polypropylene stabilization by hindered phenols e kinetic aspects

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Polymer Degradation and Stability 96 (2011) 1e11

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Polymer Degradation and Stability

journal homepage: www.elsevier .com/locate /polydegstab

Polypropylene stabilization by hindered phenols e Kinetic aspects

Emmanuel Richaud*, Bruno Fayolle, Jacques VerduArts et Metiers ParisTech, CNRS, PIMM, 151 bd de l’Hôpital, 75013 Paris, France

a r t i c l e i n f o

Article history:Received 28 September 2010Received in revised form3 November 2010Accepted 9 November 2010Available online 18 November 2010

Keywords:PolypropylenePhenolic antioxidantKinetic modelling

* Corresponding author.E-mail address: [email protected]

0141-3910/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.polymdegradstab.2010.11.011

a b s t r a c t

This article deals with polypropylene stabilization by hindered 2,6-di-tert-butylphenols. Two aspects aremainly considered: the influence of stabilizer structure, of its concentration and temperature oninduction period duration through a literature compilation completed by results obtained on PP samplesstabilized by Irganox 1010 in conditions in which physical loss was negligible. Results show that theinduction period duration is almost proportional to the phenol concentration and that the proportion-ality ratio is almost independent of the stabilizer structure in the investigated phenol family. A unique setof kinetic parameters can be therefore used to model the kinetic behaviour of all the family members.The kinetic approach can be more or less complex depending on the number of secondary processestaken into account. The results of simulations indicate that a two steps process allows generation ofa kinetic behaviour in good agreement with experimental trends regarding effects of both stabilizerconcentration and temperature on induction time.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The framework of this study is the development of a reliablelifetime prediction methods for polymer ageing by a non-empiricalway, which requires the resolution of a system of differentialequations derived from a mechanistic scheme. However, schemesfor radical chain oxidation reach complexity level for which there isno analytical solution. Numerical methods are indeed the way insuch cases but except in rare attempts [1,2], they were not used inthis filed before the beginning of 2000’s. Nevertheless, their effi-ciency was demonstrated in the case of unstabilised hydrocarbonpolymers such as polyethylene [3,4], polypropylene [5,6] or unsat-urated elastomers [7e9]. It remains now to incorporate stabilizationeffects in the model but there are at least two reasons to envisagethe failure of this attempt:

- The well-known important role of transport phenomena instabilizer performance [10,11].

- The high complexity of stabilization mechanisms.

The difficulties linked to stabilizers physical loss can be solvedby incorporating transport or loss terms in differential equations forstabilizers consumption [12,13], and literature values taken fromliterature for diffusion or volatility [14,15].

(E. Richaud).

All rights reserved.

The increased complexity of mechanistic schemes involvingstabilizer reactions is not a problem from a numerical point of view.Indeed, schemes with 15e20 equations have been successfullysolved for unstabilised unsaturated elastomers [7e9]. Hence, themain difficulty is not the ignorance of stabilization mechanisms butrather the wide variety of mechanisms reported in the literatureand the lack of consensus on their relative importance.

We have schematically the following alternative:

If all the proposedmechanisms are of comparable importance,the complexity of stabilization mechanism cannot be easilyreduced in the kinetic analysis. The probability, for two distinctstabilizing mechanisms, to have a common set of kineticparameters values, is low and each polymer-stabilizer couple isa particular case which requires a separate study.If a relatively wide stabilizer family displays common kinetic

features, then it becomes possible to envisage a reduction of thecomplexity of mechanistic schemes and the elaboration ofa unique kinetic model valid for all the members of theconsidered stabilizer family.

This work aimed to determine if 2,6-di-tert-butylphenolsconstitute a homogeneous family from a kinetic point of view,which needs first to find a set of criteria defining a stabilizer familywhich could be:

Induction time duration: This is the most interesting quantitybecause it is under the direct influence of stabilizer action and it

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E. Richaud et al. / Polymer Degradation and Stability 96 (2011) 1e112

is not very sensitive to experimental parameters such as samplethickness, sensitivity of characterization method (FTIR, oxygenabsorption, chemiluminescence, etc.). A given kinetic modelof stabilization must simulate at least the existence of aninduction period and the changes of this latter with stabilizerconcentration.Stabilizer depletion kinetics: the stabilizer is consumed during

induction period. The model must therefore simulate stabilizerdepletion curves.

Temperature effect: using physically reasonable activationenergies for the elementary reactions, the model must simulatethe global temperature effect on the induction period andstabilizer consumption rate even if the global behaviour doesnot obey Arrhenius law.

Using these hypotheses, it is now possible to check mechanisticschemes involving stabilizer, starting from the simplest one andadding complexity step by step. For this purpose, 2,6-di-tert-butylphenols constitute the most common stabilizer family. Thereis a wide consensus on the nature on the primary stabilizationevent consisting in scavenging peroxy radicals:

POO� þ AH/POOHþ A� kS1

The simplest approach here consists in assuming that theresulting radical A� is unable to propagate oxidation, which is true,and is stable [16,17], which is questionable.

It has been soon established that phenoxy radicals isomeriseinto cyclohexadienyl radicals able to participate to a wide variety ofreactions among which are dimerisation or polymerization, reac-tions with phenoxy radicals, with oxygen, or scavenging anotherperoxy radical [18e21].

The relative importance of these processes depends on thenature, the polarity and the steric hindrance of para-substituentgroups. Among these secondary processes, many have no influenceon stabilization. In contrast, scavenging of peroxy radicals couldsignificantly contribute to the stabilization effect and cannot beignored. What is their real importance? The answer to this questionwill be the aim of the second step of our approach.

2. Experimental

2.1. Materials

The stabilizer used was Irganox 1010 (denoted by AO1 in Fig. 1and AH in the kinetic analysis) supplied by Ciba SC. Samples wereprepared by a two-step procedure adapted from previous work[22,23]:

A commercial PP sample (of which the characteristics aredetailed elsewhere [24]) was purified by dissolution (polymer

0.00

0.10

0.20

0.30

0.40

0.50

0 500 1000 1500 2000 2500time (h)

[PC

=O

](m

olkg

-1)

a

Fig. 1. Oxidation kinetics at 130 (a) et 100 �C (b) for pure PP (>), PP þ 0.05

weight w2 g) into refluxing 1,2-dicholorobenzene (200 ml).After 2 min at refluxing temperature (c.a 180 �C), solution washot filtered to eliminate impurities. Methanol was dripped toselectively precipitate PP. The PP pellets were washed withethanol and dried.Antioxidant was incorporated into PP by pouring a solution of

Irganox 1010 in THF on the purified PP beads under N2 flow toquickly evaporate the solvent (mAH being the mass of addedantioxidant). The stabilized PP was pressed under 15 MPa at180 �C during 20 s. Thickness of obtained films was of the orderof 70 mm, and can be considered as low enough to neglectoxidation thickness gradients due to the kinetic control byoxygen diffusion.

Irganox 1010 weight ratios were converted into antioxidantgroup concentration (denoted by [AH]) in amorphous phase by theformula:

½AH� ¼ fAH1

1� xC,mAH=MAH

mPP=dPP(1)

- fAH being the antioxidant functionality, i.e. the number ofphenol groups per molecule.

- xC being the crystallinity ratio of films on the order of 0.5.- mAH andmPP being the respective masses of antioxidant and PP.- MAH being the molar mass of antioxidant.- dPP being the density of PP (0.95 kg l�1).- xAH being the antioxidant weight ratio ranging from 0 to 0.5%,which means that melting transition divides the stabilizerconcentration in amorphous phase by 2.

Some comparisons will be done with published data for PPstabilized with various other hindered phenols (see Resultssection).

2.2. Exposure conditions

Samples were exposed in air under atmospheric pressure at 80,100 and 130 �C.

2.3. Samples characterization

FTIR spectrophotometry was performed using a Nicolet Impact410 spectrophotometer driven byOmnic 3.1 software. 32 scanswereaveraged to obtain a 4 cm�1 resolution. The IR carbonyl absorbanceswere converted to concentrations using BeereLambert’s law witha molar absorptivity of 300 l mol�1 cm�1 at the peak maximum(1712 cm�1).

0.00

0.10

0.20

0.30

0.40

0.50

0 1000 2000 3000 4000 5000time (h)

[PC

=O

] (m

olkg

-1)

b

% (-), PP þ 0.1% (A), PP þ 0.2% (:) and PP þ 0.5% Irganox 1010 (C).

E. Richaud et al. / Polymer Degradation and Stability 96 (2011) 1e11 3

3. Results

Kinetic curves at 130 �C and 100 �C are presented in Fig. 1.Results obtained at 80 �C were presented elsewhere [25]. It is wellknown that kinetics of thermal oxidation of hydrocarbon atmoderate temperature are characterized by an induction periodafter which one observes hydroperoxides, alcohols and carbonylbuild-up, oxygen uptake and mass variation, chemiluminescence

Table 1Chemical structure of the stabilizers.

Molecule Structure

AO1C CH2 O C

O

CH2 CH2

AO2H37C18 O C

O

CH2 CH2

AO3

R

RN

N

N

O

O O

R

CH2R =

AO4CH2

R

CH3

R

CH3

R

CH3

R =

AO5CH3

OH

AO6

O

NHOH

AO7

O

OOH

AO8

O

NH NH

O

OH

emission and exothermal heat flow. Induction period durations areof the same order of magnitude whatever the measured quantity[26,27]. Starting from this observation, we have gathered data ofvarious mixtures PP þ phenolic antioxidant (see Table 1) allbelonging to the 2,6-di-tert-butylphenol family [28e36] for sampleof comparable thickness.

The induction period durations have been plotted againstconcentration of phenolic group (given by Eq. (1)) for the eight

MAH (g mol�1) fAH

OH

41176 4

OH530 1

OH783 3

OH774 3

220 1

2

636 2

2

638 2

OH 568 2


temperatures at which data were available for distinct stabilizers(see Fig. 2). The observed scatter is not surprising for sucha compilation since results differ by the sensitivity of measure-ment technique, mode of sample preparation, structure andcomposition of polypropylene (crystallinity, catalyst used forpolymerization.).

We have then calculated the “Stabilizer Efficiency factor”(denoted by SE) defined by:

SE ¼ tind � tind0½AH0�

(2)

where:

0.0E+00

1.0E+04

2.0E+04

3.0E+04

4.0E+04

5.0E+04

6.0E+04

0 0.002 0.004 0.006 0.008 0.01

[AH] (mol l-1)

t ind

(h)

PP + AO2

pure PPa b

0.0E+00

1.0E+03

2.0E+03

3.0E+03

4.0E+03

5.0E+03

6.0E+03

7.0E+03

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

[AH] (mol l-1)

t ind

(h)

pure PPPP + AO1PP + AO2PP + AO3

c

e

d

0.0E+001.0E-012.0E-013.0E-014.0E-015.0E-016.0E-017.0E-018.0E-019.0E-01

0 0.002 0.004 0.006 0.008 0.01

[AH] (mol l-1)

t ind

(h)

PP + AO1

PP + AO2

pure PP

g h

0.0E+00

1.0E+03

2.0E+03

3.0E+03

4.0E+03

5.0E+03

6.0E+03

7.0E+03

0 0.01 0.02 0.03 0.04

tdni

)h(

[AH] (mol l -1)

pure PPPP + AO1PP + AO2PP + AO3

Fig. 2. Compilation of induction time duration against stabilizer concentration at 40 �

- tind and tind0 are respectively the induction periods values forstabilized polymer and unstabilised one.

- [AH]0 is the initial stabilizer concentration of a sample of whichinduction period value is tind.

The average values and the corresponding standard deviations arereported in Table 2. These results call for the following comments:

Available standard deviation values are significantly lowerthan SE average values. Considering the diversity of the possiblesources of dispersion (initial stabilizer purity, loss during samplepreparation, effect of PP impurities or pre-oxidation), it seemsthat SE is a common characteristic of all the antioxidants under

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

3.0E+04

0 0.002 0.004 0.006 0.008 0.01

[AH] (mol l-1)

t ind

(h)

PP + AO1PP + AO2pure PP

0.0E+00

1.0E+03

2.0E+03

3.0E+03

4.0E+03

5.0E+03

6.0E+03

7.0E+03

0 0.002 0.004 0.006 0.008 0.01

[AH] (mol l-1)

tind

(h)

PP + AO1PP + AO2PP + AO3PP + AO4pure PP

0.0E+00

2.0E+02

4.0E+02

6.0E+02

8.0E+02

1.0E+03

1.2E+03

1.4E+03

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

[AH] (mol l-1)

t ind

(h)

PP + AO1PP + AO2pure PP

f

0.0E+00

2.0E+02

4.0E+02

6.0E+02

8.0E+02

1.0E+03

1.2E+03

1.4E+03

1.6E+03

0 0.002 0.004 0.006 0.008 0.01 0.012

[AH] (mol l-1)

t ind (

s)

pure PP

PP + AO1

PP + AO6

PP + AO7

C (a) 60 �C (b), 80 �C (c), 100 �C (d), 120 �C (e), 130 �C (f) 190 �C (g), 200 �C (h).

Table 2SE parameter for PP films (or model hydrocarbon) stabilized AO1 . AO8 at various temperatures. * corresponds to squalene oxidation.

T (�C) tind0 (h) AO1 AO2 AO3 AO4 AO5 AO6 AO7 AO8

200 0.015 3.5 � 0.4190 (*) 0.002 10.2 � 1.6 9.4 � 1.2 11.8 � 2.6 21.0 � 7.2190 0.003 9.3 � 1.0 9.9 � 2.1 4.8130 5 (6.0 � 2.6)�105 7.9 � 105

120 15 (5.3 � 1.1)�105 (2.4 � 0.5)�105 6.8 � 105 9.8 � 105

100 100 (5.1 � 2.7)�105 (6.1 � 2.9)�105 6.8 � 105 1.7 � 105

80 500 (9.0 � 4.0)�105 (2.4 � 0.3)�105 1.8 � 106

60 2400 (5.0 � 1.0)�106 (3.1 � 0.7)�106

40 6000 (1.2 � 0.2)�10


study and then presumably of all the 2,6-di-tert-butylphenolfamily at least in the concentration range under consideration,i.e., [AH]0 � 10�2 mol l�1.

When SE ¼ f(T) curves are available, they display clearlya maximum in the 120e130 �C interval as illustrated in Fig. 3by plotting the average induction period duration forPP þ 0.001 mol l�1 phenol.

If differences of SE values exist from one antioxidant toanother, they remain on the same order than uncertainties. Forinstance SE (AO1) appears to be lower than SE(AO2) at 60, 80and 120 �C, but the reverse is true at 100 �C and 190 �C.The stabilizers under study differ inmolarmass andmolecular

architecture and consequently in their rate of physical loss. Theexistence of a quasi-linear induction time e phenolic groupconcentration dependence indicates that physical phenomenaplay a secondary role otherwise this linearity would result froma very surprising coincidence [16].

Some theories predict the existence of a critical antioxidantconcentration below which the antioxidant is practically inef-ficient [37e39]. The above results confirm rather that there is nocritical concentration.

4. Discussion

4.1. Kinetic modelling

4.1.1. First step in kinetic modelling: Model M1

The first step in kinetic modelling consists in adding a singlestabilization event to the unstabilised polymer mechanistic schemewhich gives:

ð1uÞ POOH/2P� þ PC ¼ Oþ s k1u

ð1bÞ POOHþ POOH/P� þ POO� þ PC ¼ Oþ s k1b

-5

0

5

10

15

0.002 0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034

1/T (K-1)

tnl

dnit(

dni)h

ni

Fig. 3. Arrhenius plot of experimental induction period durations for unstabilised (,),or stabilized with 0.001 mol l�1 phenolic antioxidant PP (A). Lines correspond tokinetic modelling for pure PP (e) or stabilized one using kS1 ¼ 4.105 l mol�1 s�1 at200 �C and various activation energy values (eee: 50 kJ mol�1, e e e: 85 kJ mol�1,e - e: 150 kJ mol�1).

ð2Þ P� þ O2/POO� k2

ð3Þ POO� þ PH/POO� þ PH k3

ð4Þ P� þ P�/inactive product k4

ð5Þ POO� þ P�/inactive product k5

ð6Þ POO� þ POO�/inactive product k6

ðS1Þ POO� þ AH/POOHþ stable products kS1

- Initiation and termination processes are balanced reactions.Thismode of writing has been justified in previous publications[40,41].

- It is clear that P� react quickly with O2. However, terminationreactions involving P� (i.e. reactions (4) and (5)) were shown toplay a major role under atmospheric pressure [5].

- The Arrhenius parameters of the rate constants (except kS1which will eventually be estimated in this work) have beenpreviously determined [5,6]. They are listed in Table 3.

The following system of differential equations can be derived:

d½P��dt

¼2k1u½POOH� þ k1b½POOH�2�k2½P��½O2� þ k3½POO��½PH�� 2k4½P��2�k5½P��½POO�� ð4Þ

d½POO��dt

¼ k1b½POOH�2þk2½P��½O2� � k3½POO��½PH�

� k5½P��½POO�� 2k6½POO��2�kS1½POO��½AH� (5)

d½POOH�dt

¼ �k1u½POOH� � k1b½POOH�2þk3½POO��½PH�þ kS1½POO��½AH� (6)

v½O2�vt

¼ �k2½P��½O2� þ k6½POO��2þDO2

v2½O2�vx2

(7)

d½PH�dt

¼ �g1uk1u½POOH� � g1bk1b½POOH�2�k3½POO��½PH� (8)

v½AH�vt

¼ �kS1½POO��½AH� þ DAHv2½AH�vx2

(9)

where:

- g1u and g1b are the number of PH units consumed perrespectively unimolecular and bimolecular POOH decomposi-tion event [5].

Table 3Rate constant values (at 80 �C) and activation energy values.

k1u (s�1) k1b (l mol�1 s�1) k2 (l mol�1 s�1) k3 (l mol�1 s�1) k4 (l mol�1 s�1) k5 (l mol�1 s�1) k6 (l mol�1 s�1)1.3 � 10�8 0.5 � 10�5 1.0 � 107 6.3 � 10�2 5.0 � 1010 4.0 � 109 1.2 � 104

E1u (kJ mol�1) E1b (kJ mol�1) E2 (kJ mol�1) E3 (kJ mol�1) E4 (kJ mol�1) E5 (kJ mol�1) E6 (kJ mol�1)135 105 10 60 0 0 60

0.00

0.10

0.20

0.30

0.40

0.50

0 1000 2000 3000 4000

l lom( ]

O=C

P[1-)

time (h)

Fig. 4. Simulation of carbonyl buildeup curves at 80 �C using model M1 withparameters given in Table 3, [POOH]0 ¼ 10�3 mol l�1 (d), [POOH]0 ¼ 10�4 mol l�1

(e e), [POOH]0 ¼ 10�5 mol l�1 ($$$$).


- DO2and DAH are the respective diffusion coefficients of oxygen

and stabilizer in the polymer. For the sample thickness understudy (200 mm or lower), oxidation gradients can be neglectedand the diffusion term relative to oxygen can be suppressed inEqs. (7) and (9).

The system is solved using a commercial solver ODE23s byMatlab� using the following boundaries conditions [42] at t ¼ 0:

- ½O2� ¼ SO2� PO2

, SO2being the solubility of oxygen in PP

amorphous phase, taken equal to 1.4 � 10�8 mol l�1 Pa�1 andassumed to be temperature independent.

- [P�]0 ¼ [POO�]0 ¼ 0- [PH]0 ¼ 24 mol l�1

- [POOH] ¼ [POOH]0 depending on polymer pre-oxidation state(see later).

In the thermal oxidation at moderate temperatures, typicallyT � 120 �C for PP, the existence of an induction period indicatesa very low initiation rate, typically less than 10�12 mol l�1 s�1, at thebeginning of exposure. Among the various possible explanations ofsuch values [42], it is convenient to consider a virtual POOHconcentration ([POOH]0 s 0) kinetically equivalent to all theinitially present radical sources. It is also often convenient to take[POOH]0 ¼ 10�4 mol l�1 event though one can envisage a twodecades variation corresponding to data scatter.

The above kinetic model with these boundary conditions will becalled M1. Kinetic curves for carbonyl build-up are generated fromthe following equation:

d½PC¼ O�dt

¼ ð1�xCÞ,�gCOuk1u½POOH�þgCObk1b½POOH�2

�(10)

gCOu and gCOb being the carbonyl yields of respectively uni- andbimolecular POOH decomposition taken equal to 1 from previousstudy [43]. (1 � xC) term is included to take into account the factthat oxidation possibly occurs only in amorphous phase.

Simulations of carbonyl build-up curves are presented in Fig. 4.The stabilizing effect of phenols is an increasing function of theirreactivity, this latter being expressed by the rate constant kS1. Thedependence of induction period with kS1 and [AH]0 in model M1 isshown in Fig. 5a. For the highest initial hydroperoxide concentra-tion (10�2 mol l�1), the stabilizer is almost inefficient because it isalmost totally consumed by radicals generated by the decomposi-tion of initially present hydroperoxides of which the concentrationis on the same order or higher than the phenol concentration.Taking [POOH]0 equal to 10�3 mol l�1, convenient induction timedurations are obtained using kS1 ¼ 30 � 20 l mol�1 s�1.

The characteristics of M1 model can be summarized as follows:

It is able to generate kinetic curves with the same shape asexperimental ones.

However, the curves induction time duration versus initialstabilizer concentration display a negative concavity (Fig. 5b),which is not observed in experimental ones.

Neglecting this curvature, it could be concluded that the modelM1 is able to describe the experimental results. However, the

existence of secondary processes involving phenoxy radicals andtheir by-products cannot be ignored. We were thus interested inestimating the influence of these processes on the stabilizing effectand to refine eventually the M1 model to obtain better predictionsof induction times at every stabilizer concentrations.

4.1.2. Kinetic model M2: influence of POO� terminationby cyclohexadienonyl radicals

Phenoxy radicals A� can rearrange into cyclohexadienonylradicals B� which participate to a wide variety of reactions amongwhich combinations with peroxy radicals appear especiallyimportant because they contribute to stabilization. The simplifiedscheme could be:

ðS1Þ POO� þ AH/POOþ A� kS1

ðIsoÞ A�/B� kIso

ðS2Þ POO� þ B�/POOeB kS2

ðBÞ B�/other reactions kB

Taking into account all these processes requires new differentialequations relative to A� and B� in the scheme:

d½A��dt

¼ kS1½POO��½AH� � kIso½A�� (11)

d½B��dt

¼ kIs½A�� kS2½POO��½B�� kB½B�� (12)

Nevertheless, model M1 is not too far to give a good prediction,and addition of two functions [A�] and [B�] and three parameterskIso, kS2 and kB would lead to a situationwhere the inverse problemwould have an infinite number of solutions. We need thus todetermine independently some parameters (kIso and kB forinstance) or to simplify the scheme.

A relatively reasonable way of simplification consists in addingtwo hypotheses:

0

1000

2000

3000

4000

0 20 40 60 80 100

kS1 (l mol-1 s-1)

t ind (

h)

a

0

200

400

600

800

1000

1200

1400

1600

0.000 0.002 0.004 0.006 0.008 0.010 0.012

[AH]0 (mol l-1)

t ind (

h)

b [POOH]0 = 10-5 mol l-1

[POOH]0 = 10-4 mol l-1

[POOH]0 = 10-3 mol l-1

[POOH]0 = 10-2 mol l-1

[POOH]0 = 10-4 mol l-1

[POOH]0 = 10-3 mol l-1

[POOH]0 = 10-2 mol l-1

[POOH]0 = 10-5 mol l-1

Fig. 5. Simulations of induction period durations at 80 �C using model M1. (a): Changeswith kS1 using [AH]0 ¼ 0.005 mol l�1 (b): Changes with [AH]0 usingkS1 ¼ 20 l mol�1 s�1.

1.00

2.00

3.00

4.00

5.00

1E+00 1E+02 1E+04 1E+06 1E+08 1E+10

kS2 (l mol-1 s-1)

t ind /

t ind(k

S2 =

0) kS1 = 104 l mol-1 s-1

kS1 = 103 l mol-1 s-1

kS1 = 102 l mol-1 s-1

kS1 = 10 l mol-1 s-1

kS1 = 1 l mol-1 s-1

Fig. 6. Simulations of induction periods durations at 80 �C for PP þ phenols with[AH]0 ¼ 10�3 mol l�1.

0

2000

4000

6000

8000

10000

0.000 0.002 0.004 0.006 0.008 0.010 0.012

[AH]0 (mol l-1)

t ind

(h)

[POOH]0 = 10-5 mol l-1

[POOH]0 = 10-4 mol l-1

[POOH]0 = 10-3 mol l-1

[POOH]0 = 10-2 mol l-1

Fig. 7. Simulations of induction period durations at 80 �C using model M2 with [AH]0using kS1 ¼ 20 l mol�1 s�1 and kS2 ¼ 106 l mol�1 s�1.


The A� isomerisation into B� is almost instantaneous so thatthe stationary concentration of A� is very low and A� can beignored in the kinetic analysis.

The termination B� þ POO� predominates overall the otherreactions involving B�. Indeed, this hypothesis tends to over-estimate the stabilizing power of phenols under study. In modelM1, each phenol scavenges POO� radical meanwhile in modelM2, each phenol would scavenge two POO� radicals. The realityis probably in between.

M2 would thus involve two (balanced) reactions:

ðS1Þ POO� þ AH/POOHþ B� kS1


Reaction (S2) is a termination probably slower than termination(5) because radicals B� are resonance stabilized but is considerablyfaster than H abstraction by POO� (reaction S1):

k5> kS2[kS1 (13)

Themodel M2 has been operated with various kS1 and kS2 values(Fig. 6). It calls for the following comments:

Two regimes can be clearly distinguished:- for kS2 < 103 l mol�1 s�1, reaction (S2) has practically no effecton stabilization.

- for kS2 > 105 l mol�1 s�1, the stabilization effect of (S2) reachesan asymptotic value which increases slowly with kS1.It seems reasonable to suppose that kS2 � 105 l mol�1 s�1.

Hence (S2) plays a significant stabilizing role provided that B� isnot consumed by competitive processes and that its reactionproducts do not interfere with the oxidation chain process (seebelow).The model M2 improves the linearity of tind e [AH]0 curves

(Fig. 7). A negative concavity remains but it is less marked thanin Model M1.

4.1.3. Kinetic model M3: influence of coupling or polymerization ofcyclohexadienonyl radicals

Cyclohexadienonyl radicals B� can react by coupling, dispro-portionation or polymerization reactions [44,45] which have anindirect influence on the stabilization since they compete withtermination (S2). These processes can be tentatively represented bya single (virtual) bimolecular process [46]:

ðS3Þ B� þ B�/inactive products kS3

A first estimation can be made as follows: the induction time iscalculated from two runs of the kinetic model:

- the first one with kS2 ¼ 0- the second one with kS2 ¼ 106 l mol�1 s�1 and kS3 ¼ 0.

If the resulting induction time values are tind1 for the first run(i.e., from model M1) and tind2 for the second one (i.e., from modelM2), it is sure that whatever the kS3 value:

tind1 � tind � tind2 (14)

If tind2 and tind are on the same order of magnitude, incorpo-rating the S3 reaction into the mechanism would be an uselesscomplication, except maybe at high stabilizer concentrations.

4.1.4. Kinetic model M4: reinitiation from by e productsTermination S2 by coupling gives a peroxide which is certainly

unstable at high temperature. Its decomposition generates twoalkyl radicals able to initiate new oxidation chains:

ðS1Þ POO� þ AH/POOHþ B� kS1



ðS3Þ B� þ B�/inactive products kS3

ðS4Þ POOeB/2P� kS4

Peroxides are generally more thermally stable than corre-sponding hydroperoxides. A value of the decomposition rateconstant kS4 was reported [43]: (kS3)0 w 1014 l mol�1 s�1 andES3 w 125e150 kJ mol�1 so that it ranges between 10�9 and10�7 l mol�1 s�1 at 80 �C. Some data presented in Fig. 2, weretentatively simulated with various sets of kinetic parameters(Table 4). Indeed, kS4 increase can be compensated by kS1 increase.Incorporation of reaction (S4) in the model would be useful only toadjust kS1 value if this latter was considered too low comparedwithdata obtained for model compounds.

4.1.5. To conclude about simulation runsOur investigation is not exhaustive but it suggests that the

stabilizing effect could be relatively well represented by a combi-nation of two reactions:

ðS1Þ AHþ POO�/POOHþ B� kS1

ðS2Þ B� þ POO�/POOeB kS2

All the other reactions have only secondary effects on polymerstability. Their role could be taken into account by slight modifi-cations of kS1 and kS2 values. The same conclusionwas drawnwhentrying to model the stabilization by quinone methide generated asphenols by-products [47,48]. Let us note that the direct reactionbetween O2 and phenol surely occurs [32] but it was shown to benegligible under atmospheric pressure for PP.

It will be assumed that reaction (S2) is fully efficient i.e. thatkS2�105 lmol�1 s�1.Wehave chosen arbitrarily kS2¼106 lmol�1 s�1.We will now try to calculate the kS1 parameter from an inverseapproach [6].

12

14

16

1s-1

)

4.2. Identification of kinetic parameters

kS1 was calculated from fitting lifetime values from all abovepresented data by comparing:

- Experimental induction periods values from chem-iluminescence with simulated values for POOH build-upcurves. It can be recalled that POOH decomposition is consid-ered as the source of chemiluminescence [49,50].

- Experimental times to embrittlement with simulated time toreach MW ¼ 200 kg mol�1, which is the criterion for ductileebrittle transition in PP [51].

- Experimental and simulated induction periods for oxygenabsorption or carbonyl build-up.

Table 4Simulations of experimental value of induction period of PP þ 0.005 mol l�1 phenolat 80 �Cwith various sets of kinetic parameters. [AH]0 and [POOH]0 inmol l�1, kS1 kS2and kS3 in l mol�1 s�1, kS4 in s�1 and tind in h.

[POOH]0 [AH]0 kS1 kS2 kS3 kS4 tind

10�3 0.005 40 106 0 0 342610�3 0.005 40 106 0 10e9 340510�3 0.005 40 106 0 10e8 324010�3 0.005 43 106 0 10e8 341810�3 0.005 40 106 0 10e7 250610�3 0.005 75 106 0 10e7 3434

The initial hydroperoxide concentration [POOH]0 being a keyquantity in our modelling approach, the determination of its valuecalls for the following comments. In unstabilised polymers, it canbe in principle determined from induction time values using thekinetic model through an inverse approach [52]. For relatively cleansamples, tind was shown to be not very sensitive to [POOH]0 vari-ations [42]. A value of [POOH]0¼ 104�2 mol l�1 gives generally goodresults. It seemed to us interesting to choose a value of 10�3 mol l�1

here with a possible risk of slight underestimation of the polymerstability. This value is close to the sensitivity limit of commontitrationmethods.We don’t exclude cases where [POOH]0 would bemeasurable but, according to our experience, it is out of reach inrelatively “clean” samples. Anyhow, it can be recalled that in themodel, [POOH]0 is a “composite value” aimed to take into accountall the possible sources of radicals: hydroperoxides, dialkylper-oxides, oxygenepolymer complexes, and more generally all theimpurities or structural irregularities able to decompose intoradicals in a very short time scale compared to induction periodduration. There are thus at least two reasons to consider [POOH]0 asthe unique adjustable parameter of the model.

The crystallinity ratio xC was arbitrarily taken equal to 0 inmolten state and 0.5 in solid one considering that small variationsof xC induce only small variations of the kinetic parameters(see later).

Determined kS1 values are presented in Fig. 8. They call for thefollowing comments:

At 400 K and below kS1 values display a limited scatter (lessthan one decade). The apparent activation energy could be onthe order of 80 � 20 kJ mol�1.In the melting temperature interval (400 K < T < 450 K), kS1

value displays relatively high scatter (2e3 decades) and appearsalmost temperature independent.In liquid state at T � 450 K, the number of available data is too

low to appreciate the trends of variation.

The scatter can be discussed as follows:

Stabilizer consumption during samples processing is nottaken into account. The antioxidant concentration at thebeginning of exposure is probably lower than its nominal value.Scatter increases when approaching to the melting tempera-

ture region, in agreement with the observation of some alreadyobserved discontinuities [38,39]. A possible explanation wouldbe that the crystallinity ratio increase caused by annealing attemperatures just below Tm provokes an underestimation of“true” stabilizer concentration compared to theoretical one(Eq. (1)). The fact that tind is proportional to kS1 [AH]0 (Figs. 5 and

y = -7203.6x + 26.618

R2 = 0.5825

y = -10262x + 34.937

R2 = 0.7032

0

2

4

6

8

10

0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032

1/T (K-1)

ln k

S1

(kS

1in

l m

ol-

Fig. 8. Arrhenius plot of kS1 values determined from inverse method.


7) implies that [AH]0 underestimation is compensated by kS1overestimation in this temperature range.At elevated temperatures, kS1 could be underestimated in case

of stabilizer loss by evaporation [13]. The linearity of inductionperiod-stabilizer concentration is a pertinent criterion todetermine if volatile loss can be neglected [13], which is surelythe case for high molar mass stabilizers (for example AO1). Dataat 180 �C were available for only one stabilizer weight ratio,which prevented us from applying this simple reasoning.However, it is clear that a great part of stabilizers was lost duringprocessing or exposure given their low molar mass (c.a.�300 gmol�1). A more rigorous way for calculating stabilizationkinetic parameters bases on the simultaneous simulation ofboth PC¼O and POOH buildeup curves together with residualstabilizer concentration curve [13] which is unfortunatelygenerally not present in the compiled papers.Last, the peroxy cyclohexanedienone thermal decomposition,

neglected here (see above) could accelerate ageing at elevatedtemperatures. In other words, kS1 could be underestimated attemperatures c.a. 180e200 �C.

Despite these uncertainties, the results presented in Fig. 8 can beconsidered as an original method for estimating kS1 and its acti-vation energy. Two linear regressions were made:

- Afirst one including all available data: it gives a pre-exponentialfactor higher than 1011 l mol�1 s�1 with an activation energyclose to 60 kJ mol�1.

- A second one excluding some questionable data (in moltenstate) has a pre-exponential factor of 1013 l mol�1 s�1 with anactivation energy of about 85 kJ mol�1.

Concerning the pre-exponential factor, one can observe that itsvalue is high compared to the diffusion rate constant of particleencounter in the liquid state (109 l mol�1 s�1), which seems difficultto justify. There are two distinct explanations:

- In our case, many adjustments would be possible due to theexisting data scatter. The uncertainty in A factors is hence high.

- More fundamentally, one cannot totally exclude the possibilityof a non Arrhenius behaviour in the whole temperature range,as theorized byWaite [53] and Emanuel and Buchachenko [54]for the case of diffusion controlled reaction. Such a behaviour isexpected for a reaction between a macroradical and a moleculein relatively low concentration.

However, let usmention that pre-exponential factors formany fastreactions are many decades higher than the 109 l mol-1 s-1 limit (see[55]). Assuming in the frameof thiswork thekS1 is a genuine constant,ES1 rangesundoubtedlybetween60and85kJmol�1. This valuewillbetentatively justified in the following so as to validate the model.

5. Physical sense of kinetic parameters

5.1. Stabilizer yield kS1/k3

Identically to other substrates [46,56,57], the conditionkS1 >> k3 is verified. However, kS1 value is lower than in numerousarticles [58e60] no doubt depending on hypothesis made forkinetic model. Let us consider the ratio expressing stabilizationefficiency:

rS1r3

¼ kS1½POO��½AH�0k3½POO��½PH�0

¼ kS1½AH�0k3½PH�0

(15)

This ratio remains lower than unity but of the same order. Thefact that a significant stabilization is observed while rS1 is notstrictly higher than r3 could be explained by the positive role of(S2). Furthermore, relatively low values for kS1 in PP are expectedcompared to PE ones (a set is available in [43]) since secondaryperoxy radicals are more reactive than tertiary ones for a givensubstrate [61].

5.2. Rate constant for POO� þ A�

For the termination reaction between A� and a secondary (PEtype) POO� radical, a rate constant close to 108 l mol�1 s�1 wasreported [43] with zero activation energy. Here, PP value is 2e3decades lower in good agreement with precedent considerations.Let us recall that the kS2 value is not decisive and its precisedetermination by our approach is not easy given the low modelsensitivity to kS2.

5.3. Dependence of temperature and (S1) activation energy

Fig. 3 illustrates the temperature effect on the kinetic of oxida-tion of a stabilized PP and shows that:

- if ES1 is lower than 50 kJ mol�1, model overestimates inductionperiods durations at low temperatures.

- if ES1 is higher than 150 kJ mol�1, model underestimates thelifetime at moderate temperature.

Korcek [61] proposed a correlation between Bond DissociationEnergy (BDE) and activation energy:

E ¼ 0:55� BDEðA� HÞ � 143:9 (16)

E and BDE being expressed in kJ mol�1.Using BDE values ranging from 320 to 360 kJ mol�1 [45,62e65],

ES1 would be close to 45 kJ mol�1, which is not acceptable given theresults presented in Fig. 3. Given that the linear correlationbetween log10 k and BDE differs for the reaction between POO� andphenol hydroxyl group, and between POO� with hydrocarbons [62],a good agreement between Eq. (16) and our experimental results isillusory.

We have then used the Intersecting Parabolas Method exten-sively studied by Denisov [66]. The activation energy can be esti-mated from:

ffiffiffiffiffiEe

p¼ b,re

1� a2,

1� a,

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 1� a2

ðb,reÞ2,DHe

s !(17)

where:

- Ee is the activation energy (kJ mol�1)- 2b2 is the bond force constant of the broken bond- re characterizes the displacement of abstracted atom- bre ¼ 14.4 kJ mol�1. Let us precise that the calculation is notvery sensitive to this parameter.

- a is the ratio b/bf, bf being the strength of the formed bond.Here, a ¼ 1.014.

- DHe is the reaction enthalpy (kJ mol�1) of the reactionPOO� þ AH / POOH þ A� reaction.

Since:

- for a tertiary hydroperoxide: BDE(POO-H) ¼ 358.6 kJ mol�1

- for a phenol: BDE(AreOH) is close to 330 kJ mol�1


then : DHe ¼ �30 kJ mol�1:

�1
DHe being in any case between�10 and�30 kJ mol . Activationenergy ranges between 62 and 86 kJ mol�1. In other words, valuescalculated from exploitation of our compilation are justified by thistheoretical assessment.
6. Conclusions

This paper was dedicated to the PP stabilization by varioushindered phenol derivatives. The phenols “quasi-universal char-acter” was shown. It means that independently of their structuralcomplexity, the driving force of phenols chemical efficiency is thereaction:

POO� þ AH/POOþ A� kS1

Its activation energy for (S1) reaction is close to 70� 10 kJ mol�1

was calculated and discussed.The polymer pre-oxidation (due to severe processing or use of

recycled materials) was shown to drastically decrease the stabilizerefficiency.

The influence of further secondary reactions was then discussed.There is whether stabilization process: the termination of peroxyradicals by B� ones, or many non stabilizing processes involving B�

and phenoxy (A�) radicals. It appeared that all these processes canbe included in a single step provided that its rate constant value kS2is adjusted in order to take into account all the competitiveprocesses:

POO� þ A�/POOeA kS2

The influence of destabilizing steps, for example: POOeA / 2P�

was shown to be negligible especially in the low temperature range.

References

[1] Sommersall AC, Guillet JE. In: Klemchuck P, editor. Polymer stabilization anddegradation. Washington DC: American Chemical Society; 1985. p. 211.

[2] Verdu S, Verdu J. A new kinetic model for polypropylene thermal oxidation atmoderate temperatures. Macromolecules 1997;30(8):2262e7.

[3] Khelidj N, Colin X, Audouin L, Verdu J, Monchy-Leroy C, Prunier V. Oxidationof polyethylene under irradiation at low temperature and low dose rate. PartI- the case of "pure" radiochemical initiation. Polym Degrad Stab 2006;91(7):p1593e1597.

[4] Khelidj N, Colin X, Audouin L, Verdu J, Monchy-Leroy C, Prunier V. Oxidation ofpolyethylene under irradiation at low temperature and low dose rate. Part II.Low temperature thermal oxidation. Polym Degrad Stab 2006;91(7):1598e605.

[5] Richaud E, Farcas F, Fayolle B, Audouin L, Verdu J. Hydroperoxide build-up inthe thermal oxidation of polypropylene e a kinetic study. Polym Degrad Stab2007;92(1):118e24.

[6] Richaud E, Farcas F, Bartoloméo P, Fayolle B, Audouin L, Verdu J. Effect ofoxygen pressure on the oxidation kinetics of unstabilised polypropylene.Polym Degrad Stab 2006;91(2):398e405.

[7] Coquillat M, Verdu J, Colin X, Audouin L, Nevière R. Thermal oxidation ofpolybutadiene. Part 2: mechanistic and kinetic schemes for additive-free non-crosslinked polybutadiene. Polym Degrad Stab 2007;92(7):1334e42.

[8] Colin X, Audouin L, Verdu J. Kinetic modelling of the thermal oxidation ofpolyisoprene elastomers. Part 1: unvulcanized unstabilized polyisoprene.Polym Degrad Stab 2007;92(5):886e97.

[9] Colin X, Audouin L, Verdu J, Le Huy M. Kinetic modelling of the thermaloxidation of polyisoprene elastomers. Part 2: effect of sulfur vulcanization onmass changes and thickness distribution of oxidation products duringthermal. Polym Degrad Stab 2007;92(5):898e905.

[10] Malík J, Tuan DQ, �Spirk E. Lifetime prediction for HALS-stabilized LDPE and PP.Polym Degrad Stab 1995;47(1):1e8.

[11] Moisan JY, Lever R. Diffusion des additifs du polyéthylène V e influence sur levieillissement des polymères. Europ Polym J 1982;18:407e11.

[12] Colin X, Audouin L, Verdu J, Rozental-EvesqueM, RabaudB,Martin F, et al. Agingof polyethylene pipes transporting drinking water disinfected by chlorinedioxide. Part II-lifetime prediction. Polym Eng Sci 2009;49(8):1642e52.

[13] Richaud E, Monchy-Leroy C, Colin X, Audouin L, Verdu J. Kinetic modelling ofstabilization coupled with stabilizer loss by evaporation. Case of dithioesterstabilized polyethylene. Polym Degrad Stab 2009;94(11):2004e14.

[14] Calvert PD, Billingham NC. Loss of additives from polymers: a theoreticalmodel. J Appl Polym Sci 1979;24:357e70.

[15] Moisan JY. Diffusion des additifs du polyethylene-I. Influence de la nature dudiffusant. Eur Polym J 1980;16(10):979e87.

[16] Bair HE. Exudation of an antioxidant additive from thin polyethylene films.Polym Eng Sci 1973;13:435e9.

[17] Naskar K, Kokot D, Noordermeer JWM. Influence of various stabilizers onageing of dicumyl peroxide-cured polypropylene/ethylene-propylene-dienethermoplastic vulcanizates. Polym Degrad Stab 2004;85(2):831e9.

[18] Vulic I, Vitarelli G, Zenner JM. Structureeproperty relationships: phenolicantioxidants with high efficiency and low colour contribution. Polym DegradStab 2002;78(1):27e34.

[19] Goldberg VM, Kolesnikova NN, Paverman NG, Kavun SM, Stott PE, Gelbin ME.Thermo-oxidative degradation of linear low density poly(ethylene) in thepresence of carbon black: a kinetic approach. Polym Degrad Stab 2001;74(2):371e85.

[20] Pospí�sil J. Chemical and photochemical behaviour of phenolic antioxidants inpolymer stabilizationea state of the art report, part I. Polym Degrad Stab1993;40(2):217e32.

[21] Pospí�sil J. Chemical and photochemical behaviour of phenolic antioxidants inpolymer stabilization: a state of the art report, part II. Polym Degrad Stab1993;39(1):103e15.

[22] Aymes-Chodur C, Betz N, Legendre B, Yagoubi N. Structural and physico-chemical studies on modification of polypropylene and its polyphenolic anti-oxidant by electron beam irradiation. Polym Degrad Stab 2006;91(4):649e62.

[23] Faulkner DL. Aging of polypropylene using high oxygen pressure: influence ofsample thickness and stabilization. J Appl Polym Sci 1986;31(7):2129e38.

[24] Fayolle B, Richaud E, Verdu J, Farcas F. Embrittlement of polypropylene fibreduring thermal oxidation. J Mat Sci 2008;43(3):1026e32.

[25] Richaud E, Farcas F, Fayolle B, Audouin L, Verdu J. Accelerated ageing ofpolypropylene stabilized by phenolic antioxidants under high oxygen pres-sure. J Appl Polym Sci 2008;110(6):3313e21.

[26] Audouin L, Girois S, Achimsky L, Verdu J. Effect of temperature on the photo-oxidation of polypropylene films. Polym Degrad Stab 1998;60(1):137e43.

[27] Fayolle B, Colin X, Audouin L, Verdu J. Mechanism of degradation inducedembrittlement in polyethylene. Polym Degrad Stab 2007;92(2):231e8.

[28] Gugumus F. Effect of temperature on the lifetime of stabilized and unstabi-lized PP films. Polym Degrad Stab 1999;63(1):41e52.

[29] Schwarzenbach K, Gilg B, Muller D, Knobloch G, Pauquet JR, Rota-Graziosi P,et al. In: Zweifel H, editor. Plastics additives handbook. 5th ed. Cincinnati:Hanser Gardner Publications; 2001. p. 1.

[30] Gugumus F. Critical antioxidant concentrations in polymer oxidationeII.Experimental ‘proofs’*. Polym Degrad Stab 1998;60(1):p99e117.

[31] Tochácek J. Effect of secondary structure on physical behaviour and perfor-mance of hindered phenolic antioxidants in polypropylene. Polym DegradStab 2004;86(2):385e9.

[32] Klemchuk PP, Horng PL. Perspectives on the stabilization of hydrocarbonpolymers against thermo-oxidative degradation. Polym Degrad Stab 1984;7(3):131e51.

[33] Breese KD, Lamèthe JF, DeArmitt C. Improving synthetic hindered phenolantioxidants: learning from vitamin E. Polym Degrad Stab 2000;70(1):89e96.

[34] Jipa S, Zaharescu T, Setnescu R, Setnescu T, Herdan J, Gorghiu LM. Thermalstabilization effect of some 3,5-di-t-butyl-4-hydroxy derivatives of ethaneand ethane. Polym Test 2002;21(3):353e61.

[35] Zweifel H. In: Clough RL, Billingham NC, Gillen KT, editors. Degradation,stabilization, and lifetime prediction. Washington: American ChemicalSociety; 1993. p. 375.

[36] Matisová-Rychlá L, Rychlý R. Chemiluminescence from stabilised poly-propylene. The effect of annealing on the induction time of oxidised poly-propylene stabilised with Irganox 1010 and Irganox 1076. Polym Degrad Stab2001;73(3):393e8.

[37] Shlyapnikov YA. Some comments on the existence and nature of criticalantioxidant concentrations. Polym Degrad Stab 1997;56(3):257e60.

[38] Shlyapnikov YA, Kolesnikova NN. Variation of inhibited oxidation parametersin polyethylene melting. J Appl Polym Sci 2006;101(2):978e81.

[39] Kalinina IG, Gumargalieva KZ, Shlyapnikov YA. Variation of inhibited oxidationparameters in therangeofphase transition. J Appl PolymSci2007;104(4):2711e3.

[40] Sarrabi S, Colin X, Tcharkhtchi A. Isothermal oxidation kinetics of unstabilizedpolypropylene in the molten state. J Appl Polym Sci 2008;110(4):2030e40.

[41] Audouin L, Gueguen V, Tcharkhtchi A, Verdu J. ’Close loop’mechanistic schemesfor hydrocarbon polymer oxidation. J Polym Sci A: Polym Chem 1995;33(6):921e7.

[42] Richaud E, Colin X, Fayolle B, Audouin L, Verdu J. Induction period in the low-temperature thermal oxidation of saturated hydrocarbons: example of poly-ethylene. Int J Chem Kin 2008;40(12):769e77.

[43] Gutiérrez G, Fayolle F, Régnier G, Medina J. Thermal oxidation of clay-nano-reinforced polypropylene. Polym Degrad Stab 2010;95(9):1708e15.

[44] Pospí�sil J, Ne�sp�urek S. In: Halim Hamid S, editor. Handbook of polymerdegradation. 2nd ed. New York, Basel: Marcel Dekker Inc; 2000. p. 191.

[45] Denisov ET, Afanas’ev IB. Oxidation and antioxidants in organic chemistry andbiology. Boca Raton, London, New York, Singapore: CBC Taylor & FrancisGroup; 2005. p. 491.

[46] Zeynalov EB, Allen NS. Simultaneous determination of the content and activityof sterically hindered phenolic and amine stabilizers by means of an oxidativemodel reaction. Polym Degrad Stab 2004;85(2):847e53.


[47] Pospí�sil J, Ne�sp�urek S, Zweifel H. The role of quinone methides in thermo-stabilization of hydrocarbon polymerseI. Formation and reactivity of quinonemethides. Polym Degrad Stab 1996;54(1):7e14.

[48] Pospí�sil J, Ne�sp�urek S, Zweifel H. The role of quinone methides in thermo-stabilization of hydrocarbon polymerseII. Properties and activity mecha-nisms. Polym Degrad Stab 1996;4(1):15e21.

[49] Billingham NC, Grigg MN. The kinetic order of decomposition of polymerhydroperoxides assessed by chemiluminescence. Polym Degrad Stab 2004;83(3):441e51.

[50] Matisová-Rychlá L, Rychlý J. New approach to understanding chem-iluminescence from the decomposition of peroxidic structures in poly-propylene. Polym Degrad Stab 2000;67(3):515e25.

[51] Fayolle B, Audouin L, Verdu J. A critical molar mass separating the ductile andbrittle regimes as revealed by thermal oxidation in polypropylene. Polymer2004;45(12):4323e30.

[52] Colin X, Audouin L, Verdu J. Determination of thermal oxidation rate constantsby an inverse method. Application to polyethylene. Polym Degrad Stab2004;86(2):309e21.

[53] Waite TR. Bimolecular reaction rates in solids and liquids. J Chem Phys1960;32(1):21e3.

[54] Emanuel NM, Buchachenko AL. Chemical physics of stabilization. Utrecht:VNU Science Press; 1987. pp. 81e118.


[56] Coquillat M, Verdu J, Colin X, Audouin L, Celina M. A kinetic evaluation of thethermal oxidation of a phenol stabilised polybutadiene. Polym Degrad Stab2008;93(9):1689e94.

[57] Roginsky V. Chain-breaking antioxidant activity of natural polyphenols asdetermined during the chain oxidation of methyl linoleate in Triton X-100micelles. Arch Biochem Biophys 2003;414(2):261e70.

[58] Litwinienko G, Ingold KU. Solvent effects on the rates and mechanisms ofreaction of phenols with free radicals. Acc Chem Res 2007;40(3):222e30.

[59] Kalitchin ZD, Boneva MI, Milkova T, Todorova D. Study on the antioxidantactivity of cholesteryl esters of some phenolic acids by chemiluminescence.J Photoch Photobio B 1997;41(1e2):109e13.

[60] Valgimigli L, Amorati R, Fumo MG, DiLabio GA, Pedulli GF, Ingold KU, et al. Theunusual reaction of semiquinone radicals with molecular oxygen. J Org Chem2008;73(5):1830e41.

[61] Korcek S, Chenier JBH, Howard JA, Ingold KU. Absolute rate constants forhydrocarbon auto-oxidation - activation energies for propagation and thecorrelation of propagation rate constants. Can J Chem 1972;50:2285e97.

[62] Amorati R, Fumo MG, Menichetti S, Mugnaini V, Pedulli GF. Electronic andhydrogen bonding effects on the chain-breaking activity of sulfur-containingphenolic antioxidants. J Org Chem 2006;71(17):6325e32.

[63] Brigati G, Lucarini M, Mugnaini V, Pedulli GF. Determination of the substituenteffect on the OeH bond dissociation enthalpies of phenolic antioxidants bythe EPR radical equilibration technique. J Org Chem 2002;67(14):4828e32.

[64] Pratt DA, DiLabio GA, Mulder P, Ingold KU. Bond strengths of toluenes,anilines, and phenols: to Hammett or not. Acc Chem Res 2004;37(5):334e40.

[65] Mulder P, Saastad OW, Griller D. OeH bond dissociation energies in para-substituted phenols. J Am Chem Soc 1988;110(12):4090e2.


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