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Original papers
Materials for energy and environment, next-generation photovoltaics, and green technologies УДК 544.726 DOI: 10.17277/jamt.2023.01.pp.060-069
Selective lithium extraction from aqueous solutions by layered amorphous protonated potassium polytitanate
© Maria A. Vikulova3^, Lilia A. Maximovaa, Valeria Yu. Rudyha, Nikolay V. Gorshkova
a Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya St., Saratov, 410054, Russian Federation
И vikulovama@yandex.ru
Abstract: In this work, using a technologically simple and low-cost method, as an alternative to the known layered inorganic ion exchangers of manganese and titanate type, protonated potassium polytitanate (K0.8Hi.2Ti4.3O8.5) was obtained and studied to extract lithium from secondary natural resources. X-ray diffraction analysis confirmed the retention of the original X-ray amorphous structure of potassium polytitanate after the protonation process, which ensures good ion-exchange and adsorption capacity of the material. Functional groups of protonated potassium polytitanate, which are potential active sites for interaction with Li+ ions, were analyzed by FTIR spectroscopy. When lithium was extracted from an aqueous solution with a concentration of 0.01 mol-L-1, protonated potassium polytitanate demonstrated an equilibrium adsorption capacity of 0.52 mmol-g-1. In this case, the experimental data are in good agreement with the pseudosecond order kinetic model (R2 = 0.999). The adsorption process is described by the Freundlich isotherm and is characterized by the constant KF = 0.0013 (L)1/n(mmol)1-1/ng-1. The good selectivity of protonated potassium polytitanate with respect to Li ions in the presence ions is shown, while the adsorption capacity
is maintained at the level of 0.50-0.52 mmol-g-1.The results obtained indicate that protonated potassium polytitanate is a promising and competitive material for the extraction of Li+ ions from low concentration aqueous solutions.
Keywords: potassium polytitanate; protonation; ion exchange; lithium extraction; aqueous solutions; kinetics; adsorption isotherms; selectivity.
For citation: Vikulova MA, Maximova LA, Rudyh VYu, Gorshkov NV. Selective lithium extraction from aqueous solutions by layered amorphous protonated potassium polytitanate. Journal of Advanced Materials and Technologies. 2023;8(1):060-069. D0I:10.17277/jamt.2023.01.pp.060-069
Селективное извлечение лития из водных растворов слоистым аморфным протонированным полититанатом калия
© М. А. ВикуловаяИ, Л. А. Максимова3, В. Ю. Рудыха, Н. В. Горшков3
а Саратовский государственный технический университет, ул. Политехническая, 77, Саратов, 410054, Российская Федерация
И vikulovama@yandex.ru
Аннотация: В данной работе по технологически простой и дешевой методике в качестве альтернативы известным слоистым неорганическим ионообменникам марганцевого и титанатного типа получен и исследован протонированный полититанат калия (КадН^Тц^Ой^) в целях извлечения лития из вторичных природных ресурсов. Методом рентгеновского фазового анализа (РФА) подтверждено сохранение исходной рентгеноаморфной структуры полититаната калия после процесса протонирования, обеспечивающей хорошую ионообменную и адсорбционную способность материала. Методом инфракрасной спектроскопии проанализированы функциональные группы протонированного полититаната калия, представляющие собой потенциальные активные центры для взаимодействия с ионами О . При извлечении лития из водного раствора с концентрацией 0,01 моль/л протонированный полититанат калия продемонстрировал равновесную адсорбционную емкость 0,52 ммоль/г. При этом экспериментальные данные хорошо согласуются с кинетической моделью псевдовторого порядка (Я2 = 0,999). Адсорбционный процесс описываются изотермой Фрейндлиха и
характеризуются константой Kf = 0,0013 (л)1/"(ммоль)1 1/и/г. Показана хорошая селективность протонированного полититаната калия по отношению к ионам Li+ в присутствии ионов Na+, K+, Mg2+ и Ca2+ при сохранении адсорбционной емкости на уровне 0,50...0,52 ммоль/г. Полученные результаты свидетельствуют о том, что протонированный полититанат калия является перспективным и конкурентоспособным материалом для извлечения ионов Li из водных растворов с низкой концентрацией.
Ключевые слова: полититанат калия; протонирование; ионный обмен; извлечение лития; водные растворы; кинетика; изотермы адсорбции; селективность.
Для цитирования: Vikulova MA, Maximova LA, Rudyh VYu, Gorshkov NV. Selective lithium extraction from aqueous solutions by layered amorphous protonated potassium polytitanate. Journal of Advanced Materials and Technologies. 2023;8(1):060-069. D0I:10.17277/jamt.2023.01.pp.060-069
1. Introduction
With the current emphasis on maintaining a sustainable environment, the design, development and implementation of environmental technologies, in particular electric-powered vehicles, is a global priority. Lithium is an indispensable element in the production of electrode materials for batteries in hybrid cars and electric vehicles, as well as in portable electronics [1-8].
The favourable electrochemical characteristics of lithium are responsible for the rapidly growing demand for it. It is therefore important to utilize primary (ores and brines) and alternative secondary (clays and seawater) lithium resources with high efficiency to ensure timely and adequate supplies of lithium raw materials.
Pyrometallurgical [9-12] and hydrometallurgical [13-15] processes can be used to extract lithium from primary and secondary resources. Although pyrometallurgical processes are economical from a technical point of view, they require an intensive financial investment and are accompanied by undesirable environmental pollution.
Hydrometallurgical processes, including acid-alkali leaching followed by solvent extraction [16, 17], adsorption (ion exchange) [18, 19] and precipitation [20, 21], are considered promising methods for extracting lithium as pure carbonate (Li2CO3) and lithium hydroxide (LiOH) due to minimal energy costs and production waste. However, in solutions, lithium occurs as a cation together with other metal ions such as sodium, potassium, calcium, magnesium, etc. Therefore in the deposition method the existing impurities have to be removed before lithium is obtained. Otherwise, the product will have a lower purity due to co-deposition of other metals. Thus, for sources where the concentration of lithium ions is low and other ions are likely to be present, reactions based on adsorption and ion exchange are more effective. There are a number of inorganic ionexchange materials with exceptionally high selectivity for lithium ions alone.
Manganese-type ion exchangers based on LiMn2O4, Li4Mn5Oi2 and Li1.6Mn1.6O4 show high efficiency in the extraction of lithium ions from concentrated and dilute solutions [22-24]. However, the destruction of the manganese structure during Li+ deintercalation makes their reuse difficult [25, 26].
Many recent studies have focused on H2TiO3 metatitanic acid with layered structure due to its greater stability during lithium desorption and higher theoretical adsorption capacity [27]. It is traditionally produced by a two-step process. First, the Li2TiO3 precursor is synthesized by solid-phase [28], hydrothermal [29] or sol-gel method [30]. Li2TiO3 is then treated in acid to obtain the functional end product. The solid-phase method is preferred for industrial production due to its simplicity, cost-effectiveness and high throughput, but inadequate mixing of raw materials can lead to an inaccurate stoichiometric product, caking and large particles, which is bad for the adsorbent. Although sol-gel and hydrothermal synthesis methods provide uniform mixing of feedstocks, these techniques are relatively complex and expensive and therefore difficult to implement in industry.
In this connection, a novel technologically simple and cost-effective approach to obtaining an effective protonated form of ion exchange is proposed for the first time in this work. It uses a lithium-free precursor, potassium polytitanate, characterised by the formula K2Ti4.3O9.6 and a semi-crystalline layered structure formed by K+ cations and TiO6^ octahedra connected at different angles as a raw material. Synthesis in a hydroxide-salt melt provides the required uniformity in component mixing, and possible excess unreacted water-soluble compounds are removed by washing. The total and surface ion exchange capacities of potassium polytitanate are 134 mg-g-1 (3.43 mmol-g-1) and 16 mg-g-1 (0.42 mmol-g-1) respectively [31], which is competitive with known inorganic ion exchangers.
The aim of the work is to investigate the efficiency and selectivity of the protonated form of potassium polytitanate in the process of lithium extraction from aqueous solutions with low concentration.
2. Materials and Methods 2.1. Materials and reagents
The following reagents were used for the synthesis of potassium polytitanate: TiO2 (99.5 %, TU 2321-001-17547702-2014, Vitahim Group, Russia), KOH (analytical grade purity, Russian Standard 24363-80, LLC "Reachem", Russia) and KNO3 (analytical grade purity, Russian Standard 4217-77, LLC "Reachem", Russia). HCl (35 %, Russian Standard 3118-77, JSC "Vekton", Russia) was used for protonation of potassium polytitanate. LiCl (99.2 %, TU 6-09-3751-838, RusChem Group, Russia) was used to study lithium ion-exchange extraction. NH4OH (analytical grade purity, Russian Standard 3760-79, Sigma Tech Ltd., Russia) was used for pH correction during the ion-exchange process.
2.2. Preparation of the ion-exchange material
The synthesis of the initial potassium polytitanate (K2TiraO2ra+1 (n = 3.8-4.1)) was carried out using precursors TiO2, KOH and KNO3 at their mass ratio of 30:30:40 in the reaction mixture. This included distilled water in an amount 2:1 relative to the mass of TiO2, as a result of temperature treatment at 500 °C for 3 hours followed by washing to pH = 10.0 ± 0.5.
Protonation of potassium polytitanate was carried out using 0.1 M HCl solution by stirring the dispersion with a concentration of 20 g-L-1 at pH = 2.0 ± 0.5 for 2 hours followed by decantation and drying at 60 °C.
2.3. Characterization of the ion-exchange material
Chemical composition of the protonated sample was determined on a BRA-135F spectrometer (Burevestnik, Russia). X-ray phase analysis was carried out on diffractometer ARL X'TRA (Thermo
Scientific, Switzerland) using Cu Ka-radiation (^ = 0.15412 nm). Fourier-transform infrared spectrometer FT-801 (Simex, Russia) was used for the analysis of surface functional groups.
2.4. Investigation of the ion-exchange process
To investigate the kinetics and equilibrium state of the ion-exchange process 1 g of protonated potassium polytitanate was mixed with 100 ml of LiCl solution with Li+ ions concentration 0.005; 0.01; 0.02; 0.025 and 0.05 mol-L. The resulting mixture was incubated under constant stirring, at room temperature T = (25 ± 2) °C and pH = 8.0 by adding an aqueous solution of NH4OH. The choice of the indicated pH value during the ion-exchange process was due to the high efficiency of previously studied manganese and titanate-type ion-exchange materials under these conditions [30, 32], as well as the performance of seawater as a potential real source for lithium extraction using the obtained material [33]. The change in the concentration of Li+ ions was recorded by potentiometric method on a laboratory ionometer I-160MP (Gomel Instrumentation Plant, Republic of Belarus) with a lithium selective electrode ELIS-142Li (IzmeritelnayaTehnika, Russia) every 5, 10, 20, 30, 60, 90, 120, 150, 180, 210 and 240 min.
To study selectivity of ion-exchange material 1 g
of protonated potassium polytitanate was dispersed in
100 mL of solution, containing besides Li+ ions
(0.01 mol-L-1), the following ions: Na+, K+, Mg2+
2+ —1
and Ca with concentration of 0.004 mol-L .
Based on the results of the study, the sorption capacity of protonated potassium polytitanate (q, mmol-g—1) was calculated by the formula (1):
q = ■
C0 - Ct
V.
(1)
m
where C0 is the initial concentration of Li+ ions in solution, mmol-L—1; Ct is the concentration of Li+ ions in the solution at time t, mmol-L—1; m is the mass of protonated potassium polytitanate, g; V is the volume of solution, L.
3. Results and Discussion
3.1. Characterization of the ion-exchange material
Protonation as a method of chemical modification of layered compounds is an ionexchange replacement of interlayer cations of initial structure by hydroxonium or hydrogen cations as a result of appropriate treatment, mainly in aqueous solutions of strong inorganic acids [34, 35]. In the case of potassium polytitanates K+ cations take part in the ionic exchange compensating the negative charge of titanium-oxygen octahedrons [36, 37].
30 40 50 60 40(H) 3500 3000 250ft 2000 1500 1000 5i№
20 Wsivenumber (cm-1)
(a) (b)
Fig. 1. X-ray diffractogram (a) and IR transmission spectrum (b) of protonated potassium polytitanate
By the recalculation of X-ray fluorescence analysis data on the mass content of potassium oxides (10.4 wt. %) and titanium (89.6 wt. %) and considering the conservation of titanium mole fraction and replacement of potassium ions by hydrogen ions the obtained protonated potassium polytitanate may be described by the chemical formula Ko.8Нl.2Ti4.зO8.5.
The protonated sample is characterized by an
X-ray amorphous structure (degree of crystallinity is about 25 %). The low-intensity reflexes observed on the X-ray diffractogram relate to titanium dioxide phases of different modifications (anatase and rutile) (Fig. 1a). According to the results of the X-ray phase analysis, protonation under the specified conditions does not lead to the destruction of the X-ray amorphous structure of the original potassium polytitanate and the formation of high crystallinity phases as degradation products [38, 39].
Infrared transmission spectra of protonated potassium polytitanate reveal absorption bands, responsible for the stretching vibrations of hydroxyl groups (wide absorption band at 3750-3000 cm-1) and titanium-oxygen bonds (less prominent absorption band at 550 cm-1) as well as strain vibrations of physically adsorbed water (high intensity absorption band at 1630 cm-1) and thianol groups (paired absorption bands at 1140 and 1050 cm- ) (Fig. 1b). IR spectroscopy data feature the functional groups of protonated potassium polytitanate involved in the ion-exchange interaction with Li+ ions [40-44].
3.2. Adsorption kinetics
Two distinct stages of the investigated process can be distinguished in Fig. 2 of the kinetic dependence. During the first 20-30 min the rate
of Li ions extraction is fast, sorption capacity of protonated potassium polytitanate reaches 0.47 mmol-g-1 during the first 30 min of interaction with lithium salt solution. Then the rate of increase of q value slows down and after 2 h sorption capacity reaches its maximum value of 0.52 mmol-g-1 (lithium recovery efficiency is 52 %). The decrease in the rate of ion-exchange adsorption is due to continuous saturation of the active sites of protonated potassium polytitanate in the process of interaction with Li+ ions.
To simulate the adsorption process and to identify the limiting stage of the process, linear equations of pseudo-first order (2) and pseudo-second order (3) models have been applied [45-47]:
ln q- qt ) =ln qe- V ;
1 t —+—
qt hqe qe
(2)
(3)
mmol-g 1
0
50
100
150
200 u min
Fig. 2. Kinetics of protonated potassium polytitanate ion-exchange interaction with Li+ ions
t
0 -1
-2 -3 -4 -5
ln(qe - qt)
50
100
150
200 t, min»
y = -0.013* - 2.0251 R2 = 0.
t / qt) 400 350 300 250 200 150 100 50
y = 1.9415* + 8.6625 R2 = 0.9991
0
50
(a)
100 150 (b)
200 t, min
Fig. 3. Kinetics of protonated potassium polytitanate ion-exchange interaction with Li+ ions in coordinates of pseudo-first (a) and pseudo-second (b) order models
Table 1. Kinetic parameters of protonated potassium polytitanate ion-exchange interaction with Li+ ions
Pseudo-first order model Pseudo-second order model
R2 qe, mmol-g1 k1, min 1 R2 qe, mmol-g-1 k2, g(mmol-min)-1
0.89 0.13 0.013 0.99 0.52 0.43
where qe (mmol-g and qt (mmol-g are the number of Li+ ions subjected to ion exchange at equilibrium and at time t, respectively, k (min-1) and &2 (g(mmol min)- ) are kinetic constants of pseudofirst and pseudo-second order, respectively.
Modeling of experimental data using kinetic models shows that the pseudo-second order model (R = 0.9991) describes the process of ion-exchange interaction of protonated potassium polytitanate with Li+ ions better than the pseudo-first order kinetic model (R2 = 0.8886).
The simulation results and calculated kinetic parameters are shown in Fig. 3 and Table 1.
It is known that both kinetic models assume that a chemical exchange reaction limits the sorption process. However, if the pseudo-first order model is feasible, it should be taken into account that adsorption is preceded by diffusion. If the experimental data of the pseudo-second order model are fulfilled, the studied interaction belongs to the reaction of the second order and reacting substances interact with each other in the ratio 1:1 [48].
Consequently, the ion-exchange chemical reaction occurring between Li+ ions and functional groups of protonated potassium polytitanate —TiOH is very likely to be the limiting stage of interaction and the adsorption rate is mainly controlled by stoichiometric exchange between H+ and Li+ ions.
The rate of lithium extraction is determined by both the concentration of the alkali metal ion in solution and the number of active sites of the ion-exchange material. Most of the manganese and titanate analogues show a similar pattern in their interaction with Li+ [49-52].
The calculated equilibrium sorption capacity is 0.52 mmol-g-1, which is below the total ion exchange capacity (3.43 mmol-g-1) and slightly higher than the surface ion exchange capacity (0.42 mmol-g-1), as determined by the adapted Ming and Dixon method [53, 54]. This is mainly due to the fact that in the investigated time range the active sites of the outer surface and only a part of the inner surface of protonated potassium polytitanate participate in the ion-exchange process.
3.3. Adsorption isotherms
In addition, the Langmuir (4) and Freundlich (5) models of adsorption isotherms were used to analyze the experimental data obtained [55]:
С
Qe
1
Ce
:-+-
QK Q«
1
ln Qe = ln KF + - ln Ce,
n
(4)
(5)
Ce/Q. 30 25 20 15 10 ■ 5
R2 = 0.6201
0
6
(a)
InQe 1.5 1.0
0.5 0
-0.5 -1.0-1 -1.5
_, -2.010 Ce, mmol-L-1 -2.5.
y = 3.5813x - 6.6096 R2 = 0.9701
0.5
1.0
1.5 / 2.0 lnCe
(b)
Fig. 4. Isotherms of Li ions adsorption by protonated potassium polytitanate in coordinates of the Langmuir (a) and Freundlich (b) models
where Qe is the adsorption capacity at the time of
adsorption equilibrium, mmol-g-1; Qx is the limiting
adsorption capacity (monolayer capacity), mmol-g1; Ce is the equilibrium concentration of the solution,
mmol-L"1; KL is the adsorption equilibrium constant, L-mmol-1; n is Freundlich isotherm constant, showing the adsorption intensity; and KF is Freundlich isotherm constant, corresponding to adsorption capacity (L)1/n(mmol)1-1/ng-1.
The results show that the Freundlich model (R = 0.9701) is better suited to describe the ionexchange interaction of Li+ ions with protonated potassium polytitanate compared to the Langmuir model (R2 = 0.6201) (see Fig. 4).
The Freundlich isotherm constant showing the adsorption intensity is 0.28, which falls within the range of 0.1-0.5 for adsorption from solutions. The Kf constant is 0.0013 (L)1n(mmol)1-1/ng-1. Experimental data on Li+ adsorption involving manganese and titanate ion-exchange materials of different composition and structure show higher correlation with Langmuir isotherm than with Freundlich isotherm [50, 51, 56]. This indicates the presence of homogeneous adsorption sites, in contrast to protonated potassium polytitanate, which is characterized by a heterogeneous (external and internal) adsorption surface.
3.4. Selectivity of the ion-exchange material
The study of selectivity of protonated potassium polytitanate was carried out in solutions containing 0.01 mol-L-1 of Li+ ions and 0.004 mol-L-1of impurity ion (Na+, K+, Mg2+ or Ca2+). Extraction of lithium in the presence of the mentioned ions reaches 0.51 mmol-g-1, which is somewhat lower in comparison with the pure LiCl solution. However, the decrease of the sorption capacity does not exceed
Table 2. Selectivity of protonated potassium polytitanate with respect to lithium in the presence of impurity ions
Impurity ion Ce(Li+), mmol-L1 q, mmol-g 1
- 4.81 ± 0.2 0.52 ± 0.05
Na+ 4.94 ± 0.3 0.51 ± 0.03
K+ 4.91 ± 0.2 0.51 ± 0.03
Mg2+ 4.89 ± 0.2 0.51 ± 0.03
Ca2+ 4.96 ± 0.3 0.50 ± 0.02
4 %, which may indicate good selectivity of protonated potassium polytitanate in relation to lithium in complex chemical systems (Table 2).
The obtained value of the sorption capacity is slightly inferior to that of manganese and titanate spinels. Yet, because of the use of lithium-containing precursors and technologically complicated operations during synthesis, their cost is high and that allows considerably cheaper materials such as protonated potassium polytitanate to compete with them [31].
4. Conclusion
Protonated potassium polytitanate was obtained by treatment in hydrochloric acid solution of X-ray amorphous layered potassium polytitanate characterized by the general chemical formula K2TiraO2ra+1 (n = 3.8-4.1). The level of substitution of potassium ions in the interlayer space of the initial potassium polytanate by hydrogen ions as a result of the protonation process is estimated by using X-ray fluorescence method. The empirical formula of the obtained compound is ^.^1.2^4.308.5. According to the X-ray phase analysis data, protonation does not
e
2
4
8
lead to the destruction and crystallization of the X-ray
amorphous structure of potassium polytitanate. In the
infrared transmission spectrum a broad absorption
band responsible for vibrations of hydroxyl groups
(—OH) and an intense absorption band associated
with vibrations of thianol groups (—TiOH) are
identified. These functional groups are involved in
the ion-exchange interaction with Li+ ions in aqueous
solution. The kinetics study showed that the
equilibrium adsorption capacity of protonated
potassium polytitanate was 0.52 mmol-g—1.
The experimental data fit the kinetic model
of pseudo-second order with rate constant
k2 = 0.43 g(mmol-min)-1 which confirms the
chemical reaction as the limiting stage of the process
under investigation. The ion-exchange interaction
is described by the Freundlich adsorption
isotherm and characterized by the constant
KF = 0.0013 (L)1/n(mmol)1—1/ng—1. It was found that
protonated potassium polytitanate is selective towards
Li+ ions in the presence of both univalent (Na+, K+)
2+ 2+
and divalent cations (Mg , Ca ), keeping q at 0.50—0.51 mmol-g—1.
The simplicity of synthesis and high selectivity of protonated potassium polytitanate with respect to Li+ ions in the presence of other cations typical for natural aqueous solutions make the investigated material a promising ion-exchanger for lithium extraction from solutions.
5. Funding
The current research has been carried out with the financial support of the Russian Federation Presidential Grant no. MK-2204.2022.1.3.
6. Conflict of interests
The authors declare no conflict of interest.
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Information about the authors / Информация об авторах
Maria A. Vikulova, Cand. Sc. (Chem.), Associate Professor, Department of Chemistry and Chemical Technology of Materials, Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation; 0RCID 0000-0003-0092-6922; e-mail: vikulovama@ yandex.ru
Lilia A. Maximova, Postgraduate Student, Department of Chemistry and Chemical Technology of Materials, Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation; 0RCID 0000-0002-43515739; e-mail: liliamacsimova@mail.ru
Викулова Мария Александровна, кандидат химических наук, доцент, кафедра «Химия и химическая технология материалов», Саратовский государственный технический университет имени Гагарина Ю. А.» (СГТУ имени Гагарина Ю. А.), Саратов, Российская Федерация; ORCID 0000-0003-0092-6922; e-mail: vikulovama@yandex. ru
Максимова Лилия Алексеевна, аспирант, кафедра «Химия и химическая технология материалов», СГТУ имени Гагарина Ю. А., Саратов, Российская Федерация; ORCID 0000-0002-4351-5739; e-mail: liliamacsimova@mail.ru
Valeria Yu. Rudyh, Postgraduate Student, Department of Chemistry and Chemical Technology of Materials, Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation; 0RCID 0000-0002-21488733; e-mail: lermarik@mail.ru
Nikolay V. Gorshkov, Cand. Sc. (Eng.), Associate Professor, Department of Chemistry and Chemical Technology of Materials, Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation; 0RCID 0000-0003-3248-3257; e-mail: gorshkov.sstu@ gmail.com
Рудых Валерия Юрьевна, аспирант, кафедра «Химия и химическая технология материалов», СГТУ имени Гагарина Ю. А., Саратов, Российская Федерация; 0RCID 0000-0002-2148-8733; e-mail: lermarik@mail.ru
Горшков Николай Вячеславович, кандидат технических наук, доцент, кафедра «Химия и химическая технология материалов», СГТУ имени Гагарина Ю. А., Саратов, Российская Федерация; 0RCID 0000-00033248-3257; e-mail: gorshkov.sstu@gmail.com
Received 17 January 2023; Accepted 24 February 2023; Published 26May 2023
Copyright: © Vikulova MA, Maximova LA, Rudyh VYu, Gorshkov NV, 2023. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
