Atomic scale mechanisms controlling the oxidation of polyethylene: a first principles study
AAtomic scale mechanisms controlling the oxidation ofpolyethylene: a first principles study
Yunho Ahn a , Xavier Colin b , Guido Roma a, ∗ a Universit´e Paris-Saclay, CEA, Service de Recherches de M´etallurgie Physique, 91191Gif sur Yvette, France b PIMM, Arts et Metiers Institute of Technology, CNRS, CNAM, HESAM University,151 Boulevard de L’Hopital, 75013, Paris, France
Abstract
Understanding the degradation mechanisms of aliphatic polymers by ther-mal oxidation and radio-oxidation is very important in order to assess theirlifetime in a variety of industrial applications. We focus here on polyethy-lene as a prototypical aliphatic polymer. Kinetic models describing the timeevolution of the concentration of chain defects and radicals species in thematerial identify a relevant step in the formation and subsequent decompo-sition of transient hydroperoxides species, finally leading to carbonyl defects,in particular ketones.In this paper we first summarize the most relevant mechanistic pathsproposed in the literature for hydroperoxide formation and decompositionand, second, revisit them using first principles calculations based on Den-sity Functional Theory (DFT). We investigate the reaction paths for severalchemical reactions, for both isolated alkane molecules and a crystalline modelof polyethylene, and confirm, in some cases, the accepted activation energies;in some other cases, we challenge the accepted view finding alternative, morefavourable, reaction paths for which we estimate the activation energy. Wehighlight the influence of the environment —crystalline or not— on the out-come of some of the studied chemical reactions.A remarkable results of our calculations is that hydroxyl radicals playan important role in the decomposition of hydroperoxides. Based on ourfindings, it should be possible to improve the set of equations and parameters ∗ Corresponding author
Email address: [email protected] (Guido Roma)
Preprint to be submitted to Polymer degradation and stability February 15, 2021 a r X i v : . [ c ond - m a t . s o f t ] F e b sed in current kinetic simulations of polyethylene radio-oxidation. Keywords: polyethylene, thermal oxidation, radio-oxidation, densityfunctional theory, hydroperoxides, chemical kinetics
1. Introduction
Polyethylene (PE) is one of the most common polymers and is employedin a variety of applications such as common packaging plastic, domestic sec-tors, automobile, biomedicine, and electric cables insulation, including powercables in nuclear power plants (NPP)[1, 2, 3, 4]. During normal operationdegradation takes place through internal or external processes which end uplimiting the lifetime of the material. A crucial aging mechanism of polyethy-lene, as well as of many polymers, is oxidation; this process can be initiatedby electronic excitations produced by temperature or irradiation (UV, γ -rays,electrons, swift heavy ions)[5, 6, 7]. However, due to the complexity of the ox-idation mechanisms, many studies rely on the assumptions usually made forkinetic modelling of PE degradation [8, 9, 10, 11, 12, 13, 14, 15]. For exam-ple Niki et al. [16], in the first of a series of three papers, verified the fractionof the oxidation products by thermal decomposition based on their kineticmodels in bulk atactic polypropylene. Later, other works were devoted to thequantification of the products under thermo- and photo-oxidation conditionsby means of IR spectroscopy [17, 18, 19, 20]. In particular, carbonyl groups(namely ketones) were found to be the majority products under thermo-oxidation conditions. Despite the fact that ketones can undergo Norrish-type reactions under photochemical conditions [21], they still are majorityproducts [17]. The explanation of the kinetic path towards the formation ofketones and other carbonyl species have sparked a number of studies basedon rate theory models essentially assuming homogeneous concentration (i.e.,homogenous chemical kinetics)[15, 22, 23, 24]; in these studies, importantintermediate species include hydroperoxides (POOH groups). In a recentkinetic study by Da Cruz et al. [25, 26, 27], a new formation mechanism ofketones starting from two POOH is suggested when the bimolecular decom-position of POOH is the main source of radicals.In the last decade, the idea of investigating the elementary mechanismsof PE degradation using ab initio calculations has emerged. Although ki-netic constants and activation energies have been generally deduced fromexperiments by indirectly measuring the concentration of the products and2ssuming Arrhenius behaviour, there are reactions and processes which aredifficult to probe experimentally such as H diffusion, abstraction, or param-eters like transition ring size; the corresponding (free) energy barriers can bepredicted by first principles calculations[28, 29, 30, 31, 32, 33]. Especially,calculations have focused on the activation energy of reactions, because it cru-cially controls kinetic rate constants. However, describing PE under realisticconditions from first principles is a difficult endeavour, because of a complexmicrostructure which cannot be faithfully described by models whose sizeis limited to few tenths of atoms. Most studies focused on single molecularunits in gas phase and the search of associated transition states; other atomicenvironments such as crystalline/amorphous lamellæ of polyolefins and theirinterfaces have not, or rarely[34, 35], been tackled with ab initio methods. Inparticular, reaction processes in crystalline PE have been rarely considered,even though carbonyl defects and other species obviously affect the opticaland electrical properties by forming shallow and deep traps[34, 36, 35, 37].Besides, the formation of defects in PE during radio-oxidation occurs dueto the relatively low energy barrier for oxygen permeability, which is of theorder of 0.4 eV, diffusing from the surface all the way through the amorphousregions and to crystalline PE[38]. Not only the permeability plays a role, butalso the pristine concentration of carbonyl groups does, which in commercialPE applications can reach 0.1%, resulting from the presence of oxygen im-purities during polymerization[36]. It is therefore necessary to advance theatomic scale understanding of relevant chemical reactions through variousmodels approaching crystalline and amorphous regions and to compare themto results for gas phase molecules. In this work, guided by the kinetic schemefocusing on the production of ketones through the intermediate hydroperox-ide species, we investigate the activation energies by calculating full reactionpaths using the climbing image nudged elastic band (CI-NEB)[39] method.We discuss three main reaction pathways:i. the capture of oxygen by an alkyl radical,ii. the formation of hydroperoxides,iii. the decomposition of the latter.Two models are considered: small molecules and crystalline PE. Especially,reactions involving a hydroxyl radical are found to be particularly relevant forthe decomposition of hydroperoxides and occur spontaneously regardless ofthe position of hydroxyl radical, at variance with reactions where hydroxylsare not present. Finally, we conclude that this radical is the best candidate3eading to alkyl radical chain oxidation and the degradation of PE thanks toits reactivity.
2. Computational details
All the results presented in this paper are based on density functional the-ory (DFT). Equilibrium structures and their total energies are obtained fromthe Quantum-Espresso software package by using the PWSCF module[40].The energy barriers and reaction pathways are calculated by the climbing im-age nudged elastic band (CI-NEB) method, as implemented in the Quantum-Espresso distribution. We model amorphous regions of PE, whose density islower than the crystalline ones, by isolated molecules in large supercells (asin gas phase), while PE crystals are represented by a perfect orthorhombiclattice, as described in [37]. We will call them in the following molecularand solid models, respectively. Only the solid model is able to describe in-termolecular reactions. Pseudopotentials, norm-conserving (nc) for C and Hand both nc and ultrasoft for oxygen, were generated as described in [37] andused with the optB86b+vdW exchange-correlation (xc) functional[41] and,in some cases, with the hybrid functional vdW-DF-cx0[42].The functional optB86b+vdW includes a gradient corrected short rangexc contribution and a long-range non-local van der Waals correlation term inorder to provide a good description of van der Waals interchain interactionsin crystalline PE. In addition, for the accuracy of some specific reactions, weused the hybrid functional vdW-DF-cx0 which mixes into the same exchangepart, a portion of Hartree-Fock exchange energy to improve the description ofelectronic density localization. For molecular models, we used body-centredtetragonal unit cells in order to maximise the chain ends distance betweenperiodic images of the molecules; the unit cells were 40 ×
40 bohr wide inthe plane perpendicular to the chain and they exceeded the molecules lengthin the direction parallel to the chain so to have at least a distance of 25bohr between atoms of two different periodic images. The unit cell of thecrystalline solid is orthorhombic, containing 12 atoms, and we sampled theBZ with a 3 × × k -point mesh. To model isolated defectsin the solid we used a 2 × × × × k -point mesh. The lattice parametersof the orthorhombic unit cell in atomic units were: a=9.18 Bohr, b=13.14Bohr, and 4.84 Bohr, and for 2 × × . Results and discussion Building on previous works [31, 20] we present in Fig.1 a summary ofmost probable reaction pathways leading to the oxidation of polyethylene.We assume that alkyl radicals exist through the C-H bond dissociation by γ -irradiation (reaction 1).The reported C-H bond energies from methane to propane are in therange of 407.6-439.7 kJ/mol from experiments and 397.5-437.6 kJ/mol fromcalculations [30, 43]. After the formation of an alkyl radical, an oxygenmolecule can be captured without any energy barrier at a - • CH- site byforming a peroxy radical (reaction 2). Figure 2 presents the energy profilesof reaction 2 for both the molecular and the solid models.We checked the reaction for molecules of varying lengths and both for cap-ture far from chain end (approximately in the middle of the molecule, Fig. 2a)or at chain end (Fig. 2b). Addition of O shows barrierless energy profile notonly for the various length of alkyl chains but also for crystalline PE, withhigh exothermic enthalpies of 1.78 eV (chain centre, average), 1.75 eV (chainend, average), and 2.36 eV (PE crystal), which imply spontaneous O captureby an alkyl radical.In crystalline PE, at variance with gas phase reactions, the diffusion ofoxygen represents a limiting step. Considering the complex microstructureof PE, with crystalline and amorphous regions and interfaces between them,a full account of energy barriers for oxygen diffusion will be a study in itself.However, useful hints emerge from our calculations of a molecule in solutioninto crystalline PE. First, the molecule does not spontaneously dissociate.Second, the solution energy of the molecule (calculated with respect to pris-tine crystalline PE and a gas phase oxygen molecule) is relatively high atconstant volume, but varies considerably when varying the interchain dis-tance of PE. This can be appreciated from Fig. 3, which suggest a behavioursimilar to O in amorphous silica [44]: diffusion takes place in the amorphousmore easily than in the crystal, thanks to a wide distribution of interchainspacings; this view corroborates the usual assumption that oxygen in PEessentially diffuses through the amorphous regions[45].The typical activation energies associated to oxygen dissolving and diffus-ing for solution and diffusion in PE range from 0.35 to 0.45 eV [45]. However,in this case, this activation energy might be actually related to permeationinstead of diffusion, because, at variance with SiO where bottleneck exists5 igure 1: A summary of reaction paths leading to the (radio)-oxidation of polyethylene inthe form of ketones. Starting from the production of alkyl radicals (typically by irradia-tion, reaction 1), the capture of O molecules follows (reaction 2). The chain reaction canproceed through the formation (then decomposition) of hydroperoxides either by unimolec-ular reactions 3a-c, or by bimolecular reaction 4 and then unimomolecular or bimolecularreactions 5-11. The main stable final products are ketones and water molecules, whilehydroperoxides, hydroxyl radicals and peroxy radicals will take part in further reactions,together with alkyl and alkoxy radicals. igure 2: The capture of an oxygen molecule by an alkyl radical occurs spontaneously,as shown by the energy profiles shown here: a) capture by an alkyl radical situated ona internal carbon on alkane molecules of varying length b) capture by an alkyl radicalsituated on an end-chain carbon of alkane molecules of varying length c) capture by analkyl radical in a crystalline region of PE. between the voids where the molecule can easily sit, in PE the channelsbetween alkyl chains constitute an easy diffusion path. To check this we per-formed a NEB calculation for the migration of an oxygen molecule betweentwo equivalent neighbouring insertion sites along the channels and found amigration barrier on the order of 0.1 eV. After the capture of O by an alkyl radical (reaction 2), the reactionpathway branches into several possible channels towards the formation ofhydroperoxide groups. Let us first consider the formation of a hydroperoxideby H-abstraction from the same alkyl chain; depending on its positon it islabeled γ , β , or α (reaction 3a, 3b, and 3c). Reaction 3c does not form thehydroperoxide but a ketone and a water molecule, because its intermediateconfiguration, which is α -alkyl-hydroperoxy radical, dissociates in less than20 µ s [46, 47]. We do not consider H abstraction from more distant sites(e.g., from δ -position) because the alkyl chain is hardly bent in crystallinePE, which would presumably lead to unfavourable pathways.Figure 4 shows calculated activation energies for both molecular and solidmodels. The activation energy of H abstraction from the γ position has thelowest values among the H abstractions: it amounts to 0.84 eV and 0.82 eVfor the molecular and the solid model, respectively (Figures 4a and 4d). H ab-straction from β position shows higher energy barriers of 1.37 eV and 1.41 eV7 igure 3: Solution energy of an oxygen molecule in crystalline PE as a function of theinterchain distance. For both the red and the black curves the oxygen molecule is insertedin a model of PE with scaled in plane lattice parameters, so to modify the interchaindistance and not the dimensions along the chain. The equilibrium interchain distanceis 0.424 nm; the black curve gives the solution energy with respect to the equilibriumstructure; the red curve takes as a reference a PE crystal with the same scaled latticeparameters as that of the supercell hosting the molecule. The oxygen chemical potential,in both cases, is the energy of an isolated O molecule. igure 4: Energy profiles for reactions labeled 3a-c in Fig. 1. Panels a-c: H-abstractionsfrom γ , β , α , respectively, in a molecular model. Panels d-f: analogous reactions for crys-talline PE.Figure 5: Representative structures of the reaction whose energy profile is shown in panelf of Fig. 4, corresponding to reaction 3c of Fig. 1 as it occurs in crystalline PE. γ and β hydrogen abstraction both are endothermic, which means that a reverse re-action is more likely than the forward one, reducing the effective rate constantof hydroperoxide production. In contrast, α hydrogen abstraction is exother-mic, with the final equilibrium structure having much more stable energythan for the other two mentioned reactions. Although this reaction woulddirectly lead to ketone products as observed in thermo- or photo-oxidationof PE, it has a high activation energy (1.71 eV for the molecular model and1.54 eV for the crystal) and is thus unlikely to occur in normal conditions.In contrast with reaction 3a and 3b, showing similar behaviour in the solidand for the gas phase molecules, reaction 3c in crystalline PE leads to a dif-ferent final product: during the reaction a hydroxyl radical is produced fromP • O-OH dissociation and reacts with another neighbouring polymer chain,forming an alkyl radical and a water molecule in crystalline PE. This addi-tional process occurs spontaneously, as seen from the structural relaxation inFig. 5. Although the instability of α -alkyl-hydroperoxy radical and the reac-tivity of hydroxyl radical have already been investigated[46, 47, 48] in simplemolecular systems, not much has been done concerning these reactions incrystalline polymers nor their role in a global kinetic pathway. Regardingthe hydroxyl radical, its role in catalysing hydroperoxide formation will bediscussed in detail with reaction 9. Reactions involving additional steps aremarked by rectangles in Fig. 1.On the other hand, hydroperoxides can be formed also when the peroxyradical grabs an H atom from an adjacent polymer chain in the system. Inorder to simulate this intermolecular abstraction we chose the H atom whichis closest to the peroxy radical, in crystalline PE (reaction 4); for all bimolec-ular reactions we limited our study to the crystalline system. The calculatedactivation energy is 0.72 eV (Fig. 6). This reaction is competitive with γ -intramolecular H abstraction (Fig.4a,d) because they both contribute to theformation of a hydroperoxide. In previous kinetic modelling this sort of re-action was treated with an activation energy of 0.76 eV[15, 22], not far fromour calculated value. Calculated energy barriers can be good references for acomparison because the activation energies of intramolecular and intermolec-ular H abstraction are difficult to distinguish directly from an experimentalpoint of view. 10 igure 6: The energy profile calculated for the bimolecular reaction 4 of Fig. 1 as calculatedin crystalline PE. .3. Decomposition of hydroperoxides Reaction 5 to 9 of Fig. 1 are related to the decomposition of hydroperox-ides, which can occur both by unimolecular or bimolecular processes. At first,we can simply consider the unimolecular PO-OH bond thermal dissociation(reaction 5). As shown in Fig. 7, this reaction shows the highest activa-tion energy (2.09 eV) among the reactions in Fig. 1. From the experimentalkinetics of hydroperoxide decomposition, the contribution of this reactionis only up to 2% for temperatures below 200 o C, indicating the importanceof pseudo-unimolecular POOH decomposition such as reaction 6 when hy-droperoxide concentration is low ([PH] >> [POOH]) [33, 47, 49]. When theconcentration of POOH is small enough, reaction 6 (Fig.8) would also prevailover reaction 7 (Fig.10a). However, for the former reaction, the tradition-ally accepted reaction pathway shown in Fig. 1 comes into question. In fact,according to our calculations, it proceeds to a different product: the alkoxyradical in crystalline PE spontaneously abstracts an H atom from anotheralkyl chain, forming an alcohol as shown in Fig. 8 (this further, unexpected,step is shown in the box after reaction 6 in Fig. 1).The obtained activation energy is 1.02 eV. This reaction, among the con-sidered ones, is the one that forms the most alkyl radical chains with compar-atively low activation energy. These alkyl radicals can diffuse along or acrossthe chain. Otherwise, with the presence of oxygen, alkyl radicals do notpropagate and grab oxygen as reaction 2 by forming peroxy radical defects.We calculated the activation energy for the migration of an alkyl radicalthrough three possible atomic jumps and we show it in Fig. 9. Shimada etal. [50, 51] compared the decay rate of alkyl radicals trapped in the urea-polyethylene complex and in solution grown crystals. Although the mobilityof PE chains is higher in the urea-polyethylene complex, alkyl radicals decayat slower rate here than in the solution grown crystals, where interchain mo-tion is reduced. This finding implies that the rate of alkyl radical propagation across the chains is much faster than that along the chain in polyethylenecrystals. In agreement with such a result we find an activation energy foralkyl radical migration from chain to chain of 1.04 eV, which is much lowerthan the activation energy for alkyl migration along the chain both in themolecular and the solid models (see Fig. 9). The bimolecular decompositionof POOH (reaction 7) is relevant when the concentration of hydroperoxidesis sufficiently high or when an inhomogeneous distribution of hydroperoxidesleads to local accumulations of these groups and may become the main freeradical formation reaction[52]. Fig. 10a shows the energy profile of reaction12 igure 7: Calculated energy profile for reaction 5 of Fig. 1. igure 8: Calculated energy profile for reaction 6 of Fig. 1 in a model of crystalline PE.The calculated outcome is here different from the commonly accepted one, giving insteadtwo alkyl radicals and an alcohol, plus a water molecule. igure 9: Energy profiles for the migration of an alkyl radical. Panel a): schemes fornearest neighbor (S1) and second nearest neighbor (S2) migration along the alkane chain,and from a chain to a neighboring one (or across the chains, S3). Panels b,c: energyprofiles for migrations S1-S2 for the molecular model. Panels d,e: migrations along thechain for the solid model; panel f: migration across the chains (S3) in crystalline PE. igure 10: Energy profiles for reactions 7 (panel a) and 8 (panel b) of Fig. 1 calculatedfor crystalline PE.
7, which has a relatively high energy barrier of 1.54 eV. After the hydroper-oxide decomposition the reaction takes place depending on the existence ofthe so called cage effect —i.e., the proximity of the two radicals— and theirtendency to diffuse away from each other along the alkyl chains. When theradicals are trapped in the cage without diffusing, the reaction forms a hy-droperoxide and a ketone by abstracting the tertiary H atom of the alkoxyradical. While this process has been supposed to happen with no activationenergy, our calculation shows a small activation energy of 0.20 eV (Fig. 10b)[53, 54].Apart from the previous reaction, a hydrogen from a secondary hydroper-oxide can be attacked by other radical species resulting from the productsof other PE oxidation reactions. We considered three types of radicals: i) ahydroxyl ii) a peroxy radical, and iii) an alkyl radical. The hydroxyl radicalhas a high reactivity and easily abstracts a H atom from the alkane. DeSaint-Claire[33] reported a rate constant (10 − cm mol − s − ) of H atomabstraction by hydroxyl radical, which is much higher than that of other re-actions, but coherent with previous experimental estimations for • OH radicalreactions with alkanes[55, 56]. The induced decomposition by the radicalsamounts up to 54% of the overall hydroperoxide decomposition channel inthermo-oxidative conditions. Reactions with hydroxyl radical in crystallinePE are essential because the radical can exist not only from products of16 igure 11: Intermediate steps of reactions 9a (panels a-c) and 9b (panels d-g) of Fig. 1,showing two possible channels of hydroperoxide decomposition due to the action of ahydroxyl radical in a molecular model. The different outcome of the two reactions stemsfrom the initial position of the hydroxyl relative to the hydroperoxide group. reactions but also from outside of crystalline PE, namely the amorphousphase. Moreover, we might assume that the penetration of the hydroxylradical is comparatively lower than that of oxygen, because the • OH radicalsize is smaller than O . Therefore, we tested these reactions by putting ahydroxyl radical next to a hydroperoxide on primary and tertiary sites forreaction 9a and 9b, respectively. Reaction 9a produces a peroxy radical anda water molecule. For reaction 9b, firstly, the hydroxyl radical abstracts thetertiary H atom of the hydroperoxide. As an intermediate state an α -alkyl-hydroperoxy radical and a water molecule are formed, then the P • O-OH bondis decomposed immediately by forming a ketone and a hydroxyl radical. Boththese reactions occur spontaneously. In order to check our initial positionwe performed relaxations constraining the distance between the tertiary Hatom of the secondary hydroperoxide and the oxygen atom of the hydroxylradical; at various intermediate values. As for the oxygen capture from analkyl radical, no barrier needs to be overcome to trigger this reaction.We also verified by hybrid functional calculations the energy profile ofthose relaxations, confirming the spontaneous H-abstraction by the • OH rad-ical. Figure 11a-c and 11d-g show intermediate steps along the structuralrelaxations corresponding to reactions 9a and 9b, respectively. A hydroxylradical abstracts a H atom spontaneously, without any barrier. In partic-ular, we could see that a new hydroxyl radical is again present in the finalstate of reaction 9b; this • OH radical can react with other molecules or alkyl17 igure 12: Intermediate steps of reactions 9a (panels a-c) and 9b (panels d-i) in Fig. 1 incrystalline PE. The outcome of reaction 9b in the solid is different from the analogous onein the molecular model (Fig. 11d-g), because here the remaining • OH radical reacts witha neighbouring chain (see the arrow in panel h) giving one more water molecule (panel i). chains successively. This is important because, as we confirmed dealing withreaction 3c in crystalline PE, hydroxyl radical can be available for thesereactions to proceed spontaneously. Intermediate steps of the structural re-laxation corresponding to reaction 9a and 9b in crystalline PE are presentedin Fig. 12. While the reaction 9a in Fig. 12a-c shows the same products asits molecular model in Fig. 11a-c, the decomposed hydroxyl radical from thehydroperoxide in reaction 9b abstracts a H atom from another alkyl chainproducing an alkyl radical chain (Fig. 12d-i). The overall reaction proceedsas follows:
P OOH + • OH → P • OOH + H O → P = O + P • + 2 H O. (1)Finally, we deal with reaction 9c of Fig. 1, starting from a hydroperoxidewithout hydroxyl radical and giving a ketone and water in the final state;the corresponding activation energy is calculated by varying the number ofcarbon from 4 to 12 for comparison (Fig. 13a). In contrast with the previ-ous reactions 9a and 9b of spontaneous H abstraction, the barriers here are18 igure 13: Energy profiles calculated for reaction 9c of Fig. 1. Panel a): molecular modelsof varying sizes. Panel b): crystalline PE. quite large, regardless the size of the molecules, showing an average value of1.73 eV. The activation energy for the solid model also has the high value of2.06 eV (Fig. 13b). The energy is not far from that of reaction 5, describingthe dissociation of a PO-OH bond.Energy profiles of free radical induced decomposition of hydroperoxidesare shown in Fig.14. They both attack a tertiary hydrogen atom of a sec-ondary hydroperoxide in the same manner as in reaction 9b. Although theactivation energy of reaction 10 is higher than that for hydrogen abstrac-tion by hydroxyl radicals, we can observe that a hydroperoxide is regener-ated during the reaction; this is important during the initial stages of theoxidation[57, 58], when the formation of ketones proceeds at a constant rate.In contrast with reaction 9b and 10, the activation energy of reaction 11 ishigh and amounts to 1.54 eV. This implies that hydrogen abstraction at atertiary site is not seriously affected by an alkyl radical sitting on a nearbypolymer chain.If we consider the decomposition of hydroperoxides in absence of radi-cal attacks, the easiest path is through reaction 6, whose activation energyis 1.02 eV, all others having higher activation energies. In contrast, a hy-droxyl radical spontaneously removes the H atom of hydroperoxides, as wellas other H atoms in alkyl chains. In other words, all H abstractions re-19 igure 14: Energy profiles for hydroperoxide decomposition reactions induced by a) aperoxy radical b) an alkyl radical, sitting on a nearby polymer chain. lated to hydroxyl radical (reaction 3c, 9a, and 9b) showed barrierless energyprofiles. Especially, during the reaction 9b, a new hydroxyl radical is againgenerated after the abstraction of tertiary hydrogen, potentially triggeringa chain reaction with other alkyl radicals. Besides, a hydrogen abstractionby a peroxy radical also involves an energy barrier which is low comparedto other hydroperoxide decomposition reactions, by forming an additionalhydroperoxide as a product. Therefore, the role of peroxy and, even muchmore, hydroxyl radicals, causing chain reactions, cannot be overlooked forthe formation of ketones or other radical species and seems to be crucial forthe oxidative degradation PE.
4. Discussion
As a basis for discussion all calculated activation energies are tabulatedin Table 1.Assuming the production of alkyl radicals, and the spontaneous captureof oxygen molecules by the latter, as shown in section 3.1, the next importantstep is the formation of hydroperoxides. The reactions showing the lowestbarriers for this process are reactions 3a and 4. However, the reverse barrieris small (only a few tenths of an eV), lower than the forward barrier and ofthe diffusion barrier for the alkyl radical, suggesting that the effective rate20 able 1: Activation energies calculated in the present paper for the reactions shown inFig. 1. Energies are in eV.
Reaction Activation energy [eV]Description label in Fig. 1oxygen capture 2 γ -H abstraction 3a β -H abstraction 3b α -H abstraction 3cbimolecular H-abstraction 4unimolecular PO-OH bond cleavage 5pseudo-unimolec. POOH decomposition 6bimolecular POOH disproportionation 7bimolecular alkoxy/peroxy reaction 8POOH decomposition by • OH (1) 9aPOOH decomposition by • OH (2) 9bunimolecular POOH decomposition 9cPOOH decomposition by POO • •
11 Molecular model crystalline PEno barrier no barrier0.84 0.821.37 1.411.71 1.54– 0.722.09 –– 1.02– 1.54– 0.2no barrier no barrierno barrier no barrier1.73 (average) 2.06– 0.63– 1.54of these reactions is low, because the hydroperoxide can easily decompose inits constituents, peroxy radical and a restored alkyl chain. Another possibledirect channel of ketone formation, without hydroperoxide intermediates,could possibly stem directly from reaction 8 of Fig. 1, provided that alkoxyradical are available and get close with peroxy ones. This might be facilitatedby the reaction of hydrogen molecules with peroxy radicalsApart from the reverse reactions of 3a and 4, hydroperoxides can de-compose following reaction 6 (barrier 1.02), possibly followed by an oxygencapture by the alkyl and a subsequent reaction 8 (barrier 0.2 eV). The high-est barriers involved in those processes are not very easy to overcome at roomtemperature, although for reactions 3a and 4 the rate might be enhanced bya sufficiently large concentration of alkyl radicals. Hydroperoxide decompo-sition might be enhanced by the presence of hydroxyl radicals, however theirproduction through reactions 3c and 5 is hindered by a relatively high energybarrier ( >
5. Summary and Conclusions
Degradation mechanisms of oxidation PE were investigated by calculat-ing reaction barriers in small molecules and crystalline polyethylene. Wedivided our study in three main parts: i) oxygen capture by an alkyl radical,ii) formation of hydroperoxides, and iii) decomposition of hydroperoxides.First, oxygen reacts with alkyl radicals spontaneously, even though diffusionthrough crystalline PE might constitute a limiting step. Namely, solutionenergy of oxygen in crystalline PE is affected remarkably by interchain dis-tance. After the formation of peroxy radicals, hydroperoxides are formedby intramolecular or intermolecular H abstractions. We considered the Habstraction from α , β , and γ positions. Among the intramolecular reactions,abstraction from the γ position has the lowest activation energies, whichare 0.84 eV and 0.82 eV for molecular and solid model, respectively. Theenergy barrier of intermolecular H abstraction is 0.72 eV. Therefore, com-petition between these two reaction pathways is probable in crystalline PE.In contrast with the typical assumptions made in the literature, our cal-culations show that some reactions such as reaction 3c ( α -H abstraction),5-6 (PO-OH bond cleavage), and 9b (POOH decomposition through • OHradical), have different outcomes whether the reaction occurs in crystallinePE or in an isolated alkane molecule. In particular, in presence of hydroxylradical, further reactions take place and the activation energy of decompo-sition of hydroperoxide varies largely. Without the radical, the reaction ofbimolecular POOH decomposition leading to an alcohol, an alkyl radical anda water molecule has the minimum activation energy of 1.02 eV. For isolatedmolecules, the activation energy of the unimolecular dissociation of PO-OHis much higher, 2.09 eV. In contrast, H abstraction by hydroxyl radical isspontaneous regardless of its position, both in the crystal and on an alkanemolecule. Especially, H abstraction from a hydroperoxide in tertiary siteleads to successive reactions with other alkyl chains and finally leaves analkyl radical chain. Comparing the energy of C-H bond dissociation in purecrystalline PE, which is up to 439.7 kJ/mol, this mechanism forming alkylradical chain is much more favourable. Therefore, we conclude that, evenin presence of small concentrations of hydroxyl radicals, the reactions theyinduce may lead to a critical degradation of crystalline PE.22e believe that our study of activation energies and reaction processesprovides information at the atomic scale which can be hardly obtained byexperiments, and gives insights on polymer degradation mechanism whichare useful for further kinetic studies.
Aknowledgements
This publication was prepared in the context of the TeaM Cables project.This project has received funding from the Euratom research and trainingprogramme 2014-2018 under grant agreement No 755183. This work wasgranted access to the HPC resources of TGCC and IDRIS under the al-location 2020A0090906018 made by GENCI and under the allocation byCEA-DEN.Muriel Ferry is gratefully aknowledged for a critical reading of the manuscript.
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