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BLOCK COPOLYMER GUIDED SELF-ASSEMBLY OF NANOPARTICLES

BLOCK COPOLYMER GUIDED SELF-ASSEMBLY OF NANOPARTICLES. Rastko Sknepnek Department of Materials Science and Engineering Northwestern University. Collaborators. Dr. Joshua Anderson (at Michigan). Prof. Monica Lamm (Chemical Engineering). Prof. Joerg Schmalian (Physics).

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BLOCK COPOLYMER GUIDED SELF-ASSEMBLY OF NANOPARTICLES

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  1. BLOCK COPOLYMER GUIDED SELF-ASSEMBLY OF NANOPARTICLES RastkoSknepnek Department of Materials Science and Engineering Northwestern University

  2. Collaborators Dr. Joshua Anderson (at Michigan) Prof. Monica Lamm (Chemical Engineering) Prof. JoergSchmalian (Physics) Prof. Alex Travesset (Physics) Supported by U.S. Department of Energy Grant DE-AC02-07CH11358

  3. Outline • Why assemble nanoparticles and copolymers? • Coarse-grained model • Detailed phase diagram • Summary • Outlook • Molecular dynamics on graphics cards

  4. Motivation Growing need to control material properties at nanometer length scales. Assemble nanoparticles into ordered structures. • simple and robust approach • sufficiently versatile Use block copolymers to guide nanoparticle assembly • self-assemble at nano scales • widely available • relatively easy to manipulate Pluronic®triblock copolymer: (Wanka, et al. Macromolecules 27, 4145 (1994))

  5. Attach functional groups with affinity for nanoparticles nanoparticle Can functionalized triblocks be used to guide self-assembly of nanoparticles? coarse grain

  6. Model Nanoparticle Copolymer (CA5B7A5C) Fully flexible bead-spring chain. Minimal energy cluster of NnpLennard-Jones particles (Sloane, et al. Discrete Computational Geom. 1995) 7 hydrophobic (B) 1.2Rg 2.1Rg 2.5Rg 12 hydrophilic (A) 2 functional (C) Nnp=13 Nnp=55 Nnp=75 radius of gyration Rg=2.3s Non-bonded interactions (implicit solvent): Nanoparticle affinity eN is only tunable parameter! (set s=1, e=1, m=1)

  7. Molecular dynamics in a nutshell • Treat molecular (or molecular cluster) degrees of freedom as classical objects . • Introduce effective (classical) interaction potentials. • Numerically integrate Newton’s equations of motion: • Discretize time in steps of dt << “characteristic time scale” • Calculate forces on each particle • Ballistically propagate for time dt • Goto1. • Pros: • Can be efficiently parallelized • Preserves true dynamics • Cons: • Can be slow to reach equilibrium • Hard to implement

  8. Simulation details LAMMPS – S. Plimpton, J. Comp. Phys. 117, 1 (1995) (lammps.sandia.gov) Each simulated system contains: HOOMD – J. Anderson, et al. J. Comp. Phys. 227, 5342 (www.ameslab.gov/hoomd) • p = 600 copolymer chains • n = 40 – 270 nanoparticles of size Nnp=13(1.2Rg), 55(2.1Rg), 75(2.5Rg) • all nanoparticles in a given system are monodisperse Explore phase diagram as a function of: • nanoparticle affinity eN (eN/kBT= 1.0, 1.5, 2.0, 2.5, 3.0) • packing fraction (f = 0.15, 0.20, 0.25, 0.30, 0.35) • NVT ensemble • reduced temperature T = 1.2 • harmonic bonds, k=330es-2, r0=0.9s • time step Dt = 0.005t (t=(ms2/e)1/2) • 107 time steps • relative nanoparticle concentration (c = 0.09, 0.12, 0.146, 0.17, 0.193, 0.215, 0.235)

  9. Results 1.2Rg Sknepneket al., ACS Nano2, 1259 (2008) Square columnar order is fully suppressed and novel lamellar catenoid order appears. A very rich phase diagram. Two-dimensional square columnar order dominates phase diagram. Square columnar order yields to 2D hexagonal columnar and 3D gyroid order. eN/kBT f f f nanoparticle concentration 18% 23% 10% hexagonal hexagonal M hexagonal M M BCC BCC BCC

  10. Unconventional square columnar ordering 1.2Rg square columnar 10% 18% gyroid square columnar micellar liquid micellar liquid eN/kBT hexagonal columnar cylindrical mix disordered cylinders f f (top view) 9.5s hydrophilic hydrophobic functional nanoparticle

  11. Hexagonal ordering 1.2Rg layered hexagonal square columnar 18% 23% gyroid gyroid micellar liquid micellar liquid eN/kBT hexagonal columnar hexagonal columnar f f (top view) hydrophilic 11.5s hydrophobic functional (Toth, Regular figures, 1964) nanoparticle

  12. Extended region of gyroid ordering 1.2Rg layered hexagonal 18% 23% square columnar gyroid gyroid micellar liquid micellar liquid eN/kBT hexagonal columnar hexagonal columnar f f • gyroid order confirmed by structure factor • order shows Ia3d symmetry hydrophilic hydrophobic functional nanoparticle

  13. Lamellar catenoid order 1.2Rg (top view) lamellar catenoid 23% gyroid micellar liquid eN/kBT hexagonal columnar f simple hexagonal lattice (top view) (side view) hydrophilic hydrophobic honeycomb-like layers layered structure functional nanoparticle

  14. Cubic (CsCl) ordering 21% gyroid cubic (CsCl) 2.5Rg micellar liquid eN/kBT square columnar f (square columnar, top view) hydrophilic hydrophobic functional (cubic) nanoparticle

  15. Summary and Conclusions End-functionalized block copolymers are shown to provide an efficient strategy for assembly of nanocomposite materials. • a rich phase diagram • unconventional square columnar ordering • enhanced stability of gyroid phase eN/kBT f Sknepneket al., ACS Nano2, 1259 (2008) Anderson, et al. Phys. Rev. E 82, 021803 (2010)

  16. Outlook • Fully map phase diagram • Introduce specific details of real systems • Refine packing arguments Related projects Surface patterns and assembly of grafted nanoparticles DNA coated nanoparticles Ligand exchange on quantum dots

  17. Molecular Dynamics on Graphics Cards

  18. What does this… (IGN BioShock 3 screenshot) …have to do with this… gyroid (courtesy of J. Anderson)

  19. ~2000pixels ~1000pixels Estimate of floating point operations per second (FLOPs) to generate smooth animation: 2000x1000x50x10x100 ~ 1011 (or 100 GFLOPs!) iterations per pixel number of pixels frames per second operations per pixel

  20. Even the fastest CPU cannot handle this much load! A designated hardware is required – Graphics Processing Unit (GPU) (present in virtually all computers, including modern smart phones) Top of the line hardware: Key features: • 480 cores • 177 GB/s memory bandwidth • 1 TFLOPs single precision • Inexpensive - $450 Compared to a six-core Intel i7: • 6 cores • 17 GB/s memory bandwidth • 100 GFLOPs GTX 480 A radically different architecture!

  21. Computer graphics: Molecular dynamics: • Large amount of relatively simple computations per pixel • High data parallelization – same operations on all pixels • Large amount of relatively simple computations per particle • High data parallelization – same operations on all particles (with a bit of caveats) In 2006 NVidia Co., released CUDA and made GPU available to non-graphics applications Original developed in Alex Travesset’s group at Iowa State University. Currently main development in Sharon Glotzer’s group at University of Michigan J. A. Anderson, et al., Journal of Computational Physics 227, 5342 (2008)

  22. Real-world performance supercooled liquid tethered nanospheres tethered nanorods N=36360 N=14000 N=64000 polymer nanocomposites surfactant coated surfaces supercooled liquid N=18400 N=6908 N=20000 (courtesy of Joshua A. Anderson)

  23. People HOOMD-blue is open source! It’s being developed and used in research groups all over the world. • Latest release includes code contributions from: • J. Anderson, A. Keys, T. D. Nguyen, C. Phillips – University of Michigan • R. Sknepnek – Northwestern University • A. Travesset – Iowa State University • A. Kohlmeyer, D. Lebard, B. Levine – Temple (formerly at Penn) • I. Morozov, K. Andrey, B. Roman – Joint Institute for High Temperatures of RAS (Moscow, Russia) • Research groups developing for HOOMD-Blue: • Sharon Glotzer – University of Michigan • Alex Travesset – Iowa State University/DOE Ames Laboratory • Michael Klein – Temple (formerly at Penn) • AthanassiosPanagiotopoulos – Princeton • Monica Olvera de la Cruz – Northwestern http://codeblue.umich.edu/hoomd-blue

  24. GPU based project in Olvera de la Cruz group Surface patterns and assembly of grafted nanoparticles Ligand exchange on quantum dots (Jha, et al., J. Chem. Theory Comput. (2010)) (Guo, et al., submitted) (Donakowski, et al., J. Phys. Chem. C (2010))

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