Molecular Modeling Used as a Molecular Modeling Used as a Probe of Interactions to Study the Probe of Interactions to Study the

Polymeric Glass TransitionPolymeric Glass Transition

Armand SolderaDépartement de Chimie

HPCS May 13, 2003

ContentsContents

Tacticity

Simulation of the Amorphous Phase

Dilatometric Simulation

Energetic Analysis

Local Dynamics

Cooperativity

Conclusions

C CH2

CH3

CO O

CH3 n

HPCS May 11-14, 2003

HPCS May 11-14, 2003

Tacticity

C CH2

CH3

CO O

CH3 n

dl llll

ISOTACTIC SYNDIOTACTICTg = 45.3 °C Tg = 114 °CExperimental

Can we manage such a difference by the use of molecular modeling ?

If affirmative better understanding of the difference glass transition …

HPCS May 11-14, 2003

Simulation of the Amorphous PhaseDesign of a cubic box- From the knowledge of the density and the mass of the polymer- All the space is filled by replica of this box

Chain design- A propagation procedure (MC) is begun to design

1 polymer configuration- The chain backbone is grown step by step

looking for long range excluded volume

Periodic Boundary ConditionsEach atom coming out from one face is automatically entering through the opposite face

Relaxation ProcedureMD + minimization

;; ;

; ;

exp

exp

LRi

i i LRi i

U RTq q

q U RTη

ξη ξηξη η

η′ ′

′

−∆ ′ = −∆ ∑

RIS

HPCS May 11-14, 2003

pcff Force Field: schematic representation

connectivity+

flexibility

crossterms

non-bondingterms

HPCS May 11-14, 2003

pcff Force Field: mathematical expression

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )( )( ) ( )( ) ( )( )

' '

2 3 4 2 3 42 0 3 0 4 0 2 0 3 0 4 0

0 0 0 21 1 2 2 3 3

' 0 0 ' 0 0 0 0

0 1 2

1 cos 1 cos 2 1 cos 3

' ' ' '

( ) cos c

b

bb bb bb

V K b b K b b K b b H H H

V V V K

F b b b b F F b b

b b V V

θ

χφ χ

θθ θθ θθ

θ θ θ θ θ θ

φ φ φ φ φ φ χ

θ θ θ θ θ θ

φ

= − + − + − + − + − + −

+ − − + − − + − − +

+ − − + − − + − −

+ − +

∑ ∑

∑ ∑

∑∑ ∑∑ ∑∑[ ] [ ]

[ ] ( )( )

3 0 1 2 3'

0 1 2 3 ' 0 0'

9 6

os2 cos3 ( ' ' ) cos cos2 cos3

( ) cos cos2 cos3 cos ' 'b b

i j ij ij

i j i jij ij ij

V b b V V V

V V V K

qq A Br r r

φ φ

φθθθ φ φ θ θ

φ φ φ φ φ

θ θ φ φ φ φ θ θ θ θ

ε> >

+ + − + +

+ − + + + − −

+ + −

∑∑ ∑∑

∑∑ ∑∑∑

∑ ∑

HPCS May 11-14, 2003

Dilatometric Simulation

-50 0 50 100 150 200 250 3000.88

0.92

0.96

1.00

1.04

1.08

Isotactic PMMA

Syndiotactic PMMA

Tgsyndio= 212 °C

Tgiso= 157 °C

Spec

ific V

olum

e /cm

3 .g-1

Temperature /°C

Investigations to understandsuch a differencecan be carried out

NPT ensembleNumber of RU: 100Simulation time: 110 ps by dataforce field: pcff

12 hours in SGI O2000 /data

Simulated ∆Tg = 55 °CExpected ∆Tg = 69 °C

HPCS May 11-14, 2003

Energetic AnalysisPrinciples

- The 2 PMMA configurations have the same force field parameters - Changes in their molecular behavior will be directly linked to changes in their molecular

characteristics Energy differences

Total Energy

E(Iso)-E(Syndio)=10 kcal.mol-1

3 splits will be performed

1. Inter and intramolecular contributions2. Inside the intramolecular part3. Molecular contribution

HPCS May 11-14, 2003

Splits in the Energy Contributions

1) Total energy

2) Intramolecular Energy

3) Bending Energy

• Lennard-Jones

• electrostatic

Ar

Br

ij

ijm

ij

ijp

i j

−

>

∑

q qri j

iji j ε>∑ ( )Kθ

θ

θ θ−∑ 02 ( )[ ]R nn n1 0− −∑ cos φ φ

φbending torsion

FlexibilityConnection

( )K R RRR

−∑ 02

stretching

-35 (±8) 45 (±8)

15 (±7) 75 (±10) 15 (±5)

Intermolecular Intramolecular

Syndiotactic: 126.7° (±0.1)

Isotactic: 127.8° (±0.1)

α

θθ'C

CH2

CH3C

O OCH3

&

HPCS May 11-14, 2003

Tg Determination of PMA

C

C

C

C

HH

CH

O OCH3

θ'differencewith PMMA

-100 -50 0 50 100 150 200 250 300 3500,84

0,88

0,92

0,96

1,00

1,04

1,08

Isotactic Syndiotactic

Spec

ific

Volu

me

(cm

3 .g-1)

Temperature (°C) No differences In Tgsbetween the 2 PMAconfigurations, in agreement with experimental data

( ) ( ) ( )g g gT PMA T I PMMA T S PMMA< − < −

HPCS May 11-14, 2003

Energetic Analysis- Comparisons to PMA data -

Intermolecular energy differences

Intramolecular energy differencesIn the bending term associated with the intra-diad angle, θ’

Conclusions- Results are in agreement with the Free Volume Theory

Higher interactions between neighboring polymer chains segments will give a higher Tg

- Due to a greater aperture of θ’, the isotactic chains should be more mobile

( ) ( ) ( )θ θ θ' ' '. . .

I PMMA S PMMA PMA− > − >>° ° °127 8 126 7 118 0

( ) ( ) ( )E S PMMA E I PMMA E PMAkcal mol kca l mol kca l mol

in ter in ter in ter− > − >>− − −350 258 781 1 1. . .

Study of the local dynamics

HPCS May 11-14, 2003

Local Dynamics Analysis- Principles -

Computation of the orientation function P2- From MD, acquisition of the bond autocorrelation

function - Computation of the 2nd Legendre polynomial term

with respect to time, P2 (t)

Computation of the correlation time, τc- Fit of P2(t) with a stretching exponential, KWW

Procedure is carried out at different temperatures

Fit with a VFT equation (or WLF)

0 100 200 300 400 5000.4

0.5

0.6

0.7

0.8

0.9

1.0

t (ps)

P2

( )τc P t dt=∞

∫ 20τ

τβ βc =

Γ

1

( )τ T A BT To

=−

exp

exp −

tτ

β

( ) ( )( )P

t2

23 0 1

2=

⋅ −u u( ) ( )( )u ut ⋅ 0

Libration motions

0 200 400 600 8000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

430 K

450 K490 K

510 K

580 K

540 K

600 KP 2

t /ps

HPCS May 11-14, 2003

Local Dynamics of the BackboneFit

Results

Behavior of the 2 isomers- at T+Tg: Comparable- at T: Different

Study of the relaxation of the side chain

1.6 1.8 2.0 2.2 2.4 2.610-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

Experimental

Isotactic

Syndiotactic

τ c (s

)

1000/T (K-1)

B (kJ.mol-1)

11.9 12.8

C C

H

CH3

C O

O CH3

H

0,7 0,8 0,9 1,0 1,11E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0,01

0,1

1

10

100

τ c(s)

T /Tg

HPCS May 11-14, 2003

Local Dynamics of the Side-Chain

1.6 1.8 2.0 2.2 2.4 2.610-1110-1010-910-810-710-610-510-410-310-210-1100101102

Experimental

Isotactic

Syndiotacticτ c

(ps)

1000/T (K)

C C

H

H

CH3

C

O CH3

O

Fit

Results- Non-Arrhenian behavior, but such a relaxation corresponds to the β mode- BUT, the simulation takes into account 3 motions:

» librational modes» due to the side-chain (what we are interested in)» due to the backbone

B (kJ.mol-1)

11.5 5

HPCS May 11-14, 2003

Mobility of the side-chainNumber of transitions of the side-chainComputation of the number of transitions between the UP and DOWN states of C=O

The behavior is Arrhenian like !

0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,055,0

5,5

6,0

6,5

7,0

7,5

8,0

8,5

9,0

Syndiotactic

Isotactic

Ea=11 kJ mol-1

Ea=7 kJ mol-1

ln(fl

ip /n

s-1)

Tg/T

HPCS May 11-14, 2003

Compilation of the ResultsCorrelation times- Backbone

» Behavior of τc(C-H) is in agreement with published results:correlation times of iso PMMA are found inferior to the syndio PMMA ones

» The backbones of the 2 configurations present the same behavior at T + Tg, therefore the difference in Tgs could not be explained

- Side-Chain» The side-chains of Iso-PMMA show a greater mobility than the syndio ones» Behind this difference there lies a possible explanation of the difference in Tgs

Comparison with experimental data- From NMR experiments: compared with PEMA, PMMA showed that the greatest mobility

of the side-chains induces a decrease of the lowest correlation time of the backbone

- Consequently, a higher side-chain rotation of iso PMMA generates a greater mobility ofthe backbone, and a greater mobility of the backbone explains a lower Tg

Tg (i-PMMA) < Tg (s-PMMA)

HPCS May 11-14, 2003

Cooperativity …Cooperativity observed by molecular simulationThe stretching function:

According to the Coupling Model: where is the coupling parameter, it actually corresponds to a measure of the cooperativity

Consequently, the coupling between the side-chain and the backbone can be directly observed:

exp t β

τ −

1nβ = − n

C C

H

H

CH3

C

O CH3

O

0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45 Syndiotactic

Isotactic

β KWW

Tg/T

0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,055,0

5,5

6,0

6,5

7,0

7,5

8,0

8,5

9,0

Syndiotactic

Isotactic

Ea=11 kJ mol-1

Ea=7 kJ mol-1

ln(fl

ip /n

s-1)

Tg/T

0 ,7 0 ,8 0 ,9 1 ,0 1 ,11E -10

1E -9

1E -8

1E -7

1E -6

1E -5

1E -4

1E -3

0 ,01

0 ,1

1

10

100

τ c(s)

T g/T

backbone

HPCS May 11-14, 2003

Conclusions

The substitution of H by CH3 causes energetic variations- Augmentation of intermolecular interactions- Differenciation in the non-bonding interactions between the 2 stereomers- Aperture of the intra-diad angle to lessen side-chain interaction- Aperture of the intra-diad angle more important for the isotactic configuration

The important mobility of the isotactic side-chain induces a greater mobility of the backbone, comparatively to the syndiotactic one: This cooperativity between the side-chain and the backbone was observed using molecular simulation

Such a behavior tends to lower the Tg of the isotactic configuration

The comparison of simulated data to experimental results are in agreementwith the free volume concept to explain the difference in Tg between the two stereomers

HPCS May 11-14, 2003

Questions

Is the local scale cooperativity observed here consistent with the CRR (Coupling Rearranging Region) theory ?

Can the size or the shape of the CRR be affected by the PMMA tacticity ?

The tacticity dependent size or anisotropic shape of the CRR may be a crucial point revealed by chain confinement:

Further investigations will be performed on this topic in light of our molecular dynamics results.

( )tacticity and film thicknessgT

HPCS May 11-14, 2003

Acknowledgement

Pr. Yves GrohensUniversité de Bretagne-Sud

InsightII: Amorphous_Cell and Discover3

DL_POLY