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 CH 3 � Dilatometric Simulation C CH 2 C � Energetic Analysis O O CH 3 � Local Dynamics n � Cooperativity � Conclusions HPCS May 11-14, 2003

Tacticity CH 3 C CH 2 C O O CH 3 n l d l l l l ISOTACTIC SYNDIOTACTIC T g = 45.3 °C T g = 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 RIS � Chain design   −∆ LR exp U RT   η ; i ′ = q q - A propagation procedure (MC) is begun to design ∑ ξη ξη ; i ; i   −∆ LR q exp U RT   1 polymer configuration ′ ′ ξη η ; i ; i η ′ - 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 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 = − + − + − + θ θ − + θ θ − + θ θ − V K b b K b b K b b H H H     2 0 3 0 4 0 2 0 3 0 4 0 θ b ( ) ( ) ( ) ∑ ∑         + − φ φ − + − φ φ − + − φ φ − + χ 0 0 0 2 V 1 cos V 1 cos 2 V 1 cos 3 K         χ 1 1 2 2 3 3 φ χ ∑∑ ∑∑ ∑∑ ( )( ) ( )( ) ( )( ) + − − + θ θ − θ θ − + − θ θ − F b b b b ' ' F ' ' F b b θθ θ bb ' 0 0 ' 0 0 b 0 0 θ θ b ' ' b θ b ∑∑ [ ] ∑∑ [ ] + − φ + φ + φ + − φ + φ + φ ( b b V ) cos V c os2 V cos3 ( ' b b ' ) V cos V cos2 V cos3 0 1 2 3 0 1 2 3 φ φ b b ' ∑∑ [ ] ∑∑∑ ( )( ) + θ θ − φ + φ + φ + φ θ θ − θ θ − ( ) V cos V cos2 V cos3 K cos ' ' φθθ 0 1 2 3 ' 0 0 θ φ φ θ θ '   qq A B ∑ ∑ i j ij ij + + −   ε 9 6 r r r     > > i j i j ij ij ij HPCS May 11-14, 2003

Dilatometric Simulation NPT ensemble Number of RU: 100 12 hours in SGI O2000 / Simulation time: 110 ps by data data force field: pcff 1.08 Simulated ∆ T g = 55 °C T g sy ndio = 212 °C Expected ∆ T g = 69 °C Specific Volume /cm 3 .g -1 1.04 1.00 Syndiotactic PMMA 0.96 Isotactic PMMA Investigations to understand 0.92 such a difference T g iso = 157 °C can be carried out 0.88 -50 0 50 100 150 200 250 300 Temperature /°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 Intermolecular & Intramolecular 45 (±8) -35 (±8) Flexibility Connection • Lennard-Jones   A B ∑ ij ij −   m p r r     > i j ij ij ∑ ( ) • electrostatic 2 − [ ] K R R ( ) q q ∑ ∑ ( ) ∑ R 0 2 − φ − φ 0 i j θ − θ K θ R 1 cos n n n R 0 j ε r stretching φ θ > ij i bending torsion 2) Intramolecular Energy 75 (±10) 15 (±7) 15 (±5) CH 2 θ θ ' Syndiotactic: 126.7° (±0.1) 3) Bending Energy α C Isotactic: 127.8° (±0.1) H 3 C C OCH 3 O HPCS May 11-14, 2003

T g Determination of PMA H 1,08 H C Isotactic C 1,04 θ ' -1 ) difference Syndiotactic 3 .g C C with PMMA 1,00 Specific Volume (cm H C 0,96 OCH 3 O 0,92 0,88 0,84 -100 -50 0 50 100 150 200 250 300 350 Temperature (°C) No differences In T g s ( ) ( ) ( ) between the 2 PMA < − < − T PM A T I PM M A T S PM M A g g g configurations, in agreement with experimental data HPCS May 11-14, 2003

Energetic Analysis - Comparisons to PMA data - � Intermolecular energy differences ( ) ( ) ( ) − > − >> E S PM M A E I PM M A E PM A inter inter inter 350 − 258 − 78 − 1 1 1 kcal mol . kcal mol . kcal mol . � Intramolecular energy differences In the bending term associated with the intra-diad angle, θ ’ ( ) ( ) ( ) θ − > θ − >> θ ' I PMMA ' S PMMA ' PMA ° ° ° 127 8 . 126 7 . 118 0 . � Conclusions - Results are in agreement with the Free Volume Theory Higher interactions between neighboring polymer chains segments will give a higher T g Due to a greater aperture of θ ’, the isotactic chains should be more mobile - Study of the local dynamics HPCS May 11-14, 2003

Local Dynamics Analysis - Principles - P 2 Libration motions 1.0 � Computation of the orientation function P 2 ( ) ( ) ( ) 2 0.9 ⋅ − - From MD, acquisition of the bond autocorrelation 3 u t u 0 1 ( ) ( ) ( ) = P function t ⋅ u u 0 2 0.8 2 - Computation of the 2nd Legendre polynomial term 0.7 with respect to time, P 2 (t) 0.6  β  exp −    t    � Computation of the correlation time, τ c 0.5   τ     - Fit of P 2 (t) with a stretching exponential, KWW 0.4 0 100 200 300 400 500 t (ps)    τ Γ 1 ∞ ( ) ∫ τ c = τ c =  P t dt 2 β β   0 1 .0 0 .9 430 K 0 .8 � Procedure is carried out at different 0 .7 450 K temperatures 490 K 0 .6 0 .5 510 K P 2 0 .4 540 K 0 .3 � Fit with a VFT equation (or WLF) 580 K 0 .2   B 600 K ( ) 0 .1 τ T = A exp   0 .0 −   T T o 0 2 0 0 4 0 0 6 0 0 8 0 0 t /ps HPCS May 11-14, 2003

Local Dynamics of the Backbone � Fit 10 2 10 1 CH 3 H 10 0 B 10 -1 (kJ.mol -1 ) 10 -2 C C 10 -3 11.9 τ c (s) Experimental Syndiotactic 10 -4 H C O 10 -5 12.8 10 -6 O CH 3 10 -7 10 -8 Isotactic 10 -9 10 -10 1.6 1.8 2.0 2.2 2.4 2.6 1000/T (K -1 ) � Results 100 10 1 Behavior of the 2 isomers 0,1 0,01 - at T+T g : Comparable 1E-3 τ c (s) 1E-4 - at T: Different 1E-5 1E-6 1E-7 1E-8 1E-9 Study of the relaxation of the side chain 1E-10 0,7 0,8 0,9 1,0 1,1 T /T g HPCS May 11-14, 2003

Local Dynamics of the Side-Chain � Fit 2 1 0 1 1 0 H CH 3 0 1 0 -1 1 0 B -2 1 0 C C (kJ.mol -1 ) -3 τ c (ps) 1 0 -4 1 0 Syndiotactic Experimental 11.5 H C O -5 1 0 -6 1 0 5 -7 1 0 O CH 3 -8 1 0 -9 1 0 Isotactic -10 1 0 -11 1 0 1 .6 1 .8 2 .0 2 .2 2 .4 2 .6 1000/T (K) � 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 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 9,0 -1 8,5 E a =7 kJ mol Isotactic 8,0 -1 ) ln(flip /ns 7,5 7,0 -1 E a =11 kJ mol 6,5 6,0 Syndiotactic 5,5 5,0 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 T g /T The behavior is Arrhenian like ! HPCS May 11-14, 2003

Compilation of the Results � Correlation times - Backbone » Behavior of τ c (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 + T g , therefore the difference in T g s 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 T g s � 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 of the backbone, and a greater mobility of the backbone explains a lower T g T g (i-PMMA) < T g (s-PMMA) HPCS May 11-14, 2003