Abstract
The kinetic heterogeneity of the gadolinium-based catalytic system in 1,4-cis-polyisoprene synthesis was studied. The final form of the active site distribution function at preset accuracy was obtained by setting and solving the inverse problem of the molecular-mass distribution formation using the Tikhonov’s regularization method and numerical calculation methods. The results obtained show that there are at least three types of active sites with different kinetic activity in the system.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1070427222030120/MediaObjects/11167_2022_3442_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1070427222030120/MediaObjects/11167_2022_3442_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1070427222030120/MediaObjects/11167_2022_3442_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1070427222030120/MediaObjects/11167_2022_3442_Fig4_HTML.png)
Similar content being viewed by others
REFERENCES
Marina, N., Monakov, Y., Sabirov, Z., and Tolstikov, G., Rev. Polym. Sci. USSR, 1991, vol. 33, no. 3, pp. 387–417. https://doi.org/10.1016/0032-3950(91)90237-K
Marina, N., Monakov, Y., and Sabirov, Z., Polym. Sci., 1994, vol. 36, pp. 1404–1420.
Patent RU 2352585, Publ. 2009.
Kormer, V.A., Vasil’ev, V.A., Bubnova, S.V., and Dolinskaya, E.R., Kauchuk Rezina, 1986, no. 1, pp. 5–8.
Zhang, Z., Cui, D., Wang, B., Liu, B., and Yang, Y., in Molecular Catalysis of Rare-Earth Elements: book 137 of Structure and Bonding, Roesky, P., Ed., Berlin: Springer, 2010, pp. 49–108. https://doi.org/10.1007/430_2010_16
Friebe, L., Nuyken, O., and Obrecht, W., Adv. Polym. Sci., 2006, pp. 1–154. https://doi.org/10.1007/12_094
Levkovskaya, E.I., Bubnova, S.V., Bodrova, V.S., Drozdov, B.T., and Vasil’ev, V.A., Kauchuk Rezina, 2014, no. 1, pp. 12–15.
Levkovskaya, E.I., Bubnova, S.V., Vasil’ev, V.A., and Tsypkina, I.M., Kauchuk Rezina, 2016, no. 1, pp. 10–12.
Monakov, Y., Sigaeva, N., and Urazbaev, V., Active Sites of Polymerization. Multiplicity: Stereospecific and Kinetic Heterogeneity, Leiden: Brill Academic, 2005, pp. 369–397.
Patent RU 2668977, Publ. 2018.
Usmanov, T.S., Spivak, S.I., and Usmanov, S.M., Obratnye zadachi formirovaniya molekulyarno-massovykh raspredelenii (Inverse Problems of the Formation of Molecular-Mass Distributions), Moscow: Khimiya, 2004.
Bigaeva, L.A., Usmanov, A.S., Gaisin, F.R., and Usmanov, S.M., Bashk. Khim. Zh., 2014, vol. 21, no. 2, pp. 65–59.
Usmanov, A.S., Spivak, S.I., Nasyrov, I.Sh., and Usmanov, S.M., Sist. Upravl. Inform. Tekhnol., 2004, no. 4, pp. 34–38.
Tikhonov, A.N., Leonov, A.S., and Yagola, A.G., Nelineinye nekorrektnye zadachi (Nonlinear Ill-Posed Problems), Moscow: Nauka, 1995, pp. 91–140.
Tikhonov, A.N., Goncharskii, A.V., Stepanov, V.V., and Yagola, A.G., Chislennye metody resheniya nekorrektnykh zadach (Numerical Methods for Solving Ill-Posed Problems), Moscow: Nauka, 1990, pp. 101–156.
Usmanov, T.S., Usmanov, A.S., and Yagola, A.G., Vychisl. Met. Programm., 2006, vol. 7, no. 4, pp. 294–299.
Panteleev, A.V. and Letova, T.A., Metody optimizatsii v primerakh i zadachakh (Optimization Methods in Examples and Problems), St. Petersburg: Lan’, 2015, pp. 317–366.
Zorkal’tsev, V.I. and Mokryi, I.V., Sib. Zh. Industr. Matem., 2018, vol. 21, no. 1, pp. 11–20. https://doi.org/10.17377/sibjim.2018.21.102
Zakharov, V., Mingaleev, V., Berlin, A., Nasyrov, I., Zhavoronkov, D., and Zakharova, E., Russ. J. Phys. Chem. B, 2015, vol. 9, pp. 300–305. https://doi.org/10.1134/S199079311502013X
Deberdeev, R., Berlin, A., Dyakonov, G., Zakharov, V., and Monakov, Y., Fast Chemical Reaction in Turbulent Flows: Theory and Practice, Shawbury, Shrewsbury, Shropshire (Unnited Kingdom): Smithers Rapra, 2013, pp. 3–101.
Zakharov, V.P., Mingaleev, V.Z., Zakharova, E.M., Nasyrov, I.Sh., and Zhavoronkov, D.A., Russ. J. Appl. Chem., 2013, vol. 86, no. 6, pp. 909–913. https://doi.org/10.1134/S1070427213060219
Funding
The study was performed within the framework of the government as signment of the Ministry of Science and Higher Education of the Russian Federation (scientific theme code FZWU-2020-0027).
Author information
Authors and Affiliations
Contributions
E.N. Miftakhov: participation in setting and numerical solution of the inverse problem of the molecular-mass distribution formation and in interpretation of the results obtained; S.A. Mustafina and I.Sh. Nasyrov: setting of the research task; S.A. Mustafina: planning of the required computational experiments on solution of the inverse problem and interpretation of the calculation results obtained; I.Sh. Nasyrov: planning of the experiment on synthesis of polyisoprene samples, analysis of the experimental results; V.Yu. Faizova: synthesis of polyisoprene samples and their subsequent gel-chromatographic analysis to construct the molecular-mass distribution.
Corresponding author
Ethics declarations
The authors declare that they have no conflict of interest.
Additional information
Translated from Zhurnal Prikladnoi Khimii, No. 3, pp. 375–381, March, 2022 https://doi.org/10.31857/S0044461822030100
Rights and permissions
About this article
Cite this article
Miftakhov, E.N., Mustafina, S.A., Nasyrov, I.S. et al. Kinetic Heterogeneity of the Catalytic System Based on Gadolinium Chloride Solvate in 1,4-cis-Polyisoprene Production. Russ J Appl Chem 95, 423–429 (2022). https://doi.org/10.1134/S1070427222030120
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1070427222030120