Analysis of mathematical models for description of the fractional composition of disperse elastic fillers
https://doi.org/10.32362/2500-316X-2019-7-5-62-78
Abstract
The paper presents a comparative analysis of integral and differential mathematical models describing the particle size distribution of dispersed elastic fillers. Crushed vulcanizates obtained by high temperature shear grinding were studied as objects of research. Technogenic waste – waste passenger car tires and rubber elements of gas mask facepieces – were used as raw materials. Data on the distribution of the crushed vulcanizate particles were obtained by laser diffraction using the particle size analyzer Fritsch Analysette 22 Microtec plus (“Fritsch”, Germany). It was found that the distribution curves are unimodal asymmetric curves. Search and analysis of mathematical models were carried out using a specialized software product TableCurve 2D v5.01 (Jandel Scientific). Four- and five-parameter equations pertaining to the class of logistic models were tested to describe the integral cumulative distribution curves of the rubber powder particles. In order to justify the choice of a suitable mathematical model to describe the fractional composition of the crushed vulcanizes, the adequacy of the models was assessed, the structural characteristics of the variation series, the statistical moments of distribution and the indicators of its shape were determined. It was found that according to a number of criteria it is appropriate to use the logarithmically normal distribution function for the description and analysis of the rubber powders fractional composition. It is suggested that regardless of the nature of the feedstock, the described implementation of high temperature shear grinding provides products having an identical shape of rubber powder particles size distribution.
About the Authors
Yu. A. Naumova
MIREA – Russian Technological University
Russian Federation
Russian Federation
Dr. of Sci. (Engineering), Docent, Professor of the F.F. Koshelev Chair of Chemistry and Processing Technology of Elastomers, M.V. Lomonosov Institute of Fine Chemical Technologies,
86, Vernadskogo pr., Moscow 119571
I. V. Gordeeva
MIREA – Russian Technological University;
N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
Russian Federation
Russian Federation
Postgraduate Student of the F.F. Koshelev Chair of Chemistry and Processing Technology of Elastomers, M.V. Lomonosov Institute of Fine Chemical Technologies, 86, Vernadskogo pr., Moscow 119571;
Senior Researcher, 4, ul. Kosygina, Moscow 119991
References
1. Kablov V.F., Perfilʼev A.V., Shabanova V.P., Perfilʼev A.A. Alternative technology of manufacturing of rubber products using recycling tires products. Kauchuk i rezina = International Polymer Science and Technology. 2017; 76(3):172-175 (in Russ.).
2. Myadelets V.V., Kasperovich A.V. Investigation of the effect of surface modification of crushed vulcanizate on the nature of interaction with the elastomeric matrix. Klei. Germetiki. Tekhnologii [Glues. Sealants. Technologies]. 2018;(1):20-25 (in Russ.).
3. Nikol’skii V.G., Dudareva T.V., Krasotkina I.A., Zvereva U.G., Bekeshev V.G., Rochev V.Y., Kaplan A.M., Chekunaev N.I., Vnukova L.V., Styrikovich N.M., Gordeeva I.V. Development and properties of new nanomodifiers for road pavement. Russian Journal of Physical Chemistry. B. 2014;8(4):577-583. https://doi.org/10.1134/S1990793114040071
4. Protasov N.I. Crumb rubber: Potential that require development. Tverdye bytovie otkhody = Municipal Solid Waste. 2016;5(117):41-43 (in Russ.).
5. Bocharova O.E., Nikolsky V.G., Krasotkina I.A., Naumova Yu.A., Kozlov V.A. Elastic fillers are products of secondary processing of rubbers obtained by high-temperature shear grinding. Vestnik MITHT = Fine Chemical Technologies. 2011;6(3):23-27 (in Russ.).
6. Nigmatullina A.I., Zakirova L.Y., Lysyansky V.A. The results of the study of granulometric composition of wood fillers modern methods. Vestnik tekhnologicheskogo universiteta = Bulletin of Technological University. 2019;22(1):62-66 (in Russ.).
7. Xu R. Particle characterization: Light scattering methods. New York: Kluwer Academic Pub., 2000. 397 p.
8. Syvitski P.M. Principles, methods, and application of particle size analysis. New York: Cambridge University Press, 1991. 368 p. ISBN: 0.521.36472.8
9. Zvereva U.G. Rubber-bitumen composites based on road bitumen and active rubber powder (APDDR): preparation, structure, rheological properties, application: Cand. of Sci. (Chemistry) diss. Moscow, 2016. 149 p. (in Russ.).
10. Belov V.V., Obraztsov I.V., Ivanov V.K., Konoplev E.N. Computer implementation of scientific, technical and educational tasks. Tver: TvGTU Publ., 2015. 108 p. (in Russ.).
11. Agayants I.M. Basics of statistics in the world of chemistry. Experimental data processing. St. Petersburg: NOT Publ., 2015. 618 p. (in Russ.).
12. Davydov A.A. Dynamics of human development (Collection of articles). Official site ROS (Russian society of sociologists), 2011. Mode of access: http://www.ssa-rss.ru/index.php?page_id=22&id=53#13-free
13. Gneushev A.N., Gurchenkov A.A., Moroz I.I. Direct method of estimating parameters of two-segmented piecewise logistic curve. Vestnik MGTU im. N.E. Baumana. Ser. Priborostroenie = Herald of the Bauman Moscow State Technical University. Ser. Instrument Engineering. 2018;(1):31-48 (in Russ.).
14. Agayants I.M., Kashkinova Yu.V. Quantitative interpretation of kinetic curves. Uchenye zapiski MITHT = Scientific Proceedings of Moscow State University of Fine Chemical Technologies. 2004;(11):3-8 (in Russ.).
15. Agayants I.M., Naumova Yu.A., Kuznetsov A.S. Analysis of correlation relations in the field of rheometric studies of rubbers. Vestnik MITHT = Fine Chemical Technologies. 2013;8(1):15-19 (in Russ.).
16. Kramer G. Mathematical methods of statistics. Moscow: Mir Publ., 1975. 648 p. (in Russ.).
17. Divinets A.A., Derechennik S.S., Razumeichik V.S. Choice of probability law of distribution for model descriptions the dispersion of the filler concrete composites. Vestnik Brestskogo gosudarstvennogo tekhnicheskogo universiteta = Vestnik of Brest State Technical University. 2015;(5):54-57 (in Russ.).
Supplementary files
|
|
1. Fig. 1. The distribution of rubber powder particles by size based on averaging the results of repeated observations (sample 1): 1 the integral form of the distribution, 2 the differential form of the distribution. | |
| Subject | ||
| Type | Исследовательские инструменты | |
View
(232KB)
|
Indexing metadata ▾ | |
Review
For citations:
Naumova Yu.A., Gordeeva I.V. Analysis of mathematical models for description of the fractional composition of disperse elastic fillers. Russian Technological Journal. 2019;7(5):62-78. (In Russ.) https://doi.org/10.32362/2500-316X-2019-7-5-62-78
Views:
1443
Email this article 