Presentation on theme: "Spontaneous ordering of semiflexible polymers on nanotubes and nanospheres Simcha Srebnik Chemical Engineering Technion."— Presentation transcript:
Spontaneous ordering of semiflexible polymers on nanotubes and nanospheres Simcha Srebnik Chemical Engineering Technion
Why study semiflexible polymers? Biopolymers –double-stranded DNA –unstructured RNA –unstructured polypeptides (proteins). Semiflexible Polymers –aromatics –bulky side groups Unlike the ideal chain, there is no consistent model that describes their behavior
Polymer statistics The semiflexible chain –N=10 4, l p = 1 (ideal), 6.5 (e.g., polyacrylamide), 500 (α-helix) For flexible chains,
The wormlike chain model Kratky-Porod chains –the orientation correlation function for a worm-like chain follows an exponential decay i ii i–1 Kratky and Porod, Recl. Trav. Chim. Pays-Bas 68 (1949) 1106 sisi
Scaling of semiflexible chains The KP model accurately predicts end-to-end distance for the entire range of chain flexibility –Drawback Cannot obtain end-to-end distance distribution for comparison with experiments (S(k)) Other exact theories exist, but solution is numerical and extension to other related problems (e.g., external forces, geometrical constraints) is difficult. flexible rigid
Coarse-grained simulation Use simplified models of ‘pearl necklace’ polymer chains –Ideal ( ghost particles ) –excluded volume (hard sphere) –Lennard-Jones (soft sphere) Polymer l p /l 0 | Poly(ethylene oxide) 2.55 Poly(propylene) 36 Poly(ethylene) 3.58 Poly(methyl methacrylate) 410 Poly(vinyl chloride) 410 Poly(styrene) 515 Poly(acrylamide) 6.523 Cellulose diacetate 26230 Poly(para-benzamide) 2007000 DNA (in double helix) 30013000 Poly(benzyl-l-glutamate) (α-helix) 50030000 l p ~ 0.6
Modeling ‘ideal’ semiflexible chains Current computer resources limit our simluations to chains with ~10 2 monomers. –Develop model for analyzing conformational behavior of very long chains. –Limited to non-interacting systems. i – 1 i s i + 1 l e
Polymer adsorption on curved manifolds Noncovalent functionalization of nanotubes using polymer wrapping –Dispersion of CNTs in aqueous or organic media –Mechanical reinforcement –Fluorescent labeling –Sensors and biosensors (conjugated polymers/biopolymers) Polymer in or on spheres –DNA packaging in viruses, vesicles, or cells –Protein encapsulation –Colloidal and micellar suspensions
11 Carbon Nanotubes First reported by IIjima in 1991 (“microtubules”) –Nature 354 (1991) 56-58. –Over 5000 citations!
Examples of helical wrapping 12 B. McCarthy, J. N. Coleman. J. Phys. Chem. B, 2002, 2210 PmPV coating HupR protein on MWNTs Balavoine and Shultz. Angew. Chem., 1999, 1912 Zheng et al., Nature materials, 2 (2003)338. DNA
Forces leading to helical wrapping Molecular modeling suggests that ssDNA can bind to carbon nanotubes through -stacking, resulting in helical wrapping. (Zheng et al., Nature Materials 2 (2003) 338). Alignment of backbone aromatic rings was also thought to determine interactions between CNTs and polymers (Zaiser and coworkers, J Phys Chem B 109 (2005) 10009; Coleman and coworkers, J Phys Chem B 106 (2002) 2210-2216). –Note: all molecular modeling studies based their conclusions regarding polymers on short oligomers Shinkai and coworkers used TEM and AFM to confirm periodic helical structure of polysaccharides adsorbed on CNTs. Argue that helical pattern is observed because of their strong helix-forming nature. (JACS 127 (2005) 5875-5884) ‘General phenomenon’ argued by Baskaran et al. from studies on various polymers. (Chem Mater 17(2005)3389)
Smalley’s postulate Monolayer wrapping results from a thermodynamic drive to eliminate the hydrophobic interface between the tubes and their aqueous medium. Random adsorption is not likely to result in sufficient coverage; single tight coil would introduce significant bond-angle strain in the polymer backbone; multiple helices are the likely configuration. Smalley and coworkers, Chem Phys Lett 342 (2001) 265
Simplest MC simulation Dilute semiflexible polymer solution Impenetrable infinite cylinder Periodic boundaries LJ interactions MC moves –Reptation –Kink-jump –Pivot Metropolis acceptance –10 6 equilibration moves –Averages every 10 3 for additional 10 7 iterations Recipe: adsorption and frustration.
Potential of nanotube Surface-averaged Lennard-Jones potential between the CNT and monomers: where
The total potential energy of a given polymer configuration is given by:
Helical pitch depends on NT radius and chain flexibility Helical pitch lplp
What drives helical polymer wrapping? Hydrophobic drive? –Monolayer adsorption also achieved with weak interactions between monomers and tube for semiflexible chains –Not sufficient to induce helicity Helical polymers? –Too stringent, semiflexible polymers sufficient Helicity of nanotube ( -stacking) –Geometry (tube radius) and chain flexibility provide strong drive for helical wrapping
VIM on sphere i–1 i i+1 e s A O B Position of bead i+1 is determined from a point along the path of a great circle connecting monomer i and the intersection of line OA with the surface of the sphere.
Polymer wrapping of a sphere N=1000 monomers confined to a sphere with radius =10
Conclusions weak surface interactions are sufficient to overcome low entropy barrier of semiflexible chains and lead to monolayer adsorption helix is a stable ‘universal’ state for polymers determined solely by surface curvature (NT and sphere) and polymer bending energy. geometry determines helical pitch at intermediate radii for semiflexible chains multiple helices form due to vdW interactions between monomers which are sufficient to overcome (small) translational entropy of adsorbed chains
Conclusions (2) Available computational resources limit our simulations to relatively short chains –The semiflexible chain can be effectively modeled through a summation of energy and entropy ‘vectors’ that determine the growth or position of a monomer based solely on the two previous monomers
Acknowledgement Liora Levi Yevgeny moskovitz Hely Oizerovich Inna Gorevitz Iliya Kusner ISF Rubin Scientific and Medical Research Fund