Oxidation of polyethylene under irradiation at low temperature and low dose rate. Part I. The case of “pure” radiochemical initiation

Abstract

As part of a study on the kinetic modelling of polyethylene oxidation under irradiation at low temperature and low dose rate, this first part deals with the kinetic regime in which thermal initiation, linked to hydroperoxide decomposition, is negligible compared to radiochemical initiation due to polymer radiolysis. The kinetic analysis is based on results published 30 years ago by Decker, Mayo and Richardson. A small modification of their mechanistic scheme, consisting in the introduction of a non-terminating bimolecular combination of PO 2 radicals, leads to a more consistent set of radiochemical yield values. The most significant change is a decrease in the radiochemical yield of radicals G i from 10 to 8. At 45 °C, termination of PO 2 radicals is not very efficient: 35–40% of the PO 2 + PO 2 encounters are non-terminating, 75% of the termination events lead to peroxide bridges, the rest is a disproportionation according to the Russell mechanism. Keywords Polyethylene Irradiation Oxidation Kinetics Radiochemical yields Termination 1 Introduction This article deals with the ageing of polyethylene (PE) under irradiation at low dose rate, and low temperature, in conditions close to the use conditions of electrical insulation in nuclear plants where lifetimes of several decades are expected. In a first step, we attempt to identify the kinetic parameters corresponding to the exposure of the non-stabilised polymer, in oxygen excess (no diffusion control). In recent work [1] , the existence of two asymptotic kinetic regimes was shown: (i) the “pure” thermal oxidation regime for a dose rate I → 0. In this regime, radical formation results only from hydroperoxide decomposition. (ii) The “pure” radiochemical oxidation regime for I → ∞ . In this regime, radical formation results only from polymer radiolysis (in fact, this assumption is valid only for dose rate values higher than 0.5 Gy s −1 at temperatures lower than 50 °C [1] ). This first part of the article deals with this latter regime. Although the corresponding dose rate domain is easily accessible, and kinetic modelling is considerably simplified by the constancy of the initiation rate (which is proportional to dose rate), detailed kinetic studies of this regime are relatively scarce. Fortunately, Mayo and co-workers published in the 1970s a series of historical papers among which one, co-authored by Decker et al. [2] , deals with PE oxidation mechanisms and kinetics in the kinetic regime under consideration. The exposure conditions and film thicknesses were chosen in order to avoid complications due to oxygen diffusion control. A quasi-exhaustive quantitative analysis of propagation (hydroperoxides) and termination (peroxides, carbonyls) products allowed them to establish the main features of this kinetic regime. But this paper is especially important by its methodological aspects. The proposed approach, which will be called in the following the DMR model, has not been overtaken 30 years later. A careful reading of this article reveals, however, the existence of small discrepancies that suggest the possibility to improve both the mechanistic and the kinetic schemes. Our aim is first to show these discrepancies and then to propose a modification of the mechanistic scheme based on a reasonable hypothesis, which would lead to a fully consistent set of kinetic data. 2 Basic principles of the DMR study DMR [2] studied the radiochemically-initiated oxidation of low and high density polyethylenes at 45 °C in air, at various doses and dose rates. The samples are thin films (25 μm thick); oxidation rate was found to be insensitive to an increase in oxygen pressure so that it is assumed that oxygen is in excess and that only terminations of PO 2 radicals have to be taken into account. These terminations are supposed to be bimolecular, which is at least partially true since peroxides POOP obviously coming from bimolecular PO 2 combinations, constitute the major part of termination products. The proposed mechanistic scheme is thus: (I R ) Polymer (PH) + hν → P ( r i ) (II) P + O 2 → PO 2 ( k 2 ) (III) PO 2 + PH → PO 2 H + P ( k 3 ) (VI) PO 2 + PO 2 → inactive products + O 2 ( k 6 ) The following kinetic scheme can be derived: (1) ⅆ [ P ] ⅆ t = r i − k 2 [ O 2 ] [ P ] + k 3 [ PH ] [ PO 2 ] (2) ⅆ [ PO 2 ] ⅆ t = k 2 [ O 2 ] [ P ] − k 3 [ PH ] [ PO 2 ] − 2 k 6 [ PO 2 ] 2 (3) − ⅆ [ O 2 ] ⅆ t = k 2 [ O 2 ] [ P ] − k 6 [ PO 2 ] 2 (4) ⅆ [ POOH ] ⅆ t = k 3 [ PH ] [ PO 2 ] From the classical hypothesis of stationary state for the radical concentration, one obtains: [ PO 2 ] = ( r i 2 k 6 ) 1 / 2 so that the rates r and corresponding radiochemical yields G are given by: (5) r POOH = ⅆ [ POOH ] ⅆ t = k 3 [ PH ] ( r i 2 k 6 ) 1 / 2 → G POOH = r POOH 10 − 7 I = k 3 [ PH ] G i 1 / 2 ( 2 × 10 − 7 k 6 ) 1 / 2 I − 1 / 2 = β I − 1 / 2 (6) r ox = − ⅆ [ O 2 ] ⅆ t = r POOH + r i 2 → G ox = r ox 10 − 7 I = β I − 1 / 2 + G i 2 with β = ( k 3 [ PH ] G i 1 / 2 ) / ( 2 × 10 − 7 k 6 ) 1 / 2 Since all the oxidation products which are not hydroperoxides are termination products, it can be written: (7) G Ter = G ox − G POOH = G i 2 If, after a given exposure time t , the concentration of a given specie is [Y], the corresponding radiochemical yield G Y is calculated assuming a constant rate: (8) G Y = [ Y ] 10 − 7 I t The dose rate dependence of G Y can be ascribed: (9) G Y = α + β I − 1 / 2 where α (the “zero order” part of G Y ) is linked to initiation or termination reactions, whereas βI −1/2 (the “half order” part of G Y ) is linked to propagation. In addition to peroxides, DMR find carbonyl groups. The “zero order”...