Nanopattern of the Inner Surface of Carbon Nanotubes for Self

Jul 26, 2007 - We report a multistep Monte Carlo (MSMC) method which combines a canonical Monte Carlo (NVT) simulation for investigating the ...
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J. Phys. Chem. C 2007, 111, 11802-11805

Nanopattern of the Inner Surface of Carbon Nanotubes for Self-Assembly of Nanoparticles: A Multistep Monte Carlo Method Ran Ni, Dapeng Cao,* and Wenchuan Wang DiVision of Molecular and Materials Simulation, Key Lab of Nanomaterials, Ministry of Education, Beijing UniVersity of Chemical Technology, Beijing 100029, China ReceiVed: April 17, 2007; In Final Form: June 18, 2007

We report a multistep Monte Carlo (MSMC) method which combines a canonical Monte Carlo (NVT) simulation for investigating the nanopattern of the inner surface of a hydrophobic carbon nanotube by surfactants and a grand canonical Monte Carlo simulation (GCMC) for exploring the self-assembly of nanoparticles in the surfactant-patterned carbon nanotube, where equilibrium configuration in the NVT simulation is used as an input in the GCMC. It is found from the NVT simulation that, as a small amount of surfactant is loaded in the carbon nanotube, the surfactants are self-assembled into a “strip” pattern parallel to the axis direction rather than a “ring” pattern or a spiral pattern, because the ring pattern or spiral pattern leads to more or less loss of the surface coverage, that is, loss of the surface entropy. In addition, the GCMC simulation result suggests that the nanoparticles self-assemble into an ordered layer on the substrate of the surfactant-patterned carbon nanotube, while the nanoparticles cannot enter the unpatterned hydrophobic carbon nanotube at all because of the unfavorable properties of nanoparticle with the carbon nanotube. In summary, the MSMC provides a powerful means for the nanopattern of the inner surface of a carbon nanotube for self-assembly of nanoparticles.

Since carbon nanotubes were synthesized in 1991,1 they have been extensively applied to a lot of scientific and technological fields, including semiconductors, hydrogen energy storage,2,3 nanodevices,4 and nanoreactors.5 To better use unique chemical and physical properties of a carbon nanotube, surface modification of the carbon nanotube is often performed.6 Recently, researchers have extensively investigated the functionalization of the side wall of the carbon nanotubes,7-12 since they are good templates for adsorption of nanoparticles13,14 forming nanowires. Two main approaches considered for the surface modification are the covalent chemical approach and noncovalent attachment. The covalent chemical modification of the side wall of carbon nanotubes was carried out via enabling covalent bonding between the carbon nanotubes and the material of interest.8-10,15 It can increase the solubility of carbon nanotubes and open up the possibility of attaching other molecules to the carbon nanotubes.16,17 Examples of such covalent linkages achieved through chemical functionalization have been used in carbon nanotubes-reinforced polymer composites10,18,19 and biological systems.20,21 All covalent chemical approaches, however, may disrupt the intrinsic mechanical and electrical properties of a carbon nanotube. As a result, some researches attempted to functionalize the side wall of carbon nanotubes by the noncovalent method,7,12,22,23 which modifies the surface of the carbon nanotube via noncovalent interactions (van der Waals interaction, π stacking, etc.) and can preserve the unique properties of carbon nanotubes. The inner surface of a carbon nanotube is also important in many applications. Their large inner hollow space offers an opportunity for these investigations of fluid flow in nanoconduits,24 chemical reactions in nanosized test tubes,5 and electrical and magnetic activities in encapsulated nanowires.25,26 Several * Corresponding author. E-mail: [email protected].

methods have been developed to fill the carbon nanotubes with metals25-28 and other materials,29-31 in which these materials mostly form the discontinuous nanowires. Because of the unique conformation of the carbon nanotube, capillarity has been shown to drive wetting and filling of carbon nanotubes with liquids.30,31 However, for the liquid (i.e., Hg) whose surface tension is very large, the capillarity cannot drive it into the carbon nanotube. Therefore, Chen et al. developed an electrically activated method to induce the high surface tension liquid into the carbon nanotubes,27 and they also performed molecular simulations to illustrate the process of electrowetting.28 Motivated by the above investigations, we perform multistep Monte Carlo (MSMC) methods to investigate the nanopattern of inner surface of a hydrophobic carbon nanotube by surfactants under the van der Waals interaction and the adsorption and selfassembly of hydrophilic nanoparticle in the patterned carbon nanotube. The MSMC method contains two simulation processes. One is NVT simulation for investigating the distribution and nanopattern of surfactants in the carbon nanotube and the other is a grand canonical Monte Carlo (GCMC) simulation for exploring the adsorption and self-assembly of nanoparticles in the surfactant-patterned carbon nanotube, where the equilibrium configuration in NVT is used as an input in GCMC. In our simulations, the inner surface of the carbon nanotube is modeled as a cylindrical wall, and the surfactant molecule is represented by a linearly tangent bead chain with a fixed bonding length. To describe rigidity of the linear surfactant, the bonding angle formed by neighboring three beads is fixed at π. Figure 1 shows the schematic diagram of a surfactant molecule, where the rigid linear chain contains four beads, that is, Mb ) 4. Two beads represent the hydrophobic tail (designated as A), and the other two beads represent the hydrophilic head of a surfactant (designated as B). These beads in the surfactant have the same diameter (i.e., σA ) σB ) σ) but different van der Waals

10.1021/jp072995e CCC: $37.00 © 2007 American Chemical Society Published on Web 07/26/2007

Nanopattern of the Inner Surface of CNTs

J. Phys. Chem. C, Vol. 111, No. 32, 2007 11803

Figure 1. Schematic diagram of a surfactant; part A is the hydrophobic tail of the surfactant while part B is the hydrophilic head of the surfactant.

interactions. In addition, nanoparticle is modeled as a sphere having the same properties as bead B, but the diameter of the nanoparticle is σf. It should be mentioned that in this work we do not intend to depict a realistic system, because, to our best knowledge, no corresponding experiments have been reported in previous publications. Although the simulated case is a model system, it can provide useful information for the practical experiments. In our simulations, the interaction between the like-species beads is represented by the Lennard-Jones (LJ) 12-6 potential, and the interaction between the unlike-species beads is represented by the LJ 12 repulsive potential, given by

{

[( ) ( ) ] ()

σij 12 σij rij rij U(ri,rj) ) 12 σ ij 4/ij rij 4/ij

6

type(i) ) type(j) (1) type(i) * type(j)

where rij indicates the distance between bead i and bead j, and type(i) denotes the species of particle i (A or B); ri is the position vector of bead i. σij and /ij denote the cross size and energy interaction parameters and are obtained from the LorentzBerthelot combining rules. In addition, the interaction between the tail beads of the surfactant and the cylindrical wall of the carbon nanotube is represented by the LJ 12-6 potential, and the interactions between B-like beads (including head beads of the surfactant and the nanoparticle) and the cylindrical wall of carbon nanotube are represented by the LJ 12 repulsive potential. In the multistep method, the calculation contains two simulation steps, namely, the NVT and GCMC simulations. In the NVT simulation, the periodical boundary condition was just adopted in the axis direction (i.e., z direction), and the radius of the carbon nanotube is R ) 10σ, where σ is the diameter of the surfactant beads. The length of the simulation box was set to L ) 20σ. The packing fraction of the surfactants in the carbon nanotube is η ) (σ3 NpMb)/(6R2L) ) 0.05, which means that the number of surfactant chains is Np ) 150. The reduced interaction parameters between surfactant beads were set to 1, / / / ) B-B ) A-B ) 1. Although the likewhich means that A-A species and unlike-species interactions have the same numerical value, they bear different expressions (see eq 1). The interaction parameters between the surfactant beads and the cylindrical wall / / ) w-B ) 10, in which they also bear were set to w-A different expressions. The surfactants molecules are randomly put in the carbon nanotube at the beginning of the simulation. During the simulation, two types of trail moves were carried out: (a) the translational displacement of an entire chain and (b) the pivot rotation of an entire chain. After the above NVT simulation reached the equilibrium, we annealed the equilibrated system as an input of the following grand canonical Monte Carlo (GCMC) simulation (i.e., the second simulation process), where the chemical potential,

Figure 2. (a) Local density profiles of surfactant beads versus the distance from the center of the nanotube. (b) Conformations of the patterned carbon nanotube from axis direction.

temperature, and pore volume were specified in advance.32 That is to say, the surfactant-patterned carbon nanotube would provide as a medium for the self-assembly of nanoparticles having the same properties as the head beads of the surfactant. Here, the reduced temperature was set to T* ) T/(/k) ) 0.81 with respect to the parameters of the nanoparticles. In both the NVT and GCMC simulations, the first 5 × 107 configurations were used for equilibration, and the following 1 × 108 configurations were used for the ensemble average of thermodynamic properties of interest. As a small amount of surfactant (packing fraction, η ) 0.05) is loaded in the carbon nanotube, the local density profiles and configurations of the surfactants in the carbon nanotube are explored and shown in Figure 2. Obviously, the surfactants present an ordered distribution on the inner surface of the carbon nanotube, where two layers for the hydrophobic tails of the surfactants are near the wall of the carbon nanotube and located at the positions of r ) 8.5σ and 9.5σ, while two layers for the hydrophilic heads of the surfactants are far from the wall and located at r ) 6.8σ and 7.7σ. That is to say, the surfactants present an orientation perpendicular to the wall of the carbon nanotube from the microscopic point of view. It can be observed from Figure 2b that the surfactants do present the conformations perpendicularly oriented to the wall. Interestingly, it is found that the surfactants self-assemble into a strip pattern rather than a ring pattern or a spiral pattern in the carbon nanotube. To explore the reason why the surfactants self-assemble into the strip pattern, we show in Figure 3 the three possible nanopatterns (including spiral, ring, and strip) of the surfactants in the carbon nanotube. The surface coverage of the surfactants in the carbon nanotube is defined as C ) Scovered/Soriginal, where Soriginal denotes the original inner surface of the carbon nanotube and Scovered

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Figure 4. Adsorption isotherms of the nanoparticles with size of σf ) 2σ in the patterned and unpatterned carbon nanotubes.

Figure 3. Schematic diagrams of the three possible nanopatterns of the surfactants in the carbon nanotube: (a) spiral pattern, (b) “ring” pattern, and (c) “strip” pattern.

indicates the efficient inner surface covered by surfactants. Because of the excluded-volume effect, from the illustration of the nanopatterns in Figure 3, we can get the surface coverage of the surfactants in the spiral pattern by Cspiral ) (R - d cos θ)/R, where d is the length of the surfactants and θ is the angle between the tangential direction of the spiral curve and the xy plane. In particular, when θ ) 0, it means the ring pattern, and θ ) π/2 for the strip pattern. Therefore, in this work, the surface coverage of the surfactants in the ring pattern is 60%. It suggests that the surface coverage of 40% is lost (i.e., a lot of surface entropy is lost) if the surfactants self-assemble into the ring pattern. Actually, for the spiral pattern (i.e. 0 < θ < π/2), the surface coverage of surfactants must be less than 1, suggesting more or less loss of surface entropy. On the contrary, when the surfactants self-assemble into the strip pattern, the surface coverage of surfactants can reach Cstrip ) 1, meaning that there is no loss of the surface entropy. The above analysis is in reasonable agreement with our simulation results. Namely, the surfactants self-assemble into the strip pattern rather than the ring or spiral pattern as a small amount of surfactant is loaded in the carbon nanotube. It should be pointed out that, if the surfactants are adsorbed on the external surface of a carbon nanotube, no matter what pattern (ring, spiral, and strip patterns) the surfactants self-assemble into, surface coverage always remains as 1, suggesting no loss of surface coverage for all of the three patterns. Accordingly, adsorption of surfactants on the external surface of the carbon nanotube can self-assemble into arbitrary ones among ring, spiral, and strip patterns dependent on its loading on the external surface, which has been conformed experimentally in a previous publication.12 After the system of the surfactant-patterned carbon nanotube was annealed, we used GCMC simulation to explore adsorption and self-assembly of B type nanoparticles with size of σf in the

patterned carbon nanotube. For comparison, the adsorption behavior of the B type nanoparticles in the unpatterned carbon nanotube (i.e., the carbon nanotube without any nanopattern) was also considered. We used Γ ) 〈Finσf3〉 to denote adsorption amount of nanoparticles, where Fin is the number density of the nanoparticles in the carbon nanotube and the brackets 〈 〉 denotes the ensemble average. Figure 4 presents the adsorption isotherms of the B type nanoparticles of σf ) 2σ in patterned and unpatterned nanotubes. Impressively, adsorption of the nanoparticles in an unpatterned carbon nanotube is zero, suggesting that nanoparticles cannot enter the unpatterned carbon nanotube because of the unfavorable properties of the nanoparticle with the carbon nanotube, while the nanoparticles can enter the patterned carbon nanotube easily because the uptake of the nanoparticles in the patterned carbon nanotube increases with the chemical potential, as shown in Figure 4. That is to say, the nanopattern of the inner surface of the carbon nanotube is an important route to improve the adsorption of hydrophilic nanoparticles in the hydrophobic carbon nanotube. To further explore the microscopic distribution of the nanoparticles, Figure 5 shows the density contour and local density distribution of the nanoparticles in the cross section of the patterned carbon nanotube at the reduced chemical potential µ ) -6.5. Obviously, the local density profile of the nanoparticle presents a high peak only in the range near the surfactant-patterned substrate, while it remains zero in the other range. The above observation suggests that the adsorbed nanoparticles are basically located on the substrate of the surfactant-patterned carbon nanotube and self-assemble into an ordered layer on the substrate. Therefore, the nanopattern of the inner surface of the carbon nanotube also provides an important means for the selfassembly of hydrophilic nanoparticles in a hydrophobic carbon nanotube. This technique is in agreement with the electrically activated method inducing the high surface tension liquid into the carbon nanotube.27 In summary, by performing a multistep Monte Carlo simulation which combines a NVT simulation for investigating the distribution and nanopattern of surfactants in the carbon nanotube and a GCMC simulation for exploring the adsorption and self-assembly of nanoparticles in the surfactant-patterned carbon nanotube, it can be found that as a small amount of surfactant is loaded in the carbon nanotube, the surfactants selfassemble into a strip pattern parallel to the axis direction rather than a ring or a spiral pattern in the carbon nanotube because the ring pattern or the spiral pattern lead to more or less loss of

Nanopattern of the Inner Surface of CNTs

J. Phys. Chem. C, Vol. 111, No. 32, 2007 11805 Supporting Information Available: Calculation of surface coverage of surfactants in a spiral pattern. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 5. (a) Density contour of the nanoparticles and (b) the density distribution of the nanoparticles in the cross section of the patterned nanotube at µ* ) -6.5 and σf ) 2σ. The cylinder in b just illustrates the domain of the carbon nanotube.

the surface entropy. In addition, the simulation results indicate that the nanoparticles self-assemble into an ordered layer on the surfactant-patterned substrate. On the contrary, the nanoparticles cannot enter the unpatterned carbon nanotube at all because of the unfavorable properties of nanoparticle with the carbon nanotube. Actually, the multistep Monte Carlo method provides a powerful tool for the nanopattern of the inner surface of the carbon nanotube by surfactants and the self-assembly of nanoparticle in the surfactant-patterned carbon nanotubes. Acknowledgment. This work is supported by the National Natural Science Foundation of China (20646001), Beijing Novel Program (2006B17), the Program for New Century Excellent Talents (NCET-06-0095) from Ministry of Education, Beijing Novel Program (2006B17), and “Chemical Grid Project” and Excellent Talents Funding of Beijing University of Chemical Technology.

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