END-FUNCTIONALIZED TRIBLOCK COPOLYMERS AS A GUIDE FOR

NANOPARTICLE ORDERING

APS March Meeting 2009 March 20, 2009 1/12

Rastko Sknepnek,1 Joshua Anderson,1 Monica Lamm,2 Joerg Schmalian,1 and Alex Travesset1

1Department of Physics and Astronomy and2Department of Chemical and Biological EngineeringIowa 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:

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Can functionalized triblocks be used to guide self-assembly of nanoparticles?

coarse grain

Attach functional groups with affinity for nanoparticles

nanoparticle

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Model

Copolymer (CA5B7A5C) Nanoparticle

12 hydrophilic(A)

7 hydrophobic(B)

Fully flexible bead-spring chain. Minimal energy cluster of Nnp Lennard-Jones particles (Sloane, et al. Discrete Computational Geom. 1995)

2 functional(C) Nnp=13 Nnp=55 Nnp=75

s

radius of gyration Rg=2.3s

2.1Rg 2.5Rg1.2Rg

Non-bonded interactions (implicit solvent):

12

4

r

rUs

612

4rr

rUss

12

4

r

rUs

612

4rr

rU N

ss

Nanoparticle affinity eN is only tunable parameter!

(set s=1, e=1, m=1)

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Simulation detailsLAMMPS – S. Plimpton, J. Comp. Phys. 117, 1 (1995)

(lammps.sandia.gov)

Explore phase diagram as a function of:

• nanoparticle affinity eN

612

4rr

rU N

ss(eN/kBT = 1.0, 1.5, 2.0, 2.5, 3.0)

• packing fraction

3/6 s

L

pNnN polynp (f = 0.15, 0.20, 0.25, 0.30, 0.35)

Each simulated system contains:• 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

• relative nanoparticle concentration

polynp

np

pNnN

nNc

(c = 0.09, 0.12, 0.146, 0.17,

0.193, 0.215, 0.235)

• NVT ensemble

• reduced temperature T = 1.2

• harmonic bonds, k=330es-2, r0=0.9 s

• time step Dt = 0.005 t( =(t ms2/ )e 1/2)

• 107 time steps

HOOMD – J. Anderson, et al. J. Comp. Phys. 227, 5342 (www.ameslab.gov/hoomd)

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1.2Rg

Results

A very rich phase diagram.

nanoparticle concentration10% 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.

eN/k

BT

Sknepnek et al., ACS Nano 2, 1259 (2008)

f f f

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10% 18%

hydrophilichydrophobicfunctionalnanoparticle

(top view)

9.5s

1.2Rg

square columnar micellar

liquid

hexagonal columnar

micellarliquid

gyroid

eN/k

BT

f f

square columnar

cylindricalmix

disordered cylinders

Unconventional square columnar ordering

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Hexagonal ordering

18% 23%

hydrophilichydrophobicfunctionalnanoparticle

(top view)

(Toth, Regular figures, 1964)

11.5s

1.2Rg

micellarliquid

micellarliquid

gyroidlayered

hexagonal gyroidsquare

columnar

eN/k

BT

f f

hexagonal columnar

hexagonal columnar

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Extended region of gyroid ordering

18% 23%

hydrophilichydrophobicfunctionalnanoparticle

• gyroid order confirmed by structure factor

• order shows Ia3d symmetry

1.2Rg

square columnar

hexagonal columnar

micellarliquid

micellarliquid

gyroidgyroid

eN/k

BT

f f

hexagonal columnar

layered hexagonal

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Lamellar-catenoid ordering

23%

(top view)

(top view) (side view)

hydrophilichydrophobicfunctionalnanoparticle

simple hexagonal lattice

honeycomb-like layers

layered structure

1.2Rg

eN/k

BT

f

lamellar catenoid

hexagonal columnar

micellarliquid

gyroid

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Cubic (CsCl) ordering

21%

hydrophilichydrophobicfunctionalnanoparticle (cubic)

(square columnar, top view)

2.5Rg

micellarliquid

gyroid

square columnar

cubic (CsCl)

eN/k

BT

f

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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)

eN/k

BT

f

• a rich phase diagram • unconventional square columnar ordering• enhanced stability of gyroid phase

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