Download the full version of the article (in PDF format)
V. G. Rezanova, N. M. Rezanova
«Mathematical Modelling and Software Development to Optimize the Composition of Four-Component Nanofilled Systems»
PACS numbers: 07.05.Tp, 61.41.+e, 61.46.-w, 81.05.Zx, 81.07.Nb, 82.35.Np, 89.20.Bb
With the application of the simplex-centroid method, a plan of experiments in the studied area of factor space for the four-component heterogeneous systems is developed. The required number of points in a plan is 14. The placement of points-candidates in a simplex is performed by means of the McLeanľAnderson algorithm. To calculate the coordinates of the experiment-plan points, a program is developed in Delphi environment. The results of the experiments created a mathematical model in the form of a set of regression equations, which establishes the relationship between the content of ingredients and the properties of the four-component composition. The optimization of the composition of polypropylene/copolyamide (PP/CPA) mixture, which contains silica as a nanofiller and silicone substance as a compatibilizer, is performed using the generalized Harrington criterion. As found, the combined action of both modifying additives with a total content of 2.0 wt.% allows to realize the process of formation of the PP microfibrils within the CPA matrix and to increase the concentration of dispersed-phase component to almost 45 wt.%. Complex polypropylene filaments obtained from composition with optimized percentage are characterized by high strength, self-abrasion resistance, and hygroscopicity.
Keywords: simplex-centroid design, plan of experiment, software, mathematical model, four-component system
1. S. Thomas, R. Mishra, and N. Kalarikka, Micro and Nano Fibrillar Composites (mfcs and nfcs) from Polymer Blends (Cambridge, UK: Woodhead Publishing: 2017).
2. L. A. Utraki and C. A. Wilkie, Polymer Blends Handbook (LondonľNew Yorkľ HeidelbergľDordrecht: Springer: 2014). doi.org/10.1007/978-94-007-6064-6.
3. Vu Anh Doan and Masayuki Yamaguchi, Recent Res. Devel. Mat. Sci., 10: 59 (2013).
4. N. H. A. Tran, H. Brunig, R. Boldt et al., Polymer, 55, No. 24: 6354 (2014). doi.org/10/1016/j.polymer.2014.10.002
5. N. M. Rezanova, Yu. O. Budash, and V. P. Plavan, Innovatsiyni Tekhnologii Khimichnykh Volokon [Innovative Technologies of Chemical Fibers] (Kyiv: Kyiv National Univ. of Techn. and Design: 2017) (in Ukrainian).
6. M. V. Tsebrenko, V. G. Rezanova, and I. O. Tsebrenko, J. of Mater. Sci. and Eng., 4, No. 6: 36 (2010).
7. N. M. Rezanova, I. A. Melnyk, M. V. Tsebrenko, and A. V. Korshun, Khim. Volokna, 1: 23 (2014) (in Ukrainian).
8. K. Jin, S. Eyer, W. Dean, D. Kitto, F. S. Bates, and C. J. Ellison, Industrial and Eng. Chem. Res., 59, No. 12: 5238 (2019). https://doi.org/10.1021/acs.iecr.9b04887
9. C. J. Ellison, A. Phatak, D. W. Giles, and F. S. Bates, Polymer, 48, No. 11: 3306 (2007). doi.org/10.1016/j.polymer.2007.04.005
10. N. H. A. Tran, H. Brunig, M. A. Landwehr, R. Vogel, and G. Heinrich, J. Appl. Polym. Sci., 133: 442 (2016). doi.org/10/1002/app.44259
11. W. Li, J. Karger-Koksis, and A. K. Schlarb, Macromol. Mater. Eng., 294: 582 (2009). doi.org/10.1002/mame.200900123
12. Z. Pan, M. Zhu, Y. Chen, L. Chen, W. Wu, Ch. Yu, Z. Xu, and L. Cheng, Fibers and Polym., 3: 494 (2010). doi.org/10.1007/s12221-010-0494-x
13. V. A. Beloshenko, V. P. Plavan, N. M. Rezanova, B. M. Savchenko, and I. Vozniak, The Inter. J. of Advan. Manufact. Techn., 101: 2681 (2019). doi:10.1007/s00170-018-3152-x
14. V. G. Rezanova and M. V. Tsebrenko, Khim. Volokna, 2: 21 (2003) (in Ukrainian).
15. V. G. Rezanova and M. V. Tsebrenko, J. of Eng. Phys. and Thermophys., 81, No. 4: 766 (2009).
16. N. M. Rezanova, V. P. Plavan, L. S. Dzubenko, O. O. Sapianenko, P. P. Gorbyk, and A. V. Korshun, Nanosistemi, Nanomateriali, Nanotehnologii, 16, No. 1: 55 (2018) (in Ukrainian). https://doi.org/10.15407/nnn.16.01.055
17. N. M. Rezanova, B. M. Savchenko, V. P. Plavan, V. Yu. Bulakh, and N. V. Sova, Nanosistemi, Nanomateriali, Nanotehnologii, 15, No. 3: 559 (2017) (in Ukrainian); https://doi.org/10.15407/nnn.15.03.0559
18. N. M. Rezanova, V. P. Plavan, V. G. Rezanova, and V. M. Bohatyryov, Vlakna a Textil, 23, No. 4: 3 (2016).
19. N. M. Rezanova, V. G. Rezanova, V. P. Plavan, and O. O. Viltsaniuk, Vlakna a Textil, 24, No. 2: 37 (2017).
20. N. ╠. Rezanova, V. G. Rezanova, V. P. Plavan, and O. ╬. Viltsaniuk, Functional Mat., 26, No. 2: 389 (2019); doi.org/10.15407/fm26.02.389
21. I. G. Zedginidze, Planirovanie Ehksperimenta dlya Issledovaniya Mnogokomponentnykh Sistem [Planning an Experiment to Study Multicomponent Systems] (╠oscow: Nauka: 1976) (in Russian).
22. S. L. Akhnazarova and V. V. Kafarov, Metody Optimizatsii Ehksperimenta v Khimicheskoy Tekhnologii [Methods of Experiment Optimization in Chemical Technology] (╠oscow: High School: 1985) (in Russian).
23. N. Kultin, Osnovy Programmirovaniya v Delphi 7 [Programming Basics in Delphi 7] (St. Petersburg: BHV-Peterburg: 2012) (in Russian).
24. N. Kultin, Delphi v Primerakh i Zadachakh (3 Izd.) [Delphi in Examples and Problems (3rd Edition)] (St. Petersburg: BHV-Peterburg: 2012) (in Russian).
25. M. Flenov, Bibliya Programmista (Delphi) [Bible of programmer (Delphi)] (St. Petersburg: BHV-Peterburg: 2011) (in Russian).
26. N. Dreiper and G. Smith, Prikladnoy Regressionnyy Analiz [Applied Regression Analysis] (Moscow: Villiams: 2016) (in Russian).
27. V. Yu. Shcherban, S. ╠. Krasnitskiy, and V. G. Rezanova, Matematychni Modeli v SAPR. Obrani Rozdily ta Pryklady Zastosuvannya [Mathematical Models in SAPR. Selected Sections and Examples of Application] (Kyiv: Kyiv National Univ. of Techn. and Design: 2011) (in Ukrainian).