ordering of nanoparticles mediated by end-functionalized triblock copolymers aiche meeting...
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ORDERING OF NANOPARTICLES MEDIATED BY END-FUNCTIONALIZED
TRIBLOCK COPOLYMERS
AIChE meeting Philadelphia November 18, 2008 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
2/12
Motivation
AIChE meeting Philadelphia November 18, 2008
(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:
Can functionalized triblocks be used to guide self-assembly of nanoparticles?
3/12AIChE meeting Philadelphia November 18, 2008
coarse grain
Attach functional groups with affinity for nanoparticles
nanoparticle
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)
4/12AIChE meeting Philadelphia November 18, 2008
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
5/12AIChE meeting Philadelphia November 18, 2008
HOOMD – J. Anderson, et al. J. Comp. Phys. 227, 5342 (www.ameslab.gov/hoomd)
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.
6/12AIChE meeting Philadelphia November 18, 2008
eN/k
BT
Sknepnek et al., ACS Nano 2, 1259 (2008)
f f f
10% 18%
hydrophilichydrophobicfunctionalnanoparticle
(top view)
9.5s
7/12
1.2Rg
square columnar micellar
liquid
hexagonal columnar
micellarliquid
gyroid
eN/k
BT
f f
square columnar
cylindricalmix
disordered cylinders
AIChE meeting Philadelphia November 18, 2008
Unconventional square columnar ordering
Hexagonal ordering
18% 23%
hydrophilichydrophobicfunctionalnanoparticle
(top view)
(Toth, Regular figures, 1964)
11.5s
8/12
1.2Rg
micellarliquid
micellarliquid
gyroidlayered
hexagonal gyroidsquare
columnar
eN/k
BT
f f
hexagonal columnar
hexagonal columnar
AIChE meeting Philadelphia November 18, 2008
Extended region of gyroid ordering
18% 23%
hydrophilichydrophobicfunctionalnanoparticle
• gyroid order confirmed by structure factor
• order shows Ia3d symmetry 9/12
1.2Rg
square columnar
hexagonal columnar
micellarliquid
micellarliquid
gyroidgyroid
eN/k
BT
f f
hexagonal columnar
layered hexagonal
AIChE meeting Philadelphia November 18, 2008
Layered hexagonal ordering
23%
(top view)
(top view) (side view)
hydrophilichydrophobicfunctionalnanoparticle
simple hexagonal lattice
honeycomb-like layers
layered structure
10/12
1.2Rg
eN/k
BT
f
layered hexagonal
hexagonal columnar
micellarliquid
gyroid
AIChE meeting Philadelphia November 18, 2008
Cubic (CsCl) ordering
21%
hydrophilichydrophobicfunctionalnanoparticle (cubic)
(square columnar, top view)
11/12
2.5Rg
micellarliquid
gyroid
square columnar
cubic (CsCl)
AIChE meeting Philadelphia November 18, 2008
eN/k
BT
f
Summary and Conclusions
12/12
End-functionalized block copolymers are shown to provide an efficient strategy for assembly of
nanocomposite materials.
Sknepnek et al., ACS Nano 2, 1259 (2008)
AIChE meeting Philadelphia November 18, 2008
eN/k
BT
f
• a rich phase diagram • unconventional square columnar ordering• enhanced stability of gyroid phase