DONOSTIA INTERNATIONAL
P HYSICS CENTER
Forschungszentrum Jülich
Universidad del Pais Vasco
MD Simulations of PEO/PMMA blends
May 6th 2008
F. Alvarez, A. Arbe, Prof. J. Colmenero
M. Brodeck, Prof. D. Richter
Motivation
What is this all about?
• Eurothesis, sponsored by SoftComp, spending
time at different SoftComp labs during the PhD
 San Sebastian and Jülich
• MD-simulations of PEO and polymer blends
(PEO/PMMA) with very different Tg
• Validation of simulations by experiments (PEO)
• Analysis of fully atomistic simulations
• Rouse mode analysis
• Coarse grain simulations?
Overview
• Introduction
– Validation
• PEO/PMMA in blend
–
–
–
–
Structural properties
Self-correlation functions and non-Gaussianity
Mean Square Displacements
Rouse Modes
Introduction to the Simulation
Setup and Software
• Software by
• Simulation engine: Discover
– Periodic boundary conditions
• Densities determined by NPT-simulations
• Forcefield: COMPASS
– condensed-phase optimized
molecular potentials for
atomistic simulation studies
• Simulation time: 100 ns
Δt = 1 fs
100,000,000 steps
PEO as Homopolymer
Confirmed results
Dynamics of individual
hydrogen atoms
protonated sample*
350K - FOCUS
375K - FOCUS
400K - FOCUS
350K - PI
375K - PI
400K - PI
350K - IN16
350K - Simulation
375K - Simulation
400K - Simulation
10-8
10
w
 (s)
10
-9
Collective dynamics
deuterated sample
TOFTOF
1
1.4
1.6
1.8
2
2.2
Q=1.40
Q=1.60
Q=1.80
Q=2.00
Q=2.20
0,8
-10
0,6
10-11
-4
10
-12
10
-13
Q
0,4
0,2
10-14
0
10-15
0,1
1
-1
Q(Å )
0,01
0,1
1
10
time (ps)
*A.-C.Genix, A.Arbe, F.Alvarez, J.Colmenero, L.Willner and D.Richter, Phys.Rev.E, 2005, 72, 031808.
*M.Tyagi, A.Arbe, J.Colmenero, B.Frick and J.R.Stewart, Macromolecules, 2006, 39, 3007.
100
PEO as Homopolymer
Confirmed results
Dynamics of individual
hydrogen atoms
protonated sample*
10
-8
10
-9
350K - FOCUS
375K - FOCUS
400K - FOCUS
350K - PI
375K - PI
400K - PI
350K - IN16
350K - Simulation
375K - Simulation
400K - Simulation
-10
10-11
-4
10
-12
10
-13
10
-14
NSE
temperature corrected
1
Temperature: 400K
-1
Q=1.3, 1.5 and 1.7 A
0,8
S(Q, t)/S(Q, 0)
w
 (s)
10
Collective dynamics
deuterated sample
Q
0,6
0,4
0,2
10-15
0
0,1
1
-1
Q(Å )
0,1
1
10
time (ps)
100
1000
PEO/PMMA in blend
Introduction
*
• Simulating the blend
– 5 PEO chains
43 monomers
15 PMMA chains
25 monomers
 7170 atoms
cell size ~41.5 Å
– Density determined by NPT
Density
1,12
1,11
1,1
3
Density (g/cm )
• T: 300 (running), 350 and 400 K
• 100 ns for each temperature
• Huge data files, ~90Gb for 100ns
1,09
1,08
1,07
1,06
1,05
280
* Povray
300
320
340
360
Temperature
380
400
420
PEO/PMMA in blend
Structure
Scattering dPEO/dPMMA
1
S(Q)
0.5
0
-0.5
0.8
1.6
2.4
3.2
-1
Q (Å )
4
4.8
5.6
PEO/PMMA in blend
Structure
Scattering dPEO/dPMMA
1
Total
PEO
PMMA
PEOxPMMA
S(Q)
0.5
0
-0.5
0.8
1.6
2.4
3.2
-1
Q (Å )
4
4.8
5.6
PEO/PMMA in blend
Structure
Self density
Effective density
1
1
PEO
PMMA
PEO
PMMA
0.8
0.8

self
0.6
0.6

effective
0.4
0.2
0.4
0
0
0.2
5
10
distance (Å)
15
20
Composition of the blend (weight):
0
0
5
10
15
distance (Å)
20
25
20% PEO, 80% PMMA
PEO/PMMA in blend
Comparing the Blend with the Homopolymer
PEO in PEO/PMMA
400 K
PEO in PEO/PMMA
350 K
0.5
0.5
5 ps
50 ps
500 ps
5000 ps
50000 ps
0.4
4r G (r, t)
0.3
0.3
2
2
s
s
4r G (r, t)
0.4
5 ps
50 ps
500 ps
5000 ps
50000 ps
0.2
0.1
0.2
0.1
0
0
0
5
10
Displacement (Å)
15
20
0
5
10
Displacement (Å)
15
20
PEO/PMMA in blend
Comparing the Blend with the Homopolymer
PEO in PEO/PMMA
350 K
non-Gaussianity
0.5
0.4
5 ps
50 ps
500 ps
5000 ps
50000 ps
non-Gaussianity
0.3
0.3
2
s
4r G (r, t)
0.4
350 K
400 K
0.35
0.2
0.25
0.2
0.15
0.1
0.1
0.05
0
0
5
10
Displacement (Å)
15
20
0
0.001
0.01
4
3 r (t )
 2 (t ) 
1
2
2
5 r (t )
0.1
1
10
100
time (ps)
1000
10
4
5
10
PEO/PMMA in blend
Comparing the Blend with the Homopolymer
PEO in PEO/PMMA
350 K
non-Gaussianity
0.7
0.4
1 ps
3 ps
1000 ps
0.6
0.3
non-Gaussianity
0.5
0.4
2
s
4r G (r, t)
350 K
400 K
0.35
0.3
0.25
0.2
0.15
0.2
0.1
0.1
0.05
0
0
2
4
6
8
10
0
0.001
0.01
Displacement (Å)
4
3 r (t )
 2 (t ) 
1
2
2
5 r (t )
0.1
1
10
100
time (ps)
1000
10
4
5
10
PEO/PMMA in blend
Comparing the Blend with the Homopolymer
PEO in PEO/PMMA
400 K
non-Gaussianity
0.6
0.4
1 ps
3 ps
1000 ps
0.5
350 K
400 K
0.35
0.3
non-Gaussianity
0.3
2
s
4r G (r, t)
0.4
0.25
0.2
0.15
0.2
0.1
0.1
0.05
0
0
2
4
6
8
10
0
0.001
0.01
Displacement (Å)
4
3 r (t )
 2 (t ) 
1
2
2
5 r (t )
0.1
1
10
100
time (ps)
1000
10
4
5
10
PEO/PMMA in blend
Comparing the Blend with the Homopolymer
PEO in PEO/PMMA
350 K
non-Gaussianity
0.4
0.1
31627 ps
80000 ps
0.3
non-Gaussianity
0.08
0.06
2
s
4r G (r, t)
350 K
400 K
0.35
0.04
0.25
0.2
0.15
0.1
0.02
0.05
0
0
5
10
15
20
Displacement (Å)
25
30
0
0.001
0.01
4
3 r (t )
 2 (t ) 
1
2
2
5 r (t )
0.1
1
10
100
time (ps)
1000
10
4
5
10
PEO/PMMA in blend
Comparing the Blend with the Homopolymer
PEO in PEO/PMMA
350 K
non-Gaussianity
0.1
0.4
31627 ps
39812 ps
50000 ps
63097 ps
80000 ps
non-Gaussianity
0.3
0.06
2
s
4r G (r, t)
0.08
350 K
400 K
0.35
0.04
0.25
0.2
0.15
0.1
0.02
0.05
0
0
10
20
30
40
Displacement (Å)
50
60
0
0.001
0.01
4
3 r (t )
 2 (t ) 
1
2
2
5 r (t )
0.1
1
10
100
time (ps)
1000
10
4
5
10
PEO/PMMA in blend
Comparing the Blend with the Homopolymer
PEO in PEO/PMMA
400 K
non-Gaussianity
0.06
0.4
31627 ps
39812 ps
50000 ps
63000 ps
80000 ps
0.05
350 K
400 K
0.35
0.3
non-Gaussianity
0.03
2
s
4r G (r, t)
0.04
0.25
0.2
0.15
0.02
0.1
0.01
0.05
0
0
10
20
30
40
50
60
0
0.001
0.01
Displacement (Å)
4
3 r (t )
 2 (t ) 
1
2
2
5 r (t )
0.1
1
10
100
time (ps)
1000
10
4
5
10
PEO/PMMA in blend
MSD of PEO-hydrogens
Displacement Histograms
Comparison of homopolymer/blend at t=50 ns
Mean Square Displacement
10
0.1
homopolymer - 350 K
blend - 350 K
homopolymer - 400 K
blend - 400 K
0.08
blend - 350 K
blend - 400 K
homopolymer - 350 K
homopolymer - 400 K
1000
Slopes:
t^0.36
t^0.41
t^0.51
t^0.52
100
0.04
2
s
2
MSD (Å )
0.06
4r G (r, t)
4
10
0.02
1
0
0.1
-0.02
0
10
20
30
40
Displacement (Å)
50
60
0.01
0.01
0.1
1
10
100
time (ps)
1000
Movement of PEO atoms restricted by the rather stiff PMMA-matrix
10
4
10
5
PEO/PMMA in blend
MSD of hydrogen-atoms
PEO/PMMA at 350 K
Methyl-group
H
H C
Main-chain
1000
100
H
C
H
10
2
C
MSD (Å )
H
PEO - 350 K
PMMA-Main - 350 K
PMMA-Methyl - 350 K
PMMA-Ester - 350 K
H
H
H
H C
25
C
O
1
O
H Ester-group
Complex, stiff structure
0.1
0.01
0.01
0.1
1
10
100
time (ps)
1000
10
4
10
5
PEO/PMMA in blend
Comparing the MSD for two temperatures
PEO/PMMA at 350 and 400 K
10
2
MSD (Å )
1000 PEO - 350 K
PEO - 400 K
PMMA-Main - 350 K
PMMA-Main - 400 K
100 PMMA-Methyl - 350 K
PMMA-Methyl - 400 K
PMMA-Ester - 350 K
PMMA-Ester - 400 K
1
0.1
0.01
0.01
0.1
1
10
100
time (ps)
1000
10
4
10
5
PEO/PMMA in blend
Forming Blobs
PEO/PMMA in blend
Results – Rouse Modes
Rouse modes blend 400 K
1
We investigate the
behavior of PEO in the
blend!
0.8
0.6
1
p n
X p (t )   dn cos(
) rn (t )
N 0
N
0.4
Fourier transformation of
blob-coordinates
0.2
Nl 2
X p (t ) X p (0)  2 2 exp(t /  p )
6 p
pp
 (t)
N
0
1
10
100
1000
time (ps)
10
4
10
5
 (t )  Ae
 ( t /WW )
PEO/PMMA in blend
Results – Rouse Modes
stretching parameter 
relaxation time <>
10
p
1
107
Blend - 350K
Blend - 400K
Blend - 350K
Blend - 400K
6
-2.75
0,9
p
105
-3.87
4
p
p
-2.50
p
10

<> (ps)
0,8
0,7
1000
0,6
100
0,5
10
-2.97
p
1
0,4
1
10
p
0
10
30
20
p
Nl 2
X p (t ) X p (0)  2 2 exp((t /  )  )
6 p
40
PEO/PMMA in blend
MSD of hydrogen-atoms
PEO/PMMA at 350 K
Methyl-group
H
H C
Main-chain
1000
100
H
C
Rouse regime
H
10
2
C
MSD (Å )
H
PEO - 350 K
PMMA-Main - 350 K
PMMA-Methyl - 350 K
PMMA-Ester - 350 K
H
H
H
H C
25
C
O
1
O
H Ester-group
Complex, stiff structure
0.1
0.01
0.01
0.1
1
10
100
time (ps)
1000
10
4
10
5
PEO/PMMA in blend
MSD of hydrogen-atoms
PEO/PMMA at 400 K
Methyl-group
H
H C
Main-chain
1000
H
100
H
C
H
H
H C
Rouse regime
H
10
2
C
MSD (Å )
H
PEO - 400 K
PMMA-Main - 400 K
PMMA-Methyl - 400 K
PMMA-Ester - 400 K
25
C
O
1
O
H Ester-group
Complex, stiff structure
0.1
0.01
0.01
0.1
1
10
100
time (ps)
1000
10
4
10
5
PEO/PMMA in blend
Results – Rouse Modes
stretching parameter 
relaxation time <>
10
p
1
107
Blend - 350K
Blend - 400K
Blend - 350K
Blend - 400K
6
-2.75
0,9
p
105
-3.87
4
p
p
-2.50
p
10

<> (ps)
0,8
0,7
1000
0,6
100
0,5
10
-2.97
p
1
0,4
1
10
p
0
10
30
20
p
Nl 2
X p (t ) X p (0)  2 2 exp((t /  )  )
6 p
40
PEO/PMMA in blend
Results – Rouse Modes
stretching parameter 
relaxation time <>
10
10
7
chain
chain
chain
chain
chain
chain
chain
chain
chain
chain
6
chain 1
chain 2
chain 3
chain 4
chain 5
chain 1
chain 2
chain 3
chain 4
chain 5
0,9
0,8
p
4
1
2
3
4
5
1
2
3
4
5

<> (ps)
105
10
p
1
0,7
1000
0,6
100
0,5
10
1
0,4
10
1
0
10
p
20
30
p
Nl 2
X p (t ) X p (0)  2 2 exp((t /  )  )
6 p
40
PEO/PMMA in blend
Results – Rouse Modes
stretching parameter 
relaxation time <>
10
7
10
6
p
1
Homopolymer - 350K
Homopolymer - 400K
Blend - 350K
Blend - 400K
Homopolymer - 350K
Homopolymer - 400K
Blend - 350K
Blend - 400K
0,9
105
4
p
10

<> (ps)
0,8
0,7
1000
0,6
100
0,5
10
0,4
1
1
10
0
10
p
20
30
p
Nl 2
X p (t ) X p (0)  2 2 exp((t /  )  )
6 p
40
Conclusion
• Simulation of homopolymer validated by various
experimental techniques
• Simulation of the blend: extraction of valuable
information from full trajectories
• Development of a second peak for high Δt
Caging-effect or simulation artifact?
• Formation of blobs  Rouse mode analysis
Thank you…
• Softcomp Eurothesis Project
• DIPC, University of the Basque Country
San Sebastian
– J. Colmenero
– F. Alvarez
– A. Arbe
• Forschungszentrum Jülich
– D. Richter
relaxation time (corrected)
--10
5
10
4
Blend - 350K and 400K
1mon and 3mon
1000
100
PEOPMMA13 - 1mon
PEOPMMA9 - 1mon
PEOPMMA13 - 3mon
PEOPMMA9 - 3mon
10
1
1
10
rouse - mode
---
relaxation time (corrected)
Homopolymer - 350K and 400K
1mon and 3mon
10
5
10
4
1000
100
PEO28 - 1mon
PEO30 - 1mon
PEO28 - 3mon
PEO30 - 3mon
10
1
1
10
rouse - mode
--MSD
PEO
104
1000
Center of mass
3 blobs per momoner
1 blob per monomer
PEO (pure)
0.52
100
10
MSD
0.65
0.8
1
0.61
0,1
0,01
0,001
0,0001
0,01
0,1
1
10
100
time(ps)
1000
4
10
5
10
PEO as Homopolymer
Coarse Graining PEO
• Micro – Meso mapping
– Simplest idea: 1 monomer = 1 blob
– Obtain probabilities from MD simulations
• Bond distance
• Bond angle
• …
– Assume that the probability distributions factorize
P(l ,  ,...)  P(l ) P( ) P(...)
– Boltzmann factors of interaction potentials
U l (l )
P(l )  exp(
)
k BT
PEO as Homopolymer
Coarse Graining PEO
• Micro – Meso mapping
– Determine potentials and forces
U l (l )  ln P(l )
d
F (l )   ln P (l )
dl
–
–
–
–
Repeat for different temperatures
Compile into tables (no analytical form necessary)
Write software (or use free open source alternative)
LAMMPS – Large-scale Atomic/Molecular Massively
Parallel Simulator, lammps.sandia.gov
PEO as Homopolymer
Results – Coarse Graining
Distance between blobs
Angle between blobs
2
0,015
1,5
probability
probability
0,01
1
0,005
0,5
0
0
2
2,5
3
distance (Å)
3,5
4
0
50
100
angle
• From these probabilities we can calculate an
effective potential
150
PEO as Homopolymer
Coarse Graining – Effective Potentials
Distance between blobs
Angle between blobs
2
0,015
1,5
probability
1
0,005
0,5
0
0
2,5
3
distance (Å)
3,5
4
0
Distance between blobs
50
100
angle
150
Angle between blobs
8
8
7,5
6
7
6,5
4
Energy
2
Energy
probability
0,01
6
5,5
2
5
0
4,5
4
-2
0
2
2,5
3
distance (Å)
3,5
50
100
4
angle
150
200
PEO as Homopolymer
Coarse Graining – Non-bond interactions
Probability to find another blob
Non-bond interactions
Non-bond potential
4
1,5
3
1
Energy
probability
2
1
0,5
0
0
-1
0
2
4
8
6
Distance (Å)
10
12
14
0
2
4
6
8
Distance (Å)
10
12
14