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Understanding the Helical Wrapping of Poly(3-hexylthiophene) on Carbon Nanotubes Claudia Caddeo,*,†,‡ Claudio Melis,†,‡ Luciano Colombo,†,‡ and Alessandro Mattoni*,‡ Dipartimento di Fisica UniVersità di Cagliari, and Istituto Officina dei Materiali del CNR, Unità SLACS, Cittadella UniVersitaria, I-09042 Monserrato (Ca), Italy ReceiVed: August 5, 2010; ReVised Manuscript ReceiVed: October 27, 2010
We studied poly(3-hexylthiophene) adhesion on single-walled carbon nanotubes via molecular dynamics simulations. We provide evidence that, in absence of the solvent, the polymer tends to unwrap and align to the nanotube. The helical organization in vacuo is metastable, and its lifetime is a function of the temperature and the polymer length. A kinetic model is here proposed according to which unwrapping is thermally activated with an energy barrier as small as 0.09 eV. Our results at room temperature reproduce the experimentally observed pseudohelical morphology of the polymer and confirm the role of the nanotube chirality. Furthermore, we provide evidence of a strong stabilization effect on the wrapped configuration because of neighboring polymer chains. Introduction Hybrid blends formed by carbon nanotubes (CNT) and polymers have attracted large interest as novel structural or functional systems for applications in biology,1-4 structural engineering,5,6 and optoelectronics.7,8 In particular, when the polymer is conductive, as is the case of the conjugated poly(3hexylthiophene)(P3HT), the hybrids are important for photovoltaics and optoelectronics since they have the potential to combine the formability of P3HT to the unique transport properties of the nanotubes.9-12 Polymer/nanotube blends can be syntethized by dispersing the nanotubes into an aqueous solution containing the polymer13 provided that the latter is soluble. Solubilization is possible because the polymer coats the hydrophobic nanotubes’ surfaces and disassociates them from the aggregate form. Coating of the nanotubes is a phenomenon observed for many different soluble polymers.14 At the nanoscale, the coating corresponds to a complex organization of the polymer chains on the nanotube surface. In some cases (e.g., for stiff short polymer chains15), the polymer aligns along the carbon nanostructures, but typically the polymer wraps around the nanotube giving rise to helical structures14,16 as found, for example, for those polymers having the intrinsic property to form helices17 (e.g., some biopolymers such as DNA, alginic acid, and others). In these cases, an important role is played by intramolecular hydrogen bonds. The helical wrapping of DNA, alginic acid (AA), and amylose on CNTs18-21 has been investigated by using molecular dynamics (MD) simulations. The helical wrapping on CNTs has been also observed for soluble polymers (which do not form hydrogen bonds) in aqueous solution (e.g., poly[p-2,5-bis(3-propoxysulfonicacidsodiumsalt)phenylene]ethynylene (PPES),16 P3HT,22 and polyvinyl pyrrolidone (PVP)14). From the theoretical point of view, the importance of the solvent has been studied by Kang et al.16 that simulated the spontaneous occurrence of helical wrapping of a PPES chain on a single-wall CNT in the presence of water molecules by * To whom correspondence should be addressed. E-mail: claudia.
[email protected] (C. C.);
[email protected] (A. M.). † University of Cagliari. ‡ CNR-IOM SLACS.
MD simulations. Conversely, in the absence of the solvent, the helical self-organization of the polymer has not been found. Rather, different wrapped conformations have been in fact identified depending on the chemical nature of the monomer23-26 and on the flexibility of the polymer backbone.27 For example, flexible polymers such as poly(caprolactone) and poly(propylene) give rise to disordered configurations, while poly(acrylonitrile) tends to be aligned to the nanotube axis. These results suggest that most likely the solvent plays a major role in the helical wrapping. This is the case of P3HT, a semirigid polymer28 which is the object of the present investigation. It has been observed22 that in solution the polymer helical wrapping is possible. In particular, by analyzing single-walled carbon nanotubes (SWCNTs) with diameters as small as 1.5 nm with scanning tunneling microscopy (STM), it has been observed that single polymer chains can arrange into pseudohelical configuration with arrangements depending on the nanotube chirality. To our knowledge, no atomistic simulations of P3HT wrapping on nanotubes have been performed yet (neither on single nor on multiwalled carbon nanotubes), and several features need to be clarified. At first, the observed pseudohelical structure is still not understood, and it cannot be characterized by only using chirality considerations. Furthermore, the stability of the wrapped configuration, once the solvent has been dried, must be identified. This is important from the technological point of view because such blends operate in solvent-free environment and possible unwrapping phenomena can affect the properties of the system. Finally, understanding at the atomic scale the stability of the wrapped configuration could aid the design of highly oriented P3HT-SWCNT systems with improved conducting properties. In this work, by means of MD simulations of P3HT chains of realistic length wrapped on nanotubes, we provide evidence that, in absence of any solvent, the polymer tends to align along the nanotube. In addition, we show that the experimentally observed pseudohelical organization22 actually corresponds to a metastable configuration, whose lifetime depends on temperature and polymer length. Our results at finite temperature are in agreement with the pseudohelical morphology characterized by scanning tunneling microscopy22 confirming the role of the
10.1021/jp107370v 2010 American Chemical Society Published on Web 11/22/2010
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Caddeo et al. At any T > 100 K, the polymers were found to move along the nanotube surface thus exploring quite a few configurations differing by number of coils, coiling angles, and morphologies; all structural features depend on both L and T. The possible configurations are reported in the top panels of Figure 1. Interesting enough, no polymer desorption was observed in the thermodynmical conditions explored in the present investigation. The different morphologies are distinguished by using the alignment parameter ξ, defined as
ξ)
Figure 1. (top panels) Identified ordered (HH, H, A) and folded (C) polymer configurations. (bottom panel) Alignment parameter ξ as a function of temperature T and polymer length L. Lifetime curves (green and red lines) are identified by connecting points with identical helical lifetime (see text).
nanotube chirality. Finally, we provide evidence of a strong stabilization effect on the wrapped configuration because of neighboring polymer chains. Theoretical Framework The dispersive (i.e., van der Waals) interaction between the polymer and the carbon nanotube is here described by the sum of two-body Lennard-Jones contributions with Amber force field parameters as in ref 18. Molecular dynamics simulations were performed by using the DL_POLY parallel code.29 The simulation cells have dimensions Lx, Ly, and Lz along the x, y, and z directions, respectively, where Lx ) Ly ) 5 nm and Lz ranged in the interval 0.013-0.1 µm. Periodic boundary conditions were applied in all directions. The nanotubes were aligned along the z direction and periodically were repeated so as to represent an infinite structure. The simulated systems contained up to 2 × 104 atoms corresponding to a maximum polymer length L ∼ 0.1 µm. The equations of motion of atoms were integrated by using the velocity Verlet algorithm with a time step as small as 0.5 fs. Temperature was controlled by the Berendsen thermostat with relaxation costant f ) 0.5 ps. Results and Discussion First, we considered the case of (15, 0) zigzag nanotubes. To have an initial configuration representative of the wrapped morphology (hereafter named HH), we bent the polymer molecule into a helical shape around the nanotube and we relaxed the atomic forces until a minimum energy configuration was identified. The actual value of the coiling angle (i.e., the angle formed by the polymer backbone with respect to the nanotube axis) is ∼30°, and it was chosen according to experimental indications22 and was used for all the polymer chains investigated. After the relaxation procedure, the coiling angle in the HH configuration was found slightly changed, but the periodicity of the helix was preserved (see top left panel of Figure 1). The average polymer-nanotube distance was found to be as small as ∼0.35 nm. To study the wrapped morphology and the possible configurations at finite temperature, we annealed the HH systems for up to 4 ns in the range of temperatures 100 K < T < 1000 K. The polymer length was varied in the interval 28LP < L < 256LP, where LP is the length of the monomer, a range of lengths comparable to the experimental data.
1 NU
NU-1
∑ i)1
NU-1 b Vi · b V i+1 1 cos(θi) ) |b V i| · |b V i+1 | NU i)1
∑
(1)
where the vector b Vi connects the ith and (i + 2) equivalent sulfur atoms along the backbone, and NU is the number of periodic units of the polymer (NU ) L/2LP). According to eq 1, θi is the angle describing the bending of the polymer chain. ξ was found to vary in the range 0.6-1.0 depending on the different morphologies explored. In particular, a value ξ ∼ 0.8 is found for the HH configurations, while the largest values (ξ ∼ 1) are obtained when the polymer lies along the nanotube axis and the neighboring polymer units are aligned. Finally, a small alignment parameter (ξ ∼ 0.6) corresponds to the folded phase (C). In the bottom panel of Figure 1, the parameter ξ(L, T) is calculated as a function of the annealing temperature and chain length. Colors identify the different polymer arrangements after annealing as long as 2 ns. We evaluated the alignment parameter on a regular mesh of 7 × 6 ) 42 points, marked in Figure 1 by triangular symbols, and then interpolated the data with a thin plate spline algorithm30 to obtain the color map in Figure 1. We performed a convergency test on the number of points, and we found that when increasing the mesh from 20 to 42 points the maps are practically unaffected. For a fixed polymer length L, the above diagram shows that the ideal helical configuration (HH morphology) is stable only at very low temperature (blue region). At higher temperature, the polymer relaxes into pseudohelical structures (H) similar to the experimentally observed ones.22 By further increasing the temperature, the coils are spontaneously loosened during the dynamics and the polymer ends in the aligned morphology (A). For very high temperatures, the polymer can even fold into a cloud configuration (C). According to the above analysis, the H morphology at room temperature is only a metastable configuration, and it spontaneously changes into the aligned one. To better characterize the lifetime of the H morphology and the physical factors affecting its stability, we calculated the instantaneous number of coils g(t) of the polymer chain at time t:
1 g(t) ) 2π
NU-1
∑ i)1
1 θi ) 2π
NU-1
b V ·b V
∑ arcsin |bV i|i · |bVi+1i+1|
(2)
i)1
Vi, and NU are the same as above. At high where θi, b temperatures, any molecule unwraps and, accordingly, g(t) is found to monotonically decrease to zero during the MD run. Conversely, at lower temperatures, the unwrapping mechanism is less efficient and at the end of the simulations there is still a finite number of coils (g(t) > 0). The above picture for P3HT is in contrast with the spontaneous tendency of PPV to wrap at room temperature.31 This can be attributed
Helical Wrapping of Poly(3-hexylthiophene)
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Figure 2. Number of coils as a function of the annealing time for a 256 monomer long chain at different temperatures.
Figure 3. Unwrapping time versus temperature.
to the different chemical composition of the two polymers (e.g., PPV does not contain sulfur atoms) and to the larger rigidity of PPV which favors wrapping.27 Our atomistic data are well reproduced by an exponential function of time g(t) ∼ g(0)exp(-t/τ) where τ, hereafter referred to as the lifetime of the wrapped H morphology, depends on both T and L, and g(0) is the initial number of coils. A graph of the number of turns versus time is reported in Figure 2. It shows the time evolution of the number of turns g(t) for three different temperatures and the exponential functions used to fit data. The inverse of the lifetime ∼1/τ corresponds to the rate of unwrapping events, and it controls the kinetics. At early times, in fact, the rate of coil loss dg/dt is approximately dg/dt ∼ -1/τ. We found that the lifetime τ decreases as the temperature increases according to an Arrhenius law τ ∼ exp(Ea/kT), where Ea is the activation energy for an unwrapping event (see Figure 3). Ea was calculated to be as small as 0.09 eV. According to the above analysis, the HH morphology is stable and is distinguished from the H one at very low temperatures, while at higher temperatures, it can relax into H and eventually A configurations by overcoming the energy barrier Ea. Concerning the role of the polymer length L on the unwrapping kinetics, a linear relationship is found τ ∼ κL with a lifetime per unit of length (κ ) τ/L) that is approximately independent of L. Accordingly, in the limit Lf∞, the unwrapping kinetics is unchanged. This is shown in Figure 4, and it suggests that the lifetime per unwrapping event is approximately constant, that is, the unwrapping events are uncorrelated. This is accurately true in the early stages of the kinetics where g(t) is linear, that is, g(t) = -(1)/(τ) · t. Possible deviations can be easily incorporated into the model by introducing an exponent R in such a way that g(t) ∼ LR. The results of the above analysis can be summarized by introducing an overall T - L dependence into the kinetic model for the wrapped morphology lifetime:
τ(T, L) )
LR Ea/kT e V0
(3)
Figure 4. Unwrapping time versus polymer length.
where V0 is a suitable constant. Here, we use R ) 1. The above model correctly predicts that the lifetime of the wrapped H morphology is a continuous function of L and T, and it is longer for longer polymers and lower temperatures. A remarkable result is that such a model is able to identify the boundaries in the L - T plane (Figure 1) between the different morphologies. The points with the same lifetime τ0 give rise to the curve τ(L, T) ) const ) τ0. Different values of τ0 correspond to different curves. It is possible to choose τ0 in such a way that the corresponding curve approximately delimits the yellow region where the polymer is highly aligned (ξ > 0.98). This is obtained for τ0 ) 2 ns. The corresponding curve is reported in Figure 1 as a red line. Hereafter, all the lifetimes are normalized to τ0 ) 2 ns. Accordingly, the points on the right of the red curve (i.e., τ < 1) correspond to highly aligned polymers for which ξ > 0.98 (yellow shaded area); the points on the left (i.e., τ > 1) have a smaller degree of alignment. The case of a larger lifetime (τ ) 12) is reported for comparison (green line). The three different polymer morphologies can be identified in the L - T plane: HH (regular helix when τ . 1), H (pseudo helix when τ > 1), and A (aligned chains when τ e 1). At very high temperature, entropic contributions make a partial folding of the polymer possible, and our model is not applicable. The folded phase (C) is recognizable in the ξ color map as the dark region at high temperature and length ∼ 60LP. A snapshot of a polymer wrapped in the H morphology on a (15,0) nanotube at T ) 300 K is reported in Figure 1. It exhibits clear similarities with the experimental structure of ref 23 where different coiling angles alternate along the chain. Thus, we suggest that the experimentally observed structure corresponds to a state that, in vacuo and at room temperature, is only metastable. The theoretical results also demonstrate that the polymer morphology depends on the chirality of the nanotube as indeed also suggested by experiments22 and previous theoretical works.27 In Figure 5, we compare the results for two hybrid systems differing only by the chirality of the nanotube (the case of (15,0) zigzag and the case of a (9,9) armchair nanotube of similar radii). At T ) 300 K, both systems unwrap during 2 ns long thermal annealing, and we observe different morphologies during the run. The obtained morphologies differ qualitatively in terms of both the coiling angles and their relative abundance. In the zigzag case, the polymer forms ∼13 coils with angle ∼60° and only two with angle ∼30°, while in the armchair case, there are ∼4 coils with angle ∼45° and ∼8 coils with angle ∼30°. This implies that the SWNT chirality has an important role on the final morphology of the hybrid system. In particular, our results are in agreement with STM measurements on zigzag nanotubes.22 The observed polymer configuration presents coils of angle 33° ( 1° as we find in our models (see Figure 5, left).
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Figure 5. Polymer helical assembling on (15,0) zigzag (left) and (9,9) armchair (right) nanotubes after 0.5 ns at T ) 300 K. Only the sulfur atoms are reported for clarity as yellow balls. The insets show the details of the interdigitation of the hexyl chains and the tiophene/nanotube lattice matching.
Figure 6. Two-chain polymer/nanotube systems after 2 ns annealing at room temperature. One chain is wrapped while the other is wrapped around (left) or parallel to (right) the nanotube. The inset shows the details of the superposition of the two chains (only thiophene rings shown for clarity).
As for the predicted coiling angles in the armchair case, there is an agreement with some experiments.32 Unfortunately, the comparison is difficult since in that work the chirality of the nanotubes has not been fully characterized. The actual values of the coiling angles are determined by the thiophene/nanotube lattice matching as shown in the insets of Figure 5. An interesting feature of the wrapped conformations in both cases is the presence of clusters of two or more neighboring coils at the polymer extrema. This behavior is driven by the polymerpolymer interchain attractions, and it corresponds to an ordered interdigitation of hexyl chains (see top left inset of Figure 5). So far, we have considered systems with a single polymer chain per nanotube; however, real blends actually exhibit very high polymer density (1-0.1 wt % nanotubes22,33), and several polymer chains interact with the same nanotube. The relative polymer/nanotube density may influence in some way the stability of the helical state. For example, O’Connel et al.14 suggest multihelical wrapping as the most likely configuration for PVP. Multihelices have been experimentally observed in the P3HT case as well.22 To study the role of multiple chains, we started from a system containing one polymer chain (L )
64) helically wrapped on the nanotube (HH morphology), and we added a second chain in two different ways: (1) wrapped along the nanotube next to the first one (see Figure 6, left); (2) unwrapped and parallel to the axis of the nanotube (see Figure 6, right). The two geometries are considered in order to study the interaction of the wrapped chain with the structurally complex embedding polymer matrix in which the nanotubes are dispersed. For both systems, we observed that the second chain is able to stabilize the helical arrangement of the first chain, that is, preserved at room temperature for the whole annealing time as long as 2 ns (final configurations of the systems are reported in Figure 6). The same chain, if isolated, unwraps in a time smaller than 0.5 ns. The relative polymer/nanotube density is accordingly a key factor which gives stability to the wrapped H morphology. Conclusions In conclusion, by molecular dynamics simulations on realistically long polymer chains, we provided evidence of helical
Helical Wrapping of Poly(3-hexylthiophene) wrapping on single-wall carbon nanotubes. The helical wrapping in vacuo is found to be a metastable configuration stabilized by the interactions among neighboring polymer chains. We also showed that the nanotube chirality affects the actual coiling angles and the morphology of the helix. According to the present study, it is in principle possible to enhance the polymer-nanotube alignment by a suitable tuning of temperature, polymer density, and chain length. Acknowledgment. This work has been funded by the Italian Institute of Technology (IIT) under Project SEED “POLYPHEMO” and Regione Autonoma della Sardegna under Project “Design di nanomateriali ibridi organici/inorganici per l’energia fotovoltaica” L.R.7/2007. We acknowledge computational support by CYBERSAR (Cagliari, Italy) and CASPUR (Rome, Italy). We acknowledge Paola Castrucci (Univ. Roma Tor Vergata, Italy) and Michele Giulianini (QUT, Australia) for useful discussions. References and Notes (1) Hu, Y.; Chen, W.; Lu, L.; Liu, J.; Chang, C. ACS Nano 2010, 4, 3498–3502. (2) Landi, B. J.; Raffaelle, R. P.; Heben, M. J.; Alleman, J. L.; Derveer, W. V.; Gennett, T. Nano Lett. 2002, 2, 1329–1332. (3) Koerner, H.; Price, G.; Pearce, N. A.; Alexander, M.; Vaia, R. A. Nat. Mater. 2004, 3, 115–120. (4) Tahhan, M.; Truong, V. T.; Spinks, G. M.; Wallace, G. G. Smart Mater. Struct. 2003, 12, 626–632. (5) Ajayan, P. M.; Schadler, L. S.; Giannaris, C.; Rubio, A. AdV. Mater. 2000, 12, 751. (6) Zhang, S. H.; Zhang, N. Y.; Huang, C.; Ren, K. L.; Zhang, Q. M. AdV. Mater. 2005, 17, 1897. (7) Pradhan, B.; Setyowati, K.; Liu, H.; Waldeck, D. H.; Chen, J. Nano Lett. 2008, 8, 1142–1146. (8) Picard, L.; Lincker, F.; Kervella, Y.; Zagorska, M.; DeBettignes, R.; Peigney, A.; Flahaut, E.; Louarn, G.; Lefrant, S.; Demadrille, R.; Pron, A. J. Phys. Chem. C 2009, 113, 17347–17354. (9) Wu, M.-C.; Lin, Y.-Y.; Chen, S.; Liao, H.-C.; Wu, Y.-J.; Chen, C.-W.; Chen, Y.-F.; Su, W.-F. Chem. Phys. Lett. 2009, 468, 64–68. (10) Curran, S. A.; Ajayan, P. M.; Blau, W. J.; Carrol, D. L.; Coleman, J. N.; Dalton, A. B.; Davey, A. P.; Drury, A.; McCarty, B.; Maier, S.; Stevens, A. AdV. Mater. 1998, 10, 1091.
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