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Kikkinides ES, Enke D, Valiullin R. Gas Sorption Characterization of Porous Materials Employing a Statistical Theory for Bethe Lattices. J Phys Chem A 2024; 128:4573-4587. [PMID: 38787333 PMCID: PMC11163428 DOI: 10.1021/acs.jpca.4c02185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2024] [Revised: 05/16/2024] [Accepted: 05/16/2024] [Indexed: 05/25/2024]
Abstract
In the present work, a recently developed statistical theory for adsorption and desorption processes in mesoporous solids, modeled by random Bethe lattices, has been applied to obtain pore size distributions and interpore connectivity from sorption isotherms in real random porous materials, employing a robust and validated methodology. Using the experimental adsorption-desorption N2 isotherms at 77.4 K on Vycor glass, a porous material with random pore structure, we demonstrate the solution of the inverse problem resulting in extracted pore size distribution and interpore connectivity, notably different from the predictions of earlier theories. The results presented are corroborated by the analysis of 3D digital images of reconstructed Vycor porous glass, showing excellent agreement between the predictions of geometric analysis and the new statistical theory.
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Affiliation(s)
- E. S. Kikkinides
- Department
of Chemical Engineering, Aristotle University
of Thessaloniki, 54124 Thessaloniki, Greece
| | - D. Enke
- Faculty
of Chemistry and Mineralogy, Leipzig University, 04103 Leipzig, Germany
| | - R. Valiullin
- Faculty
of Physics and Earth System Sciences, Leipzig
University, 04103 Leipzig, Germany
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2
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Kikkinides ES, Valiullin R. A New Statistical Theory for Constructing Sorption Isotherms in Mesoporous Structures Represented by Bethe Lattices. J Phys Chem A 2023; 127:8734-8750. [PMID: 37793009 DOI: 10.1021/acs.jpca.3c04993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/06/2023]
Abstract
In the present work, a new statistical theory is developed to describe adsorption and desorption in mesoporous materials (pore sizes ranging from 2 to 50 nm) represented by pore networks in the form of Bethe lattices. The new theory is an extension of a previous theory applied for Statistically Disordered Chain Model (SDCM) structures and incorporates the cooperative effects emerging during phase transitions in pore networks. The theory is validated against simulations and algorithmic models that describe sorption of lattice and real fluids in Bethe lattices. It is seen that the pore network coordination number, or pore connectivity, z, has a significant impact on two important processes observed in pore networks: pore assisting condensation during adsorption and evaporation by percolation during desorption. The inclusion of pore connectivity in the earlier developed framework accounting for cooperativity effects is an important step, rendering the existing models to mimic fluid behavior in real materials more accurately. Hence, the new theory inherently contains all essential elements that may offer the extraction of more reliable pore size distributions utilizing both the adsorption and desorption branches of the isotherm.
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Affiliation(s)
- Eustathios S Kikkinides
- Department of Chemical Engineering, Aristotle University of Thessaloniki, University Campus, Thessaloniki 54124, Greece
| | - Rustem Valiullin
- Faculty of Physics and Earth Sciences, Felix Bloch Institute for Solid State Physics, Linnestr. 5, Leipzig 04103, Germany
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Safaripour S, Anand G, Snoeyink C. Thermodynamic Study of the Electric Field Effect on Liquid-Vapor Mixture at Equilibrium: An Analysis on a Water-Ethanol Mixture. J Phys Chem B 2023. [PMID: 37440468 DOI: 10.1021/acs.jpcb.3c01578] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/15/2023]
Abstract
In this paper, the effect of electric fields on phase equilibria through polarization is investigated. A relation is derived for the chemical potential of a system, where the electric field is localized over a liquid phase mixture in equilibrium with a vapor phase mixture. This relation is then applied to a water-ethanol mixture to explore the effect of polarization-based electric fields on the liquid phase composition. It is observed that the quadratic dependence on electric field strength produces little effect below field strengths of approx. 10 MV/m. However, above this field strength, the mole fraction of water in the liquid phase grows rapidly, increasing by a factor of 8 for a water vapor phase fraction of 0.2 and a field strength of 500 MV/m, which approaches the dielectric breakdown strength of water. Nonetheless, this field strength could be achievable with microfluidic experimental setups.
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Affiliation(s)
- Samira Safaripour
- Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, New York 14260, United States
| | - Gaurav Anand
- Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, New York 14260, United States
| | - Craig Snoeyink
- Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, New York 14260, United States
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Zill JC, Thompson ES, Nestle N, Valiullin R. Kinetics of Guest-Induced Structural Transitions in Metal-Organic-Framework MIL-53(Al)-NH 2 Probed by High-Pressure Nuclear Magnetic Resonance. J Phys Chem Lett 2023; 14:3391-3396. [PMID: 36996319 DOI: 10.1021/acs.jpclett.3c00155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
A nuclear magnetic resonance (NMR) study of a pore opening in amino-functionalized metal-organic framework (MOF) MIL-53(Al) in response to methane pressure variation is presented. Variations of both NMR signal intensities and transversal relaxation rates for methane are found to reveal hysteretic structural transitions in the MOF material, which are smeared out over broad pressure ranges. Experiments with pressure reversals upon an incomplete adsorption/desorption gave deeper insight into the microscopic transition mechanisms. These experiments have unequivocally proven that the non-stepwise pore opening/closing transitions observed in the experiments are governed by a distribution of the opening/closing pressures over different MOF crystallites, for example, due to a distribution of the crystal sizes or shapes. The slow kinetics of the structural transitions measured in the hysteresis regime revealed a complex free energy landscape for the phase transition process.
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Affiliation(s)
- Jeremias C Zill
- Felix Bloch Institute for Solid State Physics, Leipzig University, Linnéstr. 5, 04103 Leipzig, Germany
| | - Emma S Thompson
- BASF SE, Carl-Bosch-Str. 38, 67056 Ludwigshafen am Rhein, Germany
| | - Nikolaus Nestle
- BASF SE, Carl-Bosch-Str. 38, 67056 Ludwigshafen am Rhein, Germany
| | - Rustem Valiullin
- Felix Bloch Institute for Solid State Physics, Leipzig University, Linnéstr. 5, 04103 Leipzig, Germany
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Shchur Y, Beltramo G, Andrushchak AS, Vitusevich S, Huber P, Adamiv V, Teslyuk I, Boichuk N, Kityk AV. On the issue of textured crystallization of Ba(NO 3) 2 in mesoporous SiO 2: Raman spectroscopy and lattice dynamics analysis. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2022; 275:121157. [PMID: 35316625 DOI: 10.1016/j.saa.2022.121157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Revised: 03/08/2022] [Accepted: 03/11/2022] [Indexed: 06/14/2023]
Abstract
The lattice dynamics of preferentially aligned nanocrystals formed upon drying of aqueous Ba(NO3)2 solutions in a mesoporous silica glass traversed by tubular pores of approximately 12 nm are explored by Raman scattering. To interpret the experiments on the confined nanocrystals polarized Raman spectra of bulk single crystals and X-ray diffraction experiments are also performed. Since a cubic symmetry is inherent to Ba(NO3)2, a special Raman scattering geometry was utilized to separate the phonon modes of Ag and Eg species. Combining group-theory analysis and ab initio lattice dynamics calculations a full interpretation of all Raman lines of the bulk single crystal is achieved. Apart from a small confinement-induced line broadening, the peak positions and normalized peak intensities of the Raman spectra of the nanoconfined and macroscopic crystals are identical. Interestingly, the Raman scattering experiment indicates the existence of comparatively large,∼10-20 μm, single-crystalline regions of Ba(NO3)2 embedded in the porous host, near three orders of magnitude larger than the average size of single nanopores. This is contrast to the initial assumption of non-interconnected pores. It rather indicates an inter-pore propagation of the crystallization front, presumably via microporosity in the pore walls.
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Affiliation(s)
- Yaroslav Shchur
- Institute for Condensed Matter Physics, 1 Svientsitskii str., 79011 Lviv, Ukraine.
| | - Guillermo Beltramo
- Institute of Biological Information Processing Mechanobiology (IBI-2), Forschungszentrum Juelich, D-52425 Juelich, Germany
| | | | - Svetlana Vitusevich
- Institute of Bioelectronics (IBI-3), Forschungszentrum Juelich, D-52425 Juelich, Germany
| | - Patrick Huber
- Institute for Materials and X-Ray Physics, Hamburg University of Technology, Eissendorferstr. 42, 21073 Hamburg, Germany; Center for X-ray and Nano Science CXNS, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany; Center for Hybrid Nanostructures CHyN, Hamburg University, Luruper Chaussee 149, 22607 Hamburg, Germany
| | - Volodymyr Adamiv
- O.G. Vlokh Institute of Physical Optics, 23 Dragomanova str., 79005 Lviv, Ukraine
| | - Ihor Teslyuk
- O.G. Vlokh Institute of Physical Optics, 23 Dragomanova str., 79005 Lviv, Ukraine
| | - Nazarii Boichuk
- Institute of Bioelectronics (IBI-3), Forschungszentrum Juelich, D-52425 Juelich, Germany
| | - Andriy V Kityk
- Faculty of the Electrical Engineering, Czestochowa University of Technology, Al. Armii Krajowej 17, 42-200 Czestochowa, Poland
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Lazarenko MM, Zabashta YF, Alekseev AN, Yablochkova KS, Ushcats MV, Dinzhos RV, Vergun LY, Andrusenko D, Bulavin L. Melting of crystallites in a solid porous matrix and the application limits of the Gibbs-Thomson equation . J Chem Phys 2022; 157:034704. [DOI: 10.1063/5.0093327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A thermodynamic model is proposed to describe the melting of lamellar crystallite in a solid medium. This model includes a modification of the Gibbs-Thomson equation to make it applicable to the above-mentioned crystallites. The need for such modification is supported experimentally by studying the impact of the surrounding on the melting point of the crystallites. In particular, the application of the model to nanocrystals in open-porous systems makes it possible to determine the analytical relations for the melting point, the heat of melting, and the inverse effective size of the pores. The fitting of the experimental data with these functional relations then allows for the calculation of the nanocrystalline density, pressure in the nanocrystal, difference in the surface tension coefficients at the nanocrystal-matrix interface and melt-matrix interface, as well as the difference in the surface entropies per unit area at the nanocrystal-matrix and melt-matrix interfaces.
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Affiliation(s)
- Maxim M. Lazarenko
- Taras Shevchenko National University of Kyiv Faculty of Physics, Ukraine
| | - Yuri F. Zabashta
- Taras Shevchenko National University of Kyiv Faculty of Physics, Ukraine
| | | | | | | | | | - Lena Yu. Vergun
- Taras Shevchenko National University of Kyiv Faculty of Physics, Ukraine
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Morishige K. Pore Size Distribution Analysis Using Developing Hysteresis of Nitrogen in the Cylindrical Pores of Silica. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:4222-4233. [PMID: 35360908 DOI: 10.1021/acs.langmuir.1c03219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
A new method of mesopore size analysis was developed for the cylindrical pores of silica using a developing hysteresis of nitrogen measured at liquid nitrogen temperature. The method is based on the semimacroscopic approach of a modified Bonnet-Wolf model that deals with the grand potential of a vapor bubble in the cylindrical pore. It is capable of assessing correctly the pore structures of mesoporous materials with cylindrical pores using the narrow hysteresis loop of the developing hysteresis. When the mesoporous materials possess cylindrical pores of minor imperfections, two pore size distributions (PSDs) from the adsorption and desorption branches overlap. On the other hand, for cylindrical pores with an enhanced amplitude of pore corrugations and/or constrictions, PSD from the desorption branch is shifted to smaller pore sizes compared to the one from the adsorption branch, and at the same time, both the PSDs evaluated are shifted to lower pore sizes compared to the actual ones. The actual PSD can be assessed from the reversible isotherm measured at a hysteresis critical temperature. In principle, the present method may enable the determination of the PSDs from the adsorption hysteresis measured at any given temperature for mesoporous materials with cylindrical pores.
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Affiliation(s)
- Kunimitsu Morishige
- Department of Chemistry, Okayama University of Science, 1-1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan
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On the Comparative Analysis of Different Phase Coexistences in Mesoporous Materials. MATERIALS 2022; 15:ma15072350. [PMID: 35407683 PMCID: PMC8999465 DOI: 10.3390/ma15072350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Revised: 03/15/2022] [Accepted: 03/16/2022] [Indexed: 02/05/2023]
Abstract
Alterations of fluid phase transitions in porous materials are conventionally employed for the characterization of mesoporous solids. In the first approximation, this may be based on the application of the Kelvin equation for gas-liquid and the Gibbs-Thomson equation for solid-liquid phase equilibria for obtaining pore size distributions. Herein, we provide a comparative analysis of different phase coexistences measured in mesoporous silica solids with different pore sizes and morphology. Instead of comparing the resulting pore size distributions, we rather compare the transitions directly by using a common coordinate for varying the experiment's thermodynamic parameters based on the two equations mentioned. Both phase transitions in these coordinates produce comparable results for mesoporous solids of relatively large pore sizes. In contrast, marked differences are found for materials with smaller pore sizes. This illuminates the fact that, with reducing confinement sizes, thermodynamic fluctuations become increasingly important and different for different equilibria considered. In addition, we show that in the coordinate used for analysis, mercury intrusion matches perfectly with desorption and freezing transitions.
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