Abstract
The problem of oxygen and ethylene diffusion in the framework of classical Fick’s law are considered. It is assumed that the material is placed in a limited sealed container. This leads to the need to take in account the parameters of the gas in the free volume. The problem has a non-stationary and nonlinear character. The temperature of the medium is assumed to be constant. Numerical results describing the process of oxygen evacuation from polyethylene and the process of ethylene diffusion into the material are obtained. The problem of ethylene diffusion is solved for the case of the formation of molecular bonds during gamma-ray irradiation due to absorbed ethylene. The finite element method was used to solve the problems. The main characteristics of the noted processes are determined. The results are of practical value for determining the irradiated time of polyethylene, which provides the required level of crosslinking of macromolecules.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kniazev, V.K., Sidorov, N.A.: Irradiated polyethylene in engineering. Chemistry, Moskov, vol. 374 (1974)
Skroznikov, S.V.: Structural and mechanical properties formation regularities in crosslinked polyolefins for cable engineering. Ph.D. thesis. Moscov, vol. 149 (2015)
Holder, S.L., Hedenqvist, M.S., Nilsson, F.: Understanding and modelling the diffusion process of low molecular weight substances in polyethylene pipes. Water Res. 157, 301–309 (2019)
Shyichuk, A., Tokaryk, G.: Simulation-assisted evaluation of acetylene effect on macromolecular crosslinking rate under polyethylene irradiation. Macromol. Theory Simul. 12(8), 599–603 (2003)
Golubenko, I.S., Prokop’ev, O.V., Dalinkevich, A.A.: Method of radiation cross-linking polyolefin products. Russian Federation Patent no. 2004104113/04 (20016)
Oniskiv, V.D., Stolbov, V., Khatiamov, R.K.: On one control problem of the process of gamma irradiation of the polyethylene. Appl. Math. Control Sci. 3, 119–130 (2019)
Mehrer, H.: Diffusion in Solids, p. 654. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71488-0
Oniskiv, V.D., Yakovlev, A.: Some results of solving the non-stationary problem of gas diffusion in polyethylene. Appl. Math. Control Sci. 2, 41–51 (2021)
Meshkova, I.N., Ushakova, T.M., Gul’tseva, N.M.: Determination of ethylene and propylene solubility constants in polyethylene and polypropylene and their application for calculation of kinetic parameters of gas-phase and suspension homo-polymerization and copolymerization of olefins. High-Mol. Compd. Ser. A 46(12), 1996–2003 (2004)
Gerasimov, G.N., Abkin, A.D., Khomikovskii, P.M.: Mechanism of the heterogeneous polymerization of ethylene under the action of ionizing radiation. High-Mol. Compd. 5(4), 479–485 (1963)
Börjesson, A., Erdtmana, E., Ahlström, P., Berlin, M., Andersson, T., Bolton, K.: Molecular modelling of oxygen and water permeation in polyethylene. Polymer 54(12), 2988–2998 (2013)
Bekman, I.N.: The Diffusion Mathematic: School-Book, vol. 400. OntoPrint, Moskov (2016)
Kozlov, G.V., Zaikov, G.E.: Gas diffusion in semi-crystalline polyethylene and in it’s flux. High-Mol. Compd. Ser. B 45(7), 752–758 (2003)
Kozlov, G.V., Burya, A.I., Zaikov, G.E.: The structure influence on gas diffusion in polyethylene. Rep. Natl. Acad. Sci. Ukraine 2, 138–142 (2007)
Acknowledgment
The research was carried out with the financial support of the Government of the Perm Region in the framework project: “Models, methods and digital technologies for creating functional composite and polymer materials by processing them with concentrated gamma-ray streams in various gas environments” (grant № C- 26/581).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Oniskiv, V.D., Yakovlev, A.Y., Oniskiv, L.M., Gitman, I.M. (2022). Particular Problems of Gas Diffusion in Polyethylene. In: Antipova, T. (eds) Digital Science. DSIC 2021. Lecture Notes in Networks and Systems, vol 381. Springer, Cham. https://doi.org/10.1007/978-3-030-93677-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-93677-8_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-93676-1
Online ISBN: 978-3-030-93677-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)