Molecular Modeling Used as a Molecular Modeling Used as a Probe of - - PowerPoint PPT Presentation

Molecular Modeling Used as a Molecular Modeling Used as a Probe of Interactions to Study the Probe of Interactions to Study the Polymeric Glass Transition Polymeric Glass Transition

Armand Soldera

Département de Chimie

HPCS May 13, 2003

Contents Contents

Tacticity Simulation of the Amorphous Phase Dilatometric Simulation Energetic Analysis Local Dynamics Cooperativity Conclusions

C CH2 CH3 C O O CH3 n

HPCS May 11-14, 2003

HPCS May 11-14, 2003

Tacticity

C CH2 CH3 C O O CH3 n

d l l l l l

ISOTACTIC SYNDIOTACTIC Tg = 45.3 °C Tg = 114 °C

Experimental

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 Phase

Design 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 Conditions

Each atom coming out from one face is automatically entering through the opposite face

Relaxation Procedure

MD + minimization

; ; ; ; ;

exp exp

LR i i i LR i i

U RT q q q U RT

η ξη ξη ξη η η ′ ′ ′

  −∆   ′ =   −∆  

∑

RIS

HPCS May 11-14, 2003

pcff Force Field: schematic representation

connectivity + flexibility cross terms non-bonding terms

HPCS May 11-14, 2003

pcff Force Field: mathematical expression

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

( ) ( ) ( )

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

' '

2 3 4 2 3 4 2 3 4 2 3 4 2 1 1 2 2 3 3 ' ' 1 2

1 cos 1 cos 2 1 cos 3 ' ' ' ' ( ) cos c

b bb b b b b

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 χ φ χ θθ θ θ θ θ

θ θ θ θ θ θ φ φ φ φ φ φ χ θ θ θ θ θ θ φ     = − + − + − + − + − + −             + − − + − − + − − +         + − − + − − + − − + − +

∑ ∑ ∑ ∑ ∑∑ ∑∑ ∑∑

[ ] [ ] [ ] ( )( )

3 1 2 3 ' 1 2 3 ' ' 9 6

• s2

cos3 ( ' ' ) cos cos2 cos3 ( ) cos cos2 cos3 cos ' '

b b i j ij ij i j i j ij ij ij

V b b V V V V V V K qq A B r r r

φ φ φθθ θ 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

50 100 150 200 250 300 0.88 0.92 0.96 1.00 1.04 1.08

Isotactic PMMA Syndiotactic PMMA Tgsy

ndio= 212 °C

Tgiso= 157 °C Specific Volume /cm3.g-1 Temperature /°C

Investigations to understand such a difference can be carried out NPT ensemble Number of RU: 100 Simulation time: 110 ps by data force field: pcff

12 hours in SGI O2000 / data

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

HPCS May 11-14, 2003

Energetic Analysis

• Principles
• 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 contributions 2. Inside the intramolecular part 3. Molecular contribution

HPCS May 11-14, 2003

Splits in the Energy Contributions

1) Total energy

2) Intramolecular Energy 3) Bending Energy

• Lennard-Jones
• electrostatic

A r B r

ij ij m ij ij p i j

−        

>

∑

q q r

i j ij i j ε >

∑

( )

Kθ

θ

θ θ −

∑

2

( )

[ ]

R n

n n

1 − −

∑

cos φ φ

φ

bending torsion Flexibility Connection

( )

K R R

R R

−

∑

2

stretching

• 35 (±8)

45 (±8) 15 (±7) 75 (±10) 15 (±5)

Intermolecular Intramolecular

Syndiotactic: 126.7° (±0.1) Isotactic: 127.8° (±0.1)

α

θ

θ'

C CH2 C H3C O OCH3

&

HPCS May 11-14, 2003

Tg Determination of PMA

C C C C H H C H O OCH3

θ'

difference with PMMA

• 100
• 50

50 100 150 200 250 300 350 0,84 0,88 0,92 0,96 1,00 1,04 1,08

Isotactic Syndiotactic

Specific Volume (cm

3.g

• 1)

Temperature (°C)

No differences In Tgs between the 2 PMA configurations, in agreement with experimental data

( ) ( ) ( )

g g g

T PM A T I PM M A T S PM M A < − < −

HPCS May 11-14, 2003

Energetic Analysis

• Comparisons to PMA data -

Intermolecular energy differences Intramolecular energy differences

In 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 PM M A E I PM M A E PM A

kcal mol kcal mol kcal mol

inter inter inter

− > − >>

− − −

350 258 78

1 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)

100 200 300 400 500 0.4 0.5 0.6 0.7 0.8 0.9 1.0

t (ps) P2

( )

τc P t dt =

∞

∫

2

τ τ β β

c =

      Γ 1

( )

τ T A B T To = −       exp exp −               t τ

β

( ) ( )

( )

P t

2 2

3 1 2 = ⋅ − u u

( ) ( )

( )

u u t ⋅ Libration motions

2 4 6 8 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 .0

430 K 450 K 490 K 510 K 580 K 540 K 600 K

P2 t /ps

HPCS May 11-14, 2003

Local Dynamics of the Backbone

Fit 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 2.6 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

Experimental Isotactic Syndiotactic

τc (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 1,1 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,01 0,1 1 10 100

τc(s) T /T

g

HPCS May 11-14, 2003

Local Dynamics of the Side-Chain

1 .6 1 .8 2 .0 2 .2 2 .4 2 .6 1

• 11

1

• 10

1

• 9

1

• 8

1

• 7

1

• 6

1

• 5

1

• 4

1

• 3

1

• 2

1

• 1

1 1

1

1

2

Experimental Isotactic Syndiotactic

τc (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-chain

Number of transitions of the side-chain

Computation 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 1,05 5,0 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(flip /ns

• 1)

Tg/T

HPCS May 11-14, 2003

Compilation of the Results

Correlation 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
• f 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 of

the 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 simulation

The 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

• bserved:

exp t

β

τ     −           1 n β = − 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

βKWW

Tg/T

0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 5,0 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(flip /ns

• 1)

Tg/T

0,7 0,8 0,9 1,0 1,1 1E -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 agreement with 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

• f 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 thickness

g

T

HPCS May 11-14, 2003

Acknowledgement

• Pr. Yves Grohens

Université de Bretagne-Sud InsightII: Amorphous_Cell and Discover3 DL_POLY