International Journal of Materials and Chemistry

p-ISSN: 2166-5346    e-ISSN: 2166-5354

2020;  10(2): 17-22


Received: Oct. 5, 2020; Accepted: Oct. 30, 2020; Published: Nov. 5, 2020


Determination of Ammonia’s Adsorption Properties in NaLSX Zeolite by Calorimetric Method

Abdurahmonov Eldor Baratovich1, Rakhmatkarieva Firuza Gayratovna2, Ergashev Oybek Karimovich3

1Candidate of Chemical Sciences (Ph.D.) Institute of General and Inorganic Chemistry of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan

2Doctor of Chemical Sciences, Senior Researcher, Institute of General and Inorganic Chemistry of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan

3Doctor of Chemical Sciences, Namangan Institute of Engineering and Technology, Vice Rector of Innovation and Scientific Affairs, Namangan, Uzbekistan

Correspondence to: Abdurahmonov Eldor Baratovich, Candidate of Chemical Sciences (Ph.D.) Institute of General and Inorganic Chemistry of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan.


Copyright © 2020 The Author(s). Published by Scientific & Academic Publishing.

This work is licensed under the Creative Commons Attribution International License (CC BY).


The research of the molecules’ adsorption of different geometric shapes and electronic structures together with zeolites of different composition and structure arouses simultaneous interest in the research of the influence of the chemical nature of the surface of adsorbents on adsorption.Zeolites are porous crystals, their adsorption properties are physicochemical constants, therefore, it is theoretically possible to determine the micropore structure of zeolites and to calculate their interaction with the potential interacting energy adsorbate-adsorbate and adsorbate-adsorbent in zeolites. These data are of great interest for the development of the theory of adsorption forces and intermolecular interactions. Nevertheless, the calculation of the potential energy of adsorption is difficult due to the complexity of the crystal structure and the potential field in the zeolite voids. In order to determine the acidity and basicity properties of the composition, it is necessary to study the laws of adsorption of ammonia molecules. In the determination of ammonia adsorption isotherm, differential temperatures and thermokinetics in NaLSX zeolite was carried out using the method of adsorption calorimetry in a high vacuum adsorption device. They are based on differential molar entropy and free adsorption energy. The adsorption isotherm is fully described by the three-dimensional equation of the theory of volumetric micropore occupancy (VMOT). The average molar integral entropy of ammonia molecule adsorption on NaLSX zeolite is 59.64 Dj/mol*K, indicating a strong localization of ammonia molecules in NaLSX zeolite.

Keywords: Isotherm, Differential heats, Differential entropies, Thermokinetics, NaLSX zeolite, Ammonia, Adsorption calorimetry

Cite this paper: Abdurahmonov Eldor Baratovich, Rakhmatkarieva Firuza Gayratovna, Ergashev Oybek Karimovich, Determination of Ammonia’s Adsorption Properties in NaLSX Zeolite by Calorimetric Method, International Journal of Materials and Chemistry, Vol. 10 No. 2, 2020, pp. 17-22. doi: 10.5923/j.ijmc.20201002.01.

1. Introduction

The technologies for ammonia removal from wastewater are based on physicochemical and biochemical treatment methods [1]. One of these treatment methods is adsorption, which is a low-cost process. Different adsorbents, such as wheat straw biochars, pine sawdust or zeolites, can be effective in adsorbing ammonium in wastewater [2–12].
Several studies have reported on the adsorption of ammonium ions by natural or synthetic zeolitic material adsorbents as well [9–12]. Zeolite - aluminosilicate hydrate minerals with a porous, three-dimensional crystal structure are considered an excellent ion-exchange material because of their high selectivity for NH4+ due to their microstructure [2]. An adsorbent of natural zeolites possesses a polar surface and is therefore able to attract ammonium ions quickly and effectively [1]. The removal of ammonia from water was carried out by using natural and synthetic zeolites. In this research three types of natural zeolites (clinoptilolite, mordenite and ferrierite), and synthetic zeolite A were used. The different forms of zeolites such as sodium, potassium and calcium forms were investigated [9]. It was concluded that natural zeolites show high selectivity for ammonium ions with respect to other monovalent ions despite the much higher theoretical exchange capacity of zeolite A. In the study 11, the clinoptilolite was fused with sodium hydroxide prior to a hydrothermal reaction, and it was transformed to a modified zeolite Na–Y. The results were acceptable, showing that modified zeolite Na–Y exhibited a much higher uptake capacity compared with that of clinoptilolite. At an initial concentration of 250 mg/L NH4+, the ammonium ion uptake value of sample 2 was 19.29 mg/g NH4+ adsorbed, while that for sample 1 was only 10.49 mg/g1 NH4+ adsorbed.
The emergence of high-energy complexes in the adsorption of NaX zeolite ammonia is dependent on the interaction of ammonia molecules in the SIII' and SII voids in two adjacent states, two abutting sodium cations. SIII' generates heat of adsorption on cations in the void, when the extrapolation of ammonia is Н+ equal to 110 kDj/mol, ~ 90 kDj / mol, relative to the Qd curve to zero saturation [13-14].
In our research, the adsorption of ammonia molecules in various synthetic zeolites was carried out by the adsorption microcalorimetric method in a high-vacuum adsorption device, and the full thermodynamic properties of the adsorption processes were described [13-38].

2. Materials and Methods

The composition of the zeolite obtained for the study is Na96(AlO2)96(SiO2)96. The adsorption-calorimetric tip used in this study allows to reveal the detailed mechanism of adsorption processes occurring in adsorbents and catalysts, as well as obtaining adsorbents and catalysts, moreover, obtaining high-precision molar thermodynamic characteristics.
Adsorption measurements and doses of adsorbate were performed using a universal adsorption device, in the working part of which only mercury valves were used and the valves were replaced with vacuum grease [39]. The device allows to dose the adsorbate by both gas-volume and liquid-volume methods. As a calorimeter, a modified DAK 1-1 calorimeter with high accuracy and reliability was used.

3. Result and Discussion

Ammonia adsorption isotherms to NaLSX zeolite were carried out in a volumetric manner at a temperature of 303 K, Figure 1 provides the results of the experiment (1) and the re-described characteristics (2) using the equation of the volumetric saturation theory of micropores. The isotherm does not change in the same plane as the pressure increases, but rather each of them reflects the transition of one type of centers to another. The isotherm (abscissa) axis consists of a logarithmic (ln), adsorption (N) (N-supervoid and 1/8 NH3 molecule number of elementary cell) (ordinal) axis, which allows us to imagine the adsorption process over the entire pressure equilibrium range. In the adsorption of the three ammonia molecules, the isotherm line goes vertically at the initial filling of the zeolite micropores, where the isotherm ranges from ln(p/p°)=-18 to ln(p/p°)=-16,8, and the adsorption is N=3 C6H6/1/8 u.c. Na + cations in the SIII void rise sharply when adsorbed, then turns to the adsorption axis and grows to 6 NH3/1/8 u.c (SI’). In the adsorption after 6 NH3/1/8 u.c, the isotherm 18 NH3/1/8 u.c. increases with a slope to the adsorption axis and is partially saturated (SII).
Figure 1. Isotherm of ammonia adsorption in zeolite NаLSX at 303 K. 1- experimental data 2 – calculated data using the theory of volumetric micropore occupancy (VMOT)
Adsorption isotherm of ammonia in the NаLSX zeolites is satisfactorily described by three-term equation of the theory of volumetric micropore occupancy (VMOT) [40,41]:
N = 3,33exp[-(A/43,09)22] + 12,32exp[-(A/22,71)3] + 3,26exp[-(A/10,2)3],
N - adsorption in micropores NH3/1/8 u.c., А = RT ln(Po/P) - adsorption energy, kDj / mol. The parameters of the equation for the first level of the NaLSX zeolite ammonia system are: N01 = 3.33 NH3/1/8 u.c., E01 = 43.09 kDj / mol and n1=22; for the second degree N02 = 12,32 NH3/1/8 u.c., E02 = 22,71 kDj / mol and n2 = 3; and for the third degree N03 = 3.26 NH3/1/8 u.c., E03 = 10.2 kDj/mol and n3 = 3.
There is a correlation between the isotherm and the adsorption heat. Figure 2 shows a graph of the differential heat (Qd) change in the amount of ammonia adsorption (N) in NaLSX zeolite. Thermal condensation (v) of ammonia adsorption is indicated by dashed lines. The differential heat (Qd) curve has a complex wavy shape. Each fragment on the curve represents the stoichiometric ratio between the same number of adsorption centers and the number of molecules adsorbed. NaLSX zeolite contains Si/Al=1:1 ratio. According to the literature [16], the distribution of cations in the zeolite is as follows: 4 cations (in hexagonal rings connected by a cuboctahedron and a hexagonal prism) are in the 1/8 elemental cell (1/8 u.c.) of the SI position, 4 cations (in hexagonal rings connecting cupoctahedrons and large voids) are in the 1/8 elemental cell (1/8u.c.) of the SII position, and the remaining 4 cations are located in 1/8 u.c. of the SIII void (in four-membered rings of large void). There are 12 cations in 1/8 u.c. of the supervoids, or a total of 96 cations in the unit cell, according to calculations. As can be seen from the content, zeolites have a very high density.
Figure 2. Differential heats of adsorption of ammonia in zeolite NaLSX at 303 K. Horizontal dotted line - heat of condensation of ammonia at 303 K
The adsorption heat decreases to a stepped shape of the curve and is divided into 4 main fragments: 0-3 (fragment I), 3-7 (II), 7-15 (III) and 15-18 NH3/(1/8) u.c.(IV). The first high-energy fragment (0-4 NH3/(1/8)u.c.) is associated with the adsorption of ammonia to the cations in the SIII' void on the Qd curve with heat varying from 106.4 kDj/mol to 80.20 kDj/mol. These are the most suitable cations in the void because they are bound to 2-4 oxygen atoms of the forming void and therefore the adsorption goes with high heat and lasts to 2 NH3/1/8 u.c. It can therefore be assumed that the adsorption of ammonia at acidic centers H+ is in a 1: 2 ratio, then half of the number of protons and equal to 1. The total number of cations in the SIII' void is 1+3=4, which corresponds to the crystallographically determined value of the number of cations in this position. During the first molecule ammonia adsorption, 106.4 kDj/mol of heat is released. The reason for the high temperature can be explained by the fact that the cation in position SIII' is close to the entrance window, ie near the supervoid, and cations in other positions attract a small number of ammonia molecules, which takes a long time to balance the released energy. The heat of adsorption of the next molecule of ammonia decreases sharply to 90.50 kDj/mol, and we can see the stepwise decrease of 7 NH3/(1/8) u.c., from the Qd curve.
In the second fragment, 4 NH3/1/8 u.c. ammonia is sorbed, which corresponds to the number of cations in the SII or SI' position. Given that ammonia molecules do not enter sodalite voids [42], this section indicates that ammonia is adsorbed in a large void. Given the relatively high adsorption energy, it can be assumed that these centers are sodium cations that migrate from the sodalite voids to the supervoids and are localized in the open SIII void. At this stage the adsorption is 3 NH3/1/8 u.c. and 7 NH3/1/8 u.c., the adsorption differential heat decreases from 80.20 kDj/mol to 51.60 kDj/mol.
In the third fragment, the heat decreases monotonically from 51.6 to 36.6 kDj/mol with filling. Here adsorption of 8 NH3/1/8 u.c. ammonia occurs in cations at the SII position. Given that there are four Na + cations for 1/8 u.c., there are two molecules for each center.
In the fourth fragment, the adsorption heat decreases from 36.6 kDj/mol to the condensation heat, i.e., 20 kDj/mol, and 3 molecules of ammonia are adsorbed. Adsorption in this fragment goes between 15 NH3/1/8 u.c. and 18 NH3/1/8 u.c. in the range. At this stage, it is known from the differential heat of adsorption in the increasing process that 2 molecules of ammonia are sorbed at the SII position of the supervoid and 1 molecule of ammonia at the SIII position.
By extrapolating the Qd curve at the initial fillings, we obtain the adsorption of ammonia is equal to 90 kDj/mol on the Na+ cation in the SIII'state. The average adsorption heat of ammonia is equal to 75.5 kDj/mol on Na + cations in the SIII state, while that in the SII is ~ 50 kDj/mol.
The adsorption entropy calculated by the Gibbs-Helmholtz equation shows the state of ammonia molecules in zeolite. Molar differential entropy of ammonia (Fig. 3). It is much lower than the liquid ammonia entropy at NaLSX. This indicates that the mobility of ammonia in zeolite voids is severely limited.
Figure 3. Differential entropies of adsorption of ammonia in zeolite NaLSX at 303 K. Entropy of liquid ammonia is taken as zero. The horizontal dashed line is the mean integral entropy
Ammonia is adsorbed on NaLSX zeolites in the same amount but with different strength. β-voids are not available for ammonia molecules under standard conditions. Na+ cations in position SIII form four-dimensional (NH3)4/Na+ complexes in supervoids. The mobility of ammonia in the voids is lower than that of the liquid.
Figure 4 shows the equilibrium time of benzene adsorption on NaLSX zeolite. At initial fillings, the time to establish adsorption equilibrium in the NH3-NaLSX system is greatly slowed down. This is due to the fact that the zeolite takes longer to be distributed due to the voids in the pores and the zeolite pores and the large number of cations in the pores and the small amount of ammonia molecules present. It takes longer for the ammonia adsorption to reach equilibrium. Equilibrium is set at 10-16.5 hours. This process is then accelerated, slowly accelerates the rest down for N= 8 NH3/1/8.
Figure 4. Time to establish adsorption equilibrium depending on the adsorption of ammonia gases in NaLSX zeolite at 303 K
The thermokinetics of ammonia adsorption in NaLSX zeolite show that the initial ammonia molecules are slowly adsorbed, and then the adsorption equilibrium is reduced by 40 min.

4. Conclusions

At differential temperatures of ammonia adsorption, there are 4 fragments corresponding to the formation of monomeric complexes of ammonia with Na+ cations in position SIII, then SIII, the adsorption process ends with the formation of four-dimensional complexes with cations in position SII. The temperatures of ammonia adsorption with Na+ cations at positions SIII', SI' and SII are 90, 75.5 and 50 kDj/mol, respectively. The adsorption isotherm is fully described by the three-term equation of VMOT). Na+ cations in the SII position form four-dimensional (NH3)4/Na+ complexes in the supervoid. The average integral differential entropy is -59.64 J/mol*K, and the benzene molecules are adsorbed in the zeolite matrix without solid agitation. It takes a long time for the adsorption equilibrium to be established at the initial saturation. As the saturation gradually increases, the adsorption thermokinetics decreases for a few minutes.


We would like to thank the non-copyright Yakubov Y.Yu. (PhD), S.B. Lyapin for providing the necessary information in writing the article and for the doctoral students M.K. Kkhokharov and M.S. Khudoiberganov for their assistance in the experimental work. We would like to thank the authors (Rakhmatkarieva F.G., Ergashev O.K.) and the Agency for Science and Technology of the Republic of Uzbekistan for funding a total of 3 fundamental grants.


[1]  Karri, R. R., Sahu, J. N. & Chimmiri, V. Critical review of abatement of ammonia from wastewater. J. Molec. Liq. 261, 21–31. (2018).
[2]  Ramesh, K. & Reddy, D. D. Zeolites and their potential uses in agriculture. Adv. agron. 113, 219–241, (2011).
[3]  Yang, H. I. et al. Adsorption of ammonium in aqueous solutions by pine sawdust and wheat straw biochars. Envir. Sc. Pollut. Res. 25, 25638–25647, (2018).
[4]  Tian, W. et al. Remediation of aquaculture water in the estuarine wetlands using coal cinder-zeolite balls/reed wetland combination strategy. J. Envir. Manag. 181, 261–268, (2016).
[5]  Yin, H., Yang, C., Jia, Y., Chen, H. & Gu, X. Dual removal of phosphate and ammonium from high concentrations of aquaculture wastewaters using an efficient two-stage infiltration system. Sc. Total Envir. 635, 936–946, (2018).
[6]  Sànchez-Hernàndez, R., Padilla, I., Lуpez-Andrйs, S. & Lуpez-Delgado, A. Al-Waste-Based Zeolite Adsorbent Used for the Removal of Ammonium from Aqueous Solutions. Internat. J. Chem. Engineer. 1256197; (2018).
[7]  Huo, H. et al. Ammonia-nitrogen and phosphates sorption from simulated reclaimed waters by modiдed clinoptilolite. J. Hazard. Mater. 229, 292–297, (2012).
[8]  Xue, R. et al. Simultaneous removal of ammonia and N-nitrosamine precursors from high ammonia water by zeolite and powdered activated carbon. J. Environ. Sc. 64, 82–91, (2018).
[9]  Metropoulos, K., Maliou, E., Loizidou, M. & Spyrellis, N. Comparative studies between synthetic and natural zeolites for ammonium uptake. J. Environm. Sc. & Health, Part A 28, 1507–1518, (1993).
[10]  Wang, Y. F., Lin, F. & Pang, W. Q. Ammonium exchange in aqueous solution using Chinese natural clinoptilolite and modified zeolite. J. Hazard. Mater. 142, 160–164, (2007).
[11]  Markou, G., Vandamme, D. & Muylaert, K. Using natural zeolite for ammonia sorption from wastewater and as nitrogen releaser for the cultivation of Arthrospira platensis. Biores. Technol. 155, 373–378, 12.122 (2014).
[12]  Crippen, M. & Khrisnan, J. S. The combination of adsorption with modified zeolite and aquaphonic system to remove total ammonia nitrogen in fish pond. Working Paper (2016).
[13]  Rakhmatkarieva F.G., Abdurakhmonov E.B., Khudoiberganov M.S. Energetics of ammonia adsorption in NaX zeolite // Universum: chemistry and biology Issue: 6 (60), June 2019. pp. 39-43.
[14]  G.U. Rakhmatkariev, E.B. Abdurakhmonov, F.G. Rakhmatkarieva. Isotherm and differential heats of adsorption of ammonia in zeolite NaX // Composite materials. 2016. No. 2. p.39-42.
[15]  G.U. Rakhmatkariev, F.G. Usmanova, E.B. Abdurakhmonov. Isotherms and isosteric heats of adsorption of water in zeolite NaX // Chemistry journal of Uzbekistan 2013 y. # 2. Pp 11-14.
[16]  G. W. Rakhmatkariev, E.B. Abdurakhmonov, F.G. Rakhmatkarieva, G.A. Doliev. Energetics of ammonia adsorption in zeolite LiX // Chemistry journal of Uzbekistan. 2017 y. No. 5. p. 3-8.
[17]  Abdurakhmonov Eldor, Rakhmatkariev Gairat, Rakhmatkarieva Feruza, Ergashev Oybek. Adsorption-microcalorimetric investigation of benzene condition and distribution in the zeolite LiY// Austrian Journal of Technical and Natural Sciences. January – February № 1–2, 2018, pp.72-76.
[18]  Ergashev O.K., Rakhmatkarieva F.G., Abdurakhmonov E.B., Mamazhonova M.A. Ion-molecular complexes in nanostructured zeolite nitrite-sodalite // UNIVERSUM Chemistry and Biology, 2018, No. 9 (51). - pp. 14-17.
[19]  F.G. Rakhmatkarieva, E.B. Abdurakhmonov, G.U. Rakhmatkariev, Y.Yu. Yakubov. Isotherm, differential heats, entropy and time of establishment of adsorption equilibrium of ammonia in zeolite LiY // Composite materials. 2018. No. 3. p.84-82.
[20]  Rakhmatkarieva F.G., Abdurakhmonov E.B., Khudoyberganov M.S. Energetics of ammonia adsorption in NaX zeolite // Universum: chemistry and biology Issue: 6 (60), June 2019. pp. 39-43.
[21]  Rakhmatkarieva F.G., Abdurakhmonov E.B. Thermodynamics of adsorption of benzene vapors in zeolite NaX // Eurasian Union of Scientists (ESU) # 6 (63), 2019. p.42-45.
[22]  Ergashev O.K., Kokhkharov M.Kh., Abdurakhmonov E.B., Energy of adsorption of carbon dioxide in zeolite CaA // Universum: chemistry and biology: scientific journal 2019 yil No. 7 (61) pp. 23-26.
[23]  O. Ergashev, M. Koxxarov, E. Abduraxmonov. Energy of carbon dioxide gas adsorption in CaA (M-22) zeolite // FarSU scientific reports № 5. 2019 y. pp. 36-40.
[24]  Kokharov Mirzokhid Husanboevich, Axmedov Ulug’ Karimovich, Rakhmatkarieva Firuza Gayratovna, Abduraxmonov Eldor Baratovich Investigation of water sorption to Са5Na3 А zeolite at adsorption of micro calorimetric device // International Journal of Advanced Research in Science, Engineering and Technology Vol. 7, Issue 5, May 2020 yil P. 13939- 13944.
[25]  F.G. Rakhmatkarieva, E.B. Abdurakhmonov, A.O. Zhabborov, Abdurakhmonov A.B. Regularities of ammonia adsorption in nanostructured zeolite LiLSX // Universum: chemistry and biology Issue: 4 (70), p. 39-43. April 2020.
[26]  Abdurakhmonov E.B., Rakhmatkarieva F.G., Yakubov Y.Yu., Abdulkhaev T.D., Khudayberganov M.S. Differential heats of adsorption of benzene vapors in zeolite LiLSX // Universum: chemistry and biology Issue: 6 (72), pp. 60-63. June 2020.
[27]  F.G.Rakhmatkariyeva, E.B. Abdurakhmonov, Y.Y. Yakubov Volumetric Analysis of Benzene Vapor Adsorption on LiLSX Zeolite in a High Vacuum Adsorption Device // International Journal of Advanced Science and Technology Vol. 29, No. 8, (2020), pp. 3442-3448.
[28]  Abdurakhmonov Eldor Baratovich, Ergashev Oybek Karimovich. Thermokinetics of benzene adsorption in NaLSX zeolite // Universum: chemistry and biology Issue: 8 (74), pp. 5-8. August 2020.
[29]  Abdurakhmonov Eldor Baratovich Entropy of benzene adsorption in zeolite NaLSX // Universum: chemistry and biology Issue: 8 (74), pp. 12-15. August 2020.
[30]  E. B.Abdurakhmonov, F.G. Rakhmatkarieva, O.K. Ergashev, G.M. Ochilov. Energetic Characteristics Of The Process Of Adsorption Of Benzene In Zeolites NaX And NaY // International Journal of Future Generation Communication and Networking Vol. 13, No. 4, (2020), pp. 246–252.
[31]  Rakhmatkarieva F.G., Rakhmatkariev G. U., Guro V.P. Microcalorimetric study of water vapor adsorption in BaY zeolite // Austrian Journal of Technical and Natural Sciences, (Vienna, Austria), 2015, №11-12. - P. 73-77. (02.00.00 №2).
[32]  Rakhmatkarieva F.G., Rakhmatkariev G. U., Guro V. Microcalorimetric study of carbon dioxide adsorption in BaY zeolite // Austrian Journal of Technical and Natural Sciences, (Vienna, Austria), 2015, №11-12. - P. 77-81.
[33]  Rakhmatkariev G.U., Rakhmatkariev F.G. Ion-molecular complexes in nanostructured zeolite NaA // Journal "Universum" chemistry and biology, 2018, no. 11 (53). - pp. 47-50.
[34]  Rakhmatkarieva F.G., Rakhmatkariev G. U., Guro V. P. The Host/Guest Interactions in BaY Molecular Sieve: Water Adsorption // AASCIT Journals, (America), 2015, №1. - P.74-78.
[35]  Ergashev O.K., Rakhmatkarieva F.G., Abdurakhmonov E.B., Mamazhonova M.A. Ion-molecular complexes in nanostructured zeolite nitrite-sodalite // UNIVERSUM Chemistry and Biology, 2018, No. 9 (51). - pp. 14-17.
[36]  Ergashev O.K. Differential heats of water adsorption in molecular sieves of iodide sodalite // European Science Review, 2018, №11-12. - P. 310-313.
[37]  Ergashev O.K. Energy of ammonia adsorption in sodalite // Composite materials, 2018, №3. - p. 39-45.
[38]  Ergashev O.K. ammonia adsorption energy to NaI sodalite // Composite materials, 2018, №3. - p. 46-52.
[39]  Akhmedov K.S., Rakhmatkariev G.U., Khaustova A.A. Differential enthalpies of adsorption of methyl alcohol on TiO2 // Regulation of the surface properties of mineral dispersions. Ed. H.R. Rustamov. -Tashkent, 1984. -P.72-79.
[40]  Rakhmatkariev G.U., Isirikyan A.A. Complete description of adsorption isotherms by equations of the theory of volumetric filling of micropores // Izv. USSR Academy of Sciences, Ser. 1988. No. 11. P. 2644.
[41]  Dubinin M.M. Progress in Surface Membrane Science, New York 1975. Vol. 9. P. 1-70.
[42]  M. Hartmann and L. Kevan. // Chem. Rev. -99. -1999. -P. 635.