Post on 19-Dec-2015
CMBP Seminar Syracuse, February 4, 2011
BLOCK COPOLYMER GUIDED SELF-ASSEMBLY OF NANOPARTICLES
Rastko SknepnekDepartment of Materials Science and Engineering
Northwestern University
CMBP Seminar Syracuse, February 4, 2011
Supported by U.S. Department of Energy Grant DE-AC02-07CH11358
Collaborators
Dr. Joshua Anderson(at Michigan)
Prof. Monica Lamm(Chemical Engineering)
Prof. Joerg Schmalian(Physics)
Prof. Alex Travesset(Physics)
CMBP Seminar Syracuse, February 4, 2011
Outline
• Why assemble nanoparticles and copolymers?• Coarse-grained model• Detailed phase diagram• Summary• Outlook• Molecular dynamics on graphics cards
CMBP Seminar Syracuse, February 4, 2011
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:
CMBP Seminar Syracuse, February 4, 2011
Can functionalized triblocks be used to guide self-assembly of nanoparticles?
coarse grain
Attach functional groups with affinity for nanoparticles
nanoparticle
CMBP Seminar Syracuse, February 4, 2011
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)
CMBP Seminar Syracuse, February 4, 2011
Molecular dynamics in a nutshell
• Treat molecular (or molecular cluster) degrees of freedom as classical objects .
• Introduce effective (classical) interaction potentials.
• Numerically integrate Newton’s equations of motion:
i i i ijj i
m a F F
• Discretize time in steps of dt << “characteristic time scale”1. Calculate forces on each particle2. Ballistically propagate for time dt3. Goto 1.
Pros:• Can be efficiently parallelized • Preserves true dynamics
Cons:• Can be slow to reach equilibrium• Hard to implement
CMBP Seminar Syracuse, February 4, 2011
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)
CMBP Seminar Syracuse, February 4, 2011
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 lamellar catenoid order
appears.
eN/k
BT
Sknepnek et al., ACS Nano 2, 1259 (2008)
f f f
M BCC hexagonal M BCC hexagonal M BCC hexagonal
CMBP Seminar Syracuse, February 4, 2011
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
CMBP Seminar Syracuse, February 4, 2011
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
CMBP Seminar Syracuse, February 4, 2011
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
CMBP Seminar Syracuse, February 4, 2011
Lamellar catenoid order
23%
(top view)
(top view) (side view)
hydrophilichydrophobicfunctionalnanoparticle
simple hexagonal lattice
honeycomb-like layers
layered structure
1.2Rg
eN/k
BT
f
lamellarcatenoid
hexagonal columnar
micellarliquid
gyroid
CMBP Seminar Syracuse, February 4, 2011
Cubic (CsCl) ordering
21%
hydrophilichydrophobicfunctionalnanoparticle (cubic)
(square columnar, top view)
2.5Rg
micellarliquid
gyroid
square columnar
cubic (CsCl)
eN/k
BT
f
CMBP Seminar Syracuse, February 4, 2011
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
Anderson, et al. Phys. Rev. E 82, 021803 (2010)
CMBP Seminar Syracuse, February 4, 2011
Outlook
DNA coated nanoparticlesSurface patterns and assembly of grafted
nanoparticles
Ligand exchange on quantum dots
Related projects
• Fully map phase diagram• Introduce specific details of real systems• Refine packing arguments
CMBP Seminar Syracuse, February 4, 2011Condensed Matter Seminar Syracuse, February 4, 2011
Molecular Dynamics on Graphics Cards
CMBP Seminar Syracuse, February 4, 2011
What does this…
…have to do with this…
(IGN BioShock 3 screenshot)
gyroid(courtesy of J. Anderson)
CMBP Seminar Syracuse, February 4, 2011
~2000pixels~
1000
pix
els
Estimate of floating point operations per second (FLOPs) to generate smooth animation:
2000x1000x50x10x100 ~ 1011 (or 100 GFLOPs!)
number of pixels frames per second
iterations per pixel
operations per pixel
CMBP Seminar Syracuse, February 4, 2011
Even the fastest CPU cannot handle this much load!
A designated hardware is required – Graphics Processing Unit (GPU)
(present in virtually all computers, including modern smart phones)
Top of the line hardware:
GTX 480
Key features:
• 480 cores• 177 GB/s memory bandwidth• 1 TFLOPs single precision• Inexpensive - $450
Compared to a six-core Intel i7:
• 6 cores• 17 GB/s memory bandwidth• 100 GFLOPs
A radically different architecture!
CMBP Seminar Syracuse, February 4, 2011
Computer graphics:
J. A. Anderson, et al., Journal of Computational Physics 227, 5342 (2008)
• Large amount of relatively simple computations per pixel
• High data parallelization – same operations on all pixels
Molecular dynamics:
• Large amount of relatively simple computations per particle
• High data parallelization – same operations on all particles (with a bit of caveats)
In 2006 NVidia Co., released CUDA and made GPU available to non-graphics applications
Original developed in Alex Travesset’s group at Iowa State University.Currently main development in Sharon Glotzer’s group at University of Michigan
CMBP Seminar Syracuse, February 4, 2011
N=14000
N=6908 N=18400
N=36360
N=20000
N=64000
tethered nanospheres
surfactant coated surfaces
polymer nanocomposites
tethered nanorodssupercooled
liquid
supercooled liquid
(courtesy of Joshua A. Anderson)
Real-world performance
CMBP Seminar Syracuse, February 4, 2011
People
HOOMD-blue is open source!
It’s being developed and used in research groups all over the world.
Latest release includes code contributions from:• J. Anderson, A. Keys, T. D. Nguyen, C. Phillips – University of Michigan• R. Sknepnek – Northwestern University• A. Travesset – Iowa State University • A. Kohlmeyer, D. Lebard, B. Levine – Temple (formerly at Penn)• I. Morozov, K. Andrey, B. Roman – Joint Institute for High Temperatures of
RAS (Moscow, Russia)
Research groups developing for HOOMD-Blue:• Sharon Glotzer – University of Michigan• Alex Travesset – Iowa State University/DOE Ames Laboratory• Michael Klein – Temple (formerly at Penn)• Athanassios Panagiotopoulos – Princeton• Monica Olvera de la Cruz – Northwestern
http://codeblue.umich.edu/hoomd-blue