Transcript Document

Development of quantitative
coarse-grained simulation models
for polymers
Shekhar Garde & Sanat Kumar
Rensselaer Polytechnic Institute
grant number #0313101
Graduate students: Harshit Patel & Sandeep Jain
Collaborator: Hank Ashbaugh, LANL/Tulane
Education/Outreach: New Visions, MoleculariumTM
Motivation
• Polymer blend phase behavior
- Miscibility/immisciblity of polyolefins
polyethylene
atactic
-polypropylene
• Self-assembly of block copolymers to form novel
micro-structured materials
hexagonal
bicontinuous
lamellar
Hierarchy of Length and Time Scales
molecular
scale
persistance
length ~10Å
bond
length ~1Å
10 -15 to 10-12 sec
polymer
coil
~ 100 Å
10-8 to 10 -4 sec
polymer
melt/continuum
> 100 Å
O(1sec)
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?
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)
One CG particle describes
n carbons of the
detailed polymer
Coarse-grained
description (t + dt)
Basic idea
Atomistic
system ( t )
Future
work
Atomistic
system ( t + dt )
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
Coarse-graining intermolecular correlations
1.25
1
8mer-bead
1mer-bead
16mer-bead
g(r)
0.75
0.5
0.25
0
0
5
10
r (Å)
15
20
25
structural details are lost with increasing
the level (n) of coarse-graining process
Coarse Graining Intramolecular Correlations
13-intra
12-intra
14-intra
0.15
12-intra
P(r)
0.1
13-intra
0.05
0
14-intra
0
10
20
30
r (Å)
40
50
Inverse Monte Carlo simulation
choose a trial potential, e.g.,
j(r) = 0
run Monte Carlo simulation
with trial potential
jnew(r) = jold(r)
+fln[g(r)/gtarget(r)]
No
g(r) = gtarget(r) ?
Yes
update trial potential
done
Coarse Grained Potential
inter-bead
interaction
intra-bead
interaction
Etotal = Einter + Eintra
= Spairsjinter(r) + S12pairsj12intra(r)
+ S13pairsj13intra(r) + S14pairsj14intra(r) + ...
Inter-bead Interactions
inter-bead radial
distribution function
effective interaction
potential
Intra-bead Interactions
14-intra-bead
interactions
13-intra-bead
interactions
12-intra-bead
“bonded” interactions
j14(r)
j13(r)
j12(r)
10
15
6
5
10
4
0
2
5
-5
0
0
0
5
10
r (Å)
15
20
-10
0
10
20
r (Å)
30
40
0
15
30
r (Å)
45
60
Oligomer conformation distribution
radius of gyration distribution for C96
0.1
0.08
0.06
0.04
0.02
0
0
5
10
15
20
25
30
Rg (Å)
CG method reproduces conformational statistics of molecular oligomers
Radius of Gyration and Effect of Temperature
100
R = AM
<Rg >
2 1/2
(Å)
g
w
R = KM
g
10
T
1/2
w
403K 503K
KEPIC
CG 0.45 0.40
Kexpt 0.45 0.42
1
100
1000
104
M (g/mol)
105
w
excellent agreement with experiment
2Rg
Polymer Conformation Distribution
radius of gyration distribution (403K)
2
C96
C1000
C8000
ideal
P(Rg*)
1.5
1
0.5
0
0
0.5
1
1.5
2
Rg* = Rg / < Rg2 >1/2
polymer conformational space efficiently explored
Buckyball Polymer Nanocomposites
bead-ball distribution
1.25
1.5
1
j (kT)
g(r)
1
0.75
0.5
0.25
0
bead-ball interaction
0.5
0
0
5
10
15
r (Å)
20
25
0
5
10
15
r (Å)
20
25
30
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?
Water molecule
Hydra: H atom
Biological world
Mr. Carbone
Thank you!