Simulation Utilities forSoft and Hard Interfaces

Simulation Utilities forSoft and Hard Interfaces

Simulator for polymeric materials
on mesoscopic scale
based on Self-Consistent Field theory
Developed by Working Group 2 of Doi Project
T. Honda, H.Kodama, J.-R. Roan,Y.Morita, S.Urashita, R.Hasegawa, K.Yokomizo,
T.Kawakatsu, M.Doi

Position of SUSHI on length and time scale
0 sec-3 msec

GOURMET-6 μsec

MUFFIN
SUSHI-9 nsec

PASTA-12 psec

COGNAC-15 fsec
-15fm

-12pm

-9nm-6μm-3mm0mCharacteristics
The field of segment density is used to describe the system.

1. Various polymer architecture
Homo, block, star, comb, ring, any types of topology,
fixed sequence( tapered block )2. Off lattice mean field method
3. Enhanced SCF methods
Grand canonical dynamics, chemical Reaction,polyelectrolyte, etc.

4. Open source software

Characters of Components
1. Polymers
Any topologies,
Any sequences

Monomers
Specific volume,
Effective bond length,
Electric charge

Anti-symmetric block copolymer
ｂeff A=2，ｂeff B=1，NA=NB=20，χAB=0.4，
System 64×64，A：red，B:blue

2. SolventsSpecific volume

Polymers in solution

Meshes 1/2
1. Regular Mesh
One~threedimension
general purpose

2. Rectangular Mesh
One~threedimension
Interfaces

Meshes 2/2
3. Circular Mesh
One dimension
Micelles

4. Cylindrical Mesh
Two dimension
Micelles,vesicles,mushrooms,
pancakes

Boundary conditions andEnsembles
Boundary Conditions
1. Periodic boundary condition

ExamplesInfinite systems

2. Hard wall
Adsorptions, depletions, grafts

3. Reflective boundary condition

periodic systemcanonical ensemble

The boundaries for bulk systems

Ensembles
1. Canonical Ensemble
2. Grand canonical Ensemble

bulk
wall
reflective
grand canonical ensembleCalculation methods
1. Static Equilibrium Calculation
Calculates equilibrium states.
2. Dynamics Calculation
Time dependent simulation of phase separation.
3. Monte Carlo Calculation
Search for lower energy states(avoids being trapped in a local minimum)

Basic Equations
Edwards Equation for the Path Integral

Segment Density

Canonical
Ensemble
Grand CanonicalEnsemble
Segment Segment
Interaction

Self Consistent Field,: total numberof the chainin the system

Static Equilibrium Method
The segment interactions and chemical
potentials are updated at each iteration.

=−Meshes
Off lattice model
Depletion of polymer near solid wall in solution.
N=100, χ=0.5, Φbulk =0.001, dx=0.25, 0.5, and 1.
1.2

Φ/Φbulk

1.00.8

φbSolid walltheory *dx=0.25
dx=0.5dx=1.

Polymer

0.6
0.4
0.2
0.0

χ=0.5
* E.A. DiMarzio, J. Chem. Phys., 36, 2101 (1965).

Solvent

C.M.Marques and J. F. Joanny, Maxromolecules, 23,
268 (1990).

0 Grand canonical
1 system

2Z/ (3/2N)^(-1/2)

3

A polymer grafted to a wallMushroom
The mushroom shrinks with increasing χ.
Interaction parameterχs polymer-wall = 0.
χ polymer-solvent

Shrunk mushroom Swollen mushroom
χ=0.2530 N=100, χ=1.5h

Φ = 10-610-5

χ

10-4

h/a

10-3
10-2

r
10-1

00r/a

30 0r/a30

A polymer grafted to a wall
Mushrooms and Pancakes
Changes from mushroom to pancake with decreasing surface chi
parameter χs .
0.3 H

Interaction parameterχs polymer-wallχ polymer-solvent

Hh/N

N=1000.25

χχsR0.2

χs0.150.1

0.05
Single grafted polymer chain-90

in cylindrical mesh systemMushroom
χN=0.0
χN=10
χN=20
χN=30
χN=40
χN=50
χN=60
χN=70
χN=80R

Pancake-70-50
χsN-30-10

Polymers grafted to a wall
Brushes

N=100,
χ=0.25Milner, Witten and Cates, Europhys. Lett., 5, 413 (1988)

Polymers grafted to a wall
Mushrooms and Brushes
The grafted polymer should be considered as mushrooms and brush.
Interaction parameterχs polymer-wall = 0.
χ polymer-solvent

0.9

N=32

0.8

1h/N

0.7
0.60.5

χN=0
χN=3.2
χN=6.4
χN=9.6
χN=12.8
χN=16.
χN=19.2
χN=22.4
χN=25.6
χN=28.8
χN=32.

0.4
0.3
0.2
0.0001

0.001

0.01
σ0.1

Result of the 3D system

1Micelle
Associated polymer in solution
volume fraction of non-associated polymers

1.0E-01χ = 0.7
χ = 0.8
χ = 0.9
1.0E-02

1.0E-03

1.0E-04

1.0E-05
1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

total volume fraction of polymers

Volume fraction of non-associated A10B20 block copolymers as afunction of total volume fraction of block copolymers. Monomeric
solvent C is selective for B block. Interaction parameters arechosen as χAB= χAC =2.0 and χBC =χ is changed from 0.7 to 0.9.

Block copolymer
typical structures
hexagonalcubiclamellar

f=0.225
N=40，χN=20，323

f=0.5
f=0.25

Block copolymer
typical structures 1/2
Good initial guess of Self-Consistent Field is required to obtain themorphology at the global minimum of free energy.

Lamellar model

Cylinder model

One dimensional calculation

Cubic modelBlock copolymer
typical structures 2/2
Gyroid model
Using triply periodic levelsurface for initial V.
V = c ( cos x * sin y +sos y * sin z +cos z * sin x )c: scale factor

Graphics by GOURMET

http://www.msri.org/publications/sgp

Simulation Result
N=30, f=0.4, χN=14,System size = 323
Graphics by AVS

Block copolymer
Phase diagram
90
80

lamhex
bcc

70

χN

60
50
40
30
20
10
00

0.1

0.2

0.3

0.4

0.5

f

Calculated by optimizing
lattice constants

Matsen ＆ SchickPhy. Rev. Lett. , 72, 2660 (1994) .

Tapered polymer
Multi-State Path Integral
Path integral equations for K-th type monomers

AB
Sum of the path integrals

Volume fraction of K-th type segment

G.J.Fleer et al. “Polymers at Interfaces”, Chapman & Hall (1993)

Tapered polymer
9080

lamhexbcc

7060
χNｇ(x)

5040

a30

sa=1.00,χN=44

20
0.7

0.75

0.80.85
gradient

0.9

0.95

1a ( gradient of taper )
0.35

0.375

0.4

0.425
f

0.45

0.475

0.5

a=0.86,χN=44
a=0.78,χN=58, 18×18・ 3 1/2

a=0.78,χN=57, 53

Strong polyelectrolyte
A polymer solution in which almost all
the ionizable atomic groups are ionized.
SCF method
Total charge distribution is calculated bythe charge densityof the segment.

Solve the Poisson equation.
Add this electrostatic potential to Vk.
Charge − +qInteraction
parameterχ− +− +− +Strong polyelectrolyte
Phase diagram of polyelectrolyte blend; ions arelocated at each end of polymers.

Anisotropic
Multi phase2 phaseDynamics Simulation
Diffusion Equation: mobility coefficient: Lagrange multiplier for the local incompressibility
condition

Dynamics Simulation

Dynamics Simulation
Star polymer and analysis by GOURMETReaction induced phase separation
HIPS

GOAL
HIPS（High-Impact-ModifiedPolystyrene）？

Fischer and Hellman, Macromolecules 29, 2498 (1996)

Reaction induced phase separation
HIPS
Morphology of mixed PS, grafted PBs and S

Model of Salami Domain byFischer and Hellman

Block copolymer creationa block copolymer was created by areaction of A and B polymers at their ends.

Active site reaction
The volume fraction of active
group was calculated by SCF

Block copolymer creation
at interface
Matrix polymer: NA=NB=10,
reactrive and block copolymer: NA=NB= 20,
χAB=0.4, Φblock_initial=0.01

InterfaceMonte Carlo simulation
The method to study an isolated chain in a dilute
solution or a single chain in a many chain system.
AAB

B

Linking to other layers
Morphology

MUFFINχ parameters

SUSHI

PASTA

COGNAC

Multi-phase structure,
Interaction parametersSummary◇ SUSHI is a general purpose simulator of meso-scale
structures in polymeric materials.
◇ SUSHI has many functions and there is an infinite varietyof systems by combining the functions.
◇ An open source software written in C++ ;there are no restrictions to use SUSHI for your research.
We hope that SUSHI will be a useful tool for your research.

Acknowledgement
This work is supported by the national project, which has been
entrusted to the Japan Chemical Innovation Institute (JCII) bythe New Energy and Industrial Technology Development
Organization (NEDO) under METI's Program for the ScientificTechnology Development for Industries that Creates New
Industries.