1. Development of quantitative coarse-grained simulation models
for polymers
Shekhar Garde & Sanat Kumar
Rensselaer Polytechnic Institute
grant number #
Graduate students: Harshit Patel & Sandeep Jain
Collaborator: Hank Ashbaugh, LANL/Tulane
Education/Outreach: New Visions, MoleculariumTM

2. Motivation • Polymer blend phase behavior
Applications
• Polymer blend phase behavior
- Miscibility/immisciblity of polyolefins
• Self-assembly of block copolymers to form novel
micro-structured materials
atactic
-polypropylene
polyethylene
hexagonal
bicontinuous
lamellar

3. Hierarchy of Length and Time Scales
molecular
scale
polymer
coil
polymer
melt/continuum
> 100 Å
O(1sec)
persistance
length ~10Å
~ 100 Å
10-8 to sec
bond
length ~1Å
to sec

4. Coarse-graining
Examples: Lattice models or bead-spring chains, dissipative
particle dynamics methods
Basic idea: Integrate over (unimportant) degrees of freedom
How do we coarse-grain atomically detailed systems
without a significant loss of chemical information?
Do coarse-grained systems provide correct description
of structure, thermodynamics, and dynamics of a given
atomic system?

5. Coarse-graining of Polymer Simulations
Goal: To develop coarse-grained descriptions to access longer
length and timescales
How do we derive physically consistent
particle-particle interaction potentials?
Coarse-grained
description (t)
Coarse-grained
description (t + dt)
Future
work
One CG particle describes
n carbons of the
detailed polymer
Basic idea
Atomistic
system ( t )
Atomistic
system ( t + dt )

6. 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?

7. 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

8. Coarse-graining intermolecular correlations
1mer-bead
16mer-bead
8mer-bead
structural details are lost with increasing
the level (n) of coarse-graining process

9. Coarse Graining Intramolecular Correlations

10. Inverse Monte Carlo simulation
choose a trial potential, e.g.,
j(r) = 0
update trial potential
jnew(r) = jold(r)
+fln[g(r)/gtarget(r)]
run Monte Carlo simulation
with trial potential
g(r) = gtarget(r) ? No
Yes
done

11. Coarse Grained Potential
inter-bead
interaction
intra-bead
interaction
Etotal = Einter + Eintra
= Spairsjinter(r) + S12pairsj12intra(r)
+ S13pairsj13intra(r) + S14pairsj14intra(r)

12. Inter-bead Interactions
before IMC
after IMC
inter-bead radial
distribution function
effective interaction
potential

13. “bonded” interactions
Intra-bead Interactions
14-intra-bead
interactions
13-intra-bead
interactions
12-intra-bead
“bonded” interactions
j14(r)
j13(r)
j12(r)
potential (kT)
r (Å)
r (Å)
r (Å)

14. Oligomer conformation distribution
radius of gyration distribution for C96
P(Rg)
Rg (Å)
CG method reproduces conformational statistics of molecular oligomers

15. Radius of Gyration and Effect of Temperature
2Rg T
KEPIC
Kexpt
403K
0.45
2Rg
503K
0.40
0.42 CG
excellent agreement with experiment

16. Polymer Conformation Distribution
radius of gyration distribution (403K)
C96
C1000
C8000
ideal
P(Rg*)
Rg* = Rg / < Rg2 >1/2
polymer conformational space efficiently explored

17. Buckyball Polymer Nanocomposites
bead-ball distribution
bead-ball interaction
g(r)
j (kT)
r (Å)
r (Å)

18. 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?

19. Water molecule
Hydra: H atom
Biological world
Mr. Carbone

20. Thank you!