3.1 Trajectory Visualization
The molecular dynamic (MD) snapshots of the helix formation process through three polypyrrole chains and CNT are shown in Fig. 2. Each polypyrrole chain owns 60 repeat units with the length of 234.8 Å. Initially, three polypyrrole chains are parallel with each other and all of them are inserted into the one end of CNT. As the simulation time starts, due to the π-π interactions existing among the three polypyrrole chains, three polypyrrole chains fluctuate like a worm crawling. At the same time, three polypyrrole chains slide into the CNT from this end to other which is exhibited in the first 24 ps. With the time goes on, a part of the three polypyrrole chains penetrate the CNT, and the all polymer chains are twisted simultaneously. As the kinetic time continues to grow, the polymer chains twist more and more significantly, and are confined inside the carbon nanotube which lastly forms a perfect triple helix configuration. Completely the whole process needs about 90 ps. Throughout the entire process, it includes two parts: penetration and twist. The configuration changes of this process are mainly attributed to the van der Waals potential well and the π–π stacking interaction among the three polypyrrole chains and CNT.
Figure 3(a) exhibits the time evolution of total potential energy (EP) and Van der Waals energy (EvdW) for polypyrrole/carbon nanotube system. In Fig. 3(a), the curves of the total potential energy and Van der Waals energy for polypyrrole/carbon nanotube system are almost the same. Both curves show a downward trend at the first 90 ps, and then remain unchanged which means that the interaction of this system only needs 90 to reach the equilibrium. There are two inflection points in this part of curve, which can be divided into three different regions. Region I(0 ps-24 ps), two curves exhibit a great reducing trend which belongs to “penetration” process. Region II (25 ps- 90ps), the energy goes on reducing which is attributed to twist process. However, when the simulation time exceeds 90 ps (area III), the energy keeps almost the same with little fluctuation which means that the system reaches the equilibrium. These curves point out three key points: one is this whole process undergoes two stages; the second is 90 ps is a long enough for the system to reach well-equilibrated; the third is the van der Waals potential well and the π–π stacking interaction are the main driving force.
The interaction energy of polypyrrole/carbon nanotube system is shown in Fig. 3(b). To explore the origin of this difference, the interaction energy among three polypyrrole chains and CNT was calculated using the following equation:
E Interaction = E total -E polypyrrole –ECNT (1)
In this equation, EInteraction is the interaction energy of the polypyrrole/carbon nanotube system, Etotal is the total energy of the composite, Epolypyrrole is the energy of individual polymer molecules and ECNT is the energy of individual CNT.[ 24, 31]
In Figure 3(b), the curve of interaction energy can be devided into three stages similar to the reverse shape of Fig. 3(a). In stage I, the interaction energy is about -1325.8 Kcal/mol. In this process, in addition to the interactions among three polymer chains, there are also increasing interactions between polymers and carbon nanotubes. In stage II, the interaction energy among the polymer molecule and CNT still keeps increasing which gets to -2155.8 Kcal/mol. However, when the simulation time reaches 90 ps (stage III), the interaction energy remains unchanged. The conclusion is that the interaction energy among the polymer molecule and CNT is about -2155.8 Kcal/mol.
The concentration profile can give the information about the geometric parameters of the polypyrrole/CNT composite system. The 3D periodic structures can be computed through the profile of atom density within evenly spaced slices parallel to the bc, ca and ab planes. Figure 4 exhibits the concentration profiles of the final structure of the f polypyrrole/CNT composite system in the X and Y direction. [30] In Fig. 4(a), the curve of polypyrrole is surrounded by the CNT, which means that the polymer self-curls into the inside of CNT. However, the carbon nanotubes have undergone slight deformation and are no longer a perfect cylindrical structure. According to the peaks detail exhibited in Fig. 4(a), the distance between polypyrrole chain and CNT is 1.1-1.5 Å, this value is corresponded with the stacking distance of the offset face-to-face π–π stacking interaction, which suggests that the main driving force is the π–π stacking interaction.[32] In Figure 4(b), the length of CNT is about 73.8 Å, which is corresponded with the theory value of 73.79 Å. Furthermore, a little part of helix locates outside of CNT. The total length of the helix is about 86.7 Å. According to the cure of polymer in Fig. 4(b), the helix has gone through three turns.
3.2 The different number of polymer chain number
In this part, we investigate that how the chain number of polymer influences the interaction of polypyrrole/CNT composite systems. Initially, we set all the CNT with same diameter (33.90 Å) and length (73.79 Å) and the polypyrrole chain has 60 monomers with the length of 234.8 Å. All the different polypyrrole/CNT composite system just change the number of polymer chain from one, two, three, four to five. The initial and final configurations of composite and pure polymer chain are shown in Fig. 5(a). When just one polymer chain existing in this system, the whole chain curves to irregular configuration and enters into the inside of CNT. As the chain number of polymer goes on increasing from two to four, all the chains simultaneously curls to perfect helix structures. However, when the number of polymer chain exceeds five, the polymers do not have enough space to twist and only fluctuate in a wave form. The interaction energy for these different polypyrrole/CNT systems are shown in Fig. 5(b). As the number of polymer chains increases, the interaction energy between polymer and carbon nanotubes gradually increases. These are attributed to more and more van der Waals potential well and the π–π stacking interaction existing in these systems. However, when the chain number is five, the interaction energy is decreasing, this reason is that the main interaction force is between the polymers, and the force between the polymer and the carbon nanotubes is relatively small.
3.3 The length of polymer chain
The length of polymer chain also influences the final configuration of polypyrrole/CNT system. At the first time, all the CNT are set with same diameter (33.90 Å) and length (73.79 Å). The length of polypyrrole chain changes from 78.3 Å, 146.6 Å, 234.8 Å to 293.2 Å. The initial and final configurations of different polypyrrole/CNT systems are shown in Fig. 6(a). When the length of polymer is too short, the CNT have enough space to accommodate all the curled polymer chains. These can be seen in the Fig. 6(a) from I to III. However, when the length of polymer is long enough, the intense interaction exists between the polymers which make the inserted polymer far away from the CNT and lead the polymer do not enter into the CNT. The final configuration is displayed in Fig. 6(a)(IV). The interaction energy for these systems are also shown in Fig. 6(b). The longer the polymer, the stronger the interaction energy existing in these systems. If the polymer is too long, the interaction energy goes down. This is corresponded with configuration change which are shown in Fig. 6(a).
3.4 The different simulation temperature
How the simulation temperature influences the final configurations of polypyrrole/CNT system? In this part, all the CNTs and polypyrrole are set with the same parameters. Only the simulation temperature is different, which is set as 100K, 200K, 300K, 400K, 500K, respectively. The final configurations of different polypyrrole/CNT systems and pure polypyrrole chains are exhibited in Fig. 7(a). The final configurations are almost the same when the simulation temperature changes from 100K, 200 K, 300 K to 400 K. The higher the temperature, the more and more, more and more perfect multi-helical polymers are confined in carbon nanotubes. However, when the temperature is 500 K, the polymer also twists but locates outside the surface of CNT. The interaction energy for these different polypyrrole/CNT systems are also shown in Fig. 7 (b). The energy difference for these systems is very small, which is corresponded with the final configurations.