A3-3_ Natarajan.pdf

7/28/2019 A3-3_ Natarajan.pdf

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Conformation and Configuration Dependent Physical

Properties of Polymers as Influenced by ChemicalStructure: Simulations of Chains and Condensed Phase

Using Statistical Mechanics & Atomistic Models

Upendra Natarajan

Polymer Science & Engineering Division

National Chemical Laboratory

Pune, India


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Molecular Modeling of Polymers : Why ?

Understand the molecular factors to the behavior of polymers

Develop molecular-structure to property understanding

Link between chemical structure and macroscopic properties

Predictive tools for useful property prediction Fundamental understanding at the molecular level

New molecular and materials design


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Outline

Conformational Behavior & Chain Dimensions

Optical Properties of Polymer Chains

Local Structure and Properties of Amorphous Polymer Phase

Optical Birefringence of Oriented Polymers in Amorphous Phase


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BPC-1 BPC-2 Axial ring

Equatorial ring

5

6

Structure set to a controlled study of variation of local

rigidity/variation of of CD atom/linkage & Phenyl ring mobility

O O

O

BPCPC

O O

O

DMPC

O O

O

BPAPC O O

O

TMCPC

O

OODMBPC

Polycarbonates


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Conformational Properties & Chain Dimensions

Macromol. Theory Simul., 11(6), 655 (2002); Macromol. Theory Simul., 11(6), 669 (2002)J. Macromol. Sci.: Phys.(2004)

O

O

O

CH3CH3R R

modificationsstructural

Chain stiffness and dimensions are influencedby chemical groups

Calculated chain dimensions can be used tounderstand and predict polymer properties in solution

Bulkyness of substituting group and nature ofnon-bonded interactions can either increase ordecrease chain dimensions

RIS modeling

Chain dimensions:/M , /M , Cn

Torsion states: IiConformation Analysis

Polycarbonates


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Conformational Analysis, RIS ModelsChain Properties of Substituted

Polycarbonates

Chain dimensions decrease with

increase in T

Negative temperature coefficient for

all chain dimensions for all the PCs

DMPC shows slight dependence on T

Substitutions reduce chain

dimensions at all T (300 500 K)


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PolyestersWhy is there a renewed interest in polymers with aliphatic rings in thebackbone ?

Yee et al, Macromolecules 1998, 31, 5371Yee et al, Macromolecules 1999, 32, 5944Kelsey et al Macromolecules 2000, 33, 5810

As the cyclohexyl content increases,

PET/PCT copolymers exhibit ductilebehavior at lower temperatures

Improved thermal, mechanical and

optical properties

Conformational transitions of the

cyclohexyl rings facilitate chain slippage

Very limited current understanding of the conformational features in these polymers

Our objective: Understand bond level conformational features in polyestershaving cycloaliphatic rings in the main chain, formulate RIS modelsand calculate chain conformational properties

H3C CH 3

O CBDO

CC

O O

O CH2 CH2 PETO

O CC

O O

O CH2 CH2

R

R

O C

O

O CH2 CH2

O

C PCC

R=H, PCT=CH3, DMPCT

CC

O O

OO

CH 3H3C


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Methodology and RIS Models

Conformational analysis of the

bonds in the repeat unit fragmentsperformed using molecularmechanics

Bonds constrained at discretetorsional values and rest of the

molecule is allowed to relax Conformational energy includes

contributions from bonded andnon-bonded interactions

7

7

21

5 7l

T

C

C

O

O

O

O

O

H3C CH3

H3C CH3

541 2

3 4 5 67

3

8534 6

2

1

6

1

34

ll

l l l l l

I I

I II

I

TT

T TT

*

*I

II3

54321

4

H3C CH3

H3C CH3

OH3C CH3

H3C CH3

1 2I

l

1

l

1

l

1

O

O

C

21 lT1 3

l45

T2

T

T T

3

4 5

CBDO-PolyesterCBDO-PC

R = H (PCT)= CH3 (DMPCT)

I

*1

3 5

46

7

8l1

l

ll

l

ll

l2

34

5

6

7

8 9l9

8

76543

21

CH2CH2

O

O

O

O

OR

R

9

1 2

3 4 5 6 8 9*

CC

O

O

CH2O

O

CH2

O8

76543

21

9

1 2

4 5 69

10

7

10

PCC

1

3

l 2

9

8

7

64

5

ll l

l

l

l

l

l

l1 2

3 4

5

6

7

8

9

10

I

I I I I I

I

I I

I I I II I

TT

T

T

T

T

T

T

T

T

TT

T

T

T

TT


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Conformational Energy Maps

Terephthalate linkage in PCT

Terephthalate linkage in DMPCT

In PCT planar conformations of the ester linkages across the phenyl rings

In DMPCT, dicarboxylate linkage is no longer planar, but prefers skewedconformations with respect to the phenyl rings

III

I

543

21I

CH2O

O

O

O

CH2O

O

O

OH3C

CH3I1 2

3 4 5

I

I I I


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Chain Conformational Properties

r2(1022) s2(1022) C

na()

300 K 500 K 300 K 500 K 300 K 500 K 300 K 500 K

PCT 145.5 141.6 23.9 23.3 6.3 6.2 6.8 6.7

DMPCT 225.0 169.0 36.4 27.8 9.8 7.4 15.0 10.1

PCC 348.0 220.0 55.3 35.8 16.5 10.4 23.6 13.5

CBDOPolyester

1551.0 1552.2 187.1 187.2 88.3 88.4 78.6 78.7

CBDOPC

173.0 101.0 24.5 15.3 23.3 13.6 28.0 16.7

PCT exhibits lowest chain dimensions among polyesters studied here

Highly extended chain conformations for CBDO-polyester

Higher values of persistence lengths and characteristic ratio

Suggests a high level of chain rigidity in cyclobutylene containing polyesters

Chain dimensions for CBDO-PC higher than that of conventional polycarbonates

Polymer, 43, 6297 (2002); Macromol. Theory Simul., 12, 61 (2003)


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'n > 0 'n ~ 0 'n < 0

Single Chain Optical Anisotropy, J2 Birefringence in the bulk state, 'n

Properties sought

Our goal: To use Molecular Simulations & Theory to understand structure-property relationships and prediction of optical anisotropy and birefringence

BPAPCO

CO

O

CH3 CH3

SBIPCCH3 CH3

O CO

O

CH3 CH3

PS

CHCH2

Polarizability & Optical Properties of Polymer ChainsChemical Structure Anisotropy


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Molecular

fragments Electronic interactions Conformations

Repeat unit Polarizability Tensors Conformations / torsions

Conformational Averaged

Optical PropertiesPolymer chain

Conformational Properties of Polymer Chains

Polarizability & Optical Properties

Bulk phase Birefringence and material

optical properties

Our goal: To completely understand the variation of optical

anisotropy and birefringence with chemical structure and conformations


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ya

xa

X

Yxb

yb

Ia

Ib

\a\bW'

W -W

ya

xa

X

Y

-'-W

OC

O

O

'

'

,,

h bBPC ph a DMCYXD D D D

0 0 0 0 0 01 ( ) ( )

X Y ZZ ZDMCYX

CYX X Y Z

R Re eD D D [ D [

1' ' ' 0 0 0

Z ZDMCYX DMCYXX Y Z X Y ZR RD T D T

1

2

3

4

( ) (

( ( )

( ) (

( ( )

')

)

)

')

x b Z

Z x b

x a z

Z x a

T R R

T R

T R R

T R

R

R

\

I

I

\

W

W

W

W

|| ||i i P i= U I P P

Y

W 'W

ya

xa

xb

yb

\a\b'

CYX BPC

T

X'

'

'

'

X

Y

Y

X

0

0

(b) (c)

3 3 x-1 *2 J P P P P J

1 4 32 2

P P P P P4 3 2 1

trJ DD

O

O

O

( )x

R 2 1 2 (T T )

C0 (T T )

0 0 1

i i i iP

i i i i

D D

D


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14.73 6 (E) 15.03 6(A) 12.77 6

(A) 12.70 6

(E) 17.49 6

13.05 6

(A) 12.87 6(E) 15.03 6

12.93 6 19.36 6

(A) 12.95 6(E) 15.89 6

(A) 10.55 6(E) 13.57 6

11.46 6 (A) 21.86 6(E) 21.45 6

39.00 6

Higher optical anisotropy for equatorial orientation compared to axial

Anisotropy is controlled by the nature and position of the substituent and the conformation

Cyclohexyl substituted bisphenyl fragments exhibit lower optical anisotropy than diphenyl propane




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J. Phys. Chem. A., 107(1), 97 (2003)Macromolecules, 36, 2944 (2003)

Results for Optical Anisotropy of Different Chemical Structures

CH3 CH3

CH3 CH3

CH3 CH3 J2x (in units of6)

105.1

80.4

29.1

26.4

methyls on phenyl rings : reduction in anisotropy cyclohexyl ring: dramatic reduction in anisotropy linear relationship between calculated anisotropy and

melt-stress-optical coefficient (experimental)Optical anisotropy : measure of birefringence in meltstate

H3C CH3




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Amorphous Bulk Structure & Properties

Bisphenol A Polycarbonate

Bisphenol CyclohexylPolycarbonate

Calculated Quantities from SimulationsShort range structure: Structure factor (X-Ray, Neutron

scattering) orientations of specificside-groups, packing effects, RDFsSolubility parameter: cohesive energy density (thermodynamics)Free Volume : distribution & Average Free Volume

Goals: Quantify/understand how polymer chemicalatomic structure determines/controls local structure,orientations and intersegmental packingImplications on bulk(macroscopic properties) Gas permeationproperties Polymerchain dynamics Solid thermo-mechanicalproperties melt state rheologicalproperties


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Amorphous Bulk Structure & PropertiesLocal Structure & Thermodynamics

Side-group substitutions by cyclohexyl group leads to increase in free volume Rigid substituents lead to increase in free volume Methyl substituents on phenylene rings lead to decrease in free volume due

to better intermolecular packing Calculated free volume trend is in agreement with experimental

trend on mean fractional free volume


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Birefringence in Bulk Phase

Amorphous polymer Oriented polymer

Processing

Injection molding

Refractive index anisotropy induced is determined by the chemical

structure and conformation of the polymer

Birefringence is the difference in

refractive index of a material in

two different directions perpendicular

to each other.

Birefringence, 'n = n__ nA

High intrinsic birefringence

of BPAPC weakens the

signal to noise ratio and has

a detrimental effect on

the CD/DVD performance


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Birefringence using Molecular Modeling?

Molecular dynamics simulation of stress and birefringence ofPE like modelin the melt state. Cm is calculated in terms of monomer polarizability tensor

and the intrinsic monomer stress tensor,Cm (calcd) = 3.6u10-9 Pa-1

(Gao and Weiner, Macromolecules 1994)

The only polymer investigated is polyethylene No reports on determination of birefringence of polycarbonates

by atomistic simulations

Atomistic simulation of uniaxially stretched PE melt by Monte Carlo methodC78 melt = (3.15 r 0.2) u10-9 Pa-1

C200 melt = (2.35 r 0.1) u10-9 Pa-1

Exptl = 2.2u 10-9 Pa-1 for high Mw, linear, high density PE melts

(Mavrantzas and Theodorou, Macromol. Theory. Simul. 2000)


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Simulation Methodology

Uniaxial deformation of the amorphous polycarbonates in glassy state

z

yx

1. Strain is applied by changing the

cell parameters2. Cell is stretched along X direction

by 0.1 ( % strain)

3. Along Y and Z directions, the cell is

compressed in such a way to keepthe cell volume constant

4. Minimization of the deformed structure

5. Steps 1-4 performed on the new

deformed structure till 100% strain isapplied

6. Steps 1-5 performed by stretching

along Y and Z directions

Deformation performed on threeindependent structures, each stretchedalong X, Y and Z directions for each typeof polycarbonate


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Tensile Stretching of BPAPCStructure Evolution During Deformation

H = 0.2 H = 0.4 H = 0.6 H = 1.0

increase in tensile deformation

undeformed

sample z

y

x

H = 0

Orientation of BPAPC


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Orientation of BPAPC dueto Stretching

OC

O

OPh Ph

Oz-Oz

Cz-OO

Main chain is orienting parallel to thestretching axis

Carbonyl bond vector is orientingperpendicular to the stretching axis

Phenyl ring orientation behaviour is similar inall three PCs

Reorientation of the carbonate group is

different in DMPC and DMBPC


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Orientation of BPAPC dueto stretching

Shift in the population maxima towards lower angles withincrease in strain for vectors along the chain backbone

Reduction in the probability for perpendicular alignment of

the phenyl ring vector with increase in strain

Probability of the angle between the phenyl vector and stretching direction

BPAPC DMPC DMBPC


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Orientation Birefringence

22

0 229

An Nnn M

US D' '

'no is the intrinsic birefringence of the polymer (maximum birefringence of a

perfectly oriented chain), P2! is the repeat unit orientation function 'no can also be calculated using Lorenz-Lorentz equation by knowing the

polarizability anisotropy ('D)

D__DA of the repeat unit for substituted polycarbonates calculated from tensorial

addition of group polarizabilities and geometry of the chain using RIS method

Birefringence, 'n = 'nq P2!


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0.02380.3783.18DMBPC

0.04520.3865.27DMPC

0.0537

(0.05)

0.3815.54BPAPC

'nf'DRU

()

Polycarbonate

Draw ratio (extension) = 2


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Calculated birefringence for BPAPC in good agreement

with experimental values

'n : BPAPC > DMPC > DMBPC

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