Preparation of Entangled Polymer Melts of Various
Architecture for Coarse-grained Models
by Yelena R. Sliozberg and Jan W. Andzelm
ARL-TR-5679 September 2011
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Army Research Laboratory Aberdeen Proving Ground, MD 21005
ARL-TR-5679 September 2011
Preparation of Entangled Polymer Melts of Various
Architecture for Coarse-grained Models
Yelena R. Sliozberg
Oak Ridge Institute for Science and Education
Jan W. Andzelm Weapons and Materials Research Directorate, ARL
Approved for public release; distribution unlimited.
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4. TITLE AND SUBTITLE
Preparation of Entangled Polymer Melts of Various Architecture for Coarse-
grained Models
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ORISE 1120-1120-99
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6. AUTHOR(S)
Yelena R. Sliozberg and Jan W. Andzelm
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H44
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U.S. Army Research Laboratory
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Aberdeen Proving Ground, MD 21005
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ARL-TR-5679
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14. ABSTRACT
Most of the practically useful polymers have molecular weight range from 20,000 to 200,000. Mechanical properties of these
polymers are dominated by topological constraints or entanglements. Direct brute-force equilibration of well-entangled
polymers is still unattainable because of slow reptation dynamics. In this technical report, we have introduced a new fast
protocol to prepare well-equilibrated entangled polymeric systems of various compositions and architectures. Our algorithm is
simple to implement and it is general for any coarse-grained polymer model. The present preparation method exploits two
programs: gel and Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This report presents a theory
overview and a manual how to use the method.
15. SUBJECT TERMS
Ammunition, coarse-grained model, polymer builder, LAMMPS
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Yelena R. Sliozberg
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iii
Contents
List of Figures iv
Acknowledgments v
1. Overview 1
2. Models 1
2.1 Kremer-Grest Model .......................................................................................................1
2.2 DPD Polymer Model with mSRP ....................................................................................2
3. Generation of Initial Structure Using gel 3
3.1 Theoretical .......................................................................................................................3
3.2 Software Description .......................................................................................................3
4. Equilibration of the Initial Structures 12
5. Results 15
6. References 17
7. Distribution 17
iv
List of Figures
Figure 1. Schematic representation of bead-spring branched block copolymer. Different colors correspond to the different types of beads. The picture corresponds to example 1. .....4
Figure 2. Bead-spring dendrimer. Different colors correspond to the different types of beads. The picture corresponds to example 2. ......................................................................................9
Figure 3. Bead-spring dendrimer/comb polymer. Different colors correspond to the different types of beads. The picture corresponds to example 3. Some side chains are built to be rigid. .........................................................................................................................................12
Figure 4. Evolution of mean square internal distances for a melt of chain length N = 500 throughout our preparation procedure. Blue, red and green symbols correspond to the chains after initial 1000 DPD simulation with the soft (DPD) potential, after fast push-off and after 10000 LJ simulation with Lennard-Jones potential, respectively. The black symbols denote our target function obtained for the equilibrated melt, where simulation time is
LJt 6106 . .................................................................................................................16
v
Acknowledgments
This research was supported in part by an appointment to the Postgraduate Research
Participation Program at the U.S. Army Research Laboratory (ARL) administered by the Oak
Ridge Institute of Science and Education through an interagency agreement between the U.S.
Department of Energy and ARL.
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INTENTIONALLY LEFT BLANK.
1
1. Overview
Equilibration of entangled polymers is nontrivial even for a case of coarse grained chains
because of slow reptation dynamics exhibited by high molecular weight chains, where center-of-
mass diffusivity, D scaled with polymer length, N as 3.2 ND . Even with modern day parallel
computers, brute-force equilibration of well-entangled branched polymers is prohibitively
expensive. Standard method in which one starts with an ensemble of chains with the correct end-
to-end distance arranged randomly in the simulation cell and introduces the excluded volume
rapidly, leads to deformation on the intermediate length scales. Another set of long-standing
methods includes the chain connectivity altering algorithms. These bridging methods employ a
set of complex Monte Carlo (MC) moves that can be difficult to implement for branched
polymer architectures and these MC moves have very low acceptance ratio (1, 2).
New preparation protocol has been established to overcome the described difficulties. This
protocol is general to any polymer architecture and does not bring any deformation of polymer
chains. Short simulation runs with soft potential used in Dissipative Particle Dynamics (DPD) (3)
is performed for an ensemble of polymer chains with the correct end-to-end distance. After a
gradual increase of the strength of DPD potential, short simulation with target coarse-grained
potential is performed.
In this report, we adopt our method for two coarse-grained models 1) Kremer-Grest model (4)
and 2) DPD model with Segmental Repulsive Potential (mSRP) (5). However, the described
protocol is general and applicable for any coarse-grained model.
The present preparation method exploits two programs: gel and Large-scale Atomic/Molecular
Massively Parallel Simulator (LAMMPS). Gel is an in house written C program of coarse-
grained polymer builder, and LAMMPS is a molecular dynamics program from Sandia National
Laboratories (6).
2. Models
2.1 Kremer-Grest Model
Kremer-Grest model: The pair interaction between topologically nonconnected particles is
described by the standard truncated Lennard-Jones pair potential:
612612
4cc
LJrrrr
rU
, where is the depth of the potential well and is
the distance where interparticle force is zero. rc represents the cutoff distance. 6/12cr is
2
chosen, yielding so-called Weeks-Chandler-Andersen excluded volume potential, UWCA.
Topologically bound