Physico-chemical aspects of polyethylene processing in an open mixer. Part 18: Mechanisms and kinetics of trans-vinylene group formation

Numerous reactions can yield trans-vinylene groups on polyethylene oxidation. The first problem on data interpretation consists in the separation of the experimental data into components corresponding to well-defined mechanisms. This is achieved by fitting the experimental data into an equation comprising a linear and a parabolic term. The linear term corresponds to trans-vinylene formation at a constant rate from the beginning of the experiments. It can be attributed to trans-vinylene formation on direct decomposition of polyethylene peroxy radicals. The second term accounts for trans-vinylene group formation on cage reactions of various free radicals resulting from hydroperoxide decomposition.The first mechanism can be interpreted by formal homogeneous kinetics. Formation of trans-vinylene groups according to the second mechanism can be accounted for by the heterogeneous kinetics. It proceeds in parallel with the formation of alcohols and ketones. However, reaction of the double bonds with various reactive species in the oxidizing polymer melt does not only lead to a limiting value of the concentration in the advanced stages of polyethylene processing, but also affects the accuracy of the calculations already in the early stages.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 20: Additional product yields on bimolecular hydroperoxide decomposition with an alcohol group

Most products formed on polyethylene oxidation result from hydroperoxide decomposition. The product yields can be calculated for various mechanisms of hydroperoxide decomposition. This work concerns the reaction of a hydroperoxide with an alcohol group thought to be dominant in the advanced stages of polyethylene processing in the high temperature range (170-200 °C). Besides hydrogen abstraction by caged alkoxy radicals already envisaged previously, the possibility of β-scission is taken into account. This additional reaction introduces significant complexity into the reaction schemes. This is especially so because additional caged radical pairs must be included into the schemes and the calculations. It becomes possible to calculate the yields of aldehyde and vinyl groups that do not result from hydroperoxide decomposition in the absence of β-scission. The yields of the main oxidation products such as alcohols and ketones are not much affected by taking into account β-scission. The yield of aldehydes is important in the whole temperature range and increases considerably if the temperature is raised from 170 to 200 °C. It becomes more important than the ketone yield. The vinyl groups are formed in amounts corresponding roughly to 10-15% of the trans-vinylene groups in the temperature range of 170-200 °C.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 19: Mechanisms and kinetics of vinyl and vinylidene group formation

Vinyl and vinylidene group formation is detected in the initial stages of polyethylene processing. In the high temperature range (170-200 °C) the amount formed is small but significant. Formation of these double bonds is usually obscured by their rapid consumption. Bimolecular hydroperoxide decomposition does not seem to be an important source for these products in the early stages of processing. Vinyl and vinylidene group formation can be attributed mainly to intramolecular decomposition of special hydroperoxide groups. The data suggest vinyl groups to arise from secondary hydroperoxide groups formed in α-position to methyl branching. Intramolecular hydroperoxide decomposition involving a primary hydrogen atom from the methyl group yields a vinyl group and an aldehyde. Vinylidene groups seem to arise from secondary hydroperoxide groups formed in α-position to quaternary structures that necessarily include one methyl group. Intramolecular hydrogen abstraction of a primary hydrogen atom from the methyl group yields a vinylidene group and an aldehyde. The calculated rate parameters are in agreement with the thermochemical estimations relative to intramolecular abstraction of primary hydrogen atoms for both reactions. Vinyl groups are also formed on bimolecular hydroperoxide decomposition. The yield of vinylidene groups from the last reaction is negligible.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 21: Improved product yields on true bimolecular hydroperoxide decomposition

The product yields from the reaction between two hydroperoxide groups have been re-calculated. This is a consequence of the fact that β-scission of secondary alkoxy radicals cannot be neglected in the high temperature range of the polyethylene processing experiments (170-200 °C). It must be taken into account in addition to disproportionation/combination and hydrogen abstraction by alkoxy radicals. The increased complexity caused by the additional reaction results mainly from the larger number of caged radical pairs involved in the reactions and also in the calculations. Among other products it becomes possible to calculate the yields of aldehyde and vinyl groups that would not result from hydroperoxide decomposition in the absence of β-scission. The yields of the main oxidation products such as alcohols, ketones and trans-vinylene groups are reduced to some extent in comparison with the values calculated if β-scission is neglected. The vinyl group yield corresponds to slightly more than 10% of the yield of trans-vinylene groups in the temperature range of the experiments. The aldehyde yield is significantly larger than the vinyl group yield and is important in the whole temperature range examined. Main-chain scissions are important at the temperatures of the experiments. They become more important than the sum of the different combination reactions from a temperature of 200 °C on.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 23: Mechanisms and kinetics of trans-vinylene group consumption

There are many potential reactions for trans-vinylene groups in oxidizing polyethylene melts. The main possibilities are reactions with peroxy radicals, molecular oxygen, hydroperoxides and peracids. These different reactions can all contribute to the removal of trans-vinylene groups to some extent. This is especially so, for the reactions with hydroperoxides that have been found to be the dominant reactions with vinylidene and vinyl groups in the low temperature range. The reaction with peroxy radicals is thought to be as important relatively as with vinylidene groups. Therefore, the importance of the reaction is decreasing with increasing temperature. However, the most characteristic reaction for trans-vinylene groups can be detected without any doubt only in the advanced stages of processing. It is mechanical stress induced oxygen addition to the double bond. The discussion shows that the reaction should be important from the beginning of processing. The reaction cannot operate with vinyl and vinylidene groups, which are not part of the polyethylene main chain. After oxygen addition to the trans-vinylene group, the “ene” reaction yields an allylic hydroperoxide so that the double bond is not immediately removed. It is acid catalyzed hydroperoxide decomposition that leads to chain scission with aldehyde formation at the new chain ends.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 30: Formal kinetics of γ-lactone formation at a constant rate

There are only few mechanisms susceptible to explain γ-lactone formation at a constant rate. The formal kinetics based on these mechanisms proves to be a useful tool in the attempt to estimate the likeliness and possible relative amount of their contribution. The α,γ-keto-hydroperoxides formed in 4-position to hydroxyl groups are decomposed very rapidly at the temperatures of the experiments. The decomposition yields a carboxylic acid group in 4-position to the alcohol group and is first choice for explaining γ-lactone formation at a constant rate. However, the activation energy deduced from the formal kinetics developed for this mechanism is rather small with about 3.6 kcal/mol and hardly in agreement with the experimental value of 29.8 kcal/mol. This leads to the re-examination of the experimental data. Separate fitting of the data for the low temperature range yields the value of 4.1 kcal/mol. This value is sufficiently close to the value deduced from the formal kinetics to be compatible with it. The formal kinetics indicates also that on passing from air to pure oxygen the rate should increase by a factor of about 1.7. This is sufficiently close to the experimental value of about 2 for agreement. It is concluded that the mechanism examined can account for the bulk of the γ-lactone formed at a constant rate.The calculations for 1-peroxy-2,5-di-hydroperoxides and 1,4-keto-hydroperoxides do not yield conclusions that are as straightforward as those for the α,γ-keto-hydroperoxides in 4-position to hydroxyl groups. Although the estimated activation energies are roughly compatible with the experimental value for the low temperature range, the increase with the oxygen concentration is significantly larger than that observed experimentally. Hence, the contribution of these intermediates to the constant rate of γ-lactone formation can only be minor.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 31: Formal kinetics of γ-lactone formation from additional primary products

The potential contribution of primary oxidation products to γ-lactone formation in polyethylene is discussed. The 1,4,6-hydroperoxy-keto-hydroperoxides and the 1,2,5-tris-hydroperoxides are investigated in this work. Their formation and decomposition is examined with respect to γ-lactone formation at increasing rates in the initial stages and possibly at constant rates in the advanced stages of polyethylene processing. The formal kinetics based on the mechanisms is used to check the effect of the temperature and of the oxygen concentration. It is found that the activation energy calculated for the two mechanisms envisaged can account for different experimental values valid in the initial or advanced stages of polyethylene processing. However, the calculated increase of the rate on passing from air to pure oxygen is always much larger than the experimental value. Hence, the mechanisms examined can contribute to part only of the γ-lactone found experimentally. They should necessarily be complemented by additional mechanisms that show smaller increase with the oxygen concentration than that found experimentally.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 29: Experimental kinetics and mechanisms of γ-lactone formation

The experimental kinetics for γ-lactone formation shows more complexity than that for acids. Nonetheless, it can be concluded to the existence of a constant rate of formation from the beginning of the experiments with polyethylene melts. There is an additional term contributing to γ-lactone formation in the initial stages that is cubic in processing time. In the advanced stages of processing, in the high temperature range (170-200 °C), the concentration of γ-lactones increases linearly with the processing time.There are many mechanisms susceptible to give γ-lactones on polyethylene melt processing. Some of them are based on decomposition of intermediates formed directly on chain propagation. This is so for the α,γ-keto-hydroperoxides in 4-position to hydroxyl groups. Since decomposition of these intermediates is very fast, the reaction might account for a constant rate of γ-lactone formation from the beginning of polyethylene processing. Decomposition of the α,δ-keto-hydroperoxides formed on intramolecular reactions on chain propagation is not so fast as that of the α,γ-keto-hydroperoxides. Nonetheless, it might account for part of the delayed formation of γ-lactones. The same is valid for the mechanisms based on peroxidation of aldehydes and γ-hydroxy trans-vinylene groups that involve intermediates that are formed on polyethylene peroxidation. They might be important for explaining the cubic term as well as γ-lactone formation in the advanced stages of polyethylene processing.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 32: Formal kinetics of γ-lactone formation from secondary products. Heterogeneous kinetics

Oxidation of aldehydes and γ-hydroxy-trans-vinylene groups can yield γ-lactones. These intermediates account for γ-lactone formation in the advanced stages of polyethylene processing in air. The acyl-peroxy radical formed on free radical induced oxidation of aldehydes can abstract intramolecularly a δ-hydrogen atom to yield a peracid. Reaction of the alkyl radical formed in this reaction with the hydroperoxide group of the peracid gives a γ-lactone with simultaneous release of a hydroxyl radical. The calculated rate of γ-lactone formation according to the mechanism envisaged decreases slightly with increasing temperature (activation energy of about −5 kcal/mol). It is in agreement with the experiments that do not show significant activation energy in the high temperature range for the advanced stages of polyethylene processing. The calculated rate of γ-lactone formation is found to increase by a factor of about 2.7 if the processing experiments are performed in pure oxygen instead of in air. This is close to the experimental factor of about 2.Peroxidation of γ-hydroxy-trans-vinylene groups can also yield γ-lactones. The first possibility involves addition of a peroxy radical to the double bond followed by oxygen addition to the alkyl radical. This reaction possibly yields an α-peroxy-hydroperoxide. Intramolecular decomposition involving the two reactive groups of the α-peroxy-hydroperoxide can give an ozonide that on thermal decomposition yields among others an acid group in 4-position to the alcohol. The activation energy calculated is strongly negative so that the rate should decrease strongly with increasing temperature. Hence, the mechanism cannot contribute significantly to γ-lactone formation in the whole temperature range of the experiments. This is so in spite of the fact that the rate is estimated to increase by a factor of about 1.7 on passing from air to pure oxygen, which is close to the experimental value of approximately 2. The second possibility of transformation of γ-hydroxy-trans-vinylene groups is based on stress-induced oxygen addition to the double bond. Acid catalyzed decomposition of the allylic hydroperoxide that is formed in the reaction yields a pair of aldehydes with one of the aldehyde groups in 4-position to the alcohol group. Peroxidation of the aldehyde pair can give an acid group in 4-position to the hydroxyl group so that a γ-lactone can be formed. The activation energy calculated for the process is very small and the effect of the oxygen concentration corresponds to an increase by a factor of approximately 4.5 on passing from air to pure oxygen. It is postulated that simultaneous contribution by different mechanisms might well account for the experimental value of about 2.The heterogeneous kinetics discussed in detail allows for complementary data interpretation. It is especially suited for the understanding of the advanced stages of polyethylene processing, after some induction time.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 22: Mechanisms and kinetics of vinyl and vinylidene group consumption

The reactions of vinyl and vinylidene groups in oxidizing polyethylene melts are partly unexpected. The main possibilities of consumption that can be envisaged are reactions with peroxy radicals, molecular oxygen, hydroperoxides and peracids. These different reactions can all contribute to some extent to the removal of vinyl and vinylidene groups. However, the dominant reactions are quite specific for the two unsaturated groups and the temperature range. Consumption of vinylidene groups results mainly from reaction with peroxy radicals and with hydroperoxides. It decreases significantly in the high temperature range in which the hydroperoxides do not accumulate. Reaction with hydroperoxides seems also to be the dominant reaction removing vinyl groups in polyethylene melts at low temperature. The reaction with peroxy radicals seems negligible in the whole temperature range of the experiments. The increasing consumption rates in the high temperature range are attributed to dimerisation involving two vinyl groups. The same reaction is thought to account for molecular enlargement in polyethylene types with significant amounts of vinyl groups. In this respect it complements macro-alkyl radical addition to vinyl groups. The contributions of the two mechanisms to molecular enlargement are discussed.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 25: Mechanisms of aldehyde and carboxylic acid formation

Aldehydes and acids can be formed in numerous reactions in oxidizing polyethylene melts. Significant amounts of aldehydes result from β-scission of alkoxy radicals that are formed on bimolecular hydroperoxide decomposition. There are also large amounts of aldehydes expected from acid-catalyzed decomposition of allylic hydroperoxides as soon as enough acids have accumulated for efficient catalysis. There are difficulties in explaining the formation of aldehydes at a constant rate in sufficient amount for explaining the experimental data. There are much less difficulties with the constant rate of carboxylic acid formation. The α,γ-keto-hydroperoxides that are formed on chain propagation might account for the bulk of the acids formed at a constant rate.The foremost problems with the acids pertain to their formation at increasing rates in the initial as well as in the advanced stages. Formation and decomposition of α,β-di-hydroperoxides and α,γ-di-hydroperoxides is a possibility in this respect. Similarly, α,β-keto-hydroperoxides might be formed on peroxidation in the α-position to ketone groups in the advanced stages. There are considerable difficulties in elucidating the exact role of the aldehydes that are usually seen as the main precursors of the acids. Although there are many possibilities for transformation of aldehydes into acids, the free radical mechanisms envisaged usually have considerable disadvantages. These disadvantages result essentially from fast decarbonylation of acyl radicals and even faster decarboxylation of acyl-oxy radicals. Direct transformation of peracids into acids on reaction with double bonds is always a possibility. Moreover, in the low temperature range (150-160 °C) where hydroperoxides are accumulating, direct reaction of aldehydes with primary and/or secondary hydroperoxides will also yield acids.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 24: Experimental kinetics of aldehyde and carboxylic acid formation

The experimental kinetics for carboxylic acids shows more complexity than that for ketones. The fitting of the experimental results for the initial stages to the equation consisting of a linear and a quadratic term in processing time accounts well for the ketone data but not for the acid data. Instead of that, the data for the acids show fair fit to an equation containing a linear term and another term that is cubic in processing time. In the temperature range of the experiments the linear term is practically constant. The cubic term increases strongly with temperature. The combination of a linear and a quadratic term can account for the advanced stages of processing. The corresponding quadratic term shows strong increase if the processing temperature passes from 150 to 160 °C. However, for higher processing temperatures it remains constant within experimental error. The difference carbonyl absorbance measured after treatment of the polyethylene films with ammonia corresponds to the sum of the acids and aldehydes. It shows similarly complex kinetics. Some of the difficulties encountered with the experimental kinetics cannot be resolved with the data available. It is only the comparison with the formal kinetics based on potential mechanisms of product formation that allows for better understanding of the experimental results.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 26: Formal kinetics of aldehyde and carboxylic acid formation at a constant rate

Formation of carboxylic acids at a constant rate can be easily explained. It seems to result from the formation and decomposition of α,γ-keto-hydroperoxides. Formal kinetics based on formation and decomposition of these structural units is in agreement with the experimental findings. The activation energy deduced from the calculations is negligible, in agreement with the experimental data showing the constant rate to be practically temperature independent. Comparison of the acids with the hydroperoxides and ketones formed initially shows that the rate of oxygen addition to alkyl radicals is significantly smaller than in low molecular mass liquids. The same conclusion is reached on comparing directly the acids formed on decomposition of α,γ-keto-hydroperoxides in polyethylene melt and in hexadecane. The rate of oxygen addition in polyethylene melt is closer to 2 × 10⁵ than to 6 × 10⁵ (s⁻¹) that is valid in hexadecane.It is possible to attribute the relatively small amount of aldehydes that might be formed at a constant rate to different reactions of alkoxy radicals that are not in a cage with other radicals. These alkoxy radicals result from the addition of peroxy radicals to unsaturated bonds. This addition is followed mainly by epoxide formation and simultaneous release of an alkoxy radical.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 28: Formal kinetics of aldehyde and carboxylic acid formation in the advanced stages

The rate of acid formation at high temperature is constantly increasing but temperature independent. Two main mechanisms can account for this behavior in the advanced stages of polyethylene processing. The first mechanism is based on free radical induced oxidation of aldehyde pairs that are formed on acid-catalyzed decomposition of allylic hydroperoxides. The last will be formed essentially on mechanical stress-induced oxygen addition to trans-vinylene groups. Peroxidation of one of the aldehydes might yield an acyl-peroxy radical that is likely to abstract the labile hydrogen atom from the second aldehyde. The acyl radical formed in the reaction will abstract a hydroxyl group from the peracid formed in the same reaction. This yields an acid and an acyl-oxy radical that will give a primary alkyl radical on decarboxylation. The second mechanism involves oxidation of ketones and alcohols that accumulate in the oxidizing melt. Acid-catalyzed decomposition of the α-keto-hydroperoxides yields simultaneously an acid and an aldehyde. Formal kinetics based on each mechanism shows that they do not involve significant activation energy, as it is required by the experimental data. The dependency on the oxygen concentration deduced from the formal kinetics for the oxidation of aldehyde pairs is in agreement with the experiments.     

Thermolysis of polyethylene hydroperoxides in the melt, Part 10: Product yields from bimolecular and pseudo-monomolecular hydroperoxide decomposition

The quantitative aspects of some specific decomposition reactions of polyethylene hydroperoxides are re-examined. New data have shown that β-scission of primary alkoxy radicals is negligible in the temperature range of the thermolysis experiments. This is important for the true bimolecular hydroperoxide decomposition for which, in a first approximation, β-scission of primary and secondary alkoxy radicals had been taken into account. The calculation shows that the yields of the main oxidation products such as secondary alcohols, ketones, trans-vinylene groups and aldehydes are not considerably affected by the change. However, the theoretical yields of some minor products such as primary alcohols and of some combination reactions are strongly affected. For the pseudo-monomolecular hydroperoxide decomposition involving a segment of the polymer, the main novelty in comparison with previous work consists in taking into account β-scission of the secondary alkoxy radicals. It allows improving the accuracy of the calculated product yields. Moreover, all the theoretical calculations are on the same level of accuracy and can be used for comparison with the experimental product yields.     

Physico-chemical aspects of polyethylene processing in an open mixer: Part 27: Formal kinetics of aldehyde and carboxylic acid formation in the initial stages

There are many reactions susceptible to yield aldehydes and acids in polyethylene melts. It is β-scission of the alkoxy radicals formed on bimolecular hydroperoxide decomposition that is expected to be one of the main sources of the aldehydes that are formed at increasing rates in the early stages of polyethylene processing. Acid-catalyzed decomposition of allylic hydroperoxides is another source of substantial amounts of aldehydes. Formation and decomposition of α,γ- and α,β-di-hydroperoxides should yield acids. The activation energy estimated for these different processes is very large (about 57 kcal/mol) so that their contribution could be significant in the high temperature range only. This is different for the reaction of aldehydes with hydroperoxides to yield peroxy-hemiacetals. These intermediates can be expected mainly in the low temperature range where hydroperoxides are accumulating. Decomposition of the peroxy-hemiacetals gives acids as one of the main products. Free-radical induced oxidation of aldehydes is likely to yield peracids as far as oxygen addition is competitive with decarbonylation. The main problem is the transformation of the peracids into acids. The reaction with double bonds is expected to yield significantly more acids than thermal decomposition of peracids. If the last occurs, it will be followed mainly by decarboxylation. The overall activation energy for both processes of acid formation is negative (−18 to −20 kcal/mol). It is some combination of the various mechanisms examined that might account for the experimental activation energy for acid formation in the initial stages that is close to 18 kcal/mol.     

Thermolysis of polyethylene hydroperoxides in the melt, Part 12: Mechanisms and kinetics of thermolysis

The thermolysis of polyethylene hydroperoxides is attributed to the reaction of two hydroperoxide groups. This bimolecular reaction appears as a first-order reaction with the mean values of the hydroperoxide concentrations that can be used for the experimental verification of the kinetics. In low molecular mass liquids and solutions these findings would be irreconcilable. However, in polymer melts, this contradiction is more apparent than real. It is a consequence of the heterogeneous kinetics valid in polymer melts. The bimolecular reaction involves the decomposition of pairs of hydroperoxide groups that are relatively close in the elementary oxidation volumes. By diffusion these hydroperoxide groups can come close enough for reaction. From the chemical point of view the decomposition is a bimolecular reaction. However, from the kinetic point of view it is a first-order reaction of the hydroperoxide pairs. The dependency of the first-order rate on the initial hydroperoxide concentration is explained by the heterogeneous kinetics. The activation energy of the overall process can be related to the sum of the activation energies pertaining to the chemical reaction and to the diffusion process.     

Thermolysis of polyethylene hydroperoxides in the melt, Part 11: Relative yields of thermolysis products

The experimental ratios of the main products from polyethylene hydroperoxide thermolysis are examined. Comparison with the corresponding theoretical ratios calculated for different hydroperoxide decomposition reactions allows discriminating between the main hydroperoxide decomposition reactions. The experimental values can usually be explained best by the true bimolecular reaction involving two hydroperoxide groups. Mostly these values are significantly different from the theoretical ratios calculated for the bimolecular reaction with an alcohol group and for the pseudo-monomolecular reaction with a segment of the polymer. The bulk of the results points unequivocally to true bimolecular hydroperoxide decomposition for explaining thermolysis of polyethylene hydroperoxides.     

Thermolysis of polyethylene hydroperoxides in the melt. Part 9: Re-examination of the experimental kinetics of hydroperoxide decomposition

The experimental kinetics of decomposition of polyethylene hydroperoxides in the melt is re-examined. It is found that the rates determined are more accurate if only the “free” hydroperoxides are taken into account instead of the total hydroperoxides that include also the “associated” hydroperoxides. Then, decomposition of polyethylene hydroperoxides in the melt can be attributed unambiguously to a first-order reaction that is valid in the whole time range of the thermolysis experiments. Nevertheless, the first-order rate constant determined this way increases with the initial hydroperoxide concentration. This constitutes a significant difference with the first-order rate constants that are valid in low molecular mass chemistry and are independent of the initial concentration of the reacting species. It has already been concluded previously that this experimental first-order rate cannot be attributed to true monomolecular hydroperoxide decomposition. Hence, another or other reactions must be envisaged for the interpretation of the specific first-order decomposition of the hydroperoxides in polyethylene melts.     

Oxidation of polyethylene under irradiation at low temperature and low dose rate. Part II. Low temperature thermal oxidation

This paper deals with the kinetic modelling of unstabilised polyethylene thermal oxidation, particular attention being paid to the domain of low temperatures, typically below 80 °C. Experimental data show that the temperature dependence of the induction time t_i and the steady state rate of oxygen absorption r_S display a discontinuity at 80 °C. A model based on the hypothesis that this discontinuity concerns only the PO₂ bimolecular combination processes and is essentially explained by the competition between terminating and non-terminating PO₂ + PO₂ reactions, was proposed. With pertinent values of the Arrhenius parameters of the elementary reactions under consideration, the model fits well the experimental data (in the 40-200 °C temperature range) and is consistent with previously analysed results of radiochemical ageing. According to this model, 35-40% of the bimolecular PO₂ combinations would not be terminating at 45 °C and this proportion would increase with the temperature. Concerning terminations, the relative fraction of coupling processes, leading to peroxide bridges, would decrease relatively to the disproportionation processes when the temperature increases.