Molecular Dynamics Simulations of Flexible Polymer Chains

Mar 5, 2010 - The goal of this study is to explore the interface between single-walled carbon nanotubes (SWCNTs) and polymer chains with flexible back...
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Molecular Dynamics Simulations of Flexible Polymer Chains Wrapping Single-Walled Carbon Nanotubes Syamal S. Tallury and Melissa A. Pasquinelli* Fiber and Polymer Science Program/TECS, North Carolina State UniVersity, Raleigh, North Carolina 27695 ReceiVed: August 18, 2009; ReVised Manuscript ReceiVed: January 5, 2010 嘷 w This paper contains enhanced objects available on the Internet at http://pubs.acs.org/JPCB.

The goal of this study is to explore the interface between single-walled carbon nanotubes (SWCNTs) and polymer chains with flexible backbones in vacuo via molecular dynamics (MD) simulations. These simulations investigate whether the polymers prefer to wrap the SWCNT, what the molecular details of that interface are, and how the interfacial interaction is affected by the chemical composition and structure of the polymer. The simulations indicate that polymers with flexible backbones tend to wrap around the SWCNT, although not in any distinct conformation; no helical conformations were observed. PAN with the cyano side group showed a preference for transversing the length of the SWCNT rather than wrapping around its diameter, and the cyano group prefers to align parallel to the SWCNT surface. Flexible backbone polymers with bulky and aromatic side groups such as PS and PMMA prefer intrachain coiling rather than wrapping the SWCNT. Moment of inertia plots as a function of time quantify the interplay between intrachain coiling and adsorption to the SWCNT surface. Introduction The presence of carbon nanotubes (CNTs) in a material can impact the toughness, mechanical strength, crystalline morphology, and other properties like electrical conductivity. For instance, a recent study by Shi Kam and co-workers1 attenuated biological transport through a CNT with its optical properties for site-directed cancer cell destruction. The noncovalent “wrapping” of polymer chains around a CNT is an interesting phenomenon that impacts the properties of a material.2 This wrapping behavior can be utilized to solubilize3 CNTs, tune the dispersity4-6 of CNTs, drive assembly mechanisms,7 and alter the functionalization of the CNTs. For example, Chen and co-workers8 wrapped organic molecules to noncovalently functionalize CNTs for protein immobilization. Experimental evidence for polymer wrapping of CNTs has been reported. Didenko and co-workers9 utilized the wrapping of fluorescent polymers to visualize individual CNTs; electron microscopy images revealed the coiling nature of the polymers around the CNTs. Microscopy images produced by Numata and co-workers10 indicate that poly(saccharides) wrap CNTs in a distinct, helical-type structure. A similar helical-type wrapping conformation was found for poly(dialkylsilanes) in microscopy images.11 McCarthy and co-workers12 confirmed that a semiconducting conjugated polymer can wrap a CNT in a helical conformation or grow in a dendritic manner, depending on the intermolecular interactions and the existence of defects. For polymers with more flexible backbones like poly(methyl methacrylate) (PMMA), experimental studies by Bratcher and co-workers5 reveal that the polymers coat or wrap the CNT, although there was no evidence of a distinct conformation for the polymers. They therefore concluded that wrapping is a general phenomenon occurring between polymers and CNTs, although the physicochemical states of such interactions are not * To whom correspondence [email protected].

should

be

addressed.

E-mail:

well-known. The driving forces for wrapping are likely a combination of van der Waals forces,13 interactions due to electrostatics and aromaticity,8 and hydrophobic forces.14,15 An interesting molecular dynamics (MD) study by Johnson and co-workers16 predicted a conformational change in single-stranded DNA that likely occurs before wrapping to optimize the π-π interactions with the CNT. Recent work by Zheng and co-workers17 utilizes wrapping of DNA motifs for separation of CNTs. Several computational studies have been performed to investigate the interactions of polymers and CNTs. Xie and Soh18 reported in 2005 a MD simulation of a single-chain oligomer of amylose interacting with a short segment of a singlewalled carbon nanotube (SWCNT). They hypothesized from this study that the helical-like wrapping of amylose around the SWCNT allows the system to equilibrate and thus minimize its energy. Systematic MD studies of a single chain of a series of oligomers19,20 indicate that the chemical composition of the monomer unit is an important component to the conformational orientations and to the strength of interaction between the polymer and SWCNTs. Zheng and co-workers21 determined that covalent modifications of the SWCNT surface can dramatically impact the wrapping characteristics and interfacial bonding energies of poly(ethylene) (PE) oligomers. Simulations done by Wei22 on 50 chains of PE with 100 repeat units show a strong dependence of the wrapping configurations on the radius and chirality of the SWCNT. MD simulations done by Liu and co-workers23 only observed helical wrapping for single chains of oligomers with stiff backbones, which they also determined to be sensitive to the conformational arrangement of the repeat units within the chain. Naito and co-workers11 also observed different wrapping conformations from their molecular mechanics energy minimizations of poly(dialkylsilanes) depending on the flexibility of the polymer backbone. Monte Carlo simulations on semiflexible chains by Gurevitch and Srebnik24,25 indicate that ordered conformations arise from a balance between conformational

10.1021/jp908001d  2010 American Chemical Society Published on Web 03/05/2010

MD of Flexible Polymer Chains Wrapping SWCNTs

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TABLE 1: Series of Polymers Used in the Simulationsa abbreviation

name

length (Å)

MW (amu)

RU

PP PAN PS PMMA PEO PLA PCL N6

poly(propylene) poly(acrylonitrile) poly(styrene) poly(methylmethacrylate) poly(ethylene oxide) poly(lactide) poly(caprolactone) nylon-6

146 137 79 167 320 281 279 294

3822 3888 3888 3800 3828 3816 3876 3815

91 72 36 38 87 53 34 35

a The length is the approximate end-to-end length, MW is the molecular weight, and RU is the number of repeat units. The molecular weight of each polymer is relatively equivalent.

Figure 1. The repeat unit for the flexible backbone polymers used in this study. (A) Polymers with only carbons in the backbone: PP, PAN, PS, and PMMA, respectively; (B) polymers with ethers in the backbone: PEO, PLA, and PCL, respectively; and (C) a polymer with an amide in the backbone: N6. Note that PCL and N6 both have the same number of carbons in the backbone. Refer to Table 1 for the full name of each polymer.

energies, entropic penalties, and the intramolecular and intermolecular interactions. In the current study, we present a systematic study of the interaction between SWCNTs and polymers with flexible backbones. These MD simulations investigate how the interfacial interaction between the polymer and SWCNT is dependent upon the chemistry of the flexible backbone and the existence of side groups. These simulations complement those cited above by focusing on polymers with a significant number of repeat units and with distinct chemical features. We have also performed a similar analysis on polymers with stiff and semiflexible backbones.26 These simulations under vacuum conditions help in understanding the dynamics of polymer chains in the proximity of the SWCNT in a binary system and can be considered to be a mimic of a system in ideal bad solvent conditions.19,27 This is our first step toward more advanced studies such as solvent environments and in the condensed phase. Such an analysis of polymer conformations can greatly complement the existing literature on interfacial behavior of polymers with SWCNTs. Methodology Molecular Model of the Polymer Chains. A series of flexible backbone polymers was chosen for this study with varying chemical groups in the backbone and side groups. The polymers are summarized in Table 1, and the repeat unit of each polymer is depicted in Figure 1. To compare to experiments and for analysis purposes, the total molecular weight of each polymer chain was set to be approximately equivalent. The reference molecular weight was 20 repeat units of polyethylene terephthalate (PET), which is about 3850 amu. With this

molecular weight, each polymer used in this study was long enough to wrap the SWCNT at least twice. The structures of PP, PS, PAN, and PLA were built using the graphical user interface of DL_POLY, version 2.19.28 The structures for N6, PMMA, and PCL were built with MAESTRO 8.029 and then converted into the appropriate format by using the hybridize.f tool in DL_POLY. The polymers were all built in a head-to-tail configuration and in isotactic conformation. All of the polymers were equilibrated with a molecular dynamics simulation for 100 steps using a time step of 1 fs. Molecular Model of the SWCNT. The (10,0) zigzag SWCNT was built with the DL_POLY28 graphical user interface with the built-in Bucky-tube module. We chose the (10,0) zigzag-type SWCNT because it is simpler in structure than most other types and still has commendable properties.30 We used a diameter of 7.7 Å and a length of 125.0 Å. From studies based on the cohesive law theory,13 it was established that CNTs with small diameters have more van der Waals interactions than the larger-diameter CNTs. In addition, at smaller values of strains, the response of zigzag CNTs is comparable to that of other types.31 We observed that in previous studies, the SWCNT underwent little change during the simulation.32 It is also shown in some studies that the curvature of the SWCNT induced significant effects in the polymer molecule.24 Therefore, all of the simulations have been run with the SWCNT fixed along the Z-axis, meaning that all atoms in the CNT were treated as frozen particles to simplify the computational analysis of the run. Previous studies also made such approximations.16,19 To verify the validity of this approximation, we ran simulations of the same system with the SWCNT both fixed and free, and the results were qualitatively similar (results not shown). Molecular Dynamics (MD) Simulations. MD simulations were performed with DL_POLY, version 2.19.28 We used a constant number of molecules, constant volume, and constant temperature (NVT) ensemble at 300 K with no applied pressure, using the Evans Gaussian temperature constraints and the DREIDING33 force field. Cubic periodic boundary conditions were applied, and the MD box was built sufficiently large (with an edge length of 150.0 Å) to place the polymers beyond the force cutoffs of the SWCNT. We used a time step of 1 fs, an equilibration time of 0.5 ns, and a production run time of 3 ns. This time scale is sufficiently long enough to allow polymer coiling, and thus, we can study the competition between intrachain interactions and intermolecular interactions with the CNT. All cutoff radii were set to 10.0 Å. As there is no solvent applied and the box can be considered to be much larger than the binary system, the system was simulated to be in a vacuum with practically infinite volume. Because of that, these simulations do not explore all of the states of the polymer-SWCNT ensemble19,20 due to the length of the simulation time; the

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polymer could drift away from the SWCNT if given enough time and never interact with the SWCNT again. In addition, interactions of a binary system in vacuum can be correlated to characteristics in a bad solvent. Initial configurations of the SWCNT and polymer chain were created by aligning the SWCNT along the Z-axis, and then, the relaxed polymer chain was placed such that the perpendicular distance from the SWCNT was around 40 Å, implying that the polymer chain was well outside of the cutoff radius of interaction at the initial stage. The system volume was considerably high; thus, the molecules were practically isolated. Note that this starting configuration is in contrast to previous studies that placed the molecules within the interaction cutoff of the SWCNT.19,20,23 Other starting configurations were sampled to investigate whether the results were dependent on the starting geometry. The most significant difference was observed when the MD simulations at the initial configuration described above did not result in wrapping; in these instances, we attempted to “induce” wrapping by altering the orientation and by moving the polymer chain to a closer distance to the SWCNT. Such cases will be reported in the Results and Discussion section. In order to understand the physical chemical behavior in the absence of long-chain effects such as bonding constraints, simulations were performed on small molecules that correspond to the repeat unit for select polymers in this series. The adsorption of small molecular compounds on the SWCNT surface is reported in many theoretical as well as experimental studies.8,34,35 Due to the strong van der Waals behavior of SWCNTs,13 the molecules are held noncovalently to the surface. This property can be utilized to incorporate drug molecules and other relevant biomolecules with SWCNTs. The release of these small molecular weight compounds can be controlled by engineering the environment and the chemical activity of the SWCNT in the matrix.36 Some studies also have been focused toward alternative fuel technologies, where the SWCNT surface is utilized for the adsorption of gas molecules37 such as hydrogen and nitrogen. The comparison of polymer adsorption to their equivalent constituent small repeat unit molecules can yield the affinity of different chemical species toward the SWCNTs. This information could be used to tune the characteristics of nanocomposite interfaces, for instance, by adjusting the chemical composition of the polymer chains in the matrix. These simulations of the small molecules representing the chemical nature of the repeat unit of select polymers from this study were set up as follows. The molecular weight of the entire system was set to be equivalent to the corresponding polymer. The initial positions of each molecule were randomly selected. Cubic periodic boundary conditions were applied in order to allow the molecules to interact with the SWCNT to the most possible extent. Other details such as the cutoffs and time scales are the same as those for the MD simulations performed on the polymer-CNT interaction. Data Analysis Tools. The interaction energy between the SWCNT and the polymer is calculated for a specific time step according to the following equation

Einter ) Ecomplex - (ESWCNT + Epolymer)

(1)

where Einter is the interaction energy between the two molecules, Ecomplex is the energy of the polymer-SWCNT complex extracted from the MD simulation at the time step of interest, Epolymer is the energy of the polymer at infinite distance from the SWCNT, and ESWCNT is the energy of the SWCNT at infinite distance from the polymer. Note that since the atoms in the SWCNT are being held fixed in the simulations, ESWCNT will

Figure 2. Definition of the chemical group orientation angle relative to the longitudinal axis of the SWCNT.

remain constant. Ecomplex and Epolymer were calculated by running a single -step MD simulation of the isolated systems at 300 K to include only the potential energy contributions. Since the total mass of the polymer chains and SWCNT is about the same for all of the polymer chains and the atoms of the SWCNT are held fixed, the moment of inertia of each polymer can be compared relative to the longitudinal axis of the SWCNT as a function of time. The rotational moment of inertia is the total sum of masses of a polymer chain times the square of their perpendicular distance from the longitudinal axis of the SWCNT, depicted by the following equation n

MI )

∑ miri2

(2)

i)1

where i is the particle number, mi is the mass of the ith particle, and ri is the distance of the particle from the SWCNT axis. Changes in this quantity as a function of time can be correlated to the wrapping behavior of the polymers. Another useful analysis tool is the angular orientation of specific chemical groups in the polymer relative to the normal vector for the axis of the SWCNT, which is depicted in Figure 2. A vector is defined for two atoms within the polymer (such as the carbon and oxygen atoms in a carbonyl group), and the dot product between this vector and the normal vector yields the angle of orientation. Therefore, an angle of 90° indicates that the chemical entity is aligned parallel to the longitudinal axis of the SWCNT, whereas an angle of 0 or 180° indicates that it is aligned perpendicular to the SWCNT axis. Results and Discussion MD simulations were performed on a (10,10) zigzag SWCNT with a diameter of 7.7 Å and a length of 125.0 Å with cubic periodic boundary conditions. The series of polymers whose interactions with the SWCNT were simulated is listed in Table 1. After a system equilibration of 0.5 ns, the dynamics of the polymer-SWCNT system were recorded for 3.0 ns. All results below were extracted from this 3 ns production run. Time Trajectory of PCL-SWCNT Interaction. Snapshots at specific time steps along the trajectory for PCL are given in Figure 3. These snapshots depict the time evolution of the wrapping of a single chain of PCL in vacuo. At initial time steps, some interactions occur within the polymer itself, and the polymer remains coiled due to these intrachain interactions. At a later time step (within 500 ps), the polymer “finds” the SWCNT, and a portion of the chain begins to adsorb to the surface of the SWCNT. Eventually, the entire length of the polymer adsorbs onto the surface of the SWCNT. At later time steps, the polymer transverses the entire diameter of the SWCNT and also transverses a portion of the length of the SWCNT. Therefore, the polymer chain has predominant intrachain coiling,

MD of Flexible Polymer Chains Wrapping SWCNTs

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Figure 3. MD snapshots of PCL interacting with SWCNTs at (A) 350, (B) 550, (C) 950, (D) 1450, (E) 2450, and (F) 3200 ps. The colors used for the polymer represent the following atoms: carbon is aqua, hydrogen is pink, and oxygen is red.

which is later overcome by the polymer-CNT interaction, and wrapping occurs. This time evolution is similar to that for the other polymers, except for the differences noted below. Polymer Wrapping Conformations. Snapshots at a later time step (3.2 ns) for each polymer are given in Figure 4. Since all of the polymers have flexible backbones, intramolecular interactions dominate during the time trajectory before they start to interact with the SWCNT. The coiling occurs in the first few steps of the simulations and before the polymer chain starts to move toward the SWCNT. Some polymers like PS and PMMA and, to some extent, PP remain coiled within themselves, even at the later stages of the simulation. This persistence of intrachain coiling leads to the least amount of wrapping around the SWCNT. Out of all eight polymers in the series, all but three resulted in full wrapping around the diameter of the SWCNT axis, but in random conformations. PAN, with its cyano side group, had the most distinct conformation out of this series. The PAN chain aligned and transversed the axis of the SWCNT rather than wrapping around its diameter or coiling within itself. For both PS, with the aromatic side group, and PMMA, with the ester side group, the chains preferred to coil intrachain rather than

interact with the SWCNT. This lack of wrapping suggests that the barrier to break apart the intrachain coiling is likely too high under these simulated conditions; whether the barrier is entropic or enthalpic (or both) would necessitate a more comprehensive investigation than what is presented in this work. Recall that for the initial configuration of the MD system, the polymer was placed perpendicular to the SWCNT at a distance far from the interaction cutoff regime. (A parallel configuration was also tried for a subset of the polymers, and the results were independent of this orientation since the two molecules were initially at a distance far from the interaction cutoffs.) In cases where the polymer chains failed to interact with the SWCNT, like for PMMA, PP, and PS, the initial distance of separation was decreased. PP exhibited induced wrapping once its starting configuration was only about two times away from the nonbonded interaction regime; the results of this starting configuration are depicted in Figure 4A. However, PS and PMMA showed no wrapping even at this closer separation. The only way that we were able to induce wrapping of these polymers was to align the polymers along the SWCNT surface within the interaction cutoff and then confine the size of the box (results not shown) to limit the

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Figure 4. MD snapshots of polymers interacting with SWCNTs. All snapshots are at the 3.2 ns time step. (A) PP, (B) PAN, (C) PS, (D) PMMA, (E) PEO, (F) PLA, (G) PCL (same as Figure 3F), and (H) N6. Links to these MD trajectories are available in .mpg format in the HTML version of this paper. The colors used for the polymer represent the following atoms: carbon is aqua, hydrogen is pink, nitrogen is dark blue, and oxygen is red. Each of these MD trajectories is provided in .mpg format at http://www.te.ncsu.edu/mpasquinelli/movies.html.

intrachain interactions. Even then, the polymers attempted to coil intrachain rather than wrap around the diameter. Two of the polymers in this series, PP and PS, were also simulated by Liu and co-workers.23 The main differences in how the simulations were conducted are that (1) their polymer chains were under 30 Å, which is over 4 times shorter than the ones in this report; (2) the SWCNT that they used had a diameter two times larger and half of the length than what was used in this report; (3) their MD simulations were carried out for a much shorter time frame (300 ps compared to 3.5 ns); and (4) for the initial configuration, the polymers were aligned along the SWCNT axis in their simulations and within the nonbonded

potential cutoff distance, whereas we aligned them perpendicular and 4 times away from the interaction cutoffs. Note that since their polymers are not long enough to wrap entirely around the diameter of the SWCNT, that aspect of the conformation cannot be compared with our results. For PP, they found a random “snake-like” conformation along the SWCNT surface, which is comparable to Figure 4A. In addition, Figure 4A reveals that PP also prefers to transverse the entire diameter of the SWCNT but still in a random conformation. In contrast, Liu and co-workers found that PS has a comparable interaction to that of PP with the SWCNT, whereas Figure 4 indicates a significantly different behavior for PP and PS.

MD of Flexible Polymer Chains Wrapping SWCNTs

Figure 5. A zoomed-in view of Figure 4C, which highlights the π-π interactions in PS with the SWCNT and within its own chain.

This difference can likely be attributed to the different starting geometries as well as the longer polymer chains. The conformation of the PS side groups for their oligomer from ref 23 looks similar to that in Figure 5. Another observation, which can be identified in Figure 3, is that once the polymer chain starts to interact with the SWCNT, it tends to move along the length and surface of the SWCNT. Although such motions are observed for all polymers used in this study, some polymers do so with a larger amplitude. Polymer chains with side groups such as PMMA, PS, and PP translate very widely along the length of the SWCNT. PMMA and PS, which have little or no wrapping, show higher translational motion along the SWCNT axis. In contrast, polymers with large aliphatic repeat units such as N6, PLA, PEO, and PCL also exhibit wide translational motion along the surface of the SWCNT until they reach the end of the nanotube. PAN behaved differently due to its lengthwise conformation along the SWCNT length; PAN exhibited very little translational motion both along the length of the SWCNT as well as around the diameter. As a comparison of how these chemical constituents would behave without being constrained to the polymer backbone, we ran simulations of small molecules that correspond to the repeat unit of the PS, PLA, and N6 polymers. In general, the repeating unit molecules were found to be dispersed throughout the box at early times in the simulation, with some of the molecules aggregating and others sticking to the surface of the SWCNT. As time progressed, most molecules were adsorbed onto the surface, and by the end of the simulation, all of the molecules were adsorbed onto the surface. Once a molecule adsorbs onto the surface, it tends to remain there but may transverse the surface. In addition, it was never observed during these simulations that a repeat unit molecule entered the annular cavity of the SWCNT, as reported by others.18,20 This observation could

J. Phys. Chem. B, Vol. 114, No. 12, 2010 4127 be due to several reasons, the length of time for the simulations was too short, the diameter of the SWCNT was too small, the simulation box constrained the molecules from finding the cavity, or the intermolecular interactions were ideal for the molecules to prefer the exterior surface. Therefore, no comments can be made on this phenomenon. Snapshots from these small-molecule simulations are given in Figure 6 for molecules that correspond to the repeat unit of PS, PLA, and N6. These snapshots reveal strong correlations to their corresponding polymeric species in Figure 4. For Figure 6A, the aromatic rings tend to orient parallel to the SWCNT surface due to optimization of the π-π overlap. Barely any cases of overlap between two of the small molecules are observed; therefore, it appears that the small molecules prefer to have the π overlap with the SWCNT rather than among themselves when not conformationally constrained by a polymer backbone. This observation of repeat unit behavior is in contrast to what was observed for PS, where intrachain π-π interactions with the aromatic rings on the side chain seemed to dominate. The PLA repeat units in Figure 6B tended to have random conformations; therefore, some have the carbon adsorbed onto the surface, whereas others have the oxygen. Not all of the lactide molecules are adsorbed onto the surface by the end of the simulation time, in contrast to the other repeat units for the other flexible backbone polymers. The aliphatic N6 repeat units in Figure 6C indicate that both the hydrocarbon chain and the amide group adhered to the surface; thus, the molecules seem to prefer to maximize their interaction with the SWCNT surface in vacuo. N6 has a localized wrapping conformation similar to its repeat unit due to the presence of the aliphatic portions. These simulations indicate that the individual molecules have more conformational freedom yet still exhibit some orientation characteristics similar to the polymers, such as adsorption of both aromatic rings and aliphatic hydrocarbons along the SWCNT surface. The interaction energies (Einter) of the polymers with the SWCNT are reported in Table 2 and as a function of time in Figure 7. These values were calculated from eq 1, and the table contains an average of points taken every 10 ps in the trajectory in the range of 2.9 and 3.2 ns. The polymers that exhibit a significant extent of wrapping like N6 or PLA have relatively higher values of Einter. Polymers with poor wrapping behavior, such as PS and PMMA, have a significantly lesser Einter, as expected since the interfacial area is less between the polymer and SWCNT. Another method to quantify when the wrapping occurs, and the degree of adsorption through wrapping is to calculate the rotational moment of inertia of each polymer relative to the longitudinal axis of the SWCNT as a function of time. Since the molecular weight of each polymer is relatively the same,

Figure 6. MD snapshots of the repeat unit of the polymers interacting with SWCNTs. All snapshots are at the 3.2 ns time step. (A) 35 molecules of styrene (PS), (B) 53 molecules of lactic acid (PLA), and (C) 35 molecules of 6-aminohexanoic acid (N6). The colors used for the molecules represent the following atoms: carbon is aqua, hydrogen is white, nitrogen is dark blue, and oxygen is red.

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TABLE 2: Average Interaction Energy (Einter) of the Polymers with the SWCNT along with Their Respective Standard Deviationsa polymer

Einter (kcal/mol)

standard deviation

PCL N6 PLA PP PEO PAN PMMA PS

-308.9 -286.1 -278.3 -267.3 -258.4 -243.7 -112.5 -106.1

5.4 6.0 6.8 5.8 7.5 6.0 2.8 3.9

a Values were taken from the trajectory in the range of 2.9-3.2 ns at every 10 ps.

Figure 7. The interaction energy (Einter) of each polymer with the SWCNT as a function of time.

Figure 8. The moment of inertia of each polymer relative to the longitudinal axis of the SWCNT as a function of time. The inset is a zoomed-in version of the first 1 ns.

the moment of inertia can be compared directly for this series. A sudden dip in the moment of inertia with time signifies that there is a radial decrement in the position of atoms relative to the axis of the SWCNT. This type of plot for the series of polymers in this study is given in Figure 8. This plot indicates that all polymers have equilibrated their moment of inertia relative to the SWCNT by the end of the simulation. PS has the most fluctuations in the moment of inertia due to the motion of the repeat units relative to each other within the coiled chain. The moment of inertia is almost an order of magnitude larger for PS and PMMA at equilibrium due to the significant amount

Tallury and Pasquinelli of intrachain coiling and thus the lack of wrapping of the SWCNT by those polymers. Interestingly, the polymers that have the lowest moment of inertia at equilibrium are all of the polymers with an ether group in the backbone (PLA, PCL, and PEO) as well as PAN with its cyano side group. N6, which only differs from PCL by having an amino group rather than an ether group in the backbone, has a slightly higher equilibrium moment of inertia. The N6 chain tends to fold over itself more than PCL does (refer to Figure 4), causing a slight increase in the moment of inertia. The trend observed in the interaction energies shown in Figure 7 and in Table 2 is well in accordance with the qualitative estimation of the interaction based on wrapping conformational analyses such as moment of inertia studies. However, more intricate distinctions between N6, PLA, and PCL could be brought out by studying the interaction energies. At earlier times in the MD trajectory, most of the polymers reduce their moment of inertia relative to the SWCNT axis by a significant amount by around 500 ps, which can be attributed to both the intrachain coiling and the polymers being attracted toward the SWCNT. PP takes an additional 300 ps, and PLA takes an additional 800 ps. This longer time is likely due to the preference of both of these polymers for significant intrachain coiling at the onset of the simulations, but eventually, the interactions with the SWCNT causes a further decrease in the moment of inertia. For PMMA and PS, both polymers that did not wrap the SWCNT, a stepwise decrease occurs in the moment of inertia as a function of time. The first plateau can be attributed to the intrachain coiling and the second plateau to the attraction of a portion of the polymer to the SWCNT. Smaller “steps” are also observed for other polymers that tend to have some intrachain coiling at the onset, like N6 and PP. Degree of Chemical Orientation. An important aspect of the interface between the SWCNT and the polymer chain is whether chemical orientation occurs. Orientation of chemical groups such as carbonyls or aromatic rings could stabilize a wrapping configuration and thus impact the adhesion forces. In order to calculate these orientations, a vector is defined between two atoms in the polymer (such as two opposite positions in a phenyl ring), as well the normal vector for the axis of the SWCNT, and then, the angle between them is calculated. An angle of 90° indicates that the polymer entity is aligned parallel to the SWCNT surface, whereas an angle of 0 or 180° indicates that the group is perpendicular to the SWCNT surface. The analysis of chemical orientation for some of the flexible backbone polymers is given in Figure 9. Horizontal placement of the dots indicates the translational motion of the polymer chain at that time step, whereas vertical placement represents the chemical orientation of the chemical entity relative to the surface of the SWCNT. The narrow horizontal distribution for all polymers but PAN along the horizontal axis signifies the localized wrapping conformation of these polymer chains (refer to Figure 4). PAN, however, has an extended conformation along the surface of the SWCNT, thus the wide horizontal distribution in Figure 9b. For the angle of orientation, the carbonyl groups for all three polymers in Figure 9a have a wide distribution in the angles, ranging from 20 to 160° with respect to the SWCNT normal. For the chemical entities in Figure 9b, both PS and PMMA have a wide angle distribution due to poor wrapping. For PS, it can also be attributed to the balance between π-π stacking with the SWCNT and intrachain, as depicted in Figure 5. Out of all of the polymers with chemical entities, only the cyano group in PAN shows slight preferential orientation at 60-110° angles with respect to the vector normal

MD of Flexible Polymer Chains Wrapping SWCNTs

J. Phys. Chem. B, Vol. 114, No. 12, 2010 4129 Acknowledgment. The authors thank Russell Gorga and Alan Tonelli for the insightful discussions. This work was funded by start-up funds provided to M.A.P. References and Notes

Figure 9. The orientation of the chemical entities in the polymer chain relative to the normal vector from the SWCNT axis at the 2.8 ns time step. (a) Polymers that contain an ester linkage: PMMA, PLA, and PCL. (b) Other interesting chemical groups: PAN, N6, and PS. The C1-C4 vector for PS is defined as two atoms in the phenyl ring, where C1 is the atom connected to the backbone, and C4 is the atom in the para position from C1.

to the SWCNT surface, indicating that the cyano group tends to align relative to the SWCNT surface. Conclusion The simulations indicate that polymers with flexible backbones tend to adhere to the SWCNT, although not in any distinct conformation. Most of the polymers in this series tended to wrap along the diameter of the SWCNT, although no helical patterns were observed. PAN with the cyano side group showed a preference for transversing the length of the SWCNT rather than wrapping around its diameter, and the cyano group preferred to orient parallel to the SWCNT surface. Polymers with bulky and aromatic side groups such as PS and PMMA preferred intrachain coiling rather than wrapping the SWCNT. We have also performed a similar study on a series of polymers with stiffer backbones, which is the subject of another paper. It would also be interesting to repeat this study in a variety of solvent conditions as well as with multiple chains. In addition, Monte Carlo simulations using a full interaction potential could help to extract valuable details while expanding the phase space and thus may be the focus of future work.

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