Development of quantitative

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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
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Motivation
Applications
Polymer blend phase behavior -
Miscibility/immisciblity of polyolefins
Self-assembly of block copolymers to form novel
micro-structured materials
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Hierarchy of Length and Time Scales
molecular scale
polymer coil
polymer melt/continuum
gt 100 Å O(1sec)
persistance length 10Å
100 Å 10-8 to 10 -4 sec
bond length 1Å
10 -15 to 10-12 sec
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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?
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Coarse-graining of Polymer Simulations
Goal To develop coarse-grained descriptions to
access longer length and timescales
How do we derive physically consistent particle-pa
rticle 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 )
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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?
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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
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Coarse-graining intermolecular correlations
structural details are lost with increasing the
level (n) of coarse-graining process
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Coarse Graining Intramolecular Correlations
13-intra
12-intra
14-intra
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Inverse Monte Carlo simulation
g(r) gtarget(r) ?
No
Yes
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Coarse Grained Potential
inter-bead interaction
intra-bead interaction
Etotal Einter Eintra
Spairsjinter(r) S12pairsj12intra(r)
S13pairsj13intra(r) S14pairsj14intra(r) ...
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Inter-bead Interactions
before IMC
after IMC
inter-bead radial distribution function
effective interaction potential
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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)
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Oligomer conformation distribution
radius of gyration distribution for C96
P(Rg)
Rg (Å)
CG method reproduces conformational statistics of
molecular oligomers
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Radius of Gyration and Effect of Temperature
503K 0.40 0.42
CG
excellent agreement with experiment
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Polymer Conformation Distribution
radius of gyration distribution (403K)
C96 C1000 C8000 ideal
P(Rg)
Rg Rg / lt Rg2 gt1/2
polymer conformational space efficiently explored
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Buckyball Polymer Nanocomposites
bead-ball distribution
bead-ball interaction
g(r)
j (kT)
r (Å)
r (Å)
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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?
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Water molecule
Hydra H atom
Biological world
Mr. Carbone
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Thank you!