CMBP Seminar Syracuse, February 4, 2011 BLOCK COPOLYMER GUIDED SELF- ASSEMBLY OF NANOPARTICLES Rastko Sknepnek Department of Materials Science and Engineering.

CMBP Seminar Syracuse, February 4, 2011

BLOCK COPOLYMER GUIDED SELF-ASSEMBLY OF NANOPARTICLES

Rastko SknepnekDepartment of Materials Science and Engineering

Northwestern University


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)


Outline

• Why assemble nanoparticles and copolymers?• Coarse-grained model• Detailed phase diagram• Summary• Outlook• Molecular dynamics on graphics cards


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:


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

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)


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


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)


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


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


Hexagonal ordering

18% 23%


(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


Extended region of gyroid ordering

18% 23%


• 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


Lamellar catenoid order

23%

(top view)

(top view) (side view)


simple hexagonal lattice

honeycomb-like layers

layered structure

1.2Rg

eN/k

BT

f

lamellarcatenoid

hexagonal columnar

micellarliquid

gyroid


Cubic (CsCl) ordering

21%

hydrophilichydrophobicfunctionalnanoparticle (cubic)

(square columnar, top view)

2.5Rg

micellarliquid

gyroid

square columnar

cubic (CsCl)

eN/k

BT

f


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)


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


What does this…

…have to do with this…

(IGN BioShock 3 screenshot)

gyroid(courtesy of J. Anderson)


~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


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!


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


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


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


GPU based project in Olvera de la Cruz group

Surface patterns and assembly of grafted

nanoparticles

Ligand exchange on quantum dots

(Guo, et al., submitted) (Donakowski, et al., J. Phys. Chem. C (2010))

(Jha, et al., J. Chem. Theory Comput.

(2010))

CMBP Seminar Syracuse, February 4, 2011 BLOCK COPOLYMER GUIDED SELF- ASSEMBLY OF NANOPARTICLES Rastko Sknepnek Department of Materials Science and Engineering.

Documents

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radius of gyration r