R.A. Jones

Reactions of amorphous PE radical-pairs in vacuo and in acetylene: A comparison of gel fraction data with Flory-Stockmayer and atomistic modelling analyses

Abstract The radiation-induced crosslinking of linear low density polyethylene chains has been analysed theoretically using an atomistic analysis and a Flory-Stockmayer (FS) analysis. Experimentally, gel fractions greater than the theoretical maximum obtainable, assuming every radical reacts to form a crosslink (namely, D.G(R) 2 ), indicate the occurrence of chain-reactions both in the presence of acetylene and in vacuo. Based on previous studies, chain-reaction mechanisms are postulated, involving unterminated polyenes in acetylene and scission-generated vinyls in vacuo. Accordingly, numerical comparisons of the theoretical and experimental gel-fraction results, as a function of dose (D), have been used to calculate the number of ‘gel-effective’ chain-steps per initial alkyl radical generated (NCS, D) for both the atomistic and FS analyses. Both systems of analysis show that, as dose increases, NCS, D for the acetylene and in vacuo results decrease from maximum values at or just after the gel points. The decay is interpreted as resulting from the increased probability of radical-radical termination reactions towards higher levels of dose. Although there are differences between the two analyses, both give essentially the same interpretation of the experimental results. The atomistic analysis predicts maximum values of NCS, D of 9.0 in the presence of acetylene and 2.9 in vacuo. The corresponding values from the FS analysis are 9.4 and 2.8 respectively. As the dose is increased further, the atomistic analysis gives 2.1th- and 2.6th-order decays of NCS, D as functions of the dose, for the acetylene and in vacuo results respectively. The FS analysis gives, correspondingly, 2.6th- and 2.8th-order decays. General equations are developed for irradiated polymers, which relate gel fraction to the dose and the number of initial radicals generated in a pre-irradiated number-average degree of polymerization, via NCS, D.

Radiation-induced crosslinking of acetylene-impregnated polyesters

Enhanced crosslinking and reduction in chain scission are found in the amorphous regions of polycrystalline polyesters, when they are irradiated in the presence of acetylene. Increasing the chain length of the alkyl moiety is also found to decrease the extent of damaging main chain scission.

Gel fractions and chain reactions in irradiated polyethylenes

Abstract Atomistic computation, Flory–Stockmayer theory and rheological measurements have been applied to the analysis of gel-fraction data from two linear low density poly(ethylene)s (LLDPEs) irradiated and annealed either in vacuo or in the presence of acetylene. Good agreement between the three methods, as the extent of crosslinking at any given gel-fraction, confirm the presence of free radical mediated chain reactions, even during in vacuo irradiations. It is proposed that chain reactions, rather than polydispersity and structure, explain most of the deviation from ideal Charlesby–Pinner behaviour of irradiated polymers.

An investigation into the relationship between 'gel-effective' and total numbers of crosslinks in irradiated LLDPE

Rheological data for crosslinked LLDPE samples have been related to previous studies of similar materials. It has been found possible to attribute a range of time constants (λ0in) and characteristic moduli (G0i) to the ‘gel-network’ strength factor (S) of all these materials. Comparability established, the number of crosslinks estimated rheologically are compared with those computed by molecular modelling for equivalent gel fractions. Below about 0·4 gel fraction, all crosslinks are found to be effective in forming the gel. Beyond about 0·85 gel fraction, further increase in crosslinks produces only small changes in moduli; this is observed at around five crosslinks per pre-irradiated molecule. A simple power relationship is found between the rheological and ‘gel-effective’ numbers of crosslinks. A previously postulated relationship between the gel fraction and numbers of ‘gel-effective’ crosslinks appears to be universal for LLDPEs. ‘Gel-networks’ arise at low gel fractions. Rheological data suggest that there is a dose-related progression of ‘gel-network’, from initial viscoelastic polymer, through a medium containing a mobile distribution of ‘gel-networks’ of increasing size, to a temporary ‘gel-network’, still able to relax, and finally a saturated permanent network. ©1997 SCI

Computer modeling of the formation of radical pairs in amorphous high density polyethylene (HDPE)

Hydrogen atom ejection and subsequent radical pair formation have been modeled in a simple atomistic study employing a BIOSYM amorphous polyethylene macrocell. Mean radical pair distances have been obtained for various maximum hydrogen displacement vibrational cone angles (o) in the model. o angles extrapolated from these data, which correspond to experimentally determined mean radical pair distances of Dubinskii et al. (ca. 5.6 A) and Iwasaki et al. (ca. 5.75 A), are found to be close to o angles calculated from hydrogen atom ejection theory. The Dubinskii et al. mean is thought to be the best determination, because the associated model o angle (ca. o = 15°) is the closest to o * angles calculated for excited states of methane. The simple computer model thus supports the mechanism of radical pair formation in solid n-hydrocarbons and polyethylenes. In corroborating the theory for radical pair formation, the theory for polyene crosslinking termination reactions in amorphous polyethylenes irradiated in the presence of acetylene is also supported, because the mechanism requires the prior formation of radical pairs that are separated by distances of the order of those found by Dubinskii et al. The model is transferable to the study of radical-pair reactions in solid n-hydrocarbons irrespective of branching and density variations. A distribution function of radical pair distances from this model, which corresponds to the Dubinskii et al. experimentally determined mean distance, is given for amorphous HDPE.

Understanding the elastomeric properties of polymer networks

It is shown that Monte-Carlo (MC) simulations of the elastic behaviour of chains in networks using realistic rotational-isomeric-state (RIS) chain models are able to reproduce experimentally observed deviations from Gaussian network behaviour in uniaxial extension and also to interpret, quantitatively, stress-optical properties. In stress-strain behaviour, an increase in the proportion of fully extended chains with increasing macroscopic strain gives rise to a steady decrease in the rate of change of the Helmholtz energy of a network, causing a reduction in network modulus at moderate macroscopic strains. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases. To evaluate stress-optical properties, the average orientation of segments with respect to the deformation axis is calculated, taking into account the interdependence of segment orientation and chain orientation as chains become more extended and aligned under uniaxial stress. The MC method gives, in agreement with experiment, values of stress-optical coefficient that are dependent upon both deformation ratio and network-chain length. The method highlights serious shortcomings in the classical Gaussian model of stress-optical behaviour. Applications of the simulation methods to the quantitative modelling of the stress-strain behaviour of poly(dimethyl siloxane) networks and the stress-optical behaviour of polyethylene networks are described.