Computer Modeling Studies of Polymer Photooxidation and Stabilization

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Computer Modeling Studies of Polymer Photooxidation and Stabilization A. C. S O M E R S A L L and J. E. G U I L L E T Department of Chemistry, University of Toronto, Toronto, Canada M5S 1A1

A computer model has been developed which can generate realistic concentration versus time profiles of the chemical species formed during photooxidation of hydrocarbon polymers using as input data a set of elementary reactions with corresponding rate constants and initial conditions. Simulation of different mechanisms for stabilization of clear, amorphous linear polyethylene as a prototype suggests that the optimum stabilizer would be a molecularly dispersed additive in very low concentration which can trap peroxy radicals and also decompose hydroperoxides. The oxidative deterioration of most commercial polymers when exposed to sunlight has restricted their use in outdoor applications. A novel approach to the problem of predicting 20-year performance for such materials in solar photovoltaic devices has been developed in our laboratories. The process of photooxidation has been described by a qualitative model, in terms of elementary reactions with corresponding rates. A numerical integration procedure on the computer provides the predicted values of all species concentration terms over time, without any further assumptions. In principle, once the model has been verified with experimental data from accelerated and/or outdoor exposures of appropriate materials, we can have some confidence in the necessary numerical extrapolation of the solutions to very extended time periods. Moreover, manipulation of this computer model affords a novel and relatively simple means of testing common theories related to photooxidation and stabilization. The computations are derived from a chosen input block based on the literature where data are available and on experience gained from other studies of polymer photochemical reactions. Despite the problems associated with a somewhat arbitrary choice of rate constants for certain reactions, it is hoped that the study can unravel some of the complexity of the process, resolve some of the contentious issues and point the way for further experimentation. The Computer Model A complex chemical mechanism can be expressed as a system of NR elementary (fundamental) chemical reactions comprising NS different 0097-6156/85/0280-0211S07.00/0 © 1985 American Chemical Society Klemchuk; Polymer Stabilization and Degradation ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

212

POLYMER STABILIZATION AND DEGRADATION

chemical species, {Y^}, i = l , N S . The resulting mechanistic scheme takes the concise form given by v.. Y . = 0

;

j =1 , NR

i=l

(1)

in which the stoichiometric coefficients, vy , are positive for product and negative for reactant species. Furthermore, each reaction j (j = l , NR) is characterized by a rate constant k j . From the molecularity of the elementary reactions comprising the reaction scheme it is then possible to write explicit expressions for the concentration-time d e r i v a tives of all chemical species, Y j , as shown by Equation 2. In this (2) equation the product II includes only those I - values for reactant species (vjj negative). The time behavior of a derived reaction scheme can be obtained by integration of the resulting system of ordinary differential equations ( O D E ) , given a specified set of initial conditions. This yields explicit concentration-time data for all species. Generally speaking, the system of ODE is nonlinear, necessitating numerical solution. Furthermore, the rates of the individual reactions in the usual kinetic scheme commonly vary by many orders of magnitude, giving rise to the so-called stiff system of O D E . Attempts to employ classical integration algorithms require limiting the integration step size so as to keep pace with the fastest transients in the system. This has the undesirable consequence that extremely small step sizes are taken and exorbitant amounts of computing time are required to complete the problem. Clearly, for the usual chemical kinetics p r o b lem, integration algorithms especially designed to tackle a stiff system of ODE must be employed. For this work, the original Gear routine (1) and its various modifications (2) have been employed in the simulation package. Essentially, the algorithms are multi-step predictorcorrector methods utilizing the backward differencing formulation as applied by Gear with automatic error-controlled, order-step size selection. To validate our numerical procedure, the data base given for the cesium flare system (which is becoming a standard in the literature) was u s e d , and the curves generated were identical to those of Edelson (3) for the same system. T h e excellent agreement between predicted and actual rate curves showed that the program itself (irrespective of the data base) performs in a satisfactory manner. A similar computational modelling approach has been shown to be useful, for example, in studying the mechanism of low-temperature o x i dation of alkanes (4), pyrolysis of alkanes (5-7), other gas-phase r e actions (8), the formation of photochemical smog (9,10), and peroxide decomposition (11), among others. It is not uncommon to begin with all possible species and by permutation and combination derive a complete set of reactions, and then eliminate a subset by chemical

Klemchuk; Polymer Stabilization and Degradation ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

16.

SOMERSALL AND GUILLET

Computer Modeling Studies

213

intuition or by sensitivity analysis. Polymer photooxidation with over 40 different species involved is too complex a process for such an a p proach. O u r model is built up sequentially from the basic chemistry of the system and we presume that it approaches the real process in its essential elements. The Reaction Scheme A s a starting point for this computational approach to the photooxidative process in polymeric materials, we have examined the simplest prototype: neat, amorphous, linear polyethylene above its glass t r a n sition temperature. In practice, polyethylene is partially crystalline, and contains truly linear olefins, vinylidene groups, ketones and h y droperoxides in addition to the short side chains. Much insight has already been gained into the photooxidation process by conventional experimentation on such polymers (12,13), yet several important questions still remain. Several good reviews have appeared recently (14-16). A mechanistic scheme has been devised which includes most, if not all of the apparent non-trivial elementary processes. T h e 56 relevant reactions and their corresponding rates are listed in Table I and are shown schematically in Scheme I. Initiation. Three types of initiation have been considered in the model: the photolytic cleavage of ketones and/or hydroperoxide and some general fortuitous generation of alkyl radicals (such as thermal C - H homolysis, ultrasonics, mechanical treatment, ionizing radiation, e t c . ) . More often the Norrish type I cleavage of ketones has been used as standard, assuming initial ketone concentrations of 10"^M ketone. The Norrish type II process is v e r y important for chain scission but no participation is presumed in the initiation step for the suspected b i radical intermediate. Although " p u r e " saturated polyolefins should not be expected to absorb beyond 2000 the absorption m the far U V tail in the atmospheric sunlight spectrum around 3000 A has commonly been attributed to the low concentrations of ketone and/or h y d r o p e r oxide groups introduced in the commercial polymers during processing. No consideration has been given to other proposed initiation processes such as absorption by dyes, pigments, catalyst residues, oxygen a d ducts (18), charge-transfer or polynuclear aromatics absorbed from polluted urban atmospheres (19). The possibility of energy transfer from excited ketones leading to photosensitized decomposition of h y d r o peroxide (20) has also been included. The extinction coefficient for the hydroperoxide is very low but the quantum yield of cleavage is very near to u n i t y . The quantum yield for ketones is low for carbonyl incorporated in the backbone of the polymer chain, but is much higher when at a chain end or branch (21). The radicals generated are p r e sumed to have free access to oxygen, and no special cage effect in the bulk polymer has been assumed. A l l of the rates for the initiation r e actions follow directly from the absorption spectra and known photochemical quantum yields. T h e standard light intensity employed refers to the average solir intensity which is one-third of the typical peak value of 0.15 E m " h incident on a 1 mm film. 2

_ 1



214

Table I.

Data Set: Photooxidation Reaction Scheme and Activation Parameters

Reaction m a t r i x 1. 2. 3. 4. 5. 6.

Ketone — > KET*

2

0.70

x 10

0.59

x 10

0.80

x 10

8. 9.

SMKET*

Ref.

36

Ref.

37

Ref.

36

8.5

Ref.

38

2.0

Ref.

36

1U

17.0

Ref.

39

1U

17.0

Ref.

39

17

15

0.56

x 10

0.70

x 10

ROOH — >

2.0

8

SMKET*

> SMR0

SMKET* — >

0

4.8

9

Alkene + SMKetone

SMKetone — >

R0

0

+ CO

2

2

9

0

+ CH CO 3

0.32 7.

9

+ SMRCO

-> S M R 0

KET* —>

Remarks

KET*

>SMR0

SMRCO

E kcal/mol

A

x 10

13

Alkene + Acetone 0.56

x 10

0.13

x

9

RO + OH

+ RH — >

ROOH + R 0

10

9

0

10

10.

11. 12.

SMR0

0

^

+ RH

SMROOH — > SMRO + RH

0.10 x 10 > SMROOH + R 0 ^ m 0

0.10

x 10

0.13

x 10"

SMRO + OH -> SMROH + R 0

9

0

0

in

13.

RO + RH

-> ROH + R 0

0.16

x 10

1U

6.2

Ref.

39

0.16

x 10

1U

6.2

Ref.

39

9


16.



Table

I,

14.

RO

Continued

—>

SMR0

+ Aldehyde

2

0.32 15.

K E T * + ROOH

x 10

S M K E T * + ROOH

x 10

SMRCO + 0

10

x 10

10

2

SMRCO + RH — >

R0

x 10"

39

11.6

Ref.

40

11.6

Ref.

40

4

9.6

Ref.

41

7.3

Ref.

42

+ Aldehyde

9

^

19.

Ref.

> SMRCOOO 0.80

18.

17.4

> SMKetone + RO + OH 0.25

17.

16

> Ketone + RO + OH 0.25

16.

215

in

0.10 x 10 > SMRCOOOH + R 0

SMRCOOO + RH

0

10

0.10 20.

SMRCOOOH — > SMRCOO

> SMR0

+ C0

2

x 10"

cf.

36,

37

0

9

2

0.10 22.

17.0

1U

SMRCOO + OH 0.13

21.

x 10

SMRCOO + RH — >

Acid + R 0

OH + RH

0.10 + Water

x 10

6.6

15

Ref.

43

0

10

23.

-> R 0

0

^

24.

C H C O + RH

> R0

Q

0

x 10

0.10 x 10 + CH CHO

17.0 10 1U

CH CO + 0 Q

6

—>

0

1

0.10 CH COOO

Q

Q

6

CH COOOH —> Q

0.10

CH COO 3

+

RH

7.3

Ref.

42

9.6

Ref.

41

x 10

10

1U

9

17.0

cf.

36,

37

C H C O O + OH Q

0.13 28.

44

i n

0.89 x 1 0 > CH COOOH + R 0

6

27.

Ref.

Q

6

C H C O O O + RH

0.5

37

10

x 10

iU

26.

36,

Q

1

25.

cf.

x 10

> CH COOH + R 0 3

0.10

0

y

x 10 * 1

9

6.6 Continued

Ref.

43

on next


page

216


Table I.

29. 30. 31.

Continued

KET*

-> Ketone

SMKET* KET* + 0

0.10 x 10

9

0

0.10 x 10

9

0

> SMKetone —>

2

Ketone + S 0

2

0.89 x 1 0 32.

SMKET* + 0

> SMKetone + S 0

2

1 4

9.6

Ref. 41

1 4

9.6

Ref. 41

11.6

Ref. 39

15.3

Ref. 39

9

15.0

Ref 45

9

2.1

Ref. 38

8.9

Ref. 46

2

0.89 x 1 0 33.

R 0 + R0 2

—>

2

ROH + Ketone + S O 2 0.25 x 1 0

34.

R 0 + ROH ^

35.

HOO + RH

1 0

> ROOH + Ketone + HOO m

9

0.10 x 10 > HOOH + R 0

2

0.32 x 10 36.

HOO + R 0

> ROOH + S 0

2

2

0.32 x 10 37.

R 0 + Ketone

> ROOH + Peroxy CO

2

0.13 x 10

5

38.

Peroxy CO + RH

> PER OOH + R 0

39.

0.10 x 1 0 PER OOH — > PER O + OH

0.13 x 1 0 " 40.

PER O + R 0

2

—>

R0

2

+ ROOH — >

R0

0

+ SMROH

^

0 Ref. 40

11.6

Ref. 39

> ROOH + Aldehyde + HOO 1n 0.10 x 10 15.3 > ROOH + SMRCO

Ref. 39

ROOH + Ketone + OH 8

1

43.

RO

+ Aldehyde

c f . 36, 37

11.6

1 0

0.25 x ID 42.

9

17.0

DIKetone + ROOH 0.25 x 1 0

41.

2

1 0

0.25 x 1 0

i U

11.6

Ref. 40


16.



Table

44. 45. 46. 47. 48. 49. 50. 51. 52.

53. 54.

I.

Continued

R0

S 0

2

2

S0 R0

+ R0

—>

2

2

2

56.

Ref.

47

9

11.6

Ref.

39

x 10

9

11.6

Ref.

39

x 10

8

5.2

Ref.

39

x 10

0.20

x 10

14

0.16

x 10

0.16 0.16

16.0

0

5

> ROOH

> Ketone + Heat

ROOH + QD

0.80

x 10

13

9.5

Ref.

48

0.80

x 10

13

9.5

Ref.

48

0.63

x 10

15

35

Ref.

49

0.63

x 10

15

35

cf.

52

x 10

15

35

cf.

52

0.63

x 10

15

35

cf.

52

0.63

x 10

15

35

cf.

52

> PRODS R O ' + OH *

SMROOH — >

SMRO + OH

SMRCOOOH — > CHgCOOOH — > PER OOH — >

- SMProduct

10.0

0.63

12

> ROOH + Q

KET* + Q l

ROOH — >

39

x 10

> Branch

+ Alkene

+ QH

Ref.

0.38

> ROOH

+ Alkene

2

S0

°2

+ Alkene

2

SMR0 R0

-> ROOR +

2

SMRCOO + OH 0.63

55.

217

C H C O O + OH 3

PER O + OH

= product from chain cleavage, SO

=

O



Initiation

+

RH

2

Q

-> RO

fast hv -I

KETONE

-> KET*

"

0

R

' *

R

>

1

ROOH*

V e r

f a S t

y ROOH + Other products k - i o

1

- 10 "

3

Scheme I . Polyethylene photooxidaton scheme.


16.



219

Propagation. The key radical in the propagation sequence is the p e r oxy radical formed by the addition of oxygen to alkyl radicals. Molecular oxygen 0 2 ( E g ) found in nature is paramagnetic, with two parallel-spin electrons, giving it the characteristics of a biradical. A s a consequence the oxygen molecule combines very rapidly with free radicals to form the peroxy radicals (22). The solubility of oxygen in amorphous polyethylene is low (10"^M) but practically constant due to the steady diffusion of oxygen from the atmosphere to replenish what is consumed during oxidation over long periods of time. T h u s we have assumed that all carbon-centered radicals will inevitably add oxygen to form peroxy radicals so we have incorporated this step directly in those reactions involving alkyl radical products, to simplify the computation (23) . 3

The key propagation step is the abstracton of a hydrogen atom by the peroxy radical to generate a new peroxy radical and a h y d r o p e r oxide group. Alkoxy radicals and hydroxy radicals formed by cleavage of the hydroperoxide will also abstract a hydrogen atom to produce further peroxy radicals. These reactions are well studied in solution (24) and the same rates have been assumed in our model. Other r a d i cals formed in Norrish type II chain scission and subsequent reactions can also abstract hydrogen atoms to generate peroxy radicals. R e arrangement of alkoxy radicals in the $-scission process leads to aldehydes, whereas thermal cleavage of intermediates leads to small molecule fragments and products such as carbon dioxide and formaldehyde. Acids are formed in the model via the addition of oxygen to acyl r a d i cals, followed by hydrogen atom abstraction, then cleavage of the r e sulting peroxy acid and a further H-atom abstraction. Esters would develop from the condensation of acid with the alcohols formed by H atom abstraction of alkoxy radicals. In linear amorphous polyethylene, all the C - H bonds are presumed to be secondary and on the backbone of the polymer chains, with n e glect of the few chain ends. The rates of hydrogen abstraction by various radical species are taken from similar processes in solution, but subsequent processes are modified to allow for the higher internal viscosity of the medium. Termination. Just as peroxy radicals are key to the propagation sequence , so the bimolecular recombination of these radicals is the major termination process in the unstabilized polymer. The existence of an intermediate tetroxide has been established in solution (2j>). Several factors influence the competitive pathways of subsequent decomposition to form alcohols, ketone and singlet oxygen or to form alkoxy radicals which can couple before separation from the reaction center to form a peroxide. This latter process is a route to crosslinking in the case of polymeric peroxy radicals. The effect of steric control, viscosity and temperature have been studied in solution. However, in the solid phase the rates of bimolecular processes which require the mutual diffusion of the reactant groups will be limited by the diffusion process. A s a standard, we have assumed a value close to that determined from o x y gen absorption (26) and by ESR spectra (27) for oxidized polypropylene films.


220


For those bimolecular reactions that do not require mutual diffusion such as H-atom abstraction, in which one reactant is a virtual solvent, the rates are similar to solution values. The peroxy radical may react with many other species and in some cases the rate constants are even lower than the diffusion rate and hence the value is not limited in that way. Modelling Photooxidation Photooxidation of amorphous polyethylene. Figure 1 shows the general behavior predicted for exposure to different intensities of UV l i g h t . Assuming initiation by 10"^ M ketone groups and constant ambient oxygen pressure, the model shows that the C - H bonds become oxidized slowly at first and then more rapidly later o n . A 5% C - H bond (1% monomer units) oxidation level has been used to assign a point of failure which is within the range one would anticipate for marked change in mechanical properties. Under typical conditions, the time to failure (if) of unstabilized polyethylene would be three to four months in temperate climates and shorter in regions of high solar intensity. Product formation and other observations are consistent with the authors' e x perimental knowledge of polyethylene weathering (28). Table II summarizes the concentration of all chemical species in the model at the chosen time of failure. The major products are ketones, h y d r o p e r oxides, alcohols and water. The only anomaly is the relatively high concentration of hydroperoxide which the authors were unable to eliminate in their model predictions and which may point to the inadequacy of experimental methods for monitoring - O O H groups in oxidized films. The time to failure was plotted as a function of the intensity of light to find the relationship that T J « \~i one would expect for photochemical initiation producing two radical species. 9

a

s

Also, one finds that the behavior is almost unaffected by both the initiator type and concentration (Figure 2). This is not surprising for an autocatalytic process since the result is dominated by relative rates of propagation and termination. Two interesting conclusions can be drawn. F i r s t , there has been much controversy in the literature about the relative importance of the various possible mechanisms for initiation (ketone groups, h y d r o p e r oxide, catalyst residues, singlet oxygen), but the controversy is practically irrelevant if initiation does not much influence the course, rate or extent of photooxidation. Second, in terms of stabilization, minute amounts of photoinitiation will lead to practical failure so that the purification of polymers to minimize the initiating residue is not a practical alternative for stabilization. Both points underline the value of this approach to the understanding of the complex photooxidation process. Figure 3 shows the dependence of the time to failure on the rate of propagation, i . e . , the rate of hydrogen abstraction from the polymer backbone. The log-log plot is linear with a negative slope less than u n i t y . The rate of abstraction of t C - H as in branched polyethylene and ethylene copolymers would only be a factor of two to three higher than for C - H in linear polyethylene. The time to failure in these S


16.



1

CM

i

r

221

1-

i

o

—

—i°2__ fa/lure

•o c 0 -Q

1 i

0.8

o

6 c o 0.4

o E

\\ \\

\\ (f

(Q)\

\

2

i Time,

Figure 1. (c) h v / 3 ; hv x 10 .

i

i

months

Photooxidation of unstabilized P E : (a) hv/10; (b) h v / 2 ; (d) hv average daylight; (e) hv x 5; (f) hv x 10; (g)

2

-4 log

-2

0

[initiator]

Figure 2. Photooxidation of unstabilized P E : tion of initiator type and concentration.

time to failure as a func-


222

POLYMER STABILIZATION AND DEGRADATION Table II.

Concentration of A l l Species, Initially and at Failure (5% C - H Oxidation) Concentration

Species

Initial

1.

Ketone

0.1 x 10

2.

KET*

3.

SMR0

4.

Final (5% C - H oxidation) 0.39

X

10

—

0.26

X

lO"

—

0.20

X

l S

1

8

2

33.

HOO

0.20

X

i

Computer Modeling Studies of Polymer Photooxidation and Stabilization

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