Weakening of a Polyethylene Chain by Methyl Side Groups

Abstract

The effect of methyl side groups on the strength of a single polyethylene chain is calculated with Density Functional Theory. Using transition state theory, the scission rate is calculated as function of stress for bonds next to a methyl side group. The increase in the scission rate due to the presence of the side group is maximal at zero stress/strain, where it is enhanced by a factor of 5,000. This increase results from a hyperconjugation interaction between the methyl side group and the radical that is formed during the scission process. The calculated scission rate is used as input for a model in which a fiber consists of independent chains. With the help of the model we estimate how much the tensile strength of polyethylene fiber can deteriorate due to the presence of methyl side groups. The strength of the fiber is reduced with 6% for a concentration of one side group in 10 main chain carbon atoms.

Keywords:

• Polyethylene
• Chain scission
• Defects
• Side groups

Acknowledgment

This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).

Notes

^aBoudreaux has reported values of 19 PGa but at a very low level of accuracy.

^bThese numbers are total energy differences. The zero‐point motion is not accounted for.

^cAs in our previous study on ideal PE, the prefactor Ω is assumed to be independent of stress/strain. Also the effect of the side group on the prefactor is neglected, and the value that we previously obtained for ideal PE is used (see Ref. [8]). These approximations are reasonable: The change in νresulting from the shifts of a few eigenmodes is small compared to the changes resulting from a different energy barrier, as the effect of the latter is strongly amplified by the exponentiation. The prefactor was calculated in the harmonic approximation. Using classical statistics it is Ω = 2.1 × 10¹⁵s^− 1. The temperature‐dependent quantum corrections are described by an effective change of the prefactor and the energy barrier.

^dIn fact, only the component of the elongated bond along the chain axis is fixed.