][BF4]/CNT(4,4),

[Bmim][BF4]/CNT(4,4),

[Emim][BF4]/CNT(12,12), and [Bmim][BF4]/CNT(12,12) systems are represented by black, red, blue, and cyan, respectively.

Figure 2. (a) Schematic illustrations for the definitions of vectors and angles, and angle distributions of (b)

α and (c) β for the cations in the first solvation shell around the CNTs.



The colors of different systems are the same as in Figure 1.

Figure 3. Rotational TCFs Cr (t ) of (a) the cations and (b) the anions in the first solvation shell around the CNTs. The colors of different systems are the same as in Figure 1.

Figure 4. Continuous TCF S HB (t ) for the HBs between the cations and the anions in the first solvation shell around the CNTs. The inset shows the HB definition and the corresponding intermittent TCF CHB (t ) . The colors of different systems are the same as in Figure 1.


Page 28 of 33

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Figure 1. Cylindrical RDFs of (a) the cations and (b) the anions around the CNTs, as well as average interaction energies per segment in the first solvation shell with the CNTs: (c) the imidazolium rings of cations, (d) the alkyl chains of cations, and (e) the anions, as shown in the middle

schematic

illustration.

The

[Emim][BF4]/CNT(4,4),

[Bmim][BF4]/CNT(4,4),

[Emim][BF4]/CNT(12,12), and [Bmim][BF4]/CNT(12,12) systems are represented by black, red, blue, and cyan, respectively.



Figure 2. (a) Schematic illustrations for the definitions of vectors and angles, and angle distributions of (b)

α and (c) β for the cations in the first solvation shell around the CNTs.

The colors of different systems are the same as in Figure 1.


Page 30 of 33

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Figure 3. Rotational TCFs Cr (t ) of (a) the cations and (b) the anions in the first solvation shell around the CNTs. The colors of different systems are the same as in Figure 1.



Figure 4. Continuous TCF S HB (t ) for the HBs between the cations and the anions in the first solvation shell around the CNTs. The inset shows the HB definition and the corresponding intermittent TCF CHB (t ) . The colors of different systems are the same as in Figure 1.


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