A mathematical modeling of crosslinking between components of a polymer composition

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.63759

Keywords:

degree of crosslinking, polymer compositions, deformation and strength curves of polymeric films

Abstract

The paper presents a method of mathematical modeling as a most promising way to determine the structural parameters of the polymer network. In polymer systems, modeling is developed in different directions, although its capacity in studying the processes of crosslinking polymer networks is not used to full extent.

We used the interpolation method to build the 4th-degree Lagrange interpolation polynomial that allowed determining the optimal amount of a crosslinking agent. A three-factor model of crosslinking polymeric components was constructed with the use of the multiple regression equation. The model showed the main concentration of the composition components that would ensure the degree of crosslinking at an optimal level of 25–50 %. The research resulted in designing four polymer compositions. It was found that films with a crosslinking degree of 20–25 % have the relative elongation rate of 682 % and the breaking load value of 18 H.

The findings of the physical and mechanical research of films were used to build the deformation and strength curves. It was determined that when the optimal degree of crosslinking is 20–21 %, urethane-based polymer compositions (PC-2 and PC-3) have a relative elongation rate of 300–700 % and the breaking load of 40–50 MPa, which proves the dependence of the deformation the strength characteristics of films on the degree of crosslinking between the components.

The paper presents charts of the degree of crosslinking dependence on the component concentration. The constructed graphs of the response surface allow selecting the required concentrations of ingredients for obtaining polymer films with a desired crosslink density. The calculated structures of networks have proved the relevance of the suggested mathematical models (the coefficient of determination R2 equaling 0.92 and 0.98).

Author Biographies

Maria Pasichnyk, V. A. Sukhomlinsky Nikolayev National University 24 Nicholas str., Nikolaev, Ukraine, 54030

PhD, Associate Professor

Department of Chemistry and Biochemistry

Elena Kucher, V. A. Sukhomlinsky Nikolayev National University 24 Nicholas str., Nikolaev, Ukraine, 54030

PhD in Agricultural Sciences, Associate Professor

Department of laboratory diagnostics

References

  1. Zubov, P., Suhareva, L. (1982). Struktura i svoystva polimernyih pokryitiy. Moscow: Himiya, 256.
  2. Pasechnik, M. (2013). Tekstilnyie materialyi s polimernyim pokryitiem: razrabotka kompozitsionnyih sostavov i tehnologii naneseniya. Kherson: Aylant, 350.
  3. Trofimov, N., Kanovich, M., Kartashov, E. (2005). Fizika kompozitsionnyih materialov. In 2 volumes. Vol. 1. Moscow: Mir, 456.
  4. Vlasov, S., Kandyirin, L., Kuleznev, V. (2004). Osnovyi tehnologii pererabotki plastmass. Moscow: Himiya, 600.
  5. Tsivin, M. (2002). Mnogofaktornyiy eksperiment: graficheskaya interpretatsiya dannyih. Kyiv: IGiM, 120.
  6. Pyishnogray, G., Tretyakov, I., Altuhov, Yu. (2012). Matematicheskoe modelirovanie protsessa formovaniya polimernyih plenok v usloviyah dvuhosnogo rastyazheniya s uchetom teploperenosa. Prikladnaya mehanika i tehnicheskaya fizika, 53 (2), 84–90.
  7. Tarasov, V., Belyakov, E. (2011). Matematicheskoe modelirovanie protsessa neizotermicheskogo otverzhdeniya polimernyih kompozitnyih konstruktsiy. Vestnik MGTU im. N. E. Baumana. Ser. “Mashinostroenie”, 1, 113–120.
  8. Ryibalko, A., Manko, T., Rozhkovskiy, V. (2015). Matematicheskaya model protsessa otverzhdeniya izdeliy iz polimernyih kompozitnyih materialov. Voprosyi proektirovaniya i proizvodstva konstruktsiy letatelnyih apparatov, 4, 124–131.
  9. Navratil, M., Kolomaznik, K., Kresalek, V. (2007). Approach to mathematical model of the cross-linking reaction of polymer composite. AT&P journal PLUS2, 21–23.
  10. Wulkow, M. (2008). Computer Aided Modeling of Polymer Reaction Engineering-The Status of Predici, I-Simulation. Macromolecular Reaction Engineering, 2 (6), 461–494. doi: 10.1002/mren.200800024
  11. Askadskiy, A., Hohlov, A. (2009). Vvedenie v fiziko-himiyu polimerov. Moscow: Nauchnyiy mir, 384.
  12. Pasechnik, M., Kulish, I., Saribekov, G. (2010). Composition development for fabric with polymer coating. Eastern-European Journal of Enterprise Technologies, 5/6 (47), 8–12. Available at: http://journals.uran.ua/eejet/article/view/3164/2967
  13. Pasichnyk, M. (2015). Research the crosslinking density and swelling kinetics of self-crosslinkable acrylic polymers. European Science and Technology: 12th International scientific conference. Munich, 26–30.
  14. Slepchuk, I., Kulish, I., Saribekova, D. (2014). Issledovaniya vliyaniya sshivayuschih agentov na harakteristiki prostranstvennoy setki stirol-akrilovogo polimera Lacrytex 640. Tehnologiya tekstilnoy promyishlennosti, 2 (350), 83–86.
  15. Saribekova, D., Kulish, I., Slepchuk, I. (2013). Issledovanie svoystv poliuretanovoy dispersii Akvapol 12 dlya sozdaniya polimernyih pokryitiy na tekstilnyih materialah.Vestnik Hmelnitskogo natsionalnogo universiteta, 5, 101–105.
  16. Slepchuk, I., Kulish, I., Saribekov, G. (2012). Vliyanie besformaldegidnyih preparatov na protsess otverzhdeniya akrilovyih polimerov, ispolzuemyih v kompozitsionnyih otdelochnyih sostavah. Vestnik Hersonskogo natsionalnogo tehnicheskogo universiteta, 2 (45), 180–183.
  17. Abdullin, I., Gumerov, A., Shafigullin, L. (2012). Avtomatizirovannaya informatsionnaya sistema prognozirovaniya svoystv polimernyih kompozitsionnyih materialov na osnove regressionnogo analiza. Vestnik Kazanskogo tehnologicheskogo universiteta, 16, 240–243.
  18. Braun, D., Sherdon, G., Kern, V. (1976). Prakticheskoe rukovodstvo po sintezu i issledovaniyu svoystv polimerov. Moscow: Himiya, 392.
  19. Kalach, A., Zenin, Yu., Starov, V. (2015). Vliyanie strukturyi polimerov na ekspluatatsionnyie svoystva materialov. Vestnik Voronezhskogo instituta GPSMChS Rossii, 1 (14), 12–17.
  20. Lieleg, O., Claessens, M. M. A. E., Bausch, A. R. (2010). Structure and dynamics of cross-linked actin networks. Soft Matter, 6 (2), 218–225. doi: 10.1039/b912163n
  21. Lin, S., Gu, L. (2015). Influence of Crosslink Density and Stiffness on Mechanical Properties of Type I Collagen Gel. Materials, 8 (2), 551–560. doi: 10.3390/ma8020551
  22. He, J. Y. (2013). Crosslinking effect on the deformation and fracture of monodisperse polystyrene-co-divinylbenzene particles. Express Polymer Letters, 7 (4), 365–374. doi: 10.3144/expresspolymlett.2013.33
  23. Averko-Antonovich, I., Bikmullin, R. (2002). Metodyi issledovaniya svoystv polimerov. Kazan: KGTU, 503–506.
  24. Favre, E., Nguyen, Q. T., Schaetzel, P., Clément, R., Néel, J. (1993). Sorption of organic solvents into dense silicone membranes. Part 1. Validity and limitations of Flory-Huggins and related theories. J. Chem. Soc., Faraday Trans., 89 (24), 4339–4346. doi: 10.1039/ft9938904339
  25. Heinrich, G., Straube, E., Helmis, G. (1988). Rubber elasticity of polymer networks: Theories. Advances in Polymer Science, 85, 33–87. doi: 10.1007/bfb0024050

Downloads

Published

2016-04-27

How to Cite

Pasichnyk, M., & Kucher, E. (2016). A mathematical modeling of crosslinking between components of a polymer composition. Eastern-European Journal of Enterprise Technologies, 2(6(80), 4–12. https://doi.org/10.15587/1729-4061.2016.63759

Issue

Vol. 2 No. 6(80) (2016): Technology organic and inorganic substances

Section

Technology organic and inorganic substances

License

Copyright (c) 2016 Maria Pasichnyk, Elena Kucher

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.