MD Simulations of PEO/PMMA blends May 6 th 2008 F. Alvarez, A. Arbe, Prof. J. Colmenero M. Brodeck,...

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)


-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)


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


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


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


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


1 ps3 ps1000 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

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10


1 ps3 ps1000 ps

4r2 G

s(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

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20 25 30


31627 ps80000 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

0

0.02

0.04

0.06

0.08

0.1

0 10 20 30 40 50 60


31627 ps39812 ps50000 ps63097 ps80000 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

0

0.01

0.02

0.03

0.04

0.05

0.06

0 10 20 30 40 50 60


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


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


p

p


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


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


MS

D (

Å2 )

time (ps)


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


1

10

100

1000

104

105

106

107

1 10

relaxation time <>


<>

(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



p

p


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


chain 1chain 2chain 3chain 4chain 5chain 1chain 2chain 3chain 4chain 5

p

p


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


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


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


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)

MD Simulations of PEO/PMMA blends May 6 th 2008 F. Alvarez, A. Arbe, Prof. J. Colmenero M. Brodeck,...

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