1. END-FUNCTIONALIZED TRIBLOCK COPOLYMERS AS A ROBUST TEMPLATE FOR ASSEMBLY OF NANOPARTICLES Rastko Sknepnek, 1 Joshua Anderson, 1 Monica Lamm, 2 Joerg Schmalian, 1 and Alex Travesset 1 1 Department of Physics and Astronomy and 2 Department of Chemical and Biological Engineering Iowa State University and DOE Ames Laboratory APS March Meeting 2008, New Orleans March 10, 2008 1/11

2. APS March Meeting 2008, New Orleans March 10, 2008 Motivation 2/11 Growing need for complex materials with control of structure and properties on nanometer length scales. Growing need for complex materials with control of structure and properties on nanometer length scales. Need for a simple, “single-pass”, but robust fabrication technique. Need for a simple, “single-pass”, but robust fabrication technique. Our approach Nanoparticle self-assembly via end-functionalized block copolymers. Experimental results: Experimental results: successful functionalizing of Pluronic ® triblock copolymers successful functionalizing of Pluronic ® triblock copolymers successful assembly of calcium phosphate nanocomposites successful assembly of calcium phosphate nanocomposites Limited theoretical understanding of self- assembly of nanoparticle/copolymer composites, especially in solution. Limited theoretical understanding of self- assembly of nanoparticle/copolymer composites, especially in solution. Develop an understanding of mechanisms that lead to successful assembly nanocomposite materials.

3. APS March Meeting 2008, New Orleans March 10, 2008 Model Simple coarse-grained bead spring model with implicit solvent. Copolymer (CA 5 B 7 A 5 C) Nanoparticle 12 hydrophilic (A) 7 hydrophobic (B) Fully flexible bead-spring chain. Minimal energy cluster of N np Lennard-Jones particles ( Sloane, et al. Discrete Computational Geom. 1995 ) 2 functional (C) N np =13 N np =55 N np =75 radius of gyration R g =2.3  2.1R g 2.5R g 1.2R g Non-bonded interactions: Nanoparticle affinity  N is only tunable parameter! tunable parameter! (set  =1,  =1, m=1) 3/11

4. APS March Meeting 2008, New Orleans March 10, 2008 Simulation details Molecular dynamics using LAMMPS. LAMMPS – S. Plimpton, J. Comp. Phys. 117, 1 (1995) (lammps.sandia.gov) Explore phase diagram as a function of: nanoparticle affinity  N nanoparticle affinity  N (  N /k B T = 1.0, 1.5, 2.0, 2.5, 3.0) packing fraction packing fraction (  = 0.15, 0.20, 0.25, 0.30, 0.35) Each simulated system contains: p = 600 copolymer chains p = 600 copolymer chains n = 40 – 270 nanoparticles of size N np =13(1.2R g ), 55(2.1R g ), 75(2.5R g ) n = 40 – 270 nanoparticles of size N np =13(1.2R g ), 55(2.1R g ), 75(2.5R g ) all nanoparticles in a given system are monodisperse all nanoparticles in a given system are monodisperse relative nanoparticle concentration relative nanoparticle concentration (c = 0.09, 0.12, 0.146, 0.17, 0.193, 0.215, 0.235) 0.193, 0.215, 0.235) NVT ensemble NVT ensemble reduced temperature T = 1.2 reduced temperature T = 1.2 harmonic bonds, k=330  -2, r 0 =0.9  harmonic bonds, k=330  -2, r 0 =0.9  time step  t = 0.005  m      time step  t = 0.005  m      10 7 time steps 10 7 time steps 4/11

5. Results Phase diagrams for N np =13 (1.2R g ) nanoparticle concentration concentration 10% 18%23% APS March Meeting 2008, New Orleans March 10, 2008 Depending on the relative nanopaticle concentration one observes a large number of two- and three-dimensional periodic ordered structures. Two-dimensional square columnar order dominates phase diagram. Square columnar order yields to 2D hexagonal columnar and 3D gyroid order. Square columnar order is fully suppressed and novel 3D layered hexagonal order appears. 5/11 1.2R g

6. Results APS March Meeting 2008, New Orleans March 10, 2008 Square columnar ordering, N np =13 (1.2R g ) 10%18% hydrophilic hydrophobic functional nanoparticle Geometric interpretation (Toth, Regular figures, 1964) dominates phase diagram for small NP concentration dominates phase diagram for small NP concentration (top view) two-dimensional order two-dimensional order two interpenetrating “line-lattices” with lattice constant 9.5 . two interpenetrating “line-lattices” with lattice constant 9.5 . 9.5  closely related to the problem of close packing of binary disks closely related to the problem of close packing of binary disks size ratio = 0.414214 concentration = 1/2 6/11 1.2R g squarecolumnar micellarliquid gyroid hexagonal columnar micellarliquid  N /k B T   squarecolumnar cylindrical mix disorderedcylinders

7. Results Hexagonal columnar ordering, N np =13 (1.2R g ) 18%23% APS March Meeting 2008, New Orleans March 10, 2008 hydrophilic hydrophobic functional nanoparticle (top view) (Toth, Regular figures, 1964) size ratio = 0.349198 concentration = 6/7 Geometric interpretation 11.5  closely related to the problem of close packing of binary disks closely related to the problem of close packing of binary disks two-dimensional order two-dimensional order micelles form two- dimensional “line-lattice” with lattice constant 11.5  micelles form two- dimensional “line-lattice” with lattice constant 11.5  nanoparticles fill space in between nanoparticles fill space in between 7/11 1.2R g micellarliquid micellarliquid gyroid layeredhexagonal gyroid squarecolumnar  N /k B T   hexagonal columnar

8. Results Gyroid ordering, N np =13 (1.2R g ) APS March Meeting 2008, New Orleans March 10, 2008 18%23% hydrophilic hydrophobic functional nanoparticle gyroid order confirmed by structure factor gyroid order confirmed by structure factor order possess Ia3d symmetry order possess Ia3d symmetry three-dimensional order three-dimensional order micelles and nanoparticles form two interpenetrating gyroids  micelles and nanoparticles form two interpenetrating gyroids  fully connected triply periodic structures fully connected triply periodic structures nanoparticles stabilize gyroid over a wide parameter range nanoparticles stabilize gyroid over a wide parameter range 8/11 1.2R g squarecolumnar hexagonalcolumnar micellarliquid micellarliquid gyroid gyroid  N /k B T   hexagonalcolumnar layeredhexagonal

9. Results Layered hexagonal ordering, N np =13 (1.2R g ) APS March Meeting 2008, New Orleans March 10, 2008 23% (top view) (side view) hydrophilic hydrophobic functional nanoparticle simple hexagonal lattice lattice honeycomb-likelayers layered structure three-dimensional layered ordered structure three-dimensional layered ordered structure spherical micelles form simple hexagonal lattice spherical micelles form simple hexagonal lattice nanoparticles form layers that resemble honeycomb nanoparticles form layers that resemble honeycomb each nanoparticle layer is stacked between two micellar layers and vice verse. each nanoparticle layer is stacked between two micellar layers and vice verse. 9/11 1.2R g  N /k B T  layeredhexagonal hexagonalcolumnar micellarliquid gyroid

10. Results Cubic (CuCl) and square columnar orderings, N np =75 (2.5R g ) APS March Meeting 2008, New Orleans March 10, 2008 21% hydrophilic hydrophobic functional nanoparticle (cubic) (square columnar, top view) 10/11 spherical micelles and nanoparticles form two simple cubic lattices spherical micelles and nanoparticles form two simple cubic lattices cubic lattices are shifted by (a/2,a/2,a/2) with respect to each other forming a CuCl structure cubic lattices are shifted by (a/2,a/2,a/2) with respect to each other forming a CuCl structure low packing fraction  non-trivial interaction effects low packing fraction  non-trivial interaction effects 2.5R g micellarliquid gyroid squarecolumnar cubic (CuCl)

11. Summary and Conclusions APS March Meeting 2008, New Orleans March 10, 2008 11/11 Used a simple coarse grained model to study nanoparticle self-assembly mediated by end-functionalized triblock copolymers. Used a simple coarse grained model to study nanoparticle self-assembly mediated by end-functionalized triblock copolymers. Extensively studied phase diagram of the nanocomposite system as function of nanoparticle size, concentration and affinity for copolymer functional ends. Extensively studied phase diagram of the nanocomposite system as function of nanoparticle size, concentration and affinity for copolymer functional ends. Showed that end-functionalized triblock copolymer can provide a simple, but powerful strategy for assembling nanocomposite materials Showed that end-functionalized triblock copolymer can provide a simple, but powerful strategy for assembling nanocomposite materials very rich phase diagram with five distinct two- and three-dimensional ordered structures very rich phase diagram with five distinct two- and three-dimensional ordered structures each ordered structure has unique and rich properties each ordered structure has unique and rich properties easy to tune between ordered structures by changing, e.g., nanoparticle concentration easy to tune between ordered structures by changing, e.g., nanoparticle concentration End-functionalized block copolymers are shown to provide an efficient strategy for assembly of nanocomposite materials.