Interactions between Single-Walled Carbon Nanotubes and

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J. Phys. Chem. C 2008, 112, 1803-1811

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Interactions between Single-Walled Carbon Nanotubes and Polyethylene/Polypropylene/ Polystyrene/Poly(phenylacetylene)/Poly(p-phenylenevinylene) Considering Repeat Unit Arrangements and Conformations: A Molecular Dynamics Simulation Study Wei Liu, Chuan-Lu Yang,* Ying-Tao Zhu, and Mei-shan Wang Department of Physics, Ludong UniVersity, Yantai 264025, the People’s Republic of China ReceiVed: August 15, 2007; In Final Form: October 15, 2007

Although there is plenty of research work being done in the field of carbon nanotube reinforced composite materials, no special attention has been paid to the factors of the polymer’s repeat unit arrangement and conformation. In this paper we use molecular dynamics simulation based on a Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field to study the interactions between five types of polymers and (10, 10) single-walled carbon nanotubes (SWNTs). When we study the interactions, we pay special attention to the polymer’s different repeat unit arrangements and different conformations. We find that the interaction strength between the poly(phenylacetylene) molecules and SWNTs is obviously influenced by these factors, and the degree of the poly(p-phenylenevinylene) wrapping around the SWNT is associated with its repeat unit arrangement. Based on the present simulations, we think that the nanocomposite should have high mechanical properties if the polymer with an appropriate repeat unit arrangement and conformation is used to form the first layer around the SWNT.

1. Introduction Theoretical modeling1,2 and experimental measurements3,4 have shown that carbon nanotubes (CNTs) possess high tensile modulus and strength and can sustain large elastic strain. Therefore, the composite community considers that one of the anticipated applications of CNTs is ultrastrong reinforcement for high performance composite materials.5,6 Recently, remarkable enhancements in elastic modulus and strength have been achieved by adding small amounts of CNTs to polymer matrix in experiments.7-9 It is widely believed that the interfacial binding between CNTs and polymer matrix determines the efficiency of load transfer from polymer matrix to CNTs. There are many experiments indicating good interfacial binding between the CNT and polymer matrix and significant load transfer in the composites. For example, Cooper et al.10 have measured the interfacial strength by drawing out individual single-walled carbon nanotube (SWNT) ropes and multiwalled carbon nanotubes (MWNTs) bridging across holes in an epoxy matrix. Then the interfacial shear strength between MWNTs and epoxy matrix was calculated to be in the range of 35-376 MPa, whereas most of the SWNT ropes were fractured instead of being pulled out. At almost the same time when these experiments were conducted, some theoretical and computational approaches were employed to study the interfacial characteristics between CNTs and polymer matrix.11-13 Molecular mechanics modeling and molecular dynamics simulation14 were used to explore the nature of the load transfer mechanisms in CNT composites at the molecular level. Some researchers constructed molecular models of CNT-reinforced composites and calculated interfacial binding energy and interfacial shear stress or other parameters that depict the mechanical properties of the composites. Liao and Li12 * To whom correspondence should be addressed. Telephone: +86535-6672870. Fax: +86-535-6672870. E-mail: [email protected].

reported a study on the interfacial characteristics of the nanotube/ polystyrene (PS) composite system. Their simulation results suggested that the interfacial shear stress of the nanotube/ polystyrene composite system was about 160 MPa. Gou et al.13 reported their simulation results that the interfacial shear strength between SWNTs and the cured epoxy resin was up to 75 MPa, indicating that there could be an effective stress transfer from the epoxy resin to SWNTs. Many researchers have paid attention to the morphology of the polymer coating at the CNT surfaces.15-19 Lordi and Yao15 used force field based molecular mechanics calculations to determine interfacial binding energies and sliding frictional stresses between SWNTs and a range of polymer substrates. They also examined the optimized conformations of these polymers. They found that for a polymer the helical morphology wrapping around the SWNT is the most important factor for building ultrastrong nanocomposite, while the interfacial binding energy plays only a minor role. Cadek et al.16 reported that Young’s modulus of poly(vinyl alcohol) (PVA) could be increased by a factor of 2 with loading levels of less than 1% MWNTs when the crystalline polymer coating formed at the MWNT surface. However, using similar MWNTs and noncrystalline polymer resulted in much lower levels of reinforcement. It seems right that well-ordered polymer coating is crucial for effective stress transfer. McCarthy et al.17 reported their experimental observations that poly(m-phenylenevinylene-co2,5-dioctoxy-p-phenylenevinylene) (PmPV) tended to coil at well-defined angles at low coverage. Some other researchers have studied the interaction between the polymer and CNT by performing molecular dynamics (MD) simulations of one or two polymers interacting with a CNT.20,21 Although these studies cannot give bulk nanocomposite properties directly, they do present to us a clear and vivid view of the interface between the polymer and the CNT. For example, Yang et al.20 studied the interactions between PS/poly(phenylacety-

10.1021/jp076561v CCC: $40.75 © 2008 American Chemical Society Published on Web 01/24/2008

1804 J. Phys. Chem. C, Vol. 112, No. 6, 2008 lene) (PPA)/poly(p-phenylenevinylene) (PPV)/PmPV and a SWNT. They found that the specific monomer structure plays a very important role in determining the strength of interaction between the SWNT and the polymer. Based on their simulations, they suggested that polymers with backbones containing aromatic rings are promising candidates for the noncovalent binding of CNTs into composite structures. Zheng et al.21 used MD simulations to study the interaction between polyethylene (PE)/ polypropylene (PP)/polystyrene (PS)/polyaniline (PANI) and a SWNT. The influence of temperature, SWNT radius, and chirality on polymer adhesion was investigated. The results showed that the interaction between the SWNT and the polymer is strongly influenced by the specific monomer structure such as an aromatic ring. Furthermore, they conducted simulations of “filling” into the SWNT cavity by a polymer molecule due to the attractive van der Waals interaction. They thought that the possible extension of a polymer into a SWNT cavity that structurally bridged the SWNT and the polymer could be used to improve load transfer from the polymer to the SWNT. It seems to be a novel idea. From the literature mentioned above, we know that the efficiency of load transfer from polymer matrix to CNTs is in positive correlation with the interfacial binding energy and the well-ordered coating of polymers on the CNT surface is vital for effective load transfer. Thus it is reasonable to think that it should be an ideal matrix for building nanocomposites if a polymer has a helical conformation wrapping a CNT and a fairly strong adhesion to the CNT. As we know, the polymer is such a large molecule that it is characterized by different repeat unit arrangements (RUAs; we use the acronym henceforth) and a large amount of conformations from rotating around σ-bonds. Therefore, it is necessary and interesting to study the interactions between CNTs and polymers with different RUAs and different conformations. However, as far as we know, investigations concerning the issue have not been reported. Therefore, we investigate interactions between polymers and SWNTs through MD simulations, particularly considering the polymer RUAs and conformations. One of our purposes is to display the characteristics of polymers in different RUAs and with different conformations interacting with SWNTs. The other purpose is to search for a promising polymer for building a nanocomposite with high mechanical properties. In the present study, only nonbond interaction between a pristine SWNT and a polymer is considered. 2. Computational Methods 2.1. Constructions of Polymers, SWNTs. 2.1.1. Molecular Models of SWNTs. Zheng et al.21 concluded that the armchair SWNTs have the strongest adhesion with polymers in various chiral SWNTs. Two segments of (10, 10) SWNTs are considered in the present work. They have the same diameter of 13.6 Å but different lengths. The first one (represented as SWNT1) is 73.8 Å long with 1200 carbon atoms and 40 hydrogen atoms. The second one (represented as SWNT2) is 142.65 Å long with 2320 carbon atoms and 40 hydrogen atoms. Carbon atoms at both ends of them are saturated with hydrogen atoms. Each hydrogen atom has a charge of 0.127e and the carbon atom connecting them has -0.127e. Therfore, the whole SWNT segment is neutral. The initial value for each C-C bond length is 1.42 Å and for each C-H bond length is 1.10 Å. The geometric structures of the SWNTs can be relaxed in the MD simulations. 2.1.2. Molecular Models of Polymers. The five types of polymers considered are PE, PP, PS, PPA, and PPV. Their

Liu et al.

Figure 1. Chemical structures of the investigated polymers. (a) PE, (b) PP, (c) PS, (d) transPPA, (e) cisPPA, and (f) PPV.

chemical structures are provided in Figure 1. There are 10 monomers in each chain of the polymers (the number of atoms is 62, 92, 162, 142, and 142 for PE, PP, PS, PPA, and PPV, respectively). In fact, these polymers are better called oligomers; however, we would like to call them polymers in this paper. They can be looked at as small parts of the corresponding “long” polymers, and their interactions with SWNTs can be exploited to understand the primary behaviors of the “long” polymers. All the investigated polymers in present work are homopolymers. It is nonsense to talk about the RUAs of the PE molecule. Here we do not describe the PP and PS in different RUAs and with different conformations in detail. One reason is that their structures can be imagined based on the description for PPAs and PPVs in the following text. The other reason is that their conformations deriving from rotation around σ-bonds in the backbone are not important when they interact with SWNTs. There are two geometric isomers in PPA: transoidal-PPA (transPPA) and cisoidal-PPA (cisPPA). The transPPAs are described first. For the head-to-tail arrangement of repeat units, we study three different conformations in which the phenyls locate at different positions deriving from the rotation of repeat units around the σ-bonds in the backbone. In the first one, the phenyls stagger at either side of the backbone (transPPA1). In the second one, the phenyls locate at the same side of the backbone (transPPA2). In the third one, as can be seen in Figure 2a, there are two close interacting pairs in the middle part and each pair is formed by two adjacent phenyls at the same side of the backbone while the remaining phenyls locate at either side alternately (transPPA3). There are two different structures in the head-to-head arrangement according to the different cases at both ends of the backbone. There is no phenyl connecting to either carbon atom at either end of the backbone in the first structure (transPPA4), while in the second structure there are phenyls connecting to the carbon atoms at both ends of the backbone (transPPA5). In both structures, the phenyls stagger at either side of the backbone. Two different kinds of transoidal PPAs in random arrangement are considered. Three conformations (transPPA6, -7, and -8) for the first kind and two (transPPA9 and -10) for the second one are investigated. transPPA6, -7, and -8 have the same kind of random arrangement. The phenyls stagger at either side of the backbone in transPPA6 (see Figure 2b). In transPPA7 there is a close interacting pair formed by two adjacent phenyls at the same side of the backbone in the middle part, while the remaining phenyls are located at either side alternately (see Figure 2c). In transPPA8, there are three close interacting pairs

Interactions between SWNTs and PE/PP/PS/PPV

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Figure 2. Molecular models of some PPAs and PPVs with different repeat unit arrangements and conformations. (a) transPPA3, (b) transPPA6, (c) transPPA7, (d) transPPA8, (e) transPPA9, (f) transPPA10, (g) cisPPA4, (h) cisPPA5, (i) PPV1, (j) PPV2, and (k) PPV3.

1806 J. Phys. Chem. C, Vol. 112, No. 6, 2008 and each pair is formed by two adjacent phenyls at the same side of the backbone, while the remaining phenyls are located at either side alternately (see Figure 2d). transPPA9 and -10 are both in another kind of random arrangement. In transPPA9, the phenyls stagger at either side of the backbone (see Figure 2e). In the middle part of transPPA10 there are two close interacting pairs whose positions are very similar to those in transPPA3 (see Figure 2f). The cisPPAs have arrangements similar to those of transPPAs but fewer conformations. There is only one conformation for the head-to-tail arrangement considered (cisPPA1). cisPPA2 and -3 are used to represent two different structures in head-to-head arrangement. They are similar to transPPA4 and -5 in structures. In cisPPA2 there is no phenyl connecting to the carbon atom at either end, while in cisPPA3 there are phenyls connecting to the carbon atoms at both ends. The phenyls are staggered at either side of the backbone in cisPPA1, -2, and -3. cisPPA4 and -5 are used to represent two polymers in different random arrangements. In cisPPA4 the phenyls are staggered at either side of the backbone (see Figure 2g). In cisPPA5 from left to right the fourth phenyl and the sixth phenyl form a close interacting pair because of a too small interval and so do the fifth phenyl and the seventh phenyl while the remaining phenyls are located at either side alternately (see Figure 2h). There are three PPVs (PPV1, -2, and -3) illustrated in Figure 2. PPV1 is a planar structure in head-to-tail arrangement. PPV2 is a linear structure in head-to-head arrangement with aromatic rings twisting along the backbones. PPV3 is also a linear structure but in random arrangement with aromatic rings twisting along the backbones. In all these PPVs the dihedral between two aromatic rings connecting directly is about 31°, between two ethylenes connecting directly is almost 0°, and between the aromatic ring and the ethylene connecting directly is in the range 1-8°. All the polymers discussed above are optimized with the Discover module. 2.2. Computational Methods and Force Field. Materials Studio software package 3.223 is used for all calculations in this paper. MD simulations are carried out through the Discover module, using the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field. The COMPASS force field has been widely used in molecular simulation of the common organic and inorganic materials. Reference 21 has given a brief overview of the COMPASS force field. In our simulations all nonbond potentials (including the van de Waals potential and the Coulomb electrostatic potential) are treated with the atom based cutoff method. The cutoff distance is 12.5 Å. All the simulations are carried out in the constant volume and constant temperature (NVT) canonical ensemble with undefined boundary conditions, which implies that the simulated volume is actually infinite. The NVT ensemble with undefined boundary conditions is appropriate for conformational searching of the system.23 Because of the infinite volume, if the simulation time is long enough the polymer would move away eventually and never interact with the SWNT again. However, this “escape” case is extremely rare and it does not affect the results within our simulation time. The Nose-Hoover thermostat algorithm is used for temperature control. From the characteristics of this thermostat we know that MD simulations with this method produce a canonical distribution.23 We perform MD simulations at 400 K, which is a high temperature, so the molecules change their conformation rapidly. All the simulations are performed in a vacuum.

Liu et al. The time step is 0.5 fs, which is fairly short, but the duration of MD simulation can be endured by using the DELL workstation of precision 650 collocating two processors. The simulations have gone into production phase and the systems have reached equilibrium within 10 ps (20 000 steps), which can be identified from the fluctuations of the temperature and the potential energy of the system. In our simulations, the system is believed to be in equilibrium when the fluctuations of temperature and potential energy are in the range of 5-10%. Thus it is instructive and valid of the interaction energy curves (IECs) and configurations of the system deriving from the simulations since 10 ps. The simulation time is usually 100 ps, but is 200 or 300 ps when we perform a specified conformation searching. It should be noted that our simulations do not explore all the potential energy spaces of polymer-SWNT systems because of the rather short simulation time. However, the simulations do give some useful ideas about the adhesion of the polymers on the surfaces of SWNTs. As we want to study the behaviors of one polymer on the surface of the SWNT, in our interaction models the SWNTs are enough long compared with the polymers. The PE/PP/PS/ PPA molecules are all no longer than 30 Å. For example, the length of the PE in straight line shape is about 24 Å. It is appropriate to form each of these molecules and SWNT1 (initial length is 73.8 Å) into an interaction system. As the PPVs are all about 74 Å long, the PPVs-SWNT1 systems is not appropriate to study the interaction of them; SWNT2 (initial length is 142.65 Å) is used to form the interaction systems with PPVs. MD simulation can be established with the polymer initially placed beside the SWNT within the nonbond potential cutoff distance of 12.5 Å. The starting configuration for each MD simulation is a local minimum on the potential energy surface by optimizing the initial interaction system. 2.3. Interaction Energy and Interfacial Binding Energy Calculations. The interaction energy between a polymer and a SWNT can be used to describe the interaction strength between them. It is calculated according to the following equation:13

Einteraction ) Etotal - (ESWNT + Epolymer) where Einteraction is the interaction potential energy, Etotal is the total potential energy of the polymer-SWNT pair, and ESWNT is the potential energy of the SWNT when the polymer is put at infinite distance. Epolymer can be defined in the same way as ESWNT. The interfacial binding energy γ 15 is calculated as

γ)

Einteraction 2A

where A is the contact area between the polymer and the SWNT surface. A can be calculated by measuring the Connolly surface area of the polymer using a probe sphere with 6.8 Å radius, which approximates to the accessibility of a (10, 10) SWNT.15 3. Results and Discussion 3.1. PE, PP, and PS. We simulate PE and PP/PS in different RUAs (head-to-tail arrangement, two different structures in head-to-head arrangement, and two different random arrangements chosen randomly) interacting with SWNTs. We also simulate another PS with another conformation in head-to-tail arrangement interacting with SWNTs. Very similar IECs are achieved for all conformations of PPs or PSs, which means that all the investigated PPs or PSs have almost the same strong interaction with SWNTs. When a system is formed using each

Interactions between SWNTs and PE/PP/PS/PPV

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Figure 3. Interaction energy curves of PE and some PP/PS molecules interacting with SWNT at 400 K in 100 ps simulation time. Green, red, blue, cyan, and magenta lines are for PE, PP in head-to-head arrangement, PP in random arrangement, PS in head-to-tail arrangement, and PS in headto-head arrangement, respectively.

of the PPs or PSs and a SWNT, and undergoes a MD simulation course, the polymer will take such conformations by rotating around all the σ-bonds in the backbone that a similar continuous and strong interaction can be achieved during the production phase. This may be the reason that all PPs or PSs have almost the same strong interactions with SWNTs. In Figure 3 some IECs are shown. It is obvious that the PS has the strongest interaction with a SWNT in the three polymers, and the PP has a stronger interaction with a SWNT than the PE. The reason is that the atom numbers of these polymers are increasing monotonously from PE to PP to PS. As we can see in Figure 3, the average interaction energy between PS and SWNT is about 2 times that between PP and SWNT. We think the reason is that there are phenyls in PS in which the carbon atoms have the same sp2 hybridization as those carbon atoms in the SWNT. We put a PP molecule in a head-to-head arrangement beside the SWNT at a randomly chosen position and launch a MD simulation. Then we make the PP molecule rotate for the π-angle so that the other side faces the SWNT compared with its previous orientation and launch a MD simulation. Similar IECs are obtained. We also do the same work with a PS molecule in a head-to-tail arrangement and get the same result. Kisin et al.22 have studied the adhesion of styrene-co-acrylonitrile (SAN, a random copolymer having 15 styrene and 5 acrylonitrile units) on the copper surface. They found that the work of adhesion (W ) {Einteraction}/{Ac}; Ac is the van de Waals contact area between the polymer and the copper surface) is independent of the orientation of the SAN molecule on top of the copper surface. In both their cases and ours the interactions are all independent of the initial orientation of the polymer. The reason may be that such a molecule as SAN, PP, and PS is rather flexible since the backbone is made up of σ-bonds connecting all the carbon atoms. No matter whatever orientation it is located beside the SWNT (or on top of the copper surface) in the starting configuration, it will take such a conformation by rotating around the σ-bonds in the backbone that a similar continuous and strong interaction can be achieved during the production phase. Wei18 studied 50 PEs (with 100 repeating units of CH2 each) wrapping some CNTs of different radii and chiralities. He found that the PEs in the first adsorption layer around CNT (10, 0) prefer extended conformations along the tube axis. We find that the PE always adopts a zigzagged conformation on the (10, 10) SWNT surface at 400 K. It can form an extended conformation

Figure 4. Distribution of distances between the carbon atoms at both ends of PE on SWNT surface at 400 K.

to wrap the SWNT but can also adopt a folded shape. The PE prefers the extended conformation as shown by the probability function P(l) in Figure 4. The quantity l is the distance between the carbon atoms at both ends of PE. PP/PS has a zigzagged conformation on the SWNT surface. There is no helical conformation of PP/PS wrapping around the SWNT found in our simulations. The conformation of PE changes faster than that of PP/PS. The reason may be that the strong adsorption between SWNT and PP/PS hinders the motion of PP/PS. Some snapshots of PE/PP/PS interacting with a SWNT at 400 K are presented in Figure 5. 3.2. PPA and PPV. transPPA3 and cisPPA4 have the strongest interactions with SWNT, as we can see from the IECs in Figure 6. transPPA1, -2, -4, -5, -6, -7, -9, and -10 and cisPPA1, -2, and -3 have similar interaction strengths with SWNTs. transPPA8 and cisPPA5 have the weakest interactions with SWNTs. To understand these results, we must search the structures of these PPAs for answers. PPAs are all rather rigid because of the π-bonds in their backbones. The phenyls in PPA’s side chains play an important role in the interaction between PPA and SWNT. The carbon atoms in the phenyls have the same hybridization in electronic structures as those in SWNT. Yang et al.20 have studied the interactions between PS/PPA/ PmPV/PPV and SWNT. They found that the polymer would have stronger interaction with SWNT if there are more aromatic rings in the polymer approaching the SWNT surface, and the dihedrals between the planes of the aromatic rings and the surface of SWNT are more approaching 0° or 180°. They believed that the interactions of the aromatic rings in the polymer will affect the polymer’s adhesion to SWNT when the parallel alignment between two adjacent aromatic rings is not compatible

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Figure 5. Interaction snapshots of some PE/PP/PS molecules adsorbed at SWNT surface at 400 K. (a) PE, (b) another view of PE, (c) PP in head-to-tail arrangement, (d) PP in random arrangement, (e) PS in head-to-head arrangement, and (f) PS in random arrangement.

with their parallel alignment to the SWNT surface. Based on their opinion, we analyze our results as follows. As we can see from Figure 2a,g, there are very large intervals between the adjacent phenyls in the middle part of both sides of transPPA3/cisPPA4, which make the backbone more flexible. The reason that transPPA3 and cisPPA4 have the strongest interactions with SWNT is that they are so flexible to bend themselves that all their parts can approach the SWNT surface very close and the phenyls can face the surface of SWNT more easily. It surprised us that transPPA9 has a little weaker interaction with SWNT than transPPA1, -2, -4, -5, -6, -7, and -10 and cisPPA1, -2, and -3. When examining the interaction snapshots, we can find the reason. The interactions of the phenyls in transPPA9 prevent it from approaching the SWNT too closely (see Figure 7f). Although transPPA10 has a structure similar to that of transPPA3, its interaction with SWNT is weaker than that of transPPA3. The reason is that the interactions of its adjacent phenyls are still very strong for the intervals between any two adjacent phenyls are still small (see Figure 2f). transPPA2 with all the phenyls locating at the same side has a much more stable and strong interaction with SWNT, as we can see from Figure 6a. From Figure 6b we know that the interaction between cisPPA3 and SWNT is a little stronger than that between cisPPA2 and SWNT. The reason for the weak interaction between transPPA8/ cisPPA5 and SWNT is that the structure (three close interacting pairs of phenyls in transPPA8 and two such pairs in cisPPA5) hinders the approach to SWNT, as we can see from the interaction snapshots in Figure 7a-c. However, if there is only one such close interacting pair as in transPPA7 (see Figure 2c), the interaction with SWNT will be hardly affected, which can be clearly seen when we examine the average interaction energies of the production phase in the Einteraction column of Table 1. It is not important to choose carefully a precise starting configuration for a MD simulation because the simulation system will go away from the starting configuration and one cannot find any evidence of the starting configuration in the production phase.24 However, we use two different starting configurations for the transPPA8 and SWNT system (the polymer’s orientations to the SWNT are different in the two

starting configurations) and perform simulations from both of them to get more information about the interaction. The IEC of transPPA8-1 is derived from the simulation with the starting configuration that transPPA8’s one side faces the SWNT. The IEC of transPPA8-2 is derived from the simulation with the starting configuration obtained by rotating transPPA8 in the former starting configuration for the π-angle so that the other side faces the SWNT. In the first case fewer atoms can approach the SWNT so that the interaction is weaker than the second. From our simulations of many PPVs in different RUAs and with different conformations interacting with SWNT, we conclude that all PPVs have almost the same strong interactions with SWNT. The reason is that their aromatic rings locate in the backbones and all these aromatic rings can easily face the SWNT surface. There are only three IECs between different PPVs and SWNTs illustrated in Figure 6b. The degree of the PPVs’ wrapping around SWNTs is almost equal for all these in the same RUA. The PPV in the head-to-head arrangement has the greatest wrapping degree in the three RUAs. The PPV in the same random arrangement as PPV3 has an almost equal wrapping degree with the PPV in the head-to-tail arrangement. The wrapping degree can be illustrated by presenting the top snapshots in Figure 7j-l. When a simulation at 400 K is launched, the extremely high temperatures in the equilibration phase may change the essential conformation of a polymer. If we want to simulate a polymer with a specified conformation interacting with SWNT at 400 K, we can overcome the difficulty by using the following method. First we optimize the polymer-SWNT system and use the final configuration as the starting configuration to perform an NVT simulation at 200 K for 50 ps. Then we use the final configuration of the simulation at 200 K as the starting configuration to perform an NVT simulation at 250 K for 50 ps and perform NVT simulations at 300 and 350 K successively in the same way. Last, we can use the final configuration of the simulation at 350 K to launch the simulation at 400 K. This procedure is used when we perform the simulation of the interaction between SWNT and each PPV with a specified conformation. The interfacial binding energies between some polymers and SWNTs at 400 K are estimated in the following way. Einteraction

Interactions between SWNTs and PE/PP/PS/PPV

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Figure 6. Interaction energy curves of some PPA/PPV molecules interacting with SWNT at 400 K in 100 ps simulation time. (a) Curves of some transPPA and SWNT pairs: dark yellow, cyan, green, blue, orange, and magenta lines for tranPPA8-1, tranPPA8-2, transPPA9, transPPA10, transPPA2, and transPPA3, respectively. TranPPA8-1 is for the first simulation, and tranPPA8-2 is for the second. (b) Curves of some cisPPA/PPV and SWNT pairs: orange, violet, cyan, olive, magenta, red, green, and blue lines for cisPPA5, cisPPA1, cisPPA2, cisPPA3, cisPPA4, PPV3, PPV2, and PPV1, respectively.

is used as the average interaction energy in the production phase of the simulation. 2A is estimated as the whole Connelly surface area of the polymer’s conformation corresponding to the average interaction energy using a probe sphere with a 6.8 Å radius. We list the interfacial bonding energies for all PPAs (except transPPA8 and cisPPA5) and all PPVs in Table 1. As we can see from the Einteraction column, transPPA5 has a stronger interaction with SWNT than transPPA4. transPPA4 and -5 and cisPPA2 and -3 are all in a head-to-head arrangement. There are phenyls connecting to the carbon atoms at both ends of the backbones of transPPA5 and cisPPA3, which may be the reason that transPPA5/cisPPA3 has a stronger interaction with SWNT than transPPA4/cisPPA2. The interfacial binding energy of transPPA5/cisPPA3 is also larger than that of transPPA4/ cisPPA2. transPPA2 and cisPPA3 have fairly large interfacial binding energies. As we know, for linear carbon chain polymers the head-to-tail arrangement is the most common structure in the nature while cisPPA3 (head-to-head arrangement) has a larger interfacial binding energy than cisPPA1 (head-to-tail arrangement). The interfacial binding energies of transPPA3 and cisPPA4 are the largest in all PPAs. transPPA3 has a specified conformation and cisPPA4 has a specified RUA (see Figure 2a,g), so we can get more suitable structures of polymers for

nanocomposites by choosing appropriate RUAs and conformations. Lordi and Yao15 calculated the interfacial binding energies between transPPA2/cisPPA1 and (10, 10) SWNT with the molecular mechanics method. Our interfacial binding energies of transPPA2 and cisPPA1 at 400 K are both obviously smaller than their results at 0 K. The interfacial binding energies of all PPVs are almost the same in spite of their RUAs and conformations, while their wrapping degrees are associated with their RUAs. According to Wei’s discovery that the linear polymers assemble themselves into layers around CNTs, the corresponding nanocomposite is expected to have an ultrahigh performance if the polymers that have strong interactions with SWNTs and helical conformations are chosen to form the first layer around CNTs. As we can see from Figure 7, all the PPAs (except transPPA8 and cisPPA5) and PPVs have helical conformations wrapping around SWNTs, but the PSs do not have helical conformations. However, PPVs cannot interlock with each other when they are in large amounts to form bulk matter because they are very slippery polymers with no side chains. Therefore, it is reasonable to think that such polymers as the PPAs in appropriate RUAs and conformations are promising matrixes for nanocomposites. When necessary, one can choose the RUA

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Figure 7. Interaction snapshots of some PPA/PPV molecules adsorbed at SWNT surfaces at 400 K. (j)-(l) are top views. (a) View of the first simulation of transPPA8 and SWNT system. (b) View of the second simulation of transPPA8 and SWNT system. (c) cisPPA5, (d) transPPA3, (e) cisPPA4, (f) transPPA9, (g) transPPA2, (h) cisPPA3, (i) transPPA10, (j) PPV2, (k) PPV1, and (l) PPV3.

TABLE 1: Interfacial Binding Energies of Some Polymers and SWNTs at 400 K polymer

atom no.

Einteraction (eV)

2A (Å2)

γ (meV/Å2)

transPPA1 transPPA2 transPPA3 transPPA4 transPPA5 transPPA6 transPPA7 transPPA9 transPPA10 cisPPA1 cisPPA2 cisPPA3 cisPPA4 PPV1 PPV2 PPV3

142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142

2.43 2.56 2.78 2.33 2.44 2.47 2.36 2.16 2.41 2.46 2.46 2.74 3.04 4.60 4.47 4.53

859.7 831.6 857.3 897.7 900.8 881.3 891.1 841.2 830.4 870.4 867.7 896.9 941.4 1111.5 1082.9 1097.8

2.83 3.08 3.24 2.59 2.71 2.81 2.65 2.56 2.90 2.83 2.84 3.06 3.23 4.14 4.12 4.12

and change the conformation to make it more appropriate for building high performance nanocomposites. In this study we do not perform special conformational searching for the polymers or for the polymer-SWNT systems.

In fact, we just search some polymers for specified RUAs and conformations that are more suitable for building ultrastrong nanocomposites. However, our work may give some useful ideas for special conformational searching of large molecules. When

Interactions between SWNTs and PE/PP/PS/PPV exploring a molecule’s conformational space using MD simulation, one can construct a system by adding another large molecule or some small molecules and perform MD simulation on the system. During the simulation not only the kinetic energy of the objective molecule but also the interaction with other molecule(s) acts on it to change its conformation. By this means one can get some particular conformation of the objective molecule as a result of the interactions with other molecule(s). For example, we get helical conformations of the PPVs by simulating their interactions with SWNTs. 4. Conclusions The interactions of five types of polymers and (10, 10) SWNTs are investigated using MD simulations. The simulation results show that on the (10, 10) SWNT surfaces at 400 K the PE prefers extended conformations, and the PP/PS has no helical conformations, while all PPAs (except for some special structures like transPPA8 and cisPPA5) and PPVs have helical conformations. The degree of the PPV’s wrapping around a SWNT is associated with its RUA. The PPV in a head-to-head arrangement has larger wrapping degree around the SWNT than PPVs in the other two RUAs. It is also shown that the interaction energies between the PP/PS/PPV molecules and the SWNTs are almost independent of their RUAs and conformations, while the interaction strength between PPAs and SWNTs is greatly influenced by their RUAs and conformations in which the interactions of the phenyls in PPAs play an important role. It is found that a stronger interaction between the PPA and the SWNT can be achieved by choosing an appropriate RUA and conformation. We believe that such polymers as PPAs with appropriate RUAs and conformations are promising candidates for building ultrastrong nanocomposites. Acknowledgment. This work is supported by the National Natural Science Foundation of China under Grant 10674114. References and Notes (1) Salvetat, J.-P.; Briggs, G. A.; Bonard, J.-M.; Bacsa, R. R.; Kulik, A. J.; Sto¨ckli, T.; Burnham, N. A.; Forro´, L. Phys. ReV. Lett. 1999, 82, 944-947.

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