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Chiral Asymmetry of Helical Polymer Nanowires Olayinka O. Ogunro,‡,§ Kayode Karunwi,† Ishrat M. Khan,‡,§ and Xiao-Qian Wang*,† †
Department of Physics, ‡Department of Chemistry, and §Center for Functional Nanoscale Materials, Clark Atlanta University, Atlanta, Georgia 30314
ABSTRACT We have employed force-field molecular dynamics and first-principles calculations for the helical formation of isotactic poly(2-methoxystyrene) nanowires. Our calculation results reveal the self-assembly of left- and right-handed helical nanorods. The energy of the helical conformations depends on the chiral center as well as linkages among neighboring methoxy benzene groups. The implications of these results for understanding experimentally observed chiral asymmetry of left- and righthanded nanowires are discussed. Furthermore, we demonstrate that the coiled structures can effectively wrap around singled-walled carbon nanotubes. The electronic structure characteristics of these conformations are studied with use of first-principles calculations. SECTION Molecular Structure, Quantum Chemistry, General Theory
H
elices are a typical structural motif in biological molecules. The R-helix in proteins and the double helix in double-stranded DNA are well-known examples.1-4 In a living cell, the embracing of stable helical structures allows these molecules to place functional groups in specific positions and orientations, as well as keeps the polymer backbone away from the solvent, shielding it from chemical attack. The consensus of helix formation is that biological helices are stabilized by orientationally dependent hydrogen bonding, with their chirality arising from the chirality of the polymer molecule.1 Those same properties that make helical molecules so useful in living cells also make them useful in the context of nanotechnology. However, while our understanding of biological helices is satisfactory in interpreting why polypeptides and polynucleotides form helices, it does not provide sensible prescriptions for developing alternative helix-forming molecular architectures. To gain the understanding necessary to develop such prescriptions, it is desirable to consider realistic models for helix formation, which should capture the underlying physics of chiral conformations. Biological systems rely almost exclusively on supramolecular self-assembly to create complex structures that carry out diverse functions. The application of self-assembly principles gleaned from biological systems provides ways to achieve greater control over the design and construction of selfassembling molecular objects to produce artificial nanoscale devices. Motivated by the observation that many of the functions of naturally occurring macromolecules are associated with their higher structural orders,1-4 the development of synthetic polymers with biological functions has attracted a great deal of attention. Several groups have reported the preparation of synthetic polymers with higher structural order, most with helical conformations. Helical polymers have been prepared from achiral monomers, from monomers carrying pendant chiral groups, and from generating secondary conformations by helicity induction.5-8
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A series of optically active helical poly(2-methoxystyrene)s (P2MSs) have been synthesized and characterized recently.9,10 These functionalized polymers are specific to antibodies and immune receptors, thereby holding potential for controlling receptor binding and cell activation. Some of those helical polymers are potent inhibitors of receptor-mediated degranulation responses in mast cells, capable of binding to cells and affecting cellular responses. Furthermore, there are increasing amounts of experiment work on electrospun fibers of helical polymers with single-walled carbon nanotube (SWNT) contents for the purpose of developing polymeric nanostructures for therapeutics and biodiagnostics. P2MS is a non-natural rigid rod system.2,9 The 2-methoxystyrene monomer serves as an ideal building block for generating biofunctional polymer systems. In addition to its biocompatibility, surfaces prepared with helical chiral polymers demonstrate effectiveness in controlling polymer-cell interactions. Consequently, it is important to understand factors that influence the formation of helical conformation. Here we present simulation results based on a combination of force-field molecular dynamics and first-principles calculations.11 The force-field molecular dynamics is employed to obtain information regarding the conformation and the overall geometric shape of the helical polymers. Our results indicate that isotactic P2MS forms low-energy stable helical conformations. The P2MS helical polymers prefer parallel alignment of nanowires with the same chirality. Moreover, the low-energy conformations of the helical polymers depend strongly on the linkages of the monomers, especially at the starting ends. These results shed light on the experimental observations that chiral P2MS surfaces improved polymer-cell interactions as compared to achiral ones.9 Furthermore, we demonstrate that P2MS can effectively Received Date: December 15, 2009 Accepted Date: January 21, 2010 Published on Web Date: January 26, 2010
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in Figure 1 have quite different energies, although both are stable rigid rod conformations with virtually the same pitch length. It is rather unexpected to observe a lower energy of the R structure than the S one by ∼2 kcal/mol per atom. This indicates that the helical formation depends strongly on the initial positions of chiral centers with respect to terminal groups, and the helical formation process can easily “freeze” into one particular conformation. (ii) The helical polymers can form a regular pattern of parallel alignments. Our calculation on the optimized conformations of a pair of helical polymers as shown in Figure 1 indicate that the same helicity aligned polymers (R-R or S-S) are preferred, with an interaction energy 3-15 kcal/mol better than that of the opposite helicity aligned counterpart (R-S). (iii) The rigid rod conformation is semiflexible in that it can bend to form coiled wires. The helicity of the coiled wire follows the chirality of the helical polymer. As the typical helical rod consists of a few hundreds of atoms, the investigation of transition states between various conformations becomes formidable. In order to gain insight on the energetics of the helical conformations and the associated electronic structure characteristics, we constructed periodic structures. The corresponding unit cell is composed of six monomers and has 54 carbon, 60 hydrogen, and 6 oxygen, a total of 120 atoms. The periodic helical structures were investigated based on density functional theory with local density approximation (LDA) for exchange and correlation potential.15 Periodic-boundary conditions were employed with a supercell in the xy plane large enough to eliminate the interaction between neighboring structures. A double numerical basis set expansion of local orbitals implemented in the DMol3 package15 was sufficient to converge the grid integration of the charge density. It is well-known that the LDA can not properly describe long-range dispersion forces in organic molecules. However, our previous studies of similar systems11,12 indicate that the present approach is sensible in that the methoxy benzene is a small molecule and is thus less affected by dispersion corrections than larger aromatic groups. The helical R and S structures as shown in Figure 1, along with other stable low-energy conformations identified via molecular dynamics simulations, were used to construct the periodic systems with a six-monomer unit cell. The resultant unit cell was fully optimized using first-principles approach. All structures were relaxed with forces less than 0.05 eV/nm. The optimized unit cell length of 1.38 ( 0.08 nm is in good conformity with the result extracted from force-field-based molecular dynamics calculations. The average radius of the helical polymer is about 0.5 nm, in good agreement with experimental observations.9 Careful examination of various low-energy conformations indicates that the corresponding energy correlates with the sequence of neighboring methoxy benzene linkages. Closer scrutiny of the helical structures reveals that there exist two prototypical linkages between neighboring methoxy benzene groups. One type of linkage, indicated by green arrows in Figure 1, has neighboring methoxy benzene groups arranged in such a way that the torsion angle between the two groups is about 120°. The other type of linkage, indicated by red arrows,
Figure 1. Chemical formula of right- and left-handed P2MS (P2MS-R and P2MS-S, respectively), along with side views of optimized R and S helical P2MS nanowires. Each of the R and S rod structures has 32 monomers of 2-methoxystyrene (n = 32), and consists of 290 carbon, 326 hydrogen, and 32 oxygen, a total of 648 atoms. Gray, red, and white colored atoms represent carbon, oxygen, and hydrogen, respectively. Red and green arrows indicate two distinctive type of linkages that are referred to as cisand trans-linkages, respectively.
wrap around SWNTs, and thus the SWNT/P2MS nanocomposites may be utilized as components of biosensors. In view of the rapid progress made in preparing electronically active SWNT/P2MS nanocomposites by electrospinning, we have also performed first-principles calculations to investigate the electronic structure characteristics of the corresponding conformations. The helical polymers involved in the present study were constructed based on models as shown in Figure 1, with n monomers of 2-methoxystyrene. The constructed structures were subsequently optimized using simulated annealing based on MMþ force field. The classical force-field approach was thoroughly tested in our previous multiscale simulation studies of various nanostructures.11,12 For n < 20, the helical structure is not rigid, which is consistent with earlier studies on structurally similar poly(3-methyl-4-vinylpyridine) polymer systems.13 With a systematic increase of the number of monomers, the polymer forms a helix rod structure for n g 24. Illustrated in Figure 1 are the chemical formula and optimize structures of R and S conformations. In either R or S structure, approximately six consecutive 2-methoxystyrene monomers form a turn with a pitch length of 1.4 ( 0.1 nm. As can be readily observable from Figure 1, the helical polymers have a cylindrical shape, with a diameter of 0.49 ( 0.05 nm. A few remarks are immediately in order. (i) Left and righthanded helices are enantiomers, and thus each structure and its mirror image have the same energy.14 Our explicit calculations with use of the reflection confirmed that, for each stable R helical conformation, there is an isoenergy S counterpart. This implies that there exists no chirality-specific interaction in the force-field model and first-principles approach. However, it is worth mentioning that the R and S structures shown
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Figure 2. Isosurface plot of wave functions of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for a periodic P2MS-R.
has a much smaller torsion angle, typically e60°. In accordance with the distinct feature of the linkage, we refer to the two type of linkages as trans (green arrows in Figure 1) and cis (red arrows), respectively.13 The steric hindrance between the trans and cis linkage is primarily responsible for the energy differences between the R and S conformations shown in Figure 1, as the trans linkage is significantly lower in energy than the cis linkage. An important ramification of our simulation results is that the helicity of the nanorod depends crucially on the initial orientations of chiral centers with respect to the terminal groups. It is worth noting that, while the low-energy R-helix in Figure 1 has trans-linkages at both ends, the higher-energy S helix shown in Figure 1 has cis-linkages at one end. In regards to the aligned helical nanowires on the surfaces, our calculation results indicate that the parallel alignment of the same helicity nanowires leads to improved binding and ordered charge density distributions, which is useful in understanding experimental observations that chiral P2MS surfaces are effective in controlling polymer-cell interactions as compared to achiral ones. Therefore, there is significant potential in using such surfaces to develop smart materials to control and manipulate material-cell interactions. Shown in Figure 2 is the optimized P2MS-R all-trans structure, along with the extracted charge density distribution of valence band maximum and conduction band minimum, respectively. The majority of the bands of P2MS-R are flat and dispersionless, in accord with molecular orbital levels. The extracted gap for the optimized structure is about 2.1 eV. We have considered the effect of polymers interacting with a solvent using the COSMO solvation model15 and found a paucity of modification to the geometrical and electronic structures. The optimized unit cell conformation can be used to construct realistic helical polymer with variable lengths and functional groups, which will be useful for investigating the nature of ligand-receptor interactions. The all-trans conformation;either R or S;is the global minimum configuration, and the “defective” cis-linkage configuration has higher energy (∼2 kcal/mol) per atom. It appears that the degree of twist and the pattern of trans or cis linkages can be “trigged” and “memorized” during the
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Figure 3. Side view of the optimized structure of P2MS-R wrapping helically on an armchair (8,8) nanotube (green color) and the calculated band structure for helically wrapping P2MS on metallic (8,8) and semiconducting (14,0) tubes, respectively. The band center is at Γ = 0, and the band edge is at L = π/a and Χ= π/b for (8,8) and (14,0), respectively, where a = 1.297 and b = 1.278 nm. The Fermi level is shifted to 0 eV.
helix formation, which can easily freeze into a stable conformation with a certain fraction of cis linkages. An important finding from the present simulation study is that cis linkages are more readily generated in S-helical polymers, yielding higher energy nanowire conformations. These results are consistent with experimental findings in that chiral asymmetry is often observed. Specifically, the synthesized P2MS has abundant R helical polymers over S with about 2:1 ratio,9 which can be attributed to the energy differences of the stable R or S helices. Since the optical active properties of the samehelicity polymers are superior to the mixed-helicity ones, the synthesis of a preferred-helicity conformation assisted by effective catalysts is of considerable current interest.16 In this regard, our current work points to the important role played by catalysts in forming preferred-helicity conformations. The efficiency of the helical polymer could be improved by incorporating carbon nanotubes into the polymer matrix.11 Carbon nanotubes represent an intriguing class of materials for exploring nanoelectronics and nanostructured composites.11 A large variety of helical polymers can self-assemble and wrap around the nanotubes, providing a useful means for manipulating electronic transport in nanoelectronic devices. We have studied the interfacial interactions between the helical polymer and SWNTs. Our molecular dynamics results on the helical polymer P2MS interacting with SWNTs demonstrate that the semirigid helical polymer rod has certain flexibility to adjust its conformation during wrapping, and the wrapped polymer successfully adopts a helical conformation with a pitch length of about 4 nm. We depict in Figure 3 the band structure for P2MS-R helically wrapping on two prototype SWNTs: an armchair metallic (8,8) and a zigzag semiconducting (14,0). The choice of the two tubes was based
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on the fact that they have very close diameters (1.085 and 1.096 nm for (8,8) and (14,0), respectively), and the roughly commensurate feature of quarter of a pitch of the helical P2MS with the pitch of the corresponding SWNTs. When interacting with SWNTs, the helically wrapped structure increases interaction energy, which supersedes the van der Waals interaction among the SWNTs. As seen from Figure 3, the metallic or semiconducting feature, specifically the π-π* band associated with metallic armchair tubes, remains intact after the noncovalent functionalization. The superposition of dispersion bands originated from the SWNTand the flat bands that are attributed to the helical polymer leads to level hybridizations, marked with red and blue lines in Figure 3. The flat band for P2MS/(14,0) (purple line in Figure 3) indicates charge confinement on the polymer.12 Since there are about one-third metallic tubes in as-prepared samples, the incorporation of SWNTs in the formation of larger-diameter helical wires is expected to improve the conductance due to the percolation network of metallic tubes. In summary, we have performed molecular dynamics and first-principles calculations for the study of the spontaneous formation of helical polymers. Our results demonstrate that the trans and cis linkages of the neighboring methoxy benzene groups are important characteristics of the helical conformation. The folding pattern of the trans and cis linkages depends on the configurations of chiral centers at starting ends, which can readily freeze into a rod structure. Furthermore, our simulation results reveal that the helical polymers can effectively wrap around SWNTs, forming a noncovalently bonded nanohybrid. The present study provides a basis for studying the helical conformation and the associated effect on controlling cell-adhesion and growth. We remark, before closing, that it is straightforward to use this approach for novel helical polymers, and the investigation of the relevant chiral asymmetry effect will provide an important tool for developing future nanodevices.
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AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail address:
[email protected].
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ACKNOWLEDGMENT We thank B. Sannigrahi for fruitful discussions. This work was supported by the National Science Foundation (Grant Nos. DMR-0934142 and HRD-0630456) and the Army Research Office (Grant No. W911NF-06-1-0442).
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