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Further Developments in Modeling the Thermal Decomposition of Polymers

Marc R. NydenBuilding and Fire Research Laboratory

National Institute of Standards and TechnologyGaithersburg, MD 20899

marc.nyden@nist.gov

Stanislav I. Stoliarov and Phillip R. WestmorelandDept of Chemical EngineeringUniv. Massachusetts Amherst

Amherst MA 01003-3110

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Molecular Level Understanding of Materials Flammability

Sensing Film

Thermometer Plate

SiO2 Base LayerHeater

Contact Pads

Micro-Hotplate Heating Experiments

Current (mA)

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

Tem

pera

ture

(o C)

0

100

200

300

400

500

600

Col 1 vs Ps # 2 Col 1 vs PS/Clay #1

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Principles of Classical Molecular Dynamics

,,dtdp- =

qH

dtdq =

pH i

i

i

i ∂∂

∂∂

The molecular dynamics algorithm consists of numerical solution ofHamilton’s equations of motion:

where qi, pi, and mi are the coordinates, momenta, and masses of atoms

),,...,,( 321 Ni

2i

3N

i

qqqV + m2p = H ∑

V is defined by The Consistent Valence Force Field:

Vn

Vn

Vn

Vn = V bondnon

pairs

torsion

torsions

angle

angles

bond

bonds

+ + + −∑∑∑∑

5

Morse Potential

Bond Lenth

V

Bond Length

DissociationEnergy

5. Dauber-Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J.; Genest, M.; Hagler, A. T.; Structure, Function and Genetics 1988, 4: 31.

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MD Model of Thermal Degradation in Polymers

The feature that distinguishes MD_REACT from other MD codes is that it allows for the formation of new bonds from freeradical fragments that are generated when bonds in the polymer break and, thereby, accounts for the chemical reactions that play a major role in the thermal degradation process.

This is achieved using the IPC protocol to send bonding information back and forth between MD_REACT and Discover.

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Reactive Force Field

D]))r-(r(-exp-D[1 = V 2eb −α

)-(kS(ij)S(jk) = V 2ea θθθ

)]-(ncos+[1kS(kl)S(ij)S(jk) = V et φφφ

r])

rr2( - )

rr[( = V ji6

*12

*

nbδδ

ε +

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Reactive Force Field

>−

≤=

eb

e

rr)ij(D

)ij(Vrr1

)ij(S

• The atoms participating in covalent bonds become radicals when the corresponding bond orders become less than a pre-determined value.

• The program sorts through all possible bonds between these free radicals and retains those corresponding to the lowest energy subject to the constraints imposed by atomic valence rules.

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Available Reaction ChannelsR CH2

R

R

CHR RR +

RR

HH R

RR

R

H

R

HR

R

R

RR + H2

R CH2 +CH2R

H

+

R

CH3CH3

CH3 CH3

CH3

CH3 CH3CH3

CH4

CH3

CH3

CH3

CH3

CH3

CH3

CH3

Random Scission Beta - Scission

H - TransferElimination

CyclizationCrosslinking

Recombination

CH3

H

CHR

R

CH3

R

CH3

H

RR

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Interface to Discover 95

GUI

Polymerizer

ElectronicStructure

Discover 95

MolecularMechanics

MD_REACT

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Thermal Degradation of PP

pp_3000_pbc_1

Still frame from an MD simulation of the thermal degradation of a modelpolypropylene consisting of 6 polymer chains, each with 21 monomers.

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Thermal Degradation of PP

Figure 1. Major Reaction Channels in the Thermal Degradation ofPolypropylene.

RRecombination

Random ScissionCH3

+R Rn CH2

n'

CH2

R

H

H - Transfer

H

RCH2

Beta - ScissionRCH2R +

CH3

n'Rn

First OrderTermination

CH3CH3 CH3

CH3

R

CH3

CH3 CH3

CH2R

RR

H

RR

CH33

CH3

CH3

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Kinetic Model

)())(][)(2()()(

1 TZTkRTkdt

tdmtm Ii +−=

,)()(2][

0

0

mTkdTkR

t

i=

0

0

0

0 )(

)(

))()((

)()(

mdTk

Tk

mdTkTk

TkTZ

I

p

It

p →+

=

+−=

)()(

)()(2)()(

1TkTk

TZTkdt

tdmtm t

pi

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Simple Kinetic Model of Thermal Degradation Random Scission

Ea = 323 kJ/mol A = 1.5 x 1015 s-1

1/T (K)-10.00032 0.00034 0.00036 0.00038 0.00040 0.00042 0.00044 0.00046

ln(k

(T))

-11

-10

-9

-8

-7

-6

-5

Molecular dynamics dataRegression Lineslope = -38871 Kintercept = 7.308

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Simple Kinetic Model of Thermal Degradation Propagation

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Simple Kinetic Model of Thermal Degradation Propagation

Ea = 77 kJ/mol A = 5.6 x 1012 s-1

1/T (K)-14.8e-4 5.0e-4 5.2e-4 5.4e-4 5.6e-4 5.8e-4 6.0e-4 6.2e-4 6.4e-4 6.6e-4 6.8e-4

ln(k

(T))

-5

-4

-3

-2

Molecular dynamics dataRegression Lineslope = -9263 Kintercept = 1.720

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Simple Kinetic Model of Thermal Degradation Termination

Ea = 163 kJ/mol A = 3.1 x 1015 s-1

1/T (K)-14.8e-4 5.0e-4 5.2e-4 5.4e-4 5.6e-4 5.8e-4 6.0e-4 6.2e-4 6.4e-4 6.6e-4 6.8e-4

ln(k

(T))

-6

-5

-4

-3

-2

-1

Molecular dynamics dataRegression Lineslope = -19563 Kintercept = 8.053

TSimple Kinetic Model of Thermal

DegradationRate of Mass-loss from Degrading Polypropylene

)237528exp(103.5)()(

1 12

RTx

dttdm

tm−−=

Experimental Values:

Ea = 220 kJ/mol A = 19 x 1012 s-1

Bockhorn et. al., Journ Anal. and Appl. Pyrolysis 46, 1998, 1

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New Features of MD_REACT• A new mechanism that allows simultaneous rupture and

formation of bonds was introduced.• Every type of chemical reaction that involves rupture and/or

formation of σ and/or π bonds (with the exception of conjugated and aromatic systems) was included.

• All the chemical transformations are treated in the unified fashion based on the competition between energies of interatomic interactions. This approach results in more realistic model of reactions involving π bonds and eliminates the necessity of usage of special “effective” potentials for β- scission reactions.

• The CVFF forcefield is updated to accommodate decomposition of oxygen-containing polymers (in particular, PMMA). The new bond dissociation energies are obtained from CBS-QB3 calculations performed on model molecules.

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New Algorithm of MD_REACTThe following cycle is performed at every time step:

DISCOVER Integrator of Equatons of Motion

Bond-formationModule

Potential Energy and Gradient Calculation

Module

IPC

IPC

♦Effective bond order of each bond iscomputed as:

♦If [BO < Dissociation Criterion] then:BO = 0atom type = radical (R)

EnergyonDissociatiVBO bond=

DISCOVER Integrator of Equatons of Motion IPC

Bond-dissociationModule

Bond-formationModule

♦All possible covalent interactionsbetween radicals are examined.

♦The lowest energy bonds are retained:

number of bonds = valency + 1

♦If [BO > Disociation Criterion] for all the valent bonds of a radical then:

radical = regular atom type

number of bonds = valency

DISCOVER Integrator of Equatons of Motion IPC

Bond-dissociationModule

Potential Energy and Gradient Calculation

Module

For every covalent interaction with BO < Dissociation Criterion

∑∑×+ V + VBO VV torsion

torsionsangle

angles

bond =corrected

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New Algorithm of MD_REACTThe following cycle is performed at every time step:

DISCOVER Integrator of Equatons of Motion

Bond-dissociationModuleIPC

IPC

Bond-formationModule

Potential Energy and Gradient Calculation

Module

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MD Simulations

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Thermal Degradation of PMMA

pmma_2000K

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Thermal Degradation of PMMA

[CH2 monomer

3

CH3

C O

C ]

O CH33

n CH2C

CH33OC OCCH33

R. .+CH3

C O

O C3

H3

R’

CH2C=

CO

O

C

3

H3

R’ CH2

+

CH3

.

CHC=CH2

CH

.

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BE’s in MA and MMA

CH3O

OC

R

CH3

CH2C91.5

78.779.4

100.3

86.9

195

99.9

CH3O

OC

R

H

CH2C R79.7

87.5

92.5R

99.9

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Thermal Degradation of PMA

pmma_2000K

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Conclusions• The differences in the thermal degradation

chemistries of PMMA and PMA appear to be due to higher initiation temperatures required for PMA.

• Molecular modeling can be useful tool for the investigation of thermal degradation and materials flammability and the development of new and more fire resistant materials. This role will continue to expand as advances in computer technology make it possible to extend the range of applicability of molecular modeling to more complex systems.

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AcknowledgementsMD_REACT was developed as part of a CRADA betweenNIST and Accelrys Inc. (CN 1241)

Partial support for this work was provided by the FAA underInteragency Agreement DTFA0003-92-Z-0018 monitored byDr. Richard E.Lyon

MOLECVIEW was written by Dr. Glenn Forney (BFRL/NIST)

Dr. Robert Bohn (ITL/NIST) performed CBS-QB3 calculationson MMA