Emmanuel Richaud
email: emmanuel.richaud@ensam.eu

Yves Pierre

Le Gac

Jacques Verdu

THERMOOXIDATIVE AGEING OF POLYDICYCLOPENTADIENE IN GLASSY STATE

Keywords: Polydicyclopentadiene, thermal oxidation, kinetics, molecular mobility

Thermal ageing of thin films of unstabilized polydicyclopentadiene (pDCPD) at several temperatures ranging from 120 to 30°C was investigated by means of carbonyl build up by FTIR with ammonia derivatization, double bond titration, mass uptake measurement, hydroperoxides titration by iodometry and DSC coupled with sulfur dioxide treatment. In the temperature range under investigation, pDCPD is in glassy state and it oxidizes faster than common polymers oxidized at rubbery state (e.g. polydienic elastomers). Using the kinetic analysis, these results were ascribed to increased initiation rate due to catalyst residues, some possible intramolecular processes favoring propagation, or a very low termination rate of oxidation radical chains because of the control of termination reactions by macroradical diffusion.

INTRODUCTION

Most of the knowledge on polymer oxidation mechanisms and kinetics was obtained from experimental studies on elastomers [START_REF] Coquillat | Vieillissement des propergols à matrice polybutadiène : modélisation cinétique de l'oxydation[END_REF][START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF] or semi-crystalline polyolefins [START_REF] Khelidj | Oxidation of polyethylene under irradiation at low temperature and low dose rate. Part II. Low temperature thermal oxidation[END_REF][START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF]. The oxidation of all these materials occurs in a rubbery/liquid phase characterized by relatively fast cooperative segmental motions. However, some authors [START_REF] Waite | General theory of bimolecular reaction rates in solids and liquids[END_REF][START_REF] Waite | Theoretical treatment of the kinetics of diffusion-limited reactions[END_REF] have assumed that bimolecular processes between macromolecular reactive species may be disadvantaged because of low diffusivity of these species in such highly viscous matrices. In other words, radical propagation of the oxidation process would not be limited by bimolecular termination processes. It was actually observed that the ratio k p ²/k t expressing oxidizability was higher for PP than for its model compounds [START_REF] Mayo | Relative reactivities in oxidations of polypropylene and polypropylene models[END_REF]. A possible explanation is that rate constant propagation k p has same value in polypropylene (PP) and its liquid model compounds whereas termination constant k t is higher in liquids than in PP amorphous phase.

Propagation actually involves a reaction between a peroxy radical and a close monomer unit and so should not be controlled by diffusion whereas termination involves a reaction between two species (peroxy radicals) at low concentration and may be controlled by diffusion so that its rate depends sharply of the medium viscosity.

In the case of polymers in glassy state, extremely low termination rates and then extremely high oxidation rates are thus expected. Unfortunately, kinetic studies of the oxidation of glassy polymers are scarce. In the case of aromatic polymers [START_REF] Richaud | Radiochemical ageing of poly(ether ether ketone)[END_REF], significant oxidized layer (100 µm) were observed despite a slow propagation (linked to strong C-H bonds), which militates in favor of termination control by diffusion. A comparison of hydrocarbon elastomers oxidation in rubbery state with oxidation of hydrocarbon glassy polymers at the same temperature would bring another evidence of the molecular mobility effect on oxidizability. This is the reason why pDCPD has been chosen here.

pDCPD is synthetized from Ring Opening Metathesis Polymerization of dicyclopentadiene:

After thermal crosslinking [START_REF] Davidson | The polymerization of dicyclopentadiene: an investigation of mechanism[END_REF][START_REF] Dimonie | Some aspects of the thermal stability of linear polydicyclopentadiene (L-PDCPD)[END_REF][START_REF] Dimonie | Nature of the first exothermic peak on the DSC curve of linear polydicyclopentadiene obtained with a special catalytic system[END_REF], it gives a network with a glass transition temperature of c.a.

160°C used for instance in off-shore applications [START_REF] Gac | Durability of polydicyclopentadiene under high temperature, high pressure and seawater (offshore oil production conditions)[END_REF]. Apart some irregularities [START_REF] Davidson | The polymerization of dicyclopentadiene: an investigation of mechanism[END_REF][START_REF] Dimonie | Some aspects of the thermal stability of linear polydicyclopentadiene (L-PDCPD)[END_REF][START_REF] Dimonie | Nature of the first exothermic peak on the DSC curve of linear polydicyclopentadiene obtained with a special catalytic system[END_REF], its structure displays highly reactive groups: double bonds able to react by addition reactions and easily abstractable allylic hydrogens.

The present study is limited to unstabilized pDCPD thin films (not submitted to Diffusion Limited Oxidation), i.e. materials not aimed at any industrial purpose, exposed to temperatures ranging from 30 to 120°C to illustrate the specificity of oxidation in glassy state.

EXPERIMENTAL

Material

Samples were supplied as stabilized bulk material prepared by casting dicyclopentadiene into an aluminium mould preheated at 40°C. The catalyst of the metathesis polymerization is a ruthenium salicylaldimine phenylindenylidene complex. Material was cut in 20-30 µm slices using a Reichert-Jung microtome. These ones were purified by refluxing in CH 2 Cl 2 overnight. Unstabilized samples were stored in fridge prior to exposure.

Exposure conditions

Samples were exposed in ventilated ovens at various temperatures ranging from 120 to 30°C.

Characterization

Fourier Transform InfraRed spectroscopy

FTIR spectra in transmission mode were obtained on free standing films in transmission mode by averaging 4 scans at a 2 cm -1 resolution using a Frontier apparatus (Perkin Elmer) driven by Spectrum software.

SO 2 treatment

Sulfur dioxide treatments were performed by putting samples during 24 h in closed vessels in which SO 2 was in situ generated from solutions of 40 mg of Na 2 SO 3 (S0505 grade -Sigma Aldrich) in HCl (analysis grade 37% -Carlo Erba) [START_REF] Richaud | Hydroperoxide titration by DSC in thermally oxidized polypropylene[END_REF].

Iodometry

Hydroperoxides react with iodine anions in isopropanol using acetic acid for acidizing the media by the following reaction [START_REF] Gardette | Advantages and limits of hydroperoxide titration methods in solid polymers[END_REF][START_REF] Carlsson | A critical comparison of methods for hydroperoxide measurement in oxidized polyolefins[END_REF][START_REF] Scheirs | A Review of the Methods For Detecting and Characterizing Hydroperoxide Groups in Oxidized Polyolefins[END_REF]:

POOH + 2I -+ 2H +  POH + I 2 + H 2 O I 2 + I - I 3 -
A mass m (about 1 mg) of oxidized pDCPD was placed in 7 ml 10:1 isopropanol:acetic acid mixture in a bicol flask (isopropanol: ref 34959 HPLC grade purity 99.9% -Sigma Aldrich, acetic acid: ref A6283 purity > 99% -Sigma Aldrich). When the mixture reached refluxing temperature, I -was brought by adding 3 ml of a saturated solution of NaI (ref 409286 -Sigma Aldrich) saturated solution in isopropanol. After a 10 minutes reaction time, solution was analyzed by UV spectroscopy (Perkin Elmer Lambda 35) in 1 cm UV cell. Hydroperoxides concentration was thus calculated from the I 3 absorbance at 355 nm (DO 355 ) using a molar absorptivity  = 25000 l mol -1 cm -1 by the formula:

[POOH] = 0.4× DO 355 m

[POOH] being here expressed in mol kg -1 and m in mg.

DSC

Thermal analysis was performed using a Q10 DSC apparatus (TA Instrument) driven by Q Series Explorer software. DSC was first calibrated with an indium standard. Approximately 1 mg of virgin or oxidized sample was heated from 25 to 300°C in sealed aluminum pans, at a heating rate of 10°C min - 1 under an inert atmosphere obtained by purging cell with a 50 ml min -1 nitrogen flow. Results were processed using the TA Analysis software.

ThermoGravimetric Analysis

Gravimetric measurements were monitored using a TGA Q50 (TA Instrument) driven by Q Series Explorer. About 10 mg samples were placed in a Platinum pan which first heated under nitrogen till to the measurement temperature at which cell atmosphere was switched to oxygen or nitrogenoxygen mixtures (GasMix). Results were processed using TA Analysis software.

RESULTS

Gravimetric study

Mass variation has been monitored for samples exposed at 120°C under 21, 50, 75 and 100% of the atmospheric pressure (Figure 1).

Figure 1. Kinetics of mass uptake at 120°C for pDCPD under several oxygen concentrations.

The mass increases continuously which is a characteristic of unsaturated polymers [START_REF] Coquillat | Vieillissement des propergols à matrice polybutadiène : modélisation cinétique de l'oxydation[END_REF][START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF][START_REF] Coquillat | Thermal oxidation of polybutadiene. Part 1: Effect of temperature, oxygen pressure and sample thickness on the thermal oxidation of hydroxyl-terminated polybutadiene[END_REF]. The rate of mass gain is maximal shortly (1-2 min) after the beginning of exposure, and then decreases continuously.

It is possible to distinguish two periods corresponding to distinct phases of the oxidation process :

-An "initial" period, with a characteristic time of the order of 10-20 min decreasing with oxygen pressure. -A "final" period with a characteristic time at least 10 times higher than "initial" one. The mass gain reaches about 10-15% at the end of the first period that corresponds to 1 ± 0.2 oxygen atoms per initial monomer unit.

Maximum rates are almost proportional to oxygen pressure (Table 1) which will be exploited in the ''DISCUSSION'' section.

Table 1. Maximum rate of mass uptake at 120°C.

According to Table 2, pDCPD oxidizes faster and in a relatively greater extent than polybutadiene and polyisoprene, whereas the double bond concentration is 17 mol l -1 [START_REF] Coquillat | Thermal oxidation of polybutadiene. Part 1: Effect of temperature, oxygen pressure and sample thickness on the thermal oxidation of hydroxyl-terminated polybutadiene[END_REF] for polybutadiene and 27 mol l -1 for polyisoprene [START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF] versus 10 mol l -1 in pDCPD (from its theoretical structure, and even less as it will be seen below).

Table 2. Induction time (for carbonyl build up or mass uptake) t i , time to plateau (t p ), maximal mass uptake value and number of oxygen atoms grafted per monomer unit N for polybutadiene [START_REF] Coquillat | Thermal oxidation of polybutadiene. Part 1: Effect of temperature, oxygen pressure and sample thickness on the thermal oxidation of hydroxyl-terminated polybutadiene[END_REF],

polyisoprene [START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF] and pDCPD (this work).

Relative pressure

Changes in molecular structure

The DSC traces of oxidized samples reveal the growth of an exotherm centered at c.a. 150°C which disappears upon treatment by sulfur dioxide (Figure 2). concentration determined from iodometry measurements (Figure 3a). The ratio of [POOH] values over enthalpy measured by DSC gives a value for the molar enthalpy H POOH = 440 kJ mol -1 in agreement with calculations given in [START_REF] Gac | Durability of polydicyclopentadiene under high temperature, high pressure and seawater (offshore oil production conditions)[END_REF] using here values for unsaturated substrates [START_REF] Calvert | Photochemistry[END_REF].

Hydroperoxide concentrations are plotted together with concentrations in carbonyls and double bonds (Figure 3). For example, the POOH concentration at 120°C increases rapidly in the previously defined "initial" period to reach a value of about 0.8 mol l -1 after 10 min of exposure. At this time, the number of moles of dioxygen absorbed by the polymer is of the same order (Figure 1) which means that oxidation gives almost exclusively hydroperoxides in the "initial" period. After a maxima corresponding to steady state, the POOH concentration decreases because of the substrate consumption [START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF]. According to simple kinetic models [START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF][START_REF] Audouin | Close loop' mechanistic schemes for hydrocarbon polymer oxidation[END_REF], the steady state POOH concentration under oxygen excess is given by:

 000  1 h  2 h  3 h  4 h ---3 h + SO 2 (a) (b) (c) (d)
[POOH] max = 1 δ ( k 3 2 [PH] 2 k 1 k 6 ) 1/δ
Where δ = 1 or 2 is the molecularity of the POOH decomposition and k 1 is the rate constant of POOH decomposition (denoted respectively by k 1u or k 1b in the case of uni-or bimolecular decomposition).

[POOH] max is thus expected to obey Arrhenius law with an apparent activation energy:

E POOH = 2 δ E 3 - 1 δ (E 1 +E 6 )
Where E 3 , E 1 (being E 1u or E 1b in the case of uni-or bimolecular decomposition) and E 6 are the respective activation energies of propagation, initiation and termination.

[POOH] max values have been compared with polypropylene data [START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF] (Figure 4). Double bonds absorb at 965 cm -1 (molar absorptivity range from 100 [START_REF] Mcmurry | Correlation of infrared spectra[END_REF] to 168 [START_REF] Moss | Degradation and stabilization of high density polyethylene during multiple extrusions[END_REF] l mol -1 cm -1 for trans vinylene units) and at 720 cm -1 (molar absorptivity of 60 l mol -1 cm -1 for cyclohexene/cis vinylene units [START_REF] Calvert | Photochemistry[END_REF]). Their initial concentration determined from these bands is about 4 mol l -1 . It means that half of the double bonds initially present in the monomer are consumed during polymerization and thermal crosslinking [START_REF] Davidson | The polymerization of dicyclopentadiene: an investigation of mechanism[END_REF][START_REF] Dimonie | Nature of the first exothermic peak on the DSC curve of linear polydicyclopentadiene obtained with a special catalytic system[END_REF]. The remaining double bonds disappear during oxidation (Figure 3) presumably through radical additions.

Build-up of stable oxidation products

The changes of IR spectra (Figure 5) display several common features with those of other hydrocarbon polymers i.e.:

a growth of a H bonded hydroxyl band at c.a. 3400 cm )

1/T (K -1 )

a complex carbonyl band in the 1650-1750 cm -1 region, the absorptions below 1700 cm -1 indicating the presence of conjugated carbonyls coming from highly oxidizable allylic carbons.

a wide band resulting from the overlapping of several -O-Cvibrations belonging to hydroxyls, peroxides and carboxyls in the 1000-1300 cm -1 region.

Figure 5. Changes of FTIR spectra of pDCPD exposed at 120°C under air (75 min maximal duration).

Carbonyl and hydroxyl absorbances were converted into concentrations using Beer Lambert's law with  CO = 300 and  OH = 70 l mol -1 cm -1 [START_REF] Richaud | Hydroperoxide titration by DSC in thermally oxidized polypropylene[END_REF]. Ammonia treatments were also used for converting acids into ammonium carboxylates (1550 cm -1 ) and esters into amides (1650 and 3200 cm -1 ) [START_REF] Wilhelm | Infrared identification of carboxylic acids formed in polymer photooxidation[END_REF]. The simultaneous formation of ketones, carboxylic acids and esters (Figure 6) suggests the existence of a "co-oxidation" mechanism in which:

the formation of esters and carboxylic acids is ascribed to the oxidation of secondary carbons: The plot of the carbonyl concentration against hydroxyl one (Figure 7) shows that both concentrations are almost proportional. The proportionality ratio is almost temperature independent except at 30°C where it is significantly lower than at higher temperatures.

DISCUSSION

The aim of this section is to answer to the following questions:

-Can kinetic analysis allow understanding if the higher pDCPD oxidizability than polybutadiene and polyisoprene ones is due to a faster initiation or propagation in pDCPD than in polydienes or slower termination in pDCPD than in polydienes or, indeed, a combination of both causes?

-Why acids and esters, which are in principle secondary products, predominate over ketones at low temperature while ketones are largely predominant at 120°C?

Kinetic analysis of pDCPD oxidation

The following mechanistic scheme will be used for describing the oxidation of pDCPD:

(1u) POOH  2P° +  CO .P=O (k 1u ) (1b) 2 POOH  P° + POO° +  CO .P=O (k 1b ) (2) P° + O 2  POO° (k 2 ) (3) POO° + PH  POOH + P° (k 3 ) (4) P° + P°  inactive product (k 4 ) (5) P° + POO°  inactive product (k 5 ) (6) POO° + POO°  inactive product (k 6 )
The above presented model is, no doubt, a simplification for at least two reasons:

 The participation of secondary and tertiary allylic carbons, in a co-oxidation mechanism (according to the results of NH 3 treatments) is not envisaged.

 The possible radical addition to double bonds is neglected.

The oxidation rate is a hyperbolic function of oxygen concentration (this latter being proportional to oxygen pressure p) [START_REF] Verdu | Oxidative ageing of polymers[END_REF]:

r ox = α.S.p 1 + β.S.p
Where S is the coefficient of oxygen solubility in the polymer,  = k 2 .(r i /k 4 ) 1/2 and  = (k 2 /k 3 [PH]).(k 6 /k 4 ) 1/2 .

Here, the fact that r ox is almost proportional to oxygen pressure (Table 1) indicates that .S.p << 1.

The orders of magnitude for air at atmospheric pressure and about 100°C are: k 2 .S.p ~ 10 4 -10 5 s -1 and k 3 [PH] = 10-100 s -1 . Thus the above inequality involves that (k 6 /k 4 ) 1/2 ≪10 -4 to 10 -2 which provides a first constraint for the determination of rate constants.

In order to gain better insights in the pDCPD oxidative behavior, four sets of simulations runs (Figure 8) were performed. The mechanistic scheme leads to a differential system (see APPENDIX B for example) which is numerically solved to give [P°], [POO°], [POOH] or [P=O] concentrations [START_REF] Coquillat | Vieillissement des propergols à matrice polybutadiène : modélisation cinétique de l'oxydation[END_REF][START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF][START_REF] Khelidj | Oxidation of polyethylene under irradiation at low temperature and low dose rate. Part II. Low temperature thermal oxidation[END_REF][START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF].

Underlying assumptions are:

k 2 , k 3 , k 4 , k 5 and oxygen solubility S directly come from previous butadiene rubber (only secondary allylic hydrogens react) or polyisoprene (only tertiary allylic hydrogens react) [START_REF] Coquillat | Vieillissement des propergols à matrice polybutadiène : modélisation cinétique de l'oxydation[END_REF][START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF][START_REF] Coquillat | Thermal oxidation of polybutadiene. Part 1: Effect of temperature, oxygen pressure and sample thickness on the thermal oxidation of hydroxyl-terminated polybutadiene[END_REF]. Then, k 1u , k 1b , and k 6 remain the only adjustable parameters.

-Initiation is purely uni-or bimolecular, having in mind that it actually lies between the two.

-[PH] 0 is equal to twice the concentration in double bonds (determined from FTIR), [POOH] 0 = 10 -1 mol l -1 (from the initial value of the exothermal signal measured by DSC for virgin sample).

Hence, each simulation is characterized by a couple k 1u or k 1b , k 6 which will be compared with polybutadiene or polyisoprene for explaining the difference in oxidizability between pDCPD and those two polymers. The rate constants k 1u , k 1b and k 6 coming from each simulation are recalled in Table 3. Table 3. Rate constants (k 1u in s -1 , k 1b and k 6 in l mol -1 s -1 ) used for simulations given in Figure 8.

They call for the following comments:

-The carbonyl yield  CO was found in each case equal to 0.2. It seems that this apparent yield does not depend on temperature, consistently with results presented in Figure 7.

-It is easy to verify that all k 1u and k 1b values are considerably higher than those obtain in other hydrocarbon polymers [START_REF] Coquillat | Vieillissement des propergols à matrice polybutadiène : modélisation cinétique de l'oxydation[END_REF][START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF][START_REF] Khelidj | Oxidation of polyethylene under irradiation at low temperature and low dose rate. Part II. Low temperature thermal oxidation[END_REF][START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF].

k 6 is on the contrary extremely low particularly in comparison with polyisoprene and polybutadiene.

The condition k 4 >> k 6 (see APPENDIX A) is fulfilled (k 4 > 10 8 l mol -1 s -1 in each case). Its activation energy value is dramatically higher than model hydrocarbons [START_REF] Denisov | Oxidation and Antioxidants in Organic Chemistry and Biology[END_REF][START_REF] Bennett | Studies by electron spin resonance of the reactions of alkylperoxy radicals. Part 1. -Absolute rate constants for the termination reactions of alkylperoxy radicals[END_REF].

-In comparison with existing literature [START_REF] Coquillat | Vieillissement des propergols à matrice polybutadiène : modélisation cinétique de l'oxydation[END_REF][START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF][START_REF] Khelidj | Oxidation of polyethylene under irradiation at low temperature and low dose rate. Part II. Low temperature thermal oxidation[END_REF][START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF], the activation energy for initiation is relatively low whereas the termination one is relatively high. The correlation coefficient for Arrhenius plot is satisfying in the case of initiation, less for termination. However, if termination would be a diffusion controlled process (see below), its rate constant would not be a genuine constant anymore, i.e. that it would not necessarily obey Arrhenius's law. According to kinetic analysis, two reasons can explain the relatively fast oxidation of pDCPD:

Possible explanations of the high oxydability of pDCPD

-The extremely high value of initiation rate constants, irrespectively of the initiation mode.

-The very low rate constant value for the termination reaction between two POO°.

A third possible reason will be envisaged: since the oxidation rate is mainly characterized by the ratio k 3 2 /k 6 , several sets of (k 3 ,k 6 ) could lead to comparable simulations. Hence, sets with k 3 schematically 10 times higher than above reported values would be acceptable provided that k 6 is 100 times higher (which would remain here a reasonable k 6 value). Those higher k 3 values could originate in the possibility of intramolecular reactions linked to the structure of monomeric unit (having possibly some consequences on initiation).

Initiation

The elevated values of k 1u or k 1b together with the low activation energy (typically E 1b > 100 kJ mol -1 and E 1u > 130 kJ mol -1 [2-4]) suggests:

-The existence of intramolecularly favored hydroperoxides decomposition. However, such a mechanism involves an 8 members cycle.

whereas the favorable configuration is a 6 membered cycle.

O O O H O H O O H O O H
-A catalyzed POOH decomposition via redox mechanisms involving the metallic catalysts [START_REF] Davidson | The polymerization of dicyclopentadiene: an investigation of mechanism[END_REF][START_REF] Dimonie | Some aspects of the thermal stability of linear polydicyclopentadiene (L-PDCPD)[END_REF][START_REF] Dimonie | Nature of the first exothermic peak on the DSC curve of linear polydicyclopentadiene obtained with a special catalytic system[END_REF][START_REF] Abadie | New catalysts for linear polydicyclopentadiene synthesis[END_REF][START_REF] Cuia | Degradation of ROMP-based bio-renewable polymers by UV radiation[END_REF] or their degradation products, used in high quantity (in comparison with polyolefins [START_REF] Imuta | Recent Progess on single-site catalysts[END_REF] for polymerizing pDCPD.

Propagation

As previously mentioned, the structure of pDCPD could favor some intramolecular propagation step:

by hydrogen abstraction :

by double bond opening:

It is difficult, at this state of our knowledge, to appreciate the role of intramolecular propagation in the pDCPD oxidation. However, they are certainly favored in a glassy polymer characterized by a very low segmental mobility.

Termination

In polyisoprene [START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF] and polybutadiene [START_REF] Coquillat | Thermal oxidation of polybutadiene. Part 1: Effect of temperature, oxygen pressure and sample thickness on the thermal oxidation of hydroxyl-terminated polybutadiene[END_REF], an efficient non terminating bimolecular combination of POO° radicals competes with termination:

O H °O O H °O O O H O O H O O H °°OO O O ° Table 4
. Termination rate constants of pDCPD (this work) and literature data [START_REF] Colin | Kinetic modelling of the thermal oxidation of polyisoprene elastomers. Part 1: Unvulcanized unstabilized polyisoprene[END_REF][START_REF] Coquillat | Thermal oxidation of polybutadiene. Part 1: Effect of temperature, oxygen pressure and sample thickness on the thermal oxidation of hydroxyl-terminated polybutadiene[END_REF].

The termination rate constant in pDCPD is lower by several orders of magnitude than polyisoprene and polybutadiene ones. The difference is dramatic at low temperature but becomes negligible when approaching the glass transition.

Several authors [START_REF] Waite | General theory of bimolecular reaction rates in solids and liquids[END_REF][START_REF] Waite | Theoretical treatment of the kinetics of diffusion-limited reactions[END_REF][START_REF] Begum | Modeling methyl methacrylate free radical polymerization: Reaction in hydrophilic nanopores[END_REF][START_REF] Begum | Modeling methyl methacrylate free radical polymerization: Reaction in hydrophobic nanopores[END_REF][START_REF] Martins | Molecular Mechanism of Lateral Diffusion of py10-PC and Free Pyrene in Fluid DMPC Bilayers[END_REF][START_REF] Devanne | Radiochemical ageing of an amine cured epoxy network. Part II: kinetic modeling[END_REF][START_REF] Verdu | Oxidative ageing of polymers[END_REF] have proposed that the rate constant of processes involving species in low concentrations can be expressed as a function of the rate at which species actually react together and the rate at which they diffuse in the medium. According to Waite [START_REF] Waite | General theory of bimolecular reaction rates in solids and liquids[END_REF][START_REF] Waite | Theoretical treatment of the kinetics of diffusion-limited reactions[END_REF], the reactive species (here macroradicals POO°) diffuse through the medium and the reaction occurs when the distance between both reactive species become lower than a value r 0 which will be called the "cage radius". The reaction rate would be:

2 0 2 app c πDt r 1 k .c k dt dc             
Where:

k = 4r 0 N A D, r 0 is the cage radius, -D is the radical diffusion coefficient.

>CH-uni

T (°C) polyisoprene polybutadiene

This equation was applied in the case of bimolecular quenching of excited species in initial concentration c 0 [START_REF] Martins | Molecular Mechanism of Lateral Diffusion of py10-PC and Free Pyrene in Fluid DMPC Bilayers[END_REF][START_REF] Devanne | Radiochemical ageing of an amine cured epoxy network. Part II: kinetic modeling[END_REF] that are not regenerated. It fails then for thermal ageing case where POO° are continuously produced. Hence, Verdu [START_REF] Verdu | Oxidative ageing of polymers[END_REF] has recently adapted this theory:

                                 2 1 D R D C D 6 k k 2k POO V 1 1 1 1 k k With : k D = 4r o N A D V c -1 = (4N A r 0 3 ) -1
Simulations were run using k R = k 62 , i.e. supposing that the upper limit k R value in pDCPD for the terminating POO° + POO° combination in a medium of high mobility where is equal to k 62 for polyisoprene. Using a typical value of r 0 = 10 -9 m [34], curves were acceptably simulated using the D values reported in Table 5. -At this state of our knowledge, r 0 appears as an adjustable parameter while D value calculated from inverse method depends on r 0 value. For example, if r 0 is increased from 1 to 5 nm, D is almost divided by a factor 2.

-The apparent activation energy for D would be almost the same than for k 6 i.e. about 80 kJ mol -1

(Table 3).

-D is here considerably higher than values reported for PMMA [START_REF] Emanuel | Chemical Physics of Polymer Degradation and Stabilization (New Concepts in Polymer Science)[END_REF] and for epoxy [START_REF] Devanne | Radiochemical ageing of an amine cured epoxy network. Part II: kinetic modeling[END_REF]. D values are actually the minimal values below which the model turns to be insensitive to this parameter, i.e. that they might be an overestimation. To avoid this complication linked to the predominance of termination 5, it would have been necessary to study oxidation in oxygen excess regime i.e. under an oxygen pressure high enough to suppress terminations involving P° radicals and to have only POO° + POO° termination [START_REF] Richaud | Hydroperoxide build-up in the thermal oxidation of polypropylene -A kinetic study[END_REF]. In conclusion, the kinetic analysis of our data militates in favor of diffusion controlled termination kinetics for explaining the fast oxidation of pDCPD but supplementary data are required before definitively concluding.

On the nature of carbonyl species generated in pDCPD oxidation

The ratio ketones / carboxylic acids increases with temperature (Figure 6) identically to recently observed in butyl elastomer [START_REF] Pazur | Lifetime Prediction of Thermo-oxidized Copolymers of Isobutylene[END_REF]. It seems paradoxical since carboxylic acids may result from the transformation of unstable aldehydes. Some possible reasons are:

 A competition between two modes of alkoxyl (PO°) reactions i.e. disproportionation giving a ketone and β scission giving an aldehyde:

 A direct consequence of kinetic parameters values linked to the physical state of polymer. The processes responsible for aldehydes (A) or ketones (K) formation are :

initiation events i.e. uni-or bimolecular decomposition of secondary or tertiary POOH denoted by Then:

-Initiation events generate both ketones and aldehydes (and then carboxylic acids).

-Termination by POO° + POO° termination events generates rather ketones.

Since E initiation < E POO° + POO° termination (Table 3), the formation of ketones is favored when elevating temperature and carboxylic acids is favored when lowering temperatures, consistently with the exploitation of NH 3 treatments results given in Figure 6. In other words, the ratio k 5 /k 6 which is higher than unity only for thermochemical reasons, is strongly increased when the diffusion control operates.

[

3. 3 .

 3 NH 3 treatment NH 3 treatments were performed by putting samples during 24 h in closed vessels in which NH 3 was in situ generated by combining equimolar solutions of NH 4 Cl and NaOH [8].

Figure 2 .

 2 Figure 2. DSC thermograms before (full line) and after (dashed line) SO 2 treatment for pDCPD

Figure 3 .

 3 Figure 3. Changes in hydroperoxides (), carbonyl (), double bonds () for exposures at 120 (a),

  [POOH] max actually obeys Arrhenius' law. Even if PP and pDCPD straight-lines are close, it would be premature to conclude that POOH decomposition mechanisms are the same (see "DISCUSSION").

Figure 4 .

 4 Figure 4. Arrhenius diagram of POOH decomposition enthalpy for pDCPD under air (), and PP under

-Figure 6 .

 6 Figure 6. Effect of NH 3 treatment (full lines : before, dashed lines : after) for pDCPD exposed at 120°C

Figure 7 .

 7 Figure 7. Plot of total carbonyl concentration versus total hydroxyl one at 120 (), 90 (), 55 ()

Figure 8 .

 8 Figure 8. Simulation runs for carbonyl (P=O) and hydroperoxides (POOH) at 120°C (a), 90°C (b), 55°C

P-

  S OOH or P T OOH: P S OOH  P S O° + HO°  P=O A (aldehyde) → carboxylic acid P T OOH  P T O° + HO°  P=O K (ketone) P S OOH + P S OOH  P S OO° + H 2 O + P S O°  P=O A  carboxylic acid P T OOH + P T OOH  P T OO° + H 2 O + P T O°  P=O K P T OOH + P S OOH  P T OO° + H 2 O + P S O°  P=O A  carboxylic acid P S OOH + P T OOH  P S OO° + H 2 O + P T O°  P=O K termination events resulting from the combination of two POO°, giving an unstable tetroxyde POOOOP which quasi-instantaneously decomposes into "caged" alkoxy radicals PO°. Then, three routes are theoretically possible : Formation of dialkyl peroxide : [PO° + PO°] cage  POOP Disproportionation : [PO° + PO°] cage  POH + P=O Escape from the cage with β scission of alkoxyls : [PO° + PO°] cage  2PO°  2P° + 2P=O If escape from the cage is negligible because of the above evoked low segmental mobility, then the disproportionation will be the unique source of ketones: [P S O° + P S O°] cage  P S OH + P=O K [P S O° + P T O°] cage  P T OH + P=O K [P T O° + P T O°] cage disproportionation is impossible (no abstractable hydrogen atom).

k 5 >> ( 10 -

 510 10 3 ).k 6

Table 5 .

 5 POO° diffusivity D (m² s -1 ) derived from k 6 .

	T	uni	bi
	120	5.0E-11	5.0E-12
	90	7.0E-12	1.0E-12
	55	6.0E-13	5.0E-14
	28	3.0E-14	1.0E-15
	It calls for the following comments:

ACKNOWLEDGEMENTS

Carnot Arts and Carnot Edrome are gratefully acknowledged for having granted this research.

In this latter case one can define an ''apparent'' termination rate constant (see ''APPENDIX B''):

We have thus compared in Table 4:

k 6 determined in this work for tertiary C-H with k 61 and k 62 for polyisoprene in uni-or bimolecular mode (denoted by >CH-uni and >CH-bi),

k 6 determined in this work for secondary C-H with k 60 and k 6app for polybutadiene in bimolecular mode (denoted by >CH 2 bi).

CONCLUSIONS

Polycyclopentadiene oxidation was studied in glassy state by using FITR spectroscopy, chemical derivatization treatments (NH 3 , SO 2 ), hydroperoxides titration by DSC and iodometry, mass changes by TGA under several oxygen partial pressures. The comparison of pDCPD oxidation kinetics with polybutadiene and polyisoprene ones showed that pDCPD oxidized faster despite a lower concentration of double bonds. A kinetic model was used to describe oxidation kinetics, corresponding rate constants were determined from the shape of the curves. Their values were compared with those of polybutadiene and polyisoprene in order to explain high oxidizability of pDCPD: pDCPD has higher initiation rate constants, possibly ascribed to a higher concentration of metallic catalyst residues, and lower termination constants that could be due to lower segmental mobility responsible for a diffusion control of bimolecular reactions between POO° macroradicals.

Another explanation due to the peculiar structure of pDCPD favoring intramolecular processes (initiation and propagation) was also considered.

APPENDIX A

Under the assumption of long kinetic chains, it can be shown that:

Hence, the proportionality between rate of mass increase and

are negligible which is a characteristic of the oxidation regime in which termination is dominated by P° + POO° reaction [START_REF] Verdu | Oxidative ageing of polymers[END_REF]. By deriving the set of differential equations from the above scheme, and using the simplifications made by Achimsky et al. [START_REF] Achimsky | The effect of oxygen pressure on the rate of polypropylene oxidation determined by chemiluminescence[END_REF] it can be shown that, in the domain were the oxidation rate is almost proportional to oxygen pressure:


D Rasselet

A Ruellan

A Guinault

G Miquelard-Garnier

C Sollogoub

B Fayolle
email: bruno.fayolle@ensam.eu

Oxidative degradation of polylactide (PLA) and its effects on physical and mechanical properties

Keywords: Polylactic acid, polylactide, ageing, thermo-oxidation, embrittlement

The thermo-oxidative degradation of polylactide (PLA) films was studied between 70 and 150°C. It was shown that the oxidative degradation of PLA leads to a random chain scission responsible for a reduction of the molar mass. These molar mass changes affect Tg and the degree of crystalllinity, and it was found that Tg decreases according to the Fox-Flory theory whereas the degree of crystalllinity increases due to a chemicrystallization process. A correlation between molar mass and strain at break during oxidation has been established: PLA displays a brittle behaviour when M n falls below 40 kg.mol -1 in agreement with relationships linking the critical value for embrittlement with the molar mass between entanglements.

INTRODUCTION

In the market of biodegradable polymers, polylactide (PLA) is undoubtedly one of the most promising candidates for further developments since it is not only biodegradable but also produced from renewable resources, such as sugar beet and corn starch [START_REF] Auras | Poly (lactic acid): synthesis, structures, properties, processing, and applications[END_REF]. PLA can be found under several forms depending on the enantiomeric ratio of the lactic acid group, namely PLLA (poly-L-lactic acid), PDLA (poly-D-lactic acid) and the most common one, PDLLA (poly-D,L-lactic acid), each PLA having specific properties. Some of the PLA properties are comparable to the ones of conventional polymers.

Ease of processi g, echa ical properties especiall You g's odulus , glass tra sitio temperature higher than room temperature and high transparency thus make PLA a promising material for packaging and other industrial applications [START_REF] Auras | An overview of polylactides as packaging materials[END_REF]. Therefore, understanding the oxidation and thermal degradation of this polymer is of great importance, because they affect directly the physical state of the polymer and as a consequence its performance in use.

PLA performance in terms of durability are limited by multiple chemical ageing mechanisms such as thermal decomposition [START_REF] Aoyagi | Thermal degradation of poly [(R)-3-hydroxybutyrate], poly [caprolactone], and poly [(S)-lactide][END_REF][START_REF] Kopinke | Thermal decomposition of biodegradable polyesters -II. Poly (lactic acid)[END_REF][START_REF] Wachsen | Thermal degradation of poly-L-lactid -studies on kinetics, modelling and melt stabilisation[END_REF], hydrolysis [START_REF] Hakkarainen | Weight losses and molecular weight changes correlated with the evolution of hydroxyacids in simulated in vivo degradation of homo-and copolymers of PLA and PGA[END_REF][START_REF] Li | Further investigations on the hydrolytic degradation of poly (DL-lactide)[END_REF][START_REF] Zhang | Morphological behaviour of poly (lactic acid) during hydrolytic degradation[END_REF], photo oxidation [START_REF] Copinet | Effects of ultraviolet light (315 nm), temperature and relative humidity on the degradation of polylactic acid plastic films[END_REF][START_REF] Tsuji | Photodegradation of biodegradable polyesters: A comprehensive study on poly(l-lactide) and poly(-caprolactone)[END_REF],

natural weathering [START_REF] Zaidi | Effect of natural weather on the structure and properties of polylactide/Cloisite 30B nanocomposites[END_REF] and thermo oxidation at high temperature [START_REF] Badia | Assessing the MALDI-TOF MS sample preparation procedure to analyze the influence of thermo-oxidative ageing and thermo-mechanical degradation on poly (Lactide)[END_REF][START_REF] Zhou | Nanosize and microsize clay effects on the kinetics of the thermal degradation of polylactides[END_REF]. Due to biodegradable applications, numerous studies dealing with hydrolytic ageing are available (see for instance reference [START_REF] Zhang | Morphological behaviour of poly (lactic acid) during hydrolytic degradation[END_REF]). However, no studies of ageing in atmospheric conditions in the absence of water and UV light have yet been conducted. As a consequence, we focus our study only on the oxidative degradation of PLA induced at moderate temperatures (i.e. below the PLA melting temperature).

Concerning kinetics of thermal degradation in air of PLA, different assessments of activation energy (E a ) can be found in the literature. It is noteworthy that these experimental data are based on thermogravimetric measurements (TGA mainly). For example, Gupta and Deshmukh reported the degradation process above 150°C as being a single-stage type, with lactide as the major decomposition product. From isothermal TGA measurements in air, they found the overall activation energy (E a ) of the degradation to be 104-125 kJ/mol [START_REF] Gupta | Thermal oxidative degradation of poly (lactic acid), Part I: Activation energy of thermal degradation in air[END_REF][START_REF] Gupta | Thermal oxidative degradation of poly-lactic acid[END_REF].

McNeill and Leiper investigated the degradation of PLLA under both controlled heating conditions and isothermal conditions in an inert atmosphere. A first-order kinetic model enabled them to obtain an apparent activation energy of 119 ± 4 kJ.mol -1 in the temperature range 240-270°C [START_REF] Mcneill | Degradation studies of some polyesters and polycarbonatesâ-2. Polylactide: Degradation under isothermal conditions, thermal degradation mechanism and photolysis of the polymer[END_REF][START_REF] Mcneill | Degradation studies of some polyesters and polycarbonates-1. Polylactide: General features of the degradation under programmed heating conditions[END_REF]. Babanalbandi et al. reported E a values for PLLA using isothermal gravimetric analysis over the temperature range 180-280°C under nitrogen and air. Their results showed that E a for isothermal weight loss rate was between 72 to 103 kJ/mol depending on degradation conversion [START_REF] Babanalbandi | Thermal stability of poly (lactic acid) before and after -radiolysis[END_REF]. Their hypothesis was that the PLLA degradation process followed complex kinetics, even at low conversion. Liu et al. reported that the degradation of PDLLA at processing temperatures (170°C-200°C under air or nitrogen) follows a random chain scission mechanism, with two to three degradation stages depending on atmosphere and exposure temperature (higher than 160°C). They identified that E a changes (from 137 kJ/mol to 142 kJ/mol) can be associated with the various degradation stages [START_REF] Liu | Kinetics of thermo-oxidative and thermal degradation of poly (D, L-lactide)(PDLLA) at processing temperature[END_REF].

As already stated, all these data are obtained from experiments conducted at higher temperatures than the melting temperature of PLA (160°C). Therefore, it is possible that others mechanisms and kinetic behaviour take place during degradation below 160°C, i.e. in the solid state. Moreover, TGA experiments are often questionable to follow degradation since volatile products can have multiple sources (thermal decomposition, oxidation… .

The main purpose of the present work is to investigate thermal oxidation of commercial PLA (containing a small fraction, typically 5%, of D-lactide groups) below its melting temperature. The final objective of this work is to build a model based on the following steps:

1. Understanding the oxidation mechanism at temperatures below 160°C.

2. Building a kinetic model to simulate and predict macromolecular modifications independent of exposure temperature and oxygen pressure.

3. Establishing relationships between macromolecular modifications and physical/mechanical properties valid for all exposure conditions to predict the lifetime of the PLA in dry applications.

In this study, we first identify the chain scission kinetics at different temperature conditions. Thus, to the best of our knowledge, this study constitutes the first systematic investigation concerning the ageing of PLA under thermal oxidation below its melting temperature. Second, physical properties such as glass temperature and degree of crystallinity are characterized during the oxidation process in order to correlate these properties with the molar mass changes. Finally, taking into account that tensile properties are strongly dependant on the molar mass, mechanical behaviour is characterized to establish a master curve linking properties at break and molar mass during oxidation independent of any ageing conditions.

EXPERIMENTAL 1) Material and preparation of films

The poly(D,L-lactide) (PDLLA) used in this study was supplied by NatureWorks (U.S.A.). The selected grade 2002D had a D content of 4.25% [START_REF] Niaounakis | Effects of aging on the thermomechanical properties of poly (lactic acid)[END_REF], M w = 209,000 g.mol -1 , M n = 101,000 g.mol -1 , polydispersity index: M w /M n = 2.07 (obtained from SEC measurements) and a melting temperature of 155°C (obtained from DSC measurements).

Prior to processing, pellets were dried at 90°C under dried air for 4 h to remove water traces. Films were prepared from these pellets by extrusion using a single-screw MAPRE extruder of 30 mm in diameter with a barrel of length-to-diameter (L/D) ratio of [START_REF] Viebke | Degradation of polyolefin pipes in hot water applications: Simulation of the degradation process[END_REF]

2) Ageing conditions

The films were exposed in an oven under air at constant temperature of 70, 100, 130 or 150°C. Other smaller specimens (3.5×4 cm 2 ) were introduced in an autoclave at 100°C under an oxygen partial pressure of 30 bars. At chosen times, individual samples were removed from the oven or the autoclave to be characterized.

3) Characterization a) IR analysis

Infrared spectra in ATR mode were recorded with a FT-IR spectrometer Frontier (Perkin Elmer) and SPECTRA software for acquisition. Spectra were obtained using 64 scan summations and a 4 cm -1 resolution. The OMNIC software program was used to analyse the data.

b) Size exclusion chromatography (SEC)

The changes in molecular characteristics were obtained by size exclusion chromatography (SEC) using a Waters Co. equipment. It consisted of an isocratic pump (GILSON 307), a column oven (Waters Control Module II) at 35°C, an automatic sample changer (Waters 717 plus Autosampler), a Refractive Index (RI) detector (Waters 2414) and a UV photodiode array detector (Waters 2998). The analysis was performed with THF as the eluent at a flow rate of 1 ml.min -1 . The PLA solutions were prepared in THF (60 mg polymer/3 ml solvent). The Breeze software program was used for acquisition and analysis of the Waters data. Calibration of the SEC equipment was based on polystyrene standards (Shodex Standard from Showa Denko range 3070-778000 g.mol -1 ).

c) Differential scanning calorimetry (DSC)

The differential scanning calorimeter used to measure the thermal characteristics of the PLA was a Pyris 1 (Perkin Elmer). Calibration of the apparatus prior to the experiments was performed using an Indium standard. Samples of around 9 mg were cut from the films and put in 40 l sealed alu i iu pa s. All the e peri e ts were performed under dry N 2 as a protective gas (30 ml/min). Three calorimetric scans were performed for each sample at a heating/cooling rate of 10°C/min. The first heating scan, in which the thermal history was

RESULTS AND DISCUSSION

1) Identification of oxidation products

Figure 1 shows the IR spectrum modifications of PLA films exposed to oxidation at 150°C. The band assignements for neat PLA are made according to values provided in the literature [START_REF] Kister | Effects of morphology, conformation and configuration on the IR and Raman spectra of various poly (lactic acid) s[END_REF]: δ as (CH 3 ) at 1454 cm -1 , δ s (CH 3 ) at 1383 cm -1 , δ 1 (CH) at 1359 cm -1 , δ 2 (CH) at 1292-1305 cm -1 a d as (COC) at 1208 cm -1 . Only slight changes are observed which can be attributed to a secondary crystallization process, revealed by marked modifications of intensity at 955 cm -1 and 921 cm -1 . Indeed, Meaurio has shown that during PLA crystallization, the intensity of the band at 955 cm -1 , relative to the amorphous phase, decreases and that a new band appears at 921 cm -1 indicating the presence of α cr stals [START_REF] Meaurio | Infrared spectrum of poly (L-lactide): application to crystallinity studies[END_REF].

Gardette [START_REF] Gardette | Photooxidation of polylactide/calcium sulphate composites[END_REF] and Bocchini [START_REF] Bocchini | Polylactic acid and polylactic acid-based nanocomposite photooxidation[END_REF] showed that PLA photo oxidation by UV-light irradiation leads to the formation of carbonyl products, identified as anhydride functions, characterized by a new band at 1845 cm -1 . Nevertheless in our case of thermal oxidation, we have not observed new bands, especially this expected band for anhydride functions at 1845 cm -1 (Figure 1). Only the splitting of the initial carbonyl bands at 1745-1754 cm -1 , 737-754 cm -1 and 692-711 cm -1 could be observed. However, the modifications in the 690-760 cm -1 region could also be explained by crystallinity changes which lead to other conformations of the polymer. The splitting of the initial carbonyl bands at 1745-1754 cm -1 could also be linked to the presence of new carbonyl bonds, not belonging to anhydride functions, formed during the PLA oxidation. All the modifications previously described are independent of the exposure temperature. Because of the chemical structure of the PLA, no carbonyl associated with the chain scission mechanism can be detected by FTIR (as is commonly done for polyolefines), because the intrinsic PLA carbonyl band is located in the 1700-1750 cm -1 region. Nevertheless, we can assume that PLA thermal oxidative degradation follows the mechanism shown in Figure 2. This hypothesis is made considering that the tertiary CH bond shows the lowest dissociation energy and that hydroperoxides (POOH) contribute mainly to the oxidation initiation step and follow a close-loop mechanism [START_REF] Audouin | Close loop" mechanistic schemes for hydrocarbon polymer oxidation[END_REF]. To complete this mechanism, we have to consider that the structure of the PO° radical can decompose by three possible -scissions as shown in Figure 3. Among these ones, only path (1) does not produce anhydrides [START_REF] Gardette | Photooxidation of polylactide/calcium sulphate composites[END_REF].

2) Molecular weight modifications

Figure 4 shows the changes in M n and polydispersity index (PI) = M w /M n of PLA samples as a function of time during thermal oxidation at 100, 130 and 150°C. It appears that M n decreases with time for all samples suggesting strongly that a chain scission mechanism is largely predominant during oxidation (Figure 4a). One can notice that this mechanism does not exhibit an induction period, i.e. the oxidation starts from the beginning of the exposure. As expected, the rate of molar mass reduction increases with the temperature.

However, PI displays a relative stability with values between 2 and 2.5 independent of the ageing temperature (Figure 4b). In addition, no secondary peaks can be observed in the SEC chromatograms.

This strongly suggests that chain scissions occur randomly along the polymer macromolecules under thermo-oxidative conditions and validates that degradation is homogeneous through the film thickness. As a result, the molar mass drop can be attributed to a chain scission process, knowing that if depolymerisation process had occurred at the same time, this latter mechanism would have caused a remarkable PI increase in time.

According to Saito [START_REF] Saito | Effects of high energy radiation on polymers II. end-linking and gel fraction[END_REF], the number of chain scissions, s, given in mol/kg, can be expressed by the following equation:

(

where is the molar mass of the initial sample and is the molar mass of the aged sample after an exposure time t. First, by comparing ageing in air and in water at 70°C, we can conclude clearly that the hydrolysis ageing can be neglected in air. At temperatures higher than 100°C in air, ageing mechanism is undoubtedly the oxidation.

To confirm that oxidation is the predominant mechanism of degradation, exposures under 30 bars of oxygen have been performed. Figure 6 shows the change of M n for PLA samples exposed at 100°C under an oxygen partial pressure of 0.2 and 30 bars. One can observe M n of all the films exposed to an oxygen partial pressure of 30 bars decreased significantly from the beginning of exposure, the chain scission rate being dependent on the oxygen concentration into the polymer. By assuming, as a first approach, that the oxidation rate is proportional to the chain scission rate, this result suggests that oxidation occurs in air and that the oxidation rate depends on oxygen pressure as in many polymers such as polypropylene [START_REF] Richaud | Effect of oxygen pressure on the oxidation kinetics of unstabilised polypropylene[END_REF].

Analysing the data shown in Figure 5, it is possible to assess the activation energy for the oxidation rate assuming that the oxidation rate is proportional to the chain scission rate.

E a is then found close to 60 kJ.mol -1 , which is significantly lower than values reported in the literature (see Introduction). Whereas degradation kinetic are mainly assessed by following weight loss (TGA measurements), we believe that such measurements have to be used with caution to predict PLA lifetime at low temperatures.

3) T g and degree of crystallinity changes DSC measurements on PLA films exposed to oxidation at 100, 130 and 150°C were also performed. It was observed that, whatever the exposure temperature, T g tends to decrease while the melting temperature as well as the degree of crystallinity tend to increase during the oxidation process (Figure 7). It is noteworthy that DSC thermograms (not shown here) do not display any shoulder or secondary peak during the oxidation process.

Indeed, melting temperature values increase slightly with exposure time suggesting that this secondary crystallization linked to the molar mass decrease is not due to new crystals but rather to a crystallite thickening process [START_REF] Baratian | Crystallization and solid-state structure of random polylactide copolymers: poly (l-lactide-co-d-lactide) s[END_REF].

The T g decrease can be attributed without any doubt to the chain scission process occurring during oxidation. Indeed, in the case of linear polymers, T g and number average molecular weight are linked by the Fox-Flory relationship [START_REF] Fox | Second-order transition temperatures and related properties of polystyrene. I. Influence of molecular weight[END_REF] T g = T g,∞ -k/M n , where k (K.kg.mol -1 ) is the Fox-Flory constant and T g,∞ the glass transition temperature of a PLA having an infinite molar mass.

T g is plotted as a function of 1/M n in Figure 8 for all temperatures of exposure: a linear correlation is found confirming the Fox-Flory approach can be applied to predict T g changes during a chain scission process. According to Figure 8 and the Fox-Flory relationship, we can estimate a T g,∞ value of about 55°C, which is in agreement with values proposed elsewhere for PLA [START_REF] Mohanty | Natural fibers, biopolymers, and biocomposites[END_REF].

According to the DSC thermograms, it can be observed that an annealing process occurs during the first stage (roughly 48 hours) of exposure at 100, 130 and 150°C, because of the well-known PLA cold crystallisation. After this first stage, crystallinity increases slowly with the oxidation process. In other words, crystallinity increases until about 40% in these first hours of exposure to reach a regime where crystallinity is then only driven by the chain scission. Figure 7 shows the change in crystallinity for PLA samples exposed to oxidation at 100, 130 and 150°C as a function of chain scission number. It is obvious that the crystallinity increases regardless of exposure temperature. As a result, one can conclude that the degree of crystallinity is mainly governed by the chain scission process.

The phenomenon linking crystallinity and chain scission is often called chemicrystallization. Indeed, in semi-crystalline polymers the chain scission process occurs only in the amorphous phase by freeing new chain segments. These segments can then integrate the crystalline phase if they have sufficient mobility, which is the case in the rubbery state. In our case, this process are likely to occur since exposure temperatures were well above T g , knowing PLA T g are usually measured between 47 and 60°C (Figure 8).

Fayolle et al. [START_REF] Fayolle | Review: degradation-induced embrittlement in semicrystalline polymers having their amorphous phase in rubbery state[END_REF] have proposed a relationship linking chemi-crystallization and chain scissions processes, introducing the concept of crystallisation yield. This can be defined as the number y of monomer (or elementary chain segment) units entering the crystalline phase per scission event. The instantaneous value y (unitless) of this yield is given by [START_REF] Fayolle | Review: degradation-induced embrittlement in semicrystalline polymers having their amorphous phase in rubbery state[END_REF]:

(

where M m is the molar mass of the monomer unit (M m (PLA) = 72 g/mol), x c is the degree of crystallinity, and s is the number of chain scission event per mass unit.

Figure 7 allows us to assess the term ⁄ from the slope of the straight line. One can thus notice that the degree of crystallinity increases regardless of exposure temperature, and consequently the term ⁄ can be considered as a constant. Using equation ( 2), an average value of 44 for y is found, as reported in Table 1. It is noticeable that this value is very close to the ones obtained for others polymers such as PE [START_REF] Viebke | Degradation of polyolefin pipes in hot water applications: Simulation of the degradation process[END_REF] or POM [START_REF] Fayolle | Radiation aging and chemi-crystallization processes in polyoxymethylene[END_REF] (see Table 1). As a result, a prediction for the degree of crystallinity is now possible based on a chain scission kinetic model.

4) Embrittlement process

Figure 9 shows the changes in strain at break for PLA films exposed to oxidation at 100, 130 and 150°C. The strain at break before annealing is not reported in this figure since its value is close to 20%. It is noteworthy that this value, though higher than what is usually reported in the literature for PLA [START_REF] Garlotta | A literature review of poly (lactic acid)[END_REF], has already been observed by several groups especially for extruded samples [START_REF] Boufarguine | PLA/PHBV Films with Improved Mechanical and Gas Barrier Properties[END_REF][START_REF] Rathi | Toughening semicrystalline poly (lactic acid) by morphology alteration[END_REF]. During the oxidation process, strain at break values drop with increasing exposure time and reach a value close to zero after a time depending on the exposure temperature, about 150, 250 and 500 hours for 150, 130 and 100°C respectively. One can also notice that a higher exposure temperature results in a faster decrease in the tensile properties.

It is well known that mechanical properties at break of vitreous amorphous linear polymers are strongly dependent on the molar mass. In the case of semi-crystalline polymers having their amorphous phase in the rubbery state, these properties are dependent not only on the molar mass but also on the crystalline morphology (degree of crystallinity, amorphous layer thickness) [START_REF] Fayolle | Review: degradation-induced embrittlement in semicrystalline polymers having their amorphous phase in rubbery state[END_REF]. In the case of PLA, we have seen that during oxidation the molar mass decreases whereas the degree of crystallinity increases, both aspects being intimately linked. However, in our study, tensile tests have been performed at room temperature, i.e. at much lower temperature than T g (even considering its drop during oxidation). As a result, strain at break values have been measured on oxidized PLA having its amorphous phase in the glassy state. In a first approach, we propose to investigate a possible correlation between strain at break values with the degree of crystallinity or with the molar mass (see Figures 10 and 11 respectively).

Looking at figure 10, the embrittlement process cannot be correlated to the crystallinity increase (Figure 10) since the scattering of the data does not allow the building of a master curve. As a result, the degree of crystallinity does not appear to be the main parameter which governs PLA embrittlement.

Figure 11 shows strain at break as a function of number average molar mass (M n ) for the three exposure temperatures. Indeed, it has been proposed that M n is the relevant average molar mass to correlate with the failure properties for glassy linear polymers [START_REF] Dai | Fracture toughness of polymer interface reinforced with diblock copolymer: Effect of homopolymer molecular weight[END_REF].

Here, the strain at break decreases sharply when M n decreases until a critical value of about 40 kg/mol where it reaches a plateau value close to 1%. A very good correlation is obtained independently of the considered temperature of exposure, which allows building a master curve linking molar mass with failure properties independent of chain scission kinetics.

From the master curve shown in Figure 11, the following aspects can be drawn. First, strain at break values can be predicted from molar mass values which could be simulated by a kinetic model for PLA oxidation. Consequently, knowing the chain scission kinetics, it will be possible to predict the embrittlement time, in other words the time when M n is below 40 kg.mol -1 : this time is around 150h, 250h and 500h for the PLA aged at 150, 130 and 100°C respectively. One can notice that this critical mass M' C for complete embrittlement could also be applied in the case of hydrolytic ageing.

At last, the remaining question is the physical meaning of this value of 40 kg.mol -1 for M' C . For glassy amorphous polymers, it has been proposed that M' C is linked to the molar mass between entanglements. In order to predict M' C from the polymer structure, a parameter q can be defined as q = M' C /M e where M e is the entanglement molar mass. For most of amorphous polymers, q is about 5 [START_REF] Donald | Effect of molecular entanglements on craze microstructure in glassy polymers[END_REF]. On the other hand, for semi-crystalline polymers having their amorphous phase in the rubbery state, q values are much higher (close to 50 [START_REF] Dai | Fracture toughness of polymer interface reinforced with diblock copolymer: Effect of homopolymer molecular weight[END_REF]). For PLA, M e has been assessed close to 8 kg.mol -1 [START_REF] Cooper-White | Rheological properties of poly (lactides). Effect of molecular weight and temperature on the viscoelasticity of poly (l-lactic acid)[END_REF] leading to a q value close to 5. From this point of view, it appears then that PLA at room temperature is a member of the glassy amorphous family.

  and a three-section screw. The temperature profile of the six zones of the screw was 180-180-180-185-190-190°C and the speed screw was set at 40 rpm. A flat die of 200 mm in width heated at 190°C and a chill roll Haake equipment were used to manufacture films having 145 i idth a d appro i atel i a erage thick ess. The roll te perature a d the roll speed were fi ed, respecti el , at °C a d ≈ / i .

  suppressed, was performed from 0 °C to 200°C; the cooling scan went from 200°C to 0°C and the third and last heating scan from 0°C to 200°C.The thermal characteristicsglass transition temperature (T g ), cold crystallization temperature (T cc ), enthalpy of cold crystallization (ΔH cc ), melting temperature (T m ) and melting enthalpy (ΔH m )were determined from the first scan. The degree of crystallinity (x C ) of the PLA samples was calculated using a enthalpy of fusion per mole of repeating unit of perfect crystal of infinite size (totally crystalline polymer) equal to 93 J.g -1[START_REF] Fischer | Investigation of the structure of solution grown crystals of lactide copolymers by means of chemical reactions[END_REF]. d) Tensile tests Tensile properties were obtained using a universal tensile machine (Instron model 4301) with dog bone shaped samples (NF ISO 37:2005-12 type 3 standard) cut in the films along the extrusion flow direction. Dog-bone useful cross-section was then 40 microns in thickness and 4 mm in width. Prior to tensile testing, film samples were conditioned at 23°C and 50% RH (relative humidity) for 24h. Tensile tests were performed at a cross-head speed of 10 mm/min at 23°C and 50% RH.

Figure 5

 5 Figure 5 represents the evolution of s with the exposure time during thermal oxidation at 70, 100, 130 and 150°C. For comparison with hydrolytic degradation, molar mass measurements have been performed on PLA samples exposed at 70°C in water; the related chain scission number is also included in the same Figure 5.

Figure 1 :Figure 2 :

 12 Figure 1: IR spectra of PLA films in ATR mode during thermal oxidation ageing at 150°C, (normalization at 1453 cm -1 assigned to  as CH 3 ).

Figure 3 :Figure 4 :

 34 Figure 3: Possible β-scissions of the PO° radical according to [24].

Figure 5 :

 5 Figure 5: s as a function of exposure time during thermal oxidation at 70, 100, 130 and 150°C in comparison with hydrolysis at 70°C.

Figure 6 :

 6 Figure 6: Evolution of M n as a function of exposure time exposed at 100°C under an oxygen partial pressure of 0.2 () and 30 () bars.

Figure 7 :Figure 8 :

 78 Figure 7: Degree of crystallinity as a function of the number of chain scission per mass unit.

Figure 9 :Figure 10 :

 910 Figure 9: Strain at break changes as a function of exposure time during exposure at 100, 130 and 150°C under air.

Figure 11 :

 11 Figure 11: Strain at break as a function of number average molar mass (M n ) during exposure at 100, 130 and 150°C under air.

Table 1 :

 1 Chemicrystallization yield y of some polymers in thermal oxidation

			Temperature
	Polymer	Acronym		y	Reference
			(°C)
	Polylactide	PLA	100-150	44
	Polyethylene	PE	70-105	45	[33]
	Polyoxymethylene	POM	130	40-50	[34]

CONCLUSION

The thermal oxidation mechanism of PLA at low temperatures (T<160°C) leads to a random chain scission process, responsible for the decrease of the PLA molecular weight as shown by SEC measurements.

Oxidation affects the physical and mechanical properties of the polymer, in agreement with some common behaviours observed during polyolefin oxidative ageing.

Thus, the glass transition temperature T g decreases according to the Fox-Flory theory whereas the degree of crystallinity increases due to a chemi-crystallisation process. This latter process links crystallinity and chain scissions following a crystallisation yield mechanism. The determined yield value is quantitatively comparable to the ones obtained for others polymers in thermal oxidation.

It is concluded that the strain at break decrease is clearly linked to the molar mass reduction during oxidation, independent of exposure temperature. PLA displays a brittle behaviour when M n is below 40 kg.mol -1 , which is in agreement with relationships linking the critical value for embrittlement (M' C ) with the molar mass between entanglements (M e ).