END-FUNCTIONALIZED TRIBLOCK COPOLYMERS AS A GUIDE FOR NANOPARTICLE ORDERING APS March Meeting 2009 March 20, /12 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 Supported by U.S. Department of Energy Grant DE-AC02-07CH11358

Motivation (Wanka, et al. Macromolecules 27, 4145 (1994)) 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: APS March Meeting 2009 March 20, /12

Can functionalized triblocks be used to guide self-assembly of nanoparticles? coarse grain Attach functional groups with affinity for nanoparticles nanoparticle APS March Meeting 2009 March 20, /12

Model 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 ) 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 (implicit solvent): Nanoparticle affinity  N is only tunable parameter! tunable parameter! (set  =1,  =1, m=1) APS March Meeting 2009 March 20, /12

Simulation details 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 =  m      time step  t =  m      10 7 time steps 10 7 time steps HOOMD – J. Anderson, et al. J. Comp. Phys. 227, 5342 ( APS March Meeting 2009 March 20, /12

1.2R g Results A very rich phase diagram. nanoparticle concentration concentration 10% 18%23% 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.  N /k B T Sknepnek et al., ACS Nano 2, 1259 (2008)    APS March Meeting 2009 March 20, /12

10%18% hydrophilic hydrophobic functional nanoparticle (top view) 9.5  1.2R g squarecolumnar micellarliquid hexagonal columnar micellarliquid gyroid  N /k B T   squarecolumnar cylindrical mix disorderedcylinders Unconventional square columnar ordering APS March Meeting 2009 March 20, /12

Hexagonal ordering 18%23% hydrophilic hydrophobic functional nanoparticle (top view) (Toth, Regular figures, 1964) 11.5  1.2R g micellarliquid micellarliquid gyroid layeredhexagonal gyroid squarecolumnar  N /k B T   hexagonal columnar APS March Meeting 2009 March 20, /12

Extended region of gyroid ordering 18%23% hydrophilic hydrophobic functional nanoparticle gyroid order confirmed by structure factor gyroid order confirmed by structure factor order shows Ia3d symmetry order shows Ia3d symmetry 1.2R g squarecolumnar hexagonalcolumnar micellarliquid micellarliquid gyroid gyroid  N /k B T   hexagonalcolumnar layeredhexagonal APS March Meeting 2009 March 20, /12

Lamellar-catenoid ordering 23% (top view) (side view) hydrophilic hydrophobic functional nanoparticle simple hexagonal lattice lattice honeycomb-likelayers layered structure 1.2R g  N /k B T  lamellarcatenoid hexagonalcolumnar micellarliquid gyroid APS March Meeting 2009 March 20, /12

Cubic (CsCl) ordering 21% hydrophilic hydrophobic functional nanoparticle (cubic) (square columnar, top view) 2.5R g micellarliquid gyroid squarecolumnar cubic (CsCl)  N /k B T  APS March Meeting 2009 March 20, /12

Summary and Conclusions End-functionalized block copolymers are shown to provide an efficient strategy for assembly of nanocomposite materials. Sknepnek et al., ACS Nano 2, 1259 (2008)  N /k B T  a rich phase diagram a rich phase diagram unconventional square columnar ordering unconventional square columnar ordering enhanced stability of gyroid phase enhanced stability of gyroid phase APS March Meeting 2009 March 20, /12