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!
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