1. SELF-ASSEMBLY OF NANOPARTICLES VIA END-FUNCTIONALIZED TRIBLOCK COPOLYMERS Rastko Sknepnek Schatz group meeting November 3, 2008 1/17 In collaboration with: Joshua Anderson, Monica Lamm, Joerg Schmalian, and Alex Travesset  Motivation – magnetotactic bacteria  Corse grained molecular dynamics  Molecular dynamics on graphics cards

2. Schatz group meeting November 3, 2008 2/17 Motivation 500nm Magnetotactic bacteria possess ability to orient themselves in magnetic field form magnetite naonocrystals of ~50nm in size: each nanocrystal is surrounded by a membrane each nanocrystal is superparamagnetic nanocrystals form a chain which is a few hundred nanometer long (from T. Prozorov, et al. ACS Nano 1, 228 (2007))

3. Can growth and placement of magnetic nanoparticles be controlled? 3/17 Schatz group meeting November 3, 2008 Use functionalized block copolymers to guide and control nanoparticle growth. Potential applications: data storage artificial muscles drug delivery block copolymers self-assemble into ordered structures at nanometer length scales widely available and relatively easy to control a lot of “in-house” experience with functionalizing Pluronics ®.

4. (from T. Prozorov, et al. ACS Nano 1, 228 (2007)) Can we model this? What can we say about self- assembly via functionalized copolymers? 4/17 Schatz group meeting November 3, 2008 Develop a simple coarse-grained model and simulate it. Experiments on bacteria show that Mms6 peptide is present in the vesicles containing nanocrystals. (Arakaki et al., J. Biol. Chem., 278, 8745 (2003)) Experiments with Pluronic ® copolymers show that Mms6 is crucial for successful growth of magnetite nanocrystals. (T. Prozorov, et al. ACS Nano 1, 228 (2007)) Mms6: 59 amino acids – 6kDa 21 amino acid hydrophilic C-terminus and 38 amino acid hydrohibic N-terminus structure is at present unknown seems to form multimers

5. Coarse graining Reduce number of degrees of freedom by averaging sets of atoms into a single effective particle. Advantages o Simplifies the problem o Makes larger system sizes and longer times accessible to computer simulations Disadvantages o Loose information below coarse graining lengths and times o Usually possible to make only a qualitative comparison with experiments 5/17 Schatz group meeting November 3, 2008

6. 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) 6/17 Schatz group meeting November 3, 2008

7. 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 7/17 Schatz group meeting November 3, 2008

8. Results Phase diagrams for N np =13 (1.2R g ) nanoparticle concentration concentration 10% 18%23% 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. 8/17 1.2R g Schatz group meeting November 3, 2008

9. Results 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 9/17 1.2R g squarecolumnar micellarliquid gyroid hexagonal columnar micellarliquid  N /k B T   squarecolumnar cylindrical mix disorderedcylinders Schatz group meeting November 3, 2008

10. Results Hexagonal columnar ordering, N np =13 (1.2R g ) 18%23% 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 10/17 1.2R g micellarliquid micellarliquid gyroid layeredhexagonal gyroid squarecolumnar  N /k B T   hexagonal columnar Schatz group meeting November 3, 2008

11. Results Gyroid ordering, N np =13 (1.2R g ) 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 10/17 1.2R g squarecolumnar hexagonalcolumnar micellarliquid micellarliquid gyroid gyroid  N /k B T   hexagonalcolumnar layeredhexagonal Schatz group meeting November 3, 2008

12. Density profile 12/17 Hydrophobic part Nanoparticles Combined density isosurfaces Schatz group meeting November 3, 2008

13. Results Layered hexagonal ordering, N np =13 (1.2R g ) 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. 13/17 1.2R g  N /k B T  layeredhexagonal hexagonalcolumnar micellarliquid gyroid Schatz group meeting November 3, 2008

14. Results Cubic (CsCl) and square columnar orderings, N np =75 (2.5R g ) 21% hydrophilic hydrophobic functional nanoparticle (cubic) (square columnar, top view) 14/17 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 CsCl structure cubic lattices are shifted by (a/2,a/2,a/2) with respect to each other forming a CsCl structure low packing fraction  non-trivial interaction effects low packing fraction  non-trivial interaction effects 2.5R g micellarliquid gyroid squarecolumnar cubic (CsCl) Schatz group meeting November 3, 2008

15. Summary and Conclusions 15/17 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. Schatz group meeting November 3, 2008 Sknepnek et al., ACS Nano 2, 1259 (2008)

16. Molecular dynamics on graphics cards 16/17 Schatz group meeting November 3, 2008 When science meets video games… Video games: Molecular dynamics: Process large number of pixels in real time Calculate trajectories of large number of particles  A few simple operations per pixel  Pixels are independent – full data parallelization.  A few simple operations per particle  Once forces are known, updates of particles’ positions, velocities, etc. are independent of each. Can we use graphics cards to do molecular dynamics? Graphics cards are designed for games Advantages of graphics cards: widely available at low cost – less than $350 for latest NVIDIA GeForce 280GTX well supported Disadvantage: need to learn how to write programs that run on graphics cards

17. Highly Optimized Object Oriented Molecular Dynamics - HOOMD Originally developed in Prof. Alex Travesset’s group at Iowa State University, by Joshua A. Anderson. Features: performs general purpose molecular dynamics 32 optimized for speed – delivers performance equivalent of 32 fastest CPU cores. modern object oriented design makes it highly modular and easily expandable. it is free, released under open source license You can get HOOMD free of charge at: http://www.ameslab.gov/hoomd/ 17/17 Schatz group meeting November 3, 2008