Published on Web Date: January 26, 2010

r 2010 American Chemical Society 704 DOI: 10.1021/jz9004027 |J. Phys. Chem. Lett. 2010, 1, 704–707

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Chiral Asymmetry of Helical Polymer NanowiresOlayinka 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-principlescalculations for the helical formation of isotactic poly(2-methoxystyrene) nanowires.Our calculation results reveal the self-assembly of left- and right-handed helicalnanorods. The energy of the helical conformations depends on the chiral center as wellas linkages among neighboring methoxy benzene groups. The implications of theseresults for understanding experimentally observed chiral asymmetry of left- and right-handednanowiresarediscussed.Furthermore,wedemonstrate that thecoiled structurescan effectively wrap around singled-walled carbon nanotubes. The electronic structurecharacteristicsof theseconformationsarestudiedwithuseof first-principlescalculations.

SECTION Molecular Structure, Quantum Chemistry, General Theory

H elices are a typical structural motif in biologicalmolecules. The R-helix in proteins and the doublehelix in double-stranded DNA are well-known exam-

ples.1-4 In a living cell, the embracing of stable helicalstructures allows these molecules to place functional groupsin specific positions and orientations, as well as keeps thepolymer backbone away from the solvent, shielding it fromchemical attack. The consensus of helix formation is thatbiological helices are stabilized by orientationally dependenthydrogen bonding, with their chirality arising from the chir-ality of the polymer molecule.1 Those same properties thatmake helical molecules so useful in living cells also makethemuseful in the context of nanotechnology. However, whileour understanding of biological helices is satisfactory ininterpreting why polypeptides and polynucleotides formhelices, it does not provide sensible prescriptions for devel-oping alternative helix-forming molecular architectures. Togain the understanding necessary to develop such prescrip-tions, it is desirable to consider realistic models for helixformation, which should capture the underlying physics ofchiral conformations.

Biological systems rely almost exclusively on supramole-cular self-assembly to create complex structures that carry outdiverse functions. The application of self-assembly principlesgleaned from biological systems provides ways to achievegreater control over the design and construction of self-assembling molecular objects to produce artificial nanoscaledevices. Motivated by the observation that many of thefunctions of naturally occurring macromolecules are asso-ciatedwith their higher structural orders,1-4 the developmentof synthetic polymerswith biological functions has attracted agreat deal of attention. Several groups have reported thepreparation of synthetic polymers with higher structuralorder,mostwith helical conformations. Helical polymers havebeen prepared from achiral monomers, from monomerscarrying pendant chiral groups, and from generating second-ary conformations by helicity induction.5-8

A series of optically active helical poly(2-methoxystyrene)s(P2MSs) have been synthesized and characterized re-cently.9,10 These functionalized polymers are specific to anti-bodies and immune receptors, thereby holding potential forcontrolling receptor bindingand cell activation. Someof thosehelical polymers are potent inhibitors of receptor-mediateddegranulation responses in mast cells, capable of binding tocells and affecting cellular responses. Furthermore, there areincreasing amounts of experimentwork on electrospun fibersof helical polymers with single-walled carbon nanotube(SWNT) contents for the purpose of developing polymericnanostructures for therapeutics and biodiagnostics.

P2MS is a non-natural rigid rod system.2,9 The 2-methoxy-styrene monomer serves as an ideal building block forgenerating biofunctional polymer systems. In addition to itsbiocompatibility, surfaces prepared with helical chiral poly-mers demonstrate effectiveness in controlling polymer-cellinteractions. Consequently, it is important to understandfactors that influence the formation of helical conformation.

Here we present simulation results based on a combina-tion of force-field molecular dynamics and first-principlescalculations.11 The force-field molecular dynamics is em-ployed to obtain information regarding the conformationand the overall geometric shape of the helical polymers.Our results indicate that isotactic P2MS forms low-energystable helical conformations. The P2MS helical polymersprefer parallel alignment of nanowireswith the samechirality.Moreover, the low-energy conformations of the helical poly-mers depend strongly on the linkages of the monomers,especially at the starting ends. These results shed light onthe experimental observations that chiral P2MS surfacesimproved polymer-cell interactions as compared to achiralones.9 Furthermore,wedemonstrate that P2MS can effectively

Received Date: December 15, 2009Accepted Date: January 21, 2010

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wrap around SWNTs, and thus the SWNT/P2MS nanocompo-sites may be utilized as components of biosensors. In view ofthe rapid progress made in preparing electronically activeSWNT/P2MS nanocomposites by electrospinning, we havealso performed first-principles calculations to investigatethe electronic structure characteristics of the correspondingconformations.

The helical polymers involved in the present study wereconstructed based on models as shown in Figure 1, with nmonomers of 2-methoxystyrene. The constructed structureswere subsequently optimized using simulated annealingbased on MMþ force field. The classical force-field approachwas thoroughly tested in our previous multiscale simulationstudies of various nanostructures.11,12 For n< 20, the helicalstructure is not rigid, which is consistent with earlier studieson structurally similar poly(3-methyl-4-vinylpyridine) poly-mer systems.13 With a systematic increase of the number ofmonomers, the polymer forms a helix rod structure for n g24. Illustrated in Figure 1 are the chemical formula andoptimize structures of R and S conformations. In either R orS structure, approximately six consecutive 2-methoxystyrenemonomers form a turnwith a pitch length of 1.4( 0.1 nm. Ascan be readily observable from Figure 1, the helical polymershave a cylindrical shape, with a diameter of 0.49( 0.05 nm.

A few remarks are immediately in order. (i) Left and right-handed helices are enantiomers, and thus each structure andits mirror image have the same energy.14 Our explicit calcula-tions with use of the reflection confirmed that, for each stableR helical conformation, there is an isoenergy S counterpart.This implies that there exists no chirality-specific interactionin the force-field model and first-principles approach. How-ever, it is worthmentioning that the R and S structures shown

in Figure 1 have quite different energies, although both arestable rigid rod conformations with virtually the same pitchlength. It is rather unexpected to observe a lowerenergyof theR structure than the S one by ∼2 kcal/mol per atom. Thisindicates that the helical formation depends strongly on theinitial positions of chiral centers with respect to terminalgroups, and the helical formation process can easily “freeze”into oneparticular conformation. (ii)Thehelical polymers canform a regular pattern of parallel alignments. Our calculationon the optimized conformations of a pair of helical polymersas shown in Figure 1 indicate that the same helicity alignedpolymers (R-R or S-S) are preferred, with an interactionenergy 3-15 kcal/mol better than that of the opposite helicityaligned counterpart (R-S). (iii) The rigid rod conformation issemiflexible in that it can bend to form coiled wires. Thehelicity of the coiled wire follows the chirality of the helicalpolymer.

As the typical helical rod consists of a few hundreds ofatoms, the investigation of transition states between variousconformations becomes formidable. In order to gain insighton the energetics of the helical conformations and theassociated electronic structure characteristics,we constructedperiodic structures. The corresponding unit cell is composedof six monomers and has 54 carbon, 60 hydrogen, and 6oxygen, a total of 120 atoms. The periodic helical structureswere investigated based on density functional theory withlocal density approximation (LDA) for exchange and correla-tion potential.15 Periodic-boundary conditions were em-ployed with a supercell in the xy plane large enough toeliminate the interaction between neighboring structures. Adouble numerical basis set expansion of local orbitals imple-mented in the DMol3 package15 was sufficient to convergethe grid integration of the charge density. It is well-known thatthe LDA can not properly describe long-range dispersionforces in organic molecules. However, our previous studiesof similar systems11,12 indicate that the present approach issensible in that themethoxy benzene is a small molecule andis thus less affected by dispersion corrections than largeraromatic groups.

The helical R and S structures as shown in Figure 1, alongwith other stable low-energy conformations identified viamolecular dynamics simulations, were used to construct theperiodic systems with a six-monomer unit cell. The resultantunit 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 goodconformity with the result extracted from force-field-basedmolecular dynamics calculations. The average radius of thehelical polymer is about 0.5 nm, in good agreement withexperimental observations.9

Careful examination of various low-energy conformationsindicates that the corresponding energy correlates with thesequence of neighboring methoxy benzene linkages. Closerscrutiny of the helical structures reveals that there exist twoprototypical linkages between neighboringmethoxy benzenegroups. One type of linkage, indicated by green arrows inFigure 1, has neighboringmethoxy benzene groups arrangedin such away that the torsion angle between the two groups isabout 120�. Theother typeof linkage, indicatedby redarrows,

Figure 1. Chemical formula of right- and left-handed P2MS(P2MS-R and P2MS-S, respectively), along with side views ofoptimized R and S helical P2MS nanowires. Each of the R and Srod structures has 32 monomers of 2-methoxystyrene (n = 32),and consists of 290 carbon, 326 hydrogen, and 32 oxygen, a totalof 648 atoms. Gray, red, and white colored atoms representcarbon, oxygen, andhydrogen, respectively. Redand green arrowsindicate two distinctive type of linkages that are referred to as cis-and trans-linkages, respectively.

r 2010 American Chemical Society 706 DOI: 10.1021/jz9004027 |J. Phys. Chem. Lett. 2010, 1, 704–707

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has a much smaller torsion angle, typically e60�. In accor-dance with the distinct feature of the linkage, we refer to thetwo type of linkages as trans (green arrows in Figure 1) and cis(red arrows), respectively.13 The steric hindrance between thetrans and cis linkage is primarily responsible for the energydifferences between the R and S conformations shown inFigure 1, as the trans linkage is significantly lower in energythan the cis linkage.

An important ramification of our simulation results is thatthe helicity of the nanorod depends crucially on the initialorientations of chiral centers with respect to the terminalgroups. It is worth noting that, while the low-energy R-helix inFigure 1 has trans-linkages at both ends, the higher-energy Shelix shown in Figure 1 has cis-linkages at one end. In regardsto the aligned helical nanowires on the surfaces, our calcula-tion results indicate that the parallel alignment of the samehelicity nanowires leads to improved binding and orderedcharge density distributions, which is useful in understandingexperimental observations that chiral P2MS surfaces areeffective in controlling polymer-cell interactions as com-pared to achiral ones. Therefore, there is significant potentialin using such surfaces to develop smart materials to controland manipulate material-cell interactions.

Shown in Figure 2 is the optimized P2MS-R all-transstructure, alongwith the extracted charge density distributionof valence band maximum and conduction band minimum,respectively. Themajority of the bands of P2MS-R are flat anddispersionless, in accord with molecular orbital levels. Theextracted gap for the optimized structure is about 2.1 eV. Wehave considered the effect of polymers interacting with asolvent using the COSMO solvation model15 and found apaucity of modification to the geometrical and electronicstructures. The optimized unit cell conformation can be usedto construct realistic helical polymerwith variable lengths andfunctional groups, which will be useful for investigating thenature of ligand-receptor interactions.

The all-trans conformation;either R or S;is the globalminimum configuration, and the “defective” cis-linkage con-figuration has higher energy (∼2 kcal/mol) per atom. Itappears that the degree of twist and the pattern of trans orcis linkages can be “trigged” and “memorized” during the

helix formation, which can easily freeze into a stable con-formationwith a certain fraction of cis linkages. An importantfinding from the present simulation study is that cis linkagesare more readily generated in S-helical polymers, yieldinghigher energy nanowire conformations. These results areconsistent with experimental findings in that chiral asymme-try is often observed. Specifically, the synthesized P2MS hasabundant R helical polymers over S with about 2:1 ratio,9

which can be attributed to the energy differences of the stableR or S helices. Since the optical active properties of the same-helicity polymers are superior to the mixed-helicity ones, thesynthesis of a preferred-helicity conformation assisted byeffective catalysts is of considerable current interest.16 In thisregard, our current work points to the important role playedby catalysts in forming preferred-helicity conformations.

The efficiency of the helical polymer could be improved byincorporating carbon nanotubes into the polymer matrix.11

Carbon nanotubes represent an intriguing class of materialsfor exploring nanoelectronics and nanostructured compo-sites.11 A large variety of helical polymers can self-assembleandwrap around the nanotubes, providing a usefulmeans formanipulating electronic transport in nanoelectronic devices.We have studied the interfacial interactions between thehelical polymer and SWNTs. Our molecular dynamics resultson the helical polymer P2MS interacting with SWNTs demon-strate that the semirigid helical polymer rod has certainflexibility to adjust its conformation during wrapping, andthe wrapped polymer successfully adopts a helical conforma-tion with a pitch length of about 4 nm. We depict in Figure 3the band structure for P2MS-R helically wrapping on twoprototype SWNTs: an armchair metallic (8,8) and a zigzagsemiconducting (14,0). The choiceof the two tubeswasbased

Figure 2. Isosurface plot of wave functions of the highest occu-pied molecular orbital (HOMO) and the lowest unoccupied mo-lecular orbital (LUMO) for a periodic P2MS-R.

Figure 3. Side view of the optimized structure of P2MS-R wrap-ping helically on an armchair (8,8) nanotube (green color) and thecalculated band structure for helically wrapping P2MS onmetallic(8,8) and semiconducting (14,0) tubes, respectively. The bandcenter is at Γ = 0, and the band edge is at L = π/a and Χ= π/bfor (8,8) and (14,0), respectively,where a=1.297 and b=1.278nm.The Fermi level is shifted to 0 eV.

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on the fact that they have very close diameters (1.085 and1.096 nm for (8,8) and (14,0), respectively), and the roughlycommensurate feature of quarter of a pitch of the helicalP2MS with the pitch of the corresponding SWNTs. Wheninteracting with SWNTs, the helically wrapped structure in-creases interaction energy, which supersedes the van derWaals 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 intactafter the noncovalent functionalization. The superposition ofdispersionbands originated fromtheSWNTand the flat bandsthat are attributed to the helical polymer leads to levelhybridizations, marked with red and blue lines in Figure 3.The flat band for P2MS/(14,0) (purple line in Figure 3) in-dicates charge confinement on the polymer.12 Since there areabout one-third metallic tubes in as-prepared samples, theincorporation of SWNTs in the formation of larger-diameterhelical wires is expected to improve the conductance due tothe percolation network of metallic tubes.

In summary, we have performedmolecular dynamics andfirst-principles calculations for the study of the spontaneousformation of helical polymers. Our results demonstrate thatthe trans and cis linkages of the neighboring methoxy ben-zene groups are important characteristics of the helical con-formation. The folding pattern of the trans and cis linkagesdepends on the configurations of chiral centers at startingends, which can readily freeze into a rod structure. Further-more, our simulation results reveal that the helical polymerscan effectively wrap around SWNTs, forming a noncovalentlybonded nanohybrid. The present study provides a basis forstudying thehelical conformation and theassociated effect oncontrolling cell-adhesion and growth. We remark, beforeclosing, that it is straightforward to use this approach for novelhelical polymers, and the investigation of the relevant chiralasymmetry effect will provide an important tool for develop-ing future nanodevices.

AUTHOR INFORMATION

Corresponding Author:*To whom correspondence should be addressed. E-mail address:xwang@cau.edu.

ACKNOWLEDGMENT We thank B. Sannigrahi for fruitfuldiscussions. This work was supported by the National ScienceFoundation (Grant Nos. DMR-0934142 and HRD-0630456) andthe Army Research Office (Grant No. W911NF-06-1-0442).

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