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transcript
MD Simulations of PEO/PMMA blends
May 6th 2008F. Alvarez, A. Arbe, Prof. J. Colmenero
M. Brodeck, Prof. D. Richter
DONOSTIA INTERNATIONALPHYSICS CENTER
Universidad del Pais Vasco
Forschungszentrum Jülich
EurothesisEurothesis
• 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?
MotivationWhat is this all about?
Overview
• Introduction– Validation
• PEO/PMMA in blend– Structural properties– Self-correlation functions and non-Gaussianity– Mean Square Displacements– Rouse Modes
Introduction to the SimulationSetup and Software
• Software by • Simulation engine: Discover
– Periodic boundary conditions
• Densities determined by NPT-simulations• Forcefield: COMPASS
– condensed-phase optimizedmolecular potentials foratomistic simulation studies
• Simulation time: 100 nsΔt = 1 fs100,000,000 steps
PEO as HomopolymerConfirmed results
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
0,1 1
350K - FOCUS375K - FOCUS400K - FOCUS350K - PI375K - PI400K - PI350K - IN16350K - Simulation375K - Simulation400K - Simulation
w(s
)
Q(Å-1)
Q-4
Dynamics of individualhydrogen atoms
protonated sample*
0
0,2
0,4
0,6
0,8
1
0,01 0,1 1 10 100
1.41.61.822.2Q=1.40Q=1.60Q=1.80Q=2.00Q=2.20
time (ps)
Collective dynamicsdeuterated sample
TOFTOF
*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.
PEO as HomopolymerConfirmed results
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
0,1 1
350K - FOCUS375K - FOCUS400K - FOCUS350K - PI375K - PI400K - PI350K - IN16350K - Simulation375K - Simulation400K - Simulation
w(s
)
Q(Å-1)
Q-4
Dynamics of individualhydrogen atoms
protonated sample*
Collective dynamicsdeuterated sample
NSEtemperature corrected
0
0,2
0,4
0,6
0,8
1
0,1 1 10 100 1000
S(Q
, t)
/S(Q
, 0)
time (ps)
Temperature: 400K
Q=1.3, 1.5 and 1.7 A-1
PEO/PMMA in blendIntroduction
• Simulating the blend– 5 PEO chains
43 monomers15 PMMA chains25 monomers 7170 atomscell size ~41.5 Å
– Density determined by NPT
• T: 300 (running), 350 and 400 K• 100 ns for each temperature• Huge data files, ~90Gb for 100ns
1,05
1,06
1,07
1,08
1,09
1,1
1,11
1,12
280 300 320 340 360 380 400 420
Density
Den
sity
(g/
cm3)
Temperature
*
* Povray
PEO/PMMA in blendStructure
-0.5
0
0.5
1
0.8 1.6 2.4 3.2 4 4.8 5.6
Scattering dPEO/dPMMA
S(Q
)
Q (Å-1)
PEO/PMMA in blendStructure
-0.5
0
0.5
1
0.8 1.6 2.4 3.2 4 4.8 5.6
Scattering dPEO/dPMMA
TotalPEOPMMAPEOxPMMA
S(Q
)
Q (Å-1)
PEO/PMMA in blendStructure
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Effective density
PEOPMMA
e
ffec
tive
distance (Å)
Composition of the blend (weight):
20% PEO, 80% PMMA
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
Self density
PEOPMMA
se
lfdistance (Å)
PEO/PMMA in blendComparing the Blend with the Homopolymer
0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20
PEO in PEO/PMMA350 K
5 ps50 ps500 ps5000 ps50000 ps
4r2
Gs(r
, t)
Displacement (Å)
0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20
PEO in PEO/PMMA400 K
5 ps50 ps500 ps5000 ps50000 ps
4r2
Gs(r
, t)
Displacement (Å)
PEO/PMMA in blendComparing the Blend with the Homopolymer
0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20
PEO in PEO/PMMA350 K
5 ps50 ps500 ps5000 ps50000 ps
4r2
Gs(r
, t)
Displacement (Å)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.001 0.01 0.1 1 10 100 1000 104 105
non-Gaussianity
350 K400 K
no
n-G
au
ssia
nity
time (ps)
4
2 22
( )3( ) 1
5 ( )
r tt
r t
PEO/PMMA in blendComparing the Blend with the Homopolymer
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.001 0.01 0.1 1 10 100 1000 104 105
non-Gaussianity
350 K400 K
no
n-G
au
ssia
nity
time (ps)
4
2 22
( )3( ) 1
5 ( )
r tt
r t
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10
PEO in PEO/PMMA350 K
1 ps3 ps1000 ps
4r2
Gs(r
, t)
Displacement (Å)
PEO/PMMA in blendComparing the Blend with the Homopolymer
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.001 0.01 0.1 1 10 100 1000 104 105
non-Gaussianity
350 K400 K
no
n-G
au
ssia
nity
time (ps)
4
2 22
( )3( ) 1
5 ( )
r tt
r t
0
0.1
0.2
0.3
0.4
0.5
0.6
0 2 4 6 8 10
PEO in PEO/PMMA400 K
1 ps3 ps1000 ps
4r2 G
s(r, t
)
Displacement (Å)
PEO/PMMA in blendComparing the Blend with the Homopolymer
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.001 0.01 0.1 1 10 100 1000 104 105
non-Gaussianity
350 K400 K
no
n-G
au
ssia
nity
time (ps)
4
2 22
( )3( ) 1
5 ( )
r tt
r t
0
0.02
0.04
0.06
0.08
0.1
0 5 10 15 20 25 30
PEO in PEO/PMMA350 K
31627 ps80000 ps
4r2
Gs(r
, t)
Displacement (Å)
PEO/PMMA in blendComparing the Blend with the Homopolymer
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.001 0.01 0.1 1 10 100 1000 104 105
non-Gaussianity
350 K400 K
no
n-G
au
ssia
nity
time (ps)
4
2 22
( )3( ) 1
5 ( )
r tt
r t
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 50 60
PEO in PEO/PMMA350 K
31627 ps39812 ps50000 ps63097 ps80000 ps
4r2
Gs(r
, t)
Displacement (Å)
PEO/PMMA in blendComparing the Blend with the Homopolymer
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.001 0.01 0.1 1 10 100 1000 104 105
non-Gaussianity
350 K400 K
no
n-G
au
ssia
nity
time (ps)
4
2 22
( )3( ) 1
5 ( )
r tt
r t
0
0.01
0.02
0.03
0.04
0.05
0.06
0 10 20 30 40 50 60
PEO in PEO/PMMA400 K
31627 ps39812 ps50000 ps63000 ps80000 ps
4r2 G
s(r,
t)
Displacement (Å)
PEO/PMMA in blendMSD of PEO-hydrogens
-0.02
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 50 60
Displacement HistogramsComparison of homopolymer/blend at t=50 ns
homopolymer - 350 Kblend - 350 Khomopolymer - 400 Kblend - 400 K
4r2
Gs(r
, t)
Displacement (Å)
0.01
0.1
1
10
100
1000
104
0.01 0.1 1 10 100 1000 104 105
Mean Square Displacement
blend - 350 Kblend - 400 Khomopolymer - 350 Khomopolymer - 400 K
MS
D (
Å2)
time (ps)
Slopes:t^0.36t^0.41t^0.51t^0.52
Movement of PEO atoms restricted by the rather stiff PMMA-matrix
PEO/PMMA in blendMSD of hydrogen-atoms
C C
H
H
H
C
C O
OC
H
H
H
H
H
H
H
25
Methyl-group
Ester-group
Main-chain
Complex, stiff structure0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000 104 105
PEO/PMMA at 350 K
PEO - 350 KPMMA-Main - 350 KPMMA-Methyl - 350 KPMMA-Ester - 350 K
MS
D (
Å2)
time (ps)
PEO/PMMA in blendComparing the MSD for two temperatures
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000 104 105
PEO/PMMA at 350 and 400 K
PEO - 350 KPEO - 400 KPMMA-Main - 350 KPMMA-Main - 400 KPMMA-Methyl - 350 KPMMA-Methyl - 400 KPMMA-Ester - 350 KPMMA-Ester - 400 K
MS
D (
Å2 )
time (ps)
PEO/PMMA in blendForming Blobs
PEO/PMMA in blendResults – Rouse Modes
0
0.2
0.4
0.6
0.8
1
1 10 100 1000 104 105
Rouse modes blend 400 K
p
p(t)
time (ps)
We investigate the behavior of PEO in the
blend!
0
1( ) cos( ) ( )
N
p n
p nX t dn r t
N N
Fourier transformation ofblob-coordinates
2
2 2( ) (0) exp( / )
6p p p
NlX t X t
p
( / )( ) WWtt Ae
PEO/PMMA in blendResults – Rouse Modes
1
10
100
1000
104
105
106
107
1 10
relaxation time <>
Blend - 350KBlend - 400K
<>
(p
s)
p
p-2.75
p-3.87
p-2.50
p-2.97
2
2 2( ) (0) exp(( / ) )
6p p
NlX t X t
p
0,4
0,5
0,6
0,7
0,8
0,9
1
0 10 20 30 40
stretching parameter p
Blend - 350KBlend - 400K
p
p
PEO/PMMA in blendMSD of hydrogen-atoms
C C
H
H
H
C
C O
OC
H
H
H
H
H
H
H
25
Methyl-group
Ester-group
Main-chain
Complex, stiff structure0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000 104 105
PEO/PMMA at 350 K
PEO - 350 KPMMA-Main - 350 KPMMA-Methyl - 350 KPMMA-Ester - 350 K
MS
D (
Å2)
time (ps)
Rouse regime
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000 104 105
PEO/PMMA at 400 K
PEO - 400 KPMMA-Main - 400 KPMMA-Methyl - 400 KPMMA-Ester - 400 K
MS
D (
Å2 )
time (ps)
PEO/PMMA in blendMSD of hydrogen-atoms
C C
H
H
H
C
C O
OC
H
H
H
H
H
H
H
25
Methyl-group
Ester-group
Main-chain
Complex, stiff structure
Rouse regime
PEO/PMMA in blendResults – Rouse Modes
1
10
100
1000
104
105
106
107
1 10
relaxation time <>
Blend - 350KBlend - 400K
<>
(p
s)
p
p-2.75
p-3.87
p-2.50
p-2.97
2
2 2( ) (0) exp(( / ) )
6p p
NlX t X t
p
0,4
0,5
0,6
0,7
0,8
0,9
1
0 10 20 30 40
stretching parameter p
Blend - 350KBlend - 400K
p
p
PEO/PMMA in blendResults – Rouse Modes
2
2 2( ) (0) exp(( / ) )
6p p
NlX t X t
p
1
10
100
1000
104
105
106
107
1 10
relaxation time <>
chain 1chain 2chain 3chain 4chain 5chain 1chain 2chain 3chain 4chain 5
<>
(p
s)
p
0,4
0,5
0,6
0,7
0,8
0,9
1
0 10 20 30 40
stretching parameter p
chain 1chain 2chain 3chain 4chain 5chain 1chain 2chain 3chain 4chain 5
p
p
PEO/PMMA in blendResults – Rouse Modes
1
10
100
1000
104
105
106
107
1 10
relaxation time <>
Homopolymer - 350KHomopolymer - 400KBlend - 350KBlend - 400K
<>
(ps
)
p
0,4
0,5
0,6
0,7
0,8
0,9
1
0 10 20 30 40
stretching parameter p
Homopolymer - 350KHomopolymer - 400KBlend - 350KBlend - 400K
p
p
2
2 2( ) (0) exp(( / ) )
6p p
NlX t X t
p
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 ΔtCaging-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
---
1
10
100
1000
104
105
1 10
Blend - 350K and 400K1mon and 3mon
PEOPMMA13 - 1monPEOPMMA9 - 1monPEOPMMA13 - 3monPEOPMMA9 - 3mon
rela
xatio
n t
ime
(co
rre
cte
d)
rouse - mode
---
1
10
100
1000
104
105
1 10
Homopolymer - 350K and 400K1mon and 3mon
PEO28 - 1monPEO30 - 1monPEO28 - 3monPEO30 - 3mon
rela
xatio
n t
ime
(co
rre
cte
d)
rouse - mode
---
0,0001
0,001
0,01
0,1
1
10
100
1000
104
0,01 0,1 1 10 100 1000 104 105
MSDPEO
Center of mass3 blobs per momoner1 blob per monomerPEO (pure)
MS
D
time(ps)
0.8
0.61
0.65
0.52
PEO as HomopolymerCoarse 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
– Boltzmann factors of interaction potentials
( , ,...) ( ) ( ) (...)P l P l P P
( )( ) exp( )
l
B
U lP l
k T
PEO as HomopolymerCoarse Graining PEO
• Micro – Meso mapping– Determine potentials and forces
– 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
( ) ln ( )lU l P l
( ) ln ( )d
F l P ldl
PEO as HomopolymerResults – Coarse Graining
0
0,5
1
1,5
2
2 2,5 3 3,5 4
Distance between blobs
pro
bab
ility
distance (Å)
0
0,005
0,01
0,015
0 50 100 150
Angle between blobs
pro
bab
ility
angle
• From these probabilities we can calculate an effective potential
PEO as HomopolymerCoarse Graining – Effective Potentials
-2
0
2
4
6
8
2 2,5 3 3,5 4
Distance between blobs
En
erg
y
distance (Å)
4
4,5
5
5,5
6
6,5
7
7,5
8
0 50 100 150 200
Angle between blobs
Ene
rgy
angle
0
0,5
1
1,5
2
2 2,5 3 3,5 4
Distance between blobs
pro
bab
ility
distance (Å)
0
0,005
0,01
0,015
0 50 100 150
Angle between blobs
pro
bab
ility
angle
PEO as HomopolymerCoarse Graining – Non-bond interactions
0
0,5
1
1,5
0 2 4 6 8 10 12 14
Probability to find another blobNon-bond interactions
pro
bab
ility
Distance (Å)
-1
0
1
2
3
4
0 2 4 6 8 10 12 14
Non-bond potential
En
erg
y
Distance (Å)