Molecular dynamics simulations of the interactions between β-cyclodextrin derivatives and single-walled carbon nanotubes

Computational Materials Science 50 (2010) 283–290

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Molecular dynamics simulations of the interactions between b-cyclodextrin derivatives and single-walled carbon nanotubes Jinyu Pang, Guiying Xu *, Yan Bai, Shiling Yuan, Fang He, Yajing Wang, Hongyuan Sun, Aiyou Hao Key Laboratory of Colloid and Interface Chemistry, Ministry of Education, Shandong University, Jinan 250100, PR China

a r t i c l e

i n f o

Article history: Received 7 June 2010 Received in revised form 28 July 2010 Accepted 5 August 2010

Keywords: Single-walled carbon nanotube Cyclodextrin Interaction Molecular dynamics simulation

a b s t r a c t Since cyclodextrins (CDs) were discovered to be an excellent reagent to disperse carbon nanotubes (CNTs), they were used for the construction of CD/CNT based electrodes. Therefore, it is crucial to investigate the interactions between CDs and CNTs for their applications. Herein, b-cyclodextrin (b-CD) and their four derivatives, 2-O-(2-hydroxypropyl)-b-cyclodextrin (2-HP-b-CD), 6-O-(2-hydroxypropyl)b-cyclodextrin (6-HP-b-CD), 2-O-(2-hydroxybutyl)-b-cyclodextrin (2-HB-b-CD) and 6-O-(2-hydroxybutyl)-b-cyclodextrin (6-HB-b-CD), were employed to investigate the interactions with single-walled carbon nanotubes (SWNTs) both in anhydrous and aqueous conditions by molecular dynamics simulation. The results showed that the interactions between SWNTs and CDs were strongly influenced by the structures of CDs such as substituted group and position. The attractive interactions between SWNTs and CDs monotonically increased with the radius of SWNT. Van der Waals attraction was the dominating force for CDs wrapped onto the surface of the nanotube ropes. Therefore, the results could provide a fundament for the choice of CDs in their further applications. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Carbon nanotubes (CNTs), a new form of elementary carbon, are composed of graphitic sheets rolled into cylinders with nanometer, diameter and micrometer length. They have received great interest in their unique properties and wide scope of possible applications [1–4]. However, a major barrier for CNT utilization especially for single-walled carbon nanotubes (SWNTs) is their poor solubility and dispersability both in aqueous and organic media [5]. Thus, much effort has been devoted for years to prepare stable dispersions of SWNTs in different solvents. Compared to chemical modification of CNTs, noncovalent method has the advantage of no disruption of the structure and electronic property of the native tube. Cyclodextrins (CDs) are macrocyclic oligosugars commonly composed of 6, 7 or 8 glucosidic units named a-, b- and c-cyclodextrin, respectively [6]. They have a hydrophobic inner cavity and a hydrophilic outside surface, even could interact with CNTs [7]. Chen et al. [8] proposed that CDs could efficiently disperse SWNTs and they possibly adsorb at the surface of the nanotubes via Van der Waals force. Subsequently, Chambers et al. [9] and Liu et al. [10] reported the similar results. CDs adsorbed on the sur-

face of CNTs by Van der Waals force and the hydrogen-bonding interaction between adjacent CD molecules was responsible for the formation of CNT–CD complexes. CDs are excellent reagents to disperse CNTs, and their composites in the construction of CD/ CNT based electrodes [11,12] could be used as electrochemical sensor [13–15]. Therefore, it is crucial to investigate the interactions between CDs and CNTs to guide the choice of CDs in their applications. In recent years, computer simulations [16] have been widely used to investigate the ‘‘wrapping” of CNTs. It has been proved by molecular dynamics (MD) simulations that polymers [16–19] and biological macromolecules [20–22] can smoothly wrap around or insert into the nanotubes. Herein, we focused on the physisorption of CDs on SWNTs to investigate their interactions by MD simulation. b-Cyclodextrin (b-CD) and four cyclodextrin derivatives (2-HP-b-CD, 6-HP-b-CD, 2-HB-b-CD, and 6-HB-b-CD) were chosen to reveal the influence of the substituted group and position of CDs on their interacting process. The results may provide a better understanding on the mechanism of the interaction between CDs and CNTs. 2. Simulation and models

* Corresponding author. Tel.: +86 531 88365436; fax: +86 531 8856 4750. E-mail addresses: [email protected] (J. Pang), [email protected] (G. Xu), [email protected] (Y. Bai), [email protected] (S. Yuan), [email protected] (F. He), [email protected] (Y. Wang), 56832153@ qq.com (H. Sun), [email protected] (A. Hao). 0927-0256/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2010.08.016

2.1. Computational method In general, the total potential energy includes the following terms [23]:

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Etotal ¼ Evalence þ Ecross-term þ Enon-band

ð1Þ

quently, target CDs were initially placed at the side of SWNTs in two directions to simulate their adsorption on the surface of SWNTs.

where the first term (Evalence) includes a bond stretching, a twobond angle, a dihedral bond-torsion term, an inversion (or an outof-plane interaction) and a Urey–Bradlay. The effects of bond lengths and angle changes caused by the surrounding atoms are contained in the second term (Ecross-term). The third term (Enon-bond) corresponding to the interactions between non-bonded atoms includes Van der Waals, coulomb electrostatic and hydrogen bond energies. MD simulations were carried out in the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field [24], which is an ab initio force-field model and the non-bond energy is denoted as

Enon-band

X i;j

"  9  o 6 # X ro r qi qij eij 2 ij  3 ij þ r ij rij rij i;j

2.3. Interaction energy and interfacial binding energy The dynamic behavior can be illustrated by tracking the interaction energy of SWNT–CD molecules. Generally, the interaction energy is estimated from the difference between the potential energy of the complex and the energies of CD and corresponding SWNT. It is calculated according to the following equation [28]:

Einteraction ¼ Etotal  ESWNT  ECD

ð3Þ

where Etotal, ESWNT and ECD are the potential energies of the complex, individual nanotube and CD, respectively.

ð2Þ

3. Results and discussion where rij, r oij and eij are the distance, dimension and energy parameter between particles i and j, respectively. The charges of i and j are expressed as qi and qj. All the simulations were performed in the software of Material Studio 4.3 with NVT canonical ensemble and periodic boundary conditions [25]. The temperature was controlled at 298 K by the Hoover–Nose thermostat with relaxation time of 0.2 ps [26,27]. The simulations of the target systems were carried out for 200 ps, which is adequate for this system [17,19,25], with a time step of 0.001 ps to obtain the dynamic information. The dimensions of the simulation box were 4.32  4.32  4.32 nm3.

3.1. Morphology of SWNT–CDs We simulated the adsorption process of b-CD, 2-HP-b-CD, 6-HPb-CD, 2-HB-b-CD and 6-HB-b-CD in different directions on the surface of SWNT. The snapshots of the two systems, the primary hydroxyls of CD toward SWNT (S1) and the secondary hydroxyls of CD toward SWNT (S2), observed at different time steps of the simulations are shown in Figs. 2 and 3. Initially, the CDs are put near the middle of SWNT at a distance of 0.95 nm (cutoff radius). All the CDs move toward SWNT with the increase of time step until they finally wrap on the surface of the helix of SWNT. After 60 ps, all the CDs wrap onto SWNT entirely. The change ratio of the simulation temperature is less than 5%. Therefore, these systems were considered to attain the equilibrium. As we can also observe from Figs. 2 and 3, the hydroxypropyl group of HP-b-CD and the hydroxybutyl group of HB-b-CD gradually stick onto the sidewall of SWNT and almost the whole chain are attached to the outer surface of the nanotube. Subsequently, most of the hydroxypropyl and hydroxybutyl groups wrap around SWNT.

2.2. Molecular model Molecular models of SWNTs with different diameters were established from a structure database in Material Studio 4.3. The unsaturated boundary effect was avoided by adding hydrogen atoms at the ends of SWNT. Each hydrogen atom had a charge of 0.1268e and the charge of the carbon atom connecting to it was 0.1268e. Therefore, the whole SWNT segment was neutral. Each C–C and C–H bond length was 0.142 and 0.114 nm, respectively. The computer graphics of a (11, 11) SWNT model was shown in Fig. 1a, which was 4.919 nm long with 880 carbon atoms and 44 hydrogen atoms. The structures of simulated CDs (b-CD, 2-HP-b-CD, 6-HP-b-CD, 2-HB-b-CD, and 6-HB-b-CD) were shown in Fig. 1b. Since a CD molecule has two different hydroxyl groups at the two ends of its cavity, a primary (tail) and a secondary (head) hydroxyl group, it is possible that either end of CD can interact with SWNTs. Conse-

3.2. Potential energy between SWNT and CDs Potential energy evolution of SWNT and CDs is shown in Fig. 4. Although there are fluctuations through the simulation times, the change ratio in all the systems is less than 0.23% after 60 ps. SWNT/6-HP-b-CD and SWNT/6-HB-b-CD have the highest potential energies during the simulations. The substituted groups of 6-

O

OH

OR

3

2

1 O

OH

7-n

O OH

5 6

4

n

O

OH

R'O

β-CD: R=H, R'=H 2-HP-β-CD: R=CH2CHOHCH3, R'=H 6-HP-β-CD: R=H, R'=CH2CHOHCH3 2-HB-β-CD: R=CH2CHOHCH2CH3, R'=H 6-HB-β-CD: R=H, R'=CH2CHOHCH2CH3

(a)

(b)

Fig. 1. (a) Molecular model of (11, 11) SWNT (carbon and hydrogen atoms are marked in grey and white, respectively) and (b) the structures of b-CD, HB-b-CD and HP-b-CD (n = 3, substituted groups were randomly distributed).

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0 ps (a)

40 ps (a)

0 ps (b)

10 ps (b)

0 ps (c)

10 ps (c)

0 ps (d)

20 ps (d)

0 ps (e)

10 ps (e)

60 ps (a)

40 ps (b)

50 ps (c)

60 ps (d)

45 ps (e)

Fig. 2. MD simulation snapshots of the interacting process of SWNT and CDs in S1: (a) b-CD, (b) 2-HP-b-CD, (c) 6-HP-b-CD, (d) 2-HB-b-CD and (e) 6-HB-b-CD. (Oxygen atom is expressed in red, carbon atom is in grey and hydrogen atom is in white.)

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0 ps (a)

20 ps (a)

60 ps (a)

0 ps (b)

20 ps (b)

50 ps (b)

0 ps (c)

0 ps (d)

0 ps (e)

10 ps (c)

30 ps (c)

10 ps (d)

20 ps (d)

20 ps (e)

45 ps (e)

Fig. 3. MD simulation snapshots of the interacting process of SWNT and CDs in S2: (a) b-CD, (b) 2-HP-b-CD, (c) 6-HP-b-CD, (d) 2-HB-b-CD, and (e) 6-HB-b-CD.

HP-b-CD and 6-HB-b-CD are toward SWNT in S1. Possession of an attractive interaction with the surface of SWNT, they can strongly

interact with SWNT. Therefore, SWNT/6-HP-b-CD and SWNT/6HB-b-CD have much higher energies at about 44250 kcal mol1.

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The interaction energy evolution recorded every 5 ps between SWNT and CDs in S1 and S2 are shown in Fig. 5a and b, respectively. The energies decrease steeply and then show little fluctuation after 60 ps, which also indicates these systems have attained the equilibrium. In equilibrium, SWNT/6-HP-b-CD and SWNT/6HB-b-CD get the highest interaction energies in S1 of about 59 kcal mol1 (Fig. 5a). On the other hand, the energies of SWNT/2-HP-b-CD and SWNT/2-HB-b-CD in equilibrium are the highest in S2, about 63 kcal mol1 (Fig. 5b). These results indicate that the HP-b-CD and HB-b-CD with substituted groups toward SWNT have stronger interaction with SWNT. Furthermore, the interaction energies of SWNT/b-CD in the two systems decrease more slowly than the others. Therefore, the substituted group can greatly influence the interactions between SWNT and CDs. Contrasted the results of the interaction energies in S1 and S2, it is clear that higher energies are attained in S2. The head (secondary hydroxyls) of CDs on more open side is likely to wrap more closely onto SWNT. Thus, 2-HP-b-CD and 2-HB-b-CD substituted in C-2 position obtain stronger interactions with SWNT in S2. Above results suggest that the substituted position also has a strong influence on the interaction between SWNT and CDs. 3.4. Dominating force of the interactions between SWNT and CDs

Potential energy/kcal.mol

-1

To reveal the interactions between SWNT and CDs, MD simulations were also used to investigate the dominating force of CDs wrapped onto SWNT. The total and non-bond interaction energies between SWNT and CDs were calculated and listed in Table 1. Obviously, the Van der Waals interaction energies are approximate to the total energies and the coulomb energies are nearly zero. It is indicated the interaction energies are mainly attributed to the energies of the Van der Waals attraction, i.e., Van der Waals attraction is the dominating force of CDs adsorbed on the surface of SWNT. This is in well agreement with the experimental results proposed by other researches [7–10]. Furthermore, the interaction between SWNT and b-CD is weaker both in S1 and S2. HP-b-CD and HB-b-CD with substituted groups toward SWNT can more easily and completely wrap around the surface of the nanotube, corresponding to stronger interac-

44500

(11,11)SWNT/β -CD (11,11)SWNT/2-HP-β -CD (11,11)SWNT/6-HP-β -CD (11,11)SWNT/2-HB-β -CD (11,11)SWNT/6-HB-β -CD

44400 44300 44200 44100 44000

0

50

100 Time/ps

(a)

150

200

3.5. Influence of SWNT radius on CD adhesion To determine the influence of SWNT radius on the interactions between SWNT and CDs, the armchair SWNT with radius variation from 1.085 to 1.898 nm were employed and the results are shown in Fig. 6. The attractive interactions between SWNT and CDs monotonically rise with the increase of SWNT radius. Larger radius is related to a smaller curvature of surface and the cavity of CDs is a rather stiff structure. Consequently, CDs favors to interact with the SWNT in larger radius. SWNT/6-HP-b-CD and SWNT/6-HB-b-CD have much higher interaction energies in S1 due to completely wrapping onto the surface of SWNT. SWNT/2-HP-b-CD and SWNT/2-HB-b-CD have more attractive interactions in S2. Although the substituted groups of 2-HP-b-CD and 2-HB-b-CD are deviated from the CNT in S1, part of them can interact with SWNT due to Van der Waals attraction. Thus, b-CD has the weakest interaction with SWNT both in S1 and S2. It cannot be neglected that the interaction energies of SWNT/nHB-b-CD are slightly higher than the energies of SWNT/n-HP-b-CD (n = 2, 6) in S1 or S2. As result of a longer substituted chain, HB-bCD can well align parallel to the surface of the nanotube and obtain stronger interactions. The difference between the interaction energies of SWNT/6-HP-b-CD and SWNT/6-HB-b-CD is more obvious than the difference between SWNT/2-HP-b-CD and SWNT/2-HBb-CD. Furthermore, as the diameter of SWNT increases, the interaction energy of SWNT/2-HP-b-CD (or SWNT/2-HB-b-CD) is gradually close to the energy of SWNT/6-HP-b-CD (or SWNT/6-HB-b-CD) in S1, while the energy of SWNT/6-HP-b-CD (or SWNT/6-HB-b-CD) is gradually close to that of SWNT/b-CD in S2. The head of CDs on the more open side is superior direction for CDs wrapping onto SWNT, so that the substituted group in the C-2 position can well align parallel to the surface of the nanotube. However, the substituted group in the C-6 position is not easy to completely wrap onto SWNT when the diameter is larger. This result is further evidence for the influence of the substituted position on the interactions between SWNT and CDs.

-1

3.3. Interaction energy between SWNT and CDs

tions. The CDs with substituted groups in the C-2 position wrap more closely onto SWNT. This results in much stronger interactions between SWNT and 2-HP-b-CD as well as 2-HB-b-CD in S2. Due to longer chain length of substituted group at the same position, SWNT has stronger interaction with n-HB-b-CD than n-HPb-CD (n = 2, 6) in S1 or S2. Therefore, it is confirmed that the substituted group and position have great influence on the interactions between SWNT and CDs.

Potential energy/kcal.mol

On the contrary, the substituted groups of 2-HP-b-CD and 2-HBb-CD deviated SWNT in S1 cannot wrap completely onto the nanotube so that b-CD, 2-HP-b-CD and 2-HB-b-CD get lower energies at about 44105 kcal mol1. Similar results were obtained in S2, it is inferred that the substitute group of CD toward SWNT result in higher potential energy.

44500

(11,11)SWNT/ β -CD (11,11)SWNT/2-HP-β -CD (11,11)SWNT/6-HP-β -CD (11,11)SWNT/2-HB-β -CD (11,11)SWNT/6-HB-β -CD

44400 44300 44200 44100 44000

0

50

100 Time/ps

(b)

Fig. 4. Potential energy evolution between SWNT and CDs in (a) S1 and (b) S2 during 200 ps.

150

200

-20

-40

-60 0

50

100 Time/ps

150

200

Interaction energy/kcal.mol

Interaction energy/kcal.mol

(11,11)SWNT/ β -CD (11,11)SWNT/2-HP- β -CD (11,11)SWNT/6-HP- β -CD (11,11)SWNT/2-HB- β -CD (11,11)SWNT/6-HB- β -CD

0

-1

J. Pang et al. / Computational Materials Science 50 (2010) 283–290 -1

288

(11,11)SWNT/ β -CD (11,11)SWNT/2-HP- β -CD (11,11)SWNT/6-HP- β -CD (11,11)SWNT/2-HB- β -CD (11,11)SWNT/6-HB- β -CD

0 -20 -40 -60 -80

0

50

(a)

100 Time/ps

150

200

(b)

Fig. 5. Interaction energy evolution between SWNT and CDs in (a) S1 and (b) S2 during 200 ps.

a b c

Interaction energies/kcal mol1

DEtotala

DEvdwb

DEcoulombc

SWNT/b-CD S1 S2 SWNT/2-HP-b-CD S1 S2 SWNT/6-HP-b-CD S1 S2 SWNT/2-HB-b-CD S1 S2 SWNT/6-HB-b-CD S1 S2

44.78 49.81 47.33 64.95 61.32 52.89 48.46 65.49 63.34 57.07

36.80 48.62 46.74 64.33 59.73 47.36 48.04 64.65 62.54 58.40

0.10 0.012 0.051 0.047 0.080 0.067 0.083 0.078 0.082 0.0064

The total interaction energies between SWNT and CDs. The Van der Waals interaction energies. The coulomb interaction energies.

3.6. Influence of water

Interaction Energy/Kcal⋅mol-1

To investigate the interactions between CDs and CNTs, the influence of water should be taken into account. Initially, SWNT and CDs were immerged into aqueous solution constructed of 2800 water molecules. After the minimization of the initial configurations with Smart Minimizer method, the simulations were carried out for 2.0 ns in the same conditions as in anhydrous systems. The simulation time is long enough to confirm the systems achieving the equilibrium, according to the small fluctuation with a low change ratio of the simulation temperature and potential energy. As the results referred above, the substituted group and position of CDs have great influence on the interactions between CDs and

0

SWNT/ β -CD SWNT/2-HP- β -CD SWNT/6-HP- β -CD SWNT/2-HB- β -CD SWNT/6-HB- β -CD

-20 -40 -60 -80 1.0

1.2

1.4 1.6 1.8 SWNT diameter/nm

(a)

2.0

SWNT. Therefore, the five CDs in S1 were all employed to investigate the interactions with SWNT in the presence of water. Fig. 7 shows the snapshots of interacting process of SWNT and CDs in aqueous solutions observed at different time steps of the simulations. Initially, the CDs are at the side of SWNT with a distance of 0.95 nm. The simulations show that all the CDs move toward SWNT until they finally wrap onto the surface of the nanotube. After 1.5 ns, CDs wrap onto SWNT and the equilibrium is achieved. Part of the substituted chains of 6-HB-b-CD and 6-HP-b-CD are attached to the outer surface of SWNT, while the substituted groups of 2-HP-b-CD and 2-HB-b-CD are favorable to stretch into water. Although all the CDs pass through much longer simulation time to wrap on SWNT, they finally stick onto the surface of the nanotube. It is suggested that the CDs favor to interact with SWNT rather than water. Different from the results in anhydrous systems, the substituted groups of 2-HP-b-CD and 2-HB-b-CD stretch into solution and the end of the substituted chains of 6-HB-b-CD and 6-HP-b-CD deviate from SWNT toward water. However in aqueous solution, the whole hydrophobic chains of CDs generally tend to be in water rather than partly interact with SWNT. The reasons for the substituted chains of 6-HB-b-CD and 6-HP-b-CD not toward water are likely caused by the initial location. CDs cavities are parallel to the surface of SWNT and either end (head or tail) of CDs can interact with CNTs [10]. Therefore, there are possibilities for CDs wrapping onto SWNT without the alteration of the initial orientation. The substitute groups of 6-HB-b-CD and 6-HP-b-CD are toward the surface of SWNT initially, while they are prior to stretch into water and finally the end of the substitute chain deviate from SWNT. In order to

Interaction Energy/Kcal⋅mol-1

Table 1 The total and non-bond interaction energies between SWNT and CDs.

0

SWNT/ β -CD SWNT/ 2-HP- β -CD SWNT/ 6-HP- β -CD SWNT/ 2-HB- β -CD SWNT/ 6-HB- β -CD

-20 -40 -60 -80 -100 1.0

1.2

1.4 1.6 1.8 SWNT diameter/nm

(b)

Fig. 6. Interaction energies between SWNT and CDs as a function of SWNT diameter in (a) S1 and (b) S2.

2.0

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0 ns (a)

0 ns (b)

0 ns (c)

0 ns (d)

0 ns (e)

1.0 ns (a)

1.0 ns (b)

1.0 ns (c)

1.0 ns (d)

1.0 ns (e)

1.5 ns (a)

1.5 ns (b)

1.5 ns (c)

1.5 ns (d)

1.5 ns (e)

Fig. 7. MD simulation snapshots of interacting process of SWNT and CDs in S1: (a) b-CD, (b) 2-HP-b-CD, (c) 6-HP-b-CD, (d) 2-HB-b-CD and (e) 6-HB-b-CD. (For clarify, water molecules are invisible.)

prove our opinion, 6-HB-b-CD in S2 were also simulated, as shown in Fig. 8. It can be observed that the hydroxybutyl group of 6-HB-b-

CD is prone to stretch into water, which is in the same behavior as the substituted groups of 2-HP-b-CD and 2-HB-b-CD in S1. There-

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0 ns

1.0 ns

1.5 ns

Fig. 8. MD simulation snapshots of the interacting process of 6-HB-b-CD and SWNT in S2.

Table 2 Interaction energies between SWNT and CDs in the presence of water. Interaction energies/kcal mol1

DEtotal

DEvdw

DEcoulomb

SWNT/b-CD S1 SWNT/2-HP-b-CD S1 SWNT/6-HP-b-CD S1 SWNT/2-HB-b-CD S1 SWNT/6-HB-b-CD S1

42.38 43.49 50.92 44.78 54.25

41.83 42.65 51.47 43.54 55.32

0.55 1.83 1.19 1.25 1.08

fore, the substitute groups of modified CDs are favorable toward water. The interaction energies between SWNT and CDs in aqueous systems were also calculated and listed in Table 2. The interactions between SWNT and b-CD are the weakest. SWNT has stronger interaction with n-HB-b-CD than n-HP-b-CD (n = 2, 6), which is similar to the result in anhydrous systems. It is suggested that the substituted group and position have great influence on the interactions between SWNT and CDs even in the presence of water. Van der Waals attraction is also the dominating force of CDs adsorbed on the surface of SWNT in aqueous systems. Moreover, the interaction energies between SWNT and CDs are lower in aqueous systems than in anhydrous systems. This is caused by the interactions between water and CDs which own a hydrophilic outside surface [6]. Although different results occur in aqueous systems, the influence of the substituted group and position is still pronounced. Therefore, we consider that the CDs with a proper group in the appropriate position could interact strongly with CNTs in aqueous solutions. 4. Conclusions MD simulations are carried out to investigate the interactions between SWNTs and five CDs (b-CD, 2-HP-b-CD, 6-HP-b-CD, 2HB-b-CD and 6-HB-b-CD) both in anhydrous and aqueous conditions. The simulation results show that the interactions between SWNT and CDs depend on their structure. Substituted groups of CDs toward SWNTs can more easily and completely wrap around the surface of SWNTs. CDs with longer C-2 substituted chains in the secondary hydroxyls toward SWNT direction have the strongest interactions with SWNTs. Therefore, b-CD interact with SWNTs weakly relative to the other CDs. SWNTs have stronger interaction with n-HB-b-CD than n-HP-b-CD (n = 2, 6) in the same orientation (in S1 or S2). As the secondary hydroxyls toward the nanotubes, the interactions between 2-HB-b-CD and SWNTs are the strongest. Additionally, the attractive interactions between SWNTs and CDs monotonically increase with SWNT radius. CDs wrap onto the surface of carbon nanotubes by Van der Waals

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