Development of quantitative Development of quantitative coarse-grained simulation models coarse-grained simulation models

for polymersfor polymers

Shekhar Garde & Sanat KumarShekhar Garde & Sanat Kumar Rensselaer Polytechnic InstituteRensselaer Polytechnic Institute

grant number #0313101grant number #0313101

Graduate students: Harshit Patel & Sandeep JainCollaborator: Hank Ashbaugh, LANL/Tulane

Education/Outreach: New Visions, MoleculariumTM

Motivation

polyethyleneatactic -polypropylene

hexagonal lamellar

• Polymer blend phase behavior - Miscibility/immisciblity of polyolefins

• Self-assembly of block copolymers to form novel micro-structured materials

bicontinuous

Applications

Hierarchy of Length and Time Scales

molecularscale

polymercoil

polymermelt/continuum

~ 100 Å10-8 to 10 -4 sec

persistancelength ~10Å bond

length ~1Å

10 -15 to 10-12 sec

> 100 ÅO(1sec)

Coarse-graining

Basic idea: Integrate over (unimportant) degrees of freedom

Examples: Lattice models or bead-spring chains, dissipativeparticle dynamics methods

How do we coarse-grain atomically detailed systemswithout a significant loss of chemical information?

Do coarse-grained systems provide correct descriptionof structure, thermodynamics, and dynamics of a givenatomic system?

Coarse-graining of Polymer SimulationsCoarse-graining of Polymer Simulations

Goal: To develop coarse-grained descriptions to access longer length and timescales

Atomistic system ( t )

Coarse-grained description (t)

Coarse-grained description (t + dt)

Atomistic system ( t + dt )

Basic ideaOne CG particle describes

n carbons of the detailed polymer

How do we derive physically consistentparticle-particle interaction potentials?

Futurework

Coarse-graining method

• Perform molecularly detailed simulations of polymers

• Define coarse-grained beads by grouping backbone monomers

• Calculate structural correlations between coarse-grained beads

• Determine effective bead-bead interactions that reproduce coarse-grained correlations using Inverse Monte Carlo

-- uniqueness?

Detailed molecular dynamics simulations

• Classical molecular dynamics

• n-alkanes - C16 to C96 (M. Mondello et al. JCP 1998)

• 50 to 100 chains

• T = 403K P = 1 atm

• time = 5 to 10 ns

0

0.25

0.5

0.75

1

1.25

0 5 10 15 20 25

g(r)

r (Å)

1mer-bead8mer-bead16mer-bead

structural details are lost with increasingthe level (n) of coarse-graining process

Coarse-graining intermolecular correlations

Coarse Graining Intramolecular Correlations

0

0.05

0.1

0.15

0 10 20 30 40 50

P(r

)

r (Å)

12-intra

13-intra

14-intra

13-intra

14-intra12-intra

Inverse Monte Carlo simulation

g(r) = gtarget(r) ?

choose a trial potential, e.g.,(r) = 0

run Monte Carlo simulationwith trial potential

update trial potentialnew(r) = old(r)

+fln[g(r)/gtarget(r)]

done

No

Yes

Coarse Grained Potential

intra-beadinteraction

inter-beadinteraction

Etotal = Einter + Eintra

= pairsinter(r) + 12pairs12intra(r)

+ 13pairs13intra(r) + 14pairs14intra(r) + ...

inter-bead radial distribution function

effective interactionpotential

Inter-bead Interactions

before IMC

after IMC

Intra-bead Interactions

12(r) 13(r)14(r)

0

5

10

15

0 5 10 15 20-10

-5

0

5

10

0 10 20 30 40

0

2

4

6

0 15 30 45 60

pote

ntia

l (kT

)

r (Å)r (Å) r (Å)

12-intra-bead“bonded” interactions

13-intra-beadinteractions

14-intra-beadinteractions

Oligomer conformation distribution

radius of gyration distribution for C96

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20 25 30

P(R

g)

Rg (Å)

CG method reproduces conformational statistics of molecular oligomers

2RgT

KEPIC

Kexpt

403K

0.45

0.451

10

100

100 1000 104 105

<R

g2 >1/

2 (Å

)

Mw (g/mol)

Rg = KM

w

1/2

Rg = AM

w

2Rg503K

0.40

0.42

Radius of Gyration and Effect of Temperature

excellent agreement with experiment

CG

Polymer Conformation Distribution

radius of gyration distribution (403K)

C96C1000C8000ideal

Rg* = Rg / < Rg

2 >1/2

P(R

g* )

0

0.5

1

1.5

2

0 0.5 1 1.5 2

polymer conformational space efficiently explored

Buckyball Polymer Nanocomposites

0

0.25

0.5

0.75

1

1.25

0 5 10 15 20 25

0

0.5

1

1.5

0 5 10 15 20 25 30

bead-ball distribution bead-ball interaction

r (Å) r (Å)

g(r)

(k

T)

Conclusions

• CG method maps molecular scale correlations to coarse-grained potentials

• Coarse grained potential simpler than molecular potential and can be extended to polymer simulations while preserving molecular identity

• Not limited to polymeric species (e.g., buckyballs/ nanocomposites)

• Path Forward - Polyolefin blends - Block copolymer assembly - Dynamics?

Hydra: H atom

Mr. Carbone

Water molecule

Biological world

Thank you!