1
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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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2
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Ledezma Lopez GA, Verstraete JJ, Sorbier L, Glowska A, Leinekugel-Le-Cocq D, Jolimaitre E, Jallut C. Generation of γ-Alumina Digital Twins Using a Nitrogen Porosimetry Simulation. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.1c02849] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Alejandro Ledezma Lopez
- IFP Energies Nouvelles, Rond-point de l’échangeur de Solaize, BP 3, 69360 Solaize, France
- Univ Lyon, Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007 43 boulevard du 11 novembre 1918, Villeurbanne, F-69100, France
| | - Jan J. Verstraete
- IFP Energies Nouvelles, Rond-point de l’échangeur de Solaize, BP 3, 69360 Solaize, France
| | - Loïc Sorbier
- IFP Energies Nouvelles, Rond-point de l’échangeur de Solaize, BP 3, 69360 Solaize, France
| | - Aleksandra Glowska
- IFP Energies Nouvelles, Rond-point de l’échangeur de Solaize, BP 3, 69360 Solaize, France
- Centre for Nature Inspired Engineering (CNIE), University College of London, Gower Street, London, WC1E6BT, United Kingdom
| | | | - Elsa Jolimaitre
- IFP Energies Nouvelles, Rond-point de l’échangeur de Solaize, BP 3, 69360 Solaize, France
| | - Christian Jallut
- Univ Lyon, Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007 43 boulevard du 11 novembre 1918, Villeurbanne, F-69100, France
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3
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Kolesnikov AL, Budkov YA, Gor GY. Models of adsorption-induced deformation: ordered materials and beyond. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:063002. [PMID: 34666316 DOI: 10.1088/1361-648x/ac3101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 10/19/2021] [Indexed: 06/13/2023]
Abstract
Adsorption-induced deformation is a change in geometrical dimensions of an adsorbent material caused by gas or liquid adsorption on its surface. This phenomenon is universal and sensitive to adsorbent properties, which makes its prediction a challenging task. However, the pure academic interest is complemented by its importance in a number of engineering applications with porous materials characterization among them. Similar to classical adsorption-based characterization methods, the deformation-based ones rely on the quality of the underlying theoretical framework. This fact stimulates the recent development of qualitative and quantitative models toward the more detailed description of a solid material, e.g. account of non-convex and corrugated pores, calculations of adsorption stress in realistic three-dimension solid structures, the extension of the existing models to new geometries, etc. The present review focuses on the theoretical description of adsorption-induced deformation in micro and mesoporous materials. We are aiming to cover recent theoretical works describing the deformation of both ordered and disordered porous bodies.
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Affiliation(s)
- A L Kolesnikov
- Institut für Nichtklassische Chemie e.V., Permoserstr. 15, 04318 Leipzig, Germany
| | - Yu A Budkov
- School of Applied Mathematics, Tikhonov Moscow Institute of Electronics and Mathematics, HSE University, Tallinskaya St. 34, 123458 Moscow, Russia
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Academicheskaya St. 1, 153045 Ivanovo, Russia
| | - G Y Gor
- Otto H. York Department Chemical and Materials Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, United States of America
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4
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Aguilar-Huerta E, Cordero-Sánchez S, Rojas-González F, Villegas-Cortez J. Description of the thickness of the adsorbed layer, identification of the instability characteristics of the liquid–vapour interface and assessment of criticality in elliptical pores through the Broekhoff de Boer theory. ADSORPTION 2021. [DOI: 10.1007/s10450-021-00326-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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5
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Morishige K. Revisiting the Nature of Adsorption and Desorption Branches: Temperature Dependence of Adsorption Hysteresis in Ordered Mesoporous Silica. ACS OMEGA 2021; 6:15964-15974. [PMID: 34179641 PMCID: PMC8223431 DOI: 10.1021/acsomega.1c01643] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
To gain a deeper understanding as to the nature of the adsorption hysteresis due to capillary condensation of nitrogen in ordered mesoporous silicas, we calculated the temperature dependences of the activated condensation, equilibrium transition, and activated desorption pressures for nitrogen in spherical and cylindrical silica pores with several different pore sizes on the basis of semimacroscopic continuum models. The results clearly indicate that the models capture the exact nature of capillary condensation and evaporation phenomena of a fluid in cagelike and cylindrical mesopores. The temperature dependences of the adsorption hysteresis of nitrogen measured confirm previous theoretical predictions for cylindrical pores: for the ordered mesoporous silicas with cylindrical mesopores at least greater than ∼7 nm in diameter, the capillary condensation takes place via a nucleation process followed by a growth process of a bridging meniscus at pressures higher than the equilibrium transition, while the capillary evaporation takes place via a receding meniscus from pore ends at the equilibrium. For SBA-15 and MCM-41 with smaller mesopore sizes, on the other hand, the capillary condensation takes place close to the equilibrium transition pressures, while the capillary evaporation takes place at pressures lower than the equilibrium, owing to single pore blocking due to corrugation of the cylindrical pores. We discuss the effect of curvature on surface tension in capillary condensation, as well as the relation between a change in the mechanisms of adsorption and desorption and the pore corrugation in the cylindrical pores.
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Affiliation(s)
- Kunimitsu Morishige
- Department of Chemistry, Okayama University of Science, 1-1 Rida-cho, Kita-ku, Okayama 700-0005, Japan
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6
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Maximov MA, Molina M, Gor GY. The effect of interconnections on gas adsorption in materials with spherical mesopores: A Monte Carlo simulation study. J Chem Phys 2021; 154:114706. [PMID: 33752360 DOI: 10.1063/5.0040763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Gas adsorption is a standard method for measuring pore-size distributions of nanoporous materials. This method is often based on assuming the pores as separate entities of a certain simple shape: slit-like, cylindrical, or spherical. Here, we study the effect of interconnections on gas adsorption in materials with spherical pores, such as three-dimensionally ordered mesoporous (3DOm) carbons. We consider interconnected systems with two, four, and six windows of various sizes. We propose a simple method based on the integration of solid-fluid interactions to take into account these windows. We used Monte Carlo simulations to model argon adsorption at the normal boiling point and obtained adsorption isotherms for the range of systems. For a system with two windows, we obtained a remarkably smooth transition from the spherical to cylindrical isotherm. Depending on the size and number of windows, our system resembles both spherical and cylindrical pores. These windows can drastically shift the point of capillary condensation and result in pore-size distributions that are very different from the ones based on a spherical pore model. Our results can be further used for modeling fluids in a system of interconnected pores using Monte Carlo and density functional theory methods.
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Affiliation(s)
- Max A Maximov
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, 323 Dr. Martin Luther King Jr. Blvd., Newark, New Jersey 07102, USA
| | - Marcos Molina
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, 323 Dr. Martin Luther King Jr. Blvd., Newark, New Jersey 07102, USA
| | - Gennady Y Gor
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, 323 Dr. Martin Luther King Jr. Blvd., Newark, New Jersey 07102, USA
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7
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Kolesnikov AL, Budkov YA, Gor GY. Adsorption-induced deformation of mesoporous materials with corrugated cylindrical pores. J Chem Phys 2020; 153:194703. [PMID: 33218228 DOI: 10.1063/5.0025473] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mesoporous materials play an important role both in engineering applications and in fundamental research of confined fluids. Adsorption goes hand in hand with the deformation of the absorbent, which has positive and negative sides. It can cause sample aging or can be used in sensing technology. Here, we report the theoretical study of adsorption-induced deformation of the model mesoporous material with ordered corrugated cylindrical pores. Using the classical density functional theory in the local density approximation, we compared the solvation pressure in corrugated and cylindrical pores for nitrogen at sub- and super-critical temperatures. Our results demonstrate qualitative differences between solvation pressures in the two geometries at sub-critical temperatures. The deviations are attributed to the formation of liquid bridges in corrugated pores. However, at super-critical temperatures, there is no abrupt bridge formation and corrugation does not qualitatively change solvation pressure isotherms. We believe that these results could help in the analysis of an adsorption-induced deformation of the materials with distorted pores.
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Affiliation(s)
- A L Kolesnikov
- Institut für Nichtklassische Chemie e.V., Permoserstr. 15, 04318 Leipzig, Germany
| | - Yu A Budkov
- School of Applied Mathematics, Tikhonov Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Tallinskaya St. 34, 123458 Moscow, Russia
| | - G Y Gor
- Otto H. York Department Chemical and Materials Engineering, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102, USA
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8
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Ludescher L, Morak R, Braxmeier S, Putz F, Hüsing N, Reichenauer G, Paris O. Hierarchically organized materials with ordered mesopores: adsorption isotherm and adsorption-induced deformation from small-angle scattering. Phys Chem Chem Phys 2020; 22:12713-12723. [PMID: 32462146 DOI: 10.1039/d0cp01026j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
In situ small angle scattering is used to study the pore filling mechanism and the adsorption induced deformation of a silica sample with hierarchical porosity upon water adsorption. The high structural order of the cylindrical mesopores on a 2D hexagonal lattice allows obtaining adsorption induced strains from the shift of the corresponding Bragg peaks measured by in situ small-angle X-ray scattering (SAXS). However, apparent strains due to scattering contrast induced changes of the Bragg peak shapes emerge in SAXS. In contrast, small-angle neutron scattering (SANS) allows determining the real adsorption induced strains by employing a H2O/D2O adsorbate with net coherent scattering length density of zero. This allows separating the apparent strains from the real strains experimentally and comparing them with strains obtained from model calculations of the SAXS intensity. It is shown that the apparent strains cannot be described at all by a simple mesopore model of film growth and capillary condensation. A hierarchical model taking the scattering of the micropores and the outer surface of the mesoporous struts in the hierarchically porous sample properly into account, together with a modified mesopore filling mechanism based on a corona model, leads to satisfactory description of both, the adsorption isotherm and the measured apparent strains as derived by SAXS.
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Affiliation(s)
- Lukas Ludescher
- Institute of Physics, Montanuniversität Leoben, Franz-Josef Strasse 18, 8700, Leoben, Austria.
| | - Roland Morak
- Institute of Physics, Montanuniversität Leoben, Franz-Josef Strasse 18, 8700, Leoben, Austria.
| | - Stephan Braxmeier
- Bavarian Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Wuerzburg, Germany
| | - Florian Putz
- Chemistry and Physics of Materials, Paris Lodron University Salzburg, Jakob-Haringer Str. 2a, 5020 Salzburg, Austria
| | - Nicola Hüsing
- Chemistry and Physics of Materials, Paris Lodron University Salzburg, Jakob-Haringer Str. 2a, 5020 Salzburg, Austria
| | - Gudrun Reichenauer
- Bavarian Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Wuerzburg, Germany
| | - Oskar Paris
- Institute of Physics, Montanuniversität Leoben, Franz-Josef Strasse 18, 8700, Leoben, Austria.
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9
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Maximov MA, Galukhin AV, Gor GY. Pore-Size Distribution of Silica Colloidal Crystals from Nitrogen Adsorption Isotherms. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:14975-14982. [PMID: 31633940 DOI: 10.1021/acs.langmuir.9b02252] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Silica colloidal crystals are face-centered cubic structures comprised of silica spheres with the diameters ranging between tens and hundreds of nanometers. The voids between the spheres form pores, which can be probed by nitrogen adsorption porosimetry. Here, we prepared two mesoporous samples and a macroporous reference sample and then measured nitrogen adsorption and desorption isotherms for further characterization. We proposed a straightforward procedure for calculation of the pore-size distribution of silica colloidal crystals from nitrogen adsorption isotherms. The procedure is based on the adsorption integral equation solution with a kernel of theoretical isotherms, consistent with the procedure used for many other porous materials. The solution is carried out using the non-negative least squares (NNLS) regression with Tikhonov regularization. The kernel of mesoporous isotherms is built on the basis of the macroscopic Derjaguin-Broekhoff-de Boer (DBdB) theory of capillary condensation considering the voids as a network of spheres. Application of our procedure for the analysis of the adsorption branches of experimental isotherms resulted in bimodal distributions, where the modes matched well with the sizes of the voids in the colloidal crystals face centered cubic structure: the main mode corresponds to the octahedral voids and the second mode to the tetrahedral voids. Furthermore, we modified the surface of the samples with organics and repeated the characterization procedure for the modified samples. The resulting pore-size distribution for the samples with the modified surface matched the original one quite closely. It demonstrates the procedure as a simple and efficient technique to estimate the pore-size distribution and justifies the spherical shape approximation for the voids in the silica colloidal crystals.
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Affiliation(s)
- Max A Maximov
- Otto H. York Department of Chemical and Materials Engineering , New Jersey Institute of Technology , 323 Dr. Martin Luther King Jr. Blvd , Newark , New Jersey 07102 , United States
| | - Andrey V Galukhin
- Alexander Butlerov Institute of Chemistry , Kazan Federal University , Kremlevskaya Str. 18 , 420008 Kazan , Russian Federation
| | - Gennady Y Gor
- Otto H. York Department of Chemical and Materials Engineering , New Jersey Institute of Technology , 323 Dr. Martin Luther King Jr. Blvd , Newark , New Jersey 07102 , United States
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10
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Gommes CJ, Asset T, Drnec J. Small-angle scattering by supported nanoparticles: exact results and useful approximations. J Appl Crystallogr 2019. [DOI: 10.1107/s1600576719003935] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
In functional materials, nanoparticles are often dispersed in a porous support for the purpose of stabilizing them. This makes their characterization by small-angle scattering challenging because the signal comprises contributions from the nanoparticles of interest, from the inert support and from their cross-correlation. Exact analytical expressions for all three contributions are derived in the case of a Gaussian-field model of the porous support, with nanoparticles randomly distributed over the surface. For low nanoparticle loading, the expressions simplify to the addition of properly scaled support and particle scattering. For higher loadings, however, the cross-correlation cannot be ignored. Two approximations are introduced, which capture correlation effects in cases where the pores of the support are much larger or only slightly larger than the nanoparticles. The methods of the paper are illustrated with the small-angle X-ray scattering analysis of hollow metallic nanoparticles supported on porous carbon.
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11
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Enninful HRNB, Schneider D, Hoppe A, König S, Fröba M, Enke D, Valiullin R. Comparative Gas Sorption and Cryoporometry Study of Mesoporous Glass Structure: Application of the Serially Connected Pore Model. Front Chem 2019; 7:230. [PMID: 31041305 PMCID: PMC6476905 DOI: 10.3389/fchem.2019.00230] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Accepted: 03/25/2019] [Indexed: 11/13/2022] Open
Abstract
Nitrogen sorption and melting and freezing of water in a small pore size mesoporous glass with irregular pore structure is studied. The analysis of the experimentally obtained data is performed using the recently developed serially connected pore model (SCPM). The model intrinsically incorporates structural disorder by introducing coupling between nucleation and phase growth mechanisms in geometrically disordered mesopore spaces. It is shown that, in contrast to the independent pore models prevailing in the literature, SCPM self-consistently describes not only boundary transitions, but also the entire family of the scanning transitions. The scanning behavior is shown to be very sensitive to microscopic details of the fluid phase distribution within the porous materials, hence can be used to check the validity of the thermodynamic models and to improve the structural analysis. We show excellent quantitative agreement between the structural information evaluated from the cryoporometry and gas sorption data using SCPM.
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Affiliation(s)
- Henry R N B Enninful
- Faculty of Physics and Earth Sciences, Felix Bloch Institute for Solid State Physics, Leipzig University, Leipzig, Germany
| | - Daniel Schneider
- Faculty of Physics and Earth Sciences, Felix Bloch Institute for Solid State Physics, Leipzig University, Leipzig, Germany
| | - Antonia Hoppe
- Faculty of Chemistry and Mineralogy, Institute of Chemical Technology, Leipzig University, Leipzig, Germany
| | - Sandra König
- Institute of Inorganic and Applied Chemistry, University of Hamburg, Hamburg, Germany
| | - Michael Fröba
- Institute of Inorganic and Applied Chemistry, University of Hamburg, Hamburg, Germany
| | - Dirk Enke
- Faculty of Chemistry and Mineralogy, Institute of Chemical Technology, Leipzig University, Leipzig, Germany
| | - Rustem Valiullin
- Faculty of Physics and Earth Sciences, Felix Bloch Institute for Solid State Physics, Leipzig University, Leipzig, Germany
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12
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Gommes CJ, Roberts AP. Stochastic analysis of capillary condensation in disordered mesopores. Phys Chem Chem Phys 2018; 20:13646-13659. [PMID: 29737990 DOI: 10.1039/c8cp01628c] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Most mesoporous materials of practical interest are inherently disordered, which has a significant impact on the condensation and evaporation of vapours in their pores. Traditionally, the effect of disorder is theoretically analyzed in a perturbative approach whereby slight elements of disorder (constriction, corrugation) are added to geometrically ideal pores. We propose an alternative approach, which consists of using a stochastic geometrical model to describe both the porous material and the condensate within the pores. This is done through a multiphase generalisation of the standard Gaussian random field model of disordered materials. The model parameters characterising the condensate provide a low-dimensional approximation of its configuration space, and we use a Derjaguin-Broekhoff-de Boer approximation to calculate the free-energy landscape. Our analysis notably questions the existence of vapour-like metastable states in realistically disordered mesoporous materials. Beyond capillary condensation, our general methodology is applicable to a broad array of confined phenomena.
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Affiliation(s)
- Cedric J Gommes
- Department of Chemical Engineering, University of Liège, Allée du Six Août, 3, B-4000 Liège, Belgium.
| | - Anthony P Roberts
- School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia
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13
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Desgranges C, Delhommelle J. Free energy calculations along entropic pathways. III. Nucleation of capillary bridges and bubbles. J Chem Phys 2017. [DOI: 10.1063/1.4982943] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, University of North Dakota, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, University of North Dakota, Grand Forks, North Dakota 58202, USA
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14
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Hofmann T, Wallacher D, Perlich J, Koyiloth Vayalil S, Huber P. Formation of Periodically Arranged Nanobubbles in Mesopores: Capillary Bridge Formation and Cavitation during Sorption and Solidification in an Hierarchical Porous SBA-15 Matrix. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:2928-2936. [PMID: 26940230 DOI: 10.1021/acs.langmuir.5b04560] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We report synchrotron-based small-angle X-ray scattering experiments on a template-grown porous silica matrix (Santa Barbara Amorphous-15) upon in situ sorption of fluorinated pentane C5F12 along with volumetric gas sorption isotherm measurements. Within the mean-field model of Saam and Cole for vapor condensation in cylindrical pores, a nitrogen and C5F12 sorption isotherm is well described by a bimodal pore radius distribution dominated by meso- and micropores with 3.4 and 1.6 nm mean radius, respectively. In the scattering experiments, two different periodicities become evident. One of them (d1 = 11.5 nm) reflects the next nearest neighbor distance in a 2D-hexagonal lattice of tubular mesopores. A second periodicity (d2 = 11.4 nm) found during in situ sorption and freezing experiments is traced back to a superstructure along the cylindrical mesopores. It is compatible with periodic pore corrugations found in electron tomograms of empty SBA-15 by Gommes et al. ( Chem. Mater. 2009, 21, 1311 - 1317). A Rayleigh-Plateau instability occurring at the cylindrical blockcopolymer micelles characteristic of the SBA-15 templating process quantitatively accounts for the superstructure and thus the spatial periodicity of the pore wall corrugation. The consequences of this peculiar morphological feature on the spatial arrangement of C5F12, in particular the formation of periodically arranged nanobubbles (or voids) upon adsorption, desorption, and freezing of liquids, are discussed in terms of capillary bridge formation and cavitation in tubular but periodically corrugated pores.
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Affiliation(s)
- Tommy Hofmann
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH , D-12489 Berlin, Germany
| | - Dirk Wallacher
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH , D-12489 Berlin, Germany
| | - Jan Perlich
- Deutsches Elektronen Synchrotron , D-22607 Hamburg, Germany
| | | | - Patrick Huber
- Technische Universität Hamburg , D-21073 Hamburg, Germany
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15
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Secret E, Wu CC, Chaix A, Galarneau A, Gonzalez P, Cot D, Sailor MJ, Jestin J, Zanotti JM, Cunin F, Coasne B. Control of the Pore Texture in Nanoporous Silicon via Chemical Dissolution. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:8121-8128. [PMID: 26135844 DOI: 10.1021/acs.langmuir.5b01518] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The surface and textural properties of porous silicon (pSi) control many of its physical properties essential to its performance in key applications such as optoelectronics, energy storage, luminescence, sensing, and drug delivery. Here, we combine experimental and theoretical tools to demonstrate that the surface roughness at the nanometer scale of pSi can be tuned in a controlled fashion using partial thermal oxidation followed by removal of the resulting silicon oxide layer with hydrofluoric acid (HF) solution. Such a process is shown to smooth the pSi surface by means of nitrogen adsorption, electron microscopy, and small-angle X-ray and neutron scattering. Statistical mechanics Monte Carlo simulations, which are consistent with the experimental data, support the interpretation that the pore surface is initially rough and that the oxidation/oxide removal procedure diminishes the surface roughness while increasing the pore diameter. As a specific example considered in this work, the initial roughness ξ ∼ 3.2 nm of pSi pores having a diameter of 7.6 nm can be decreased to 1.0 nm following the simple procedure above. This study allows envisioning the design of pSi samples with optimal surface properties toward a specific process.
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Affiliation(s)
- Emilie Secret
- †UMR 5253 CNRS/UM/ENSCM, Institut Charles Gerhardt Montpellier, 8 rue de l'Ecole Normale, 34296 Montpellier, France
| | - Chia-Chen Wu
- ‡Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093-0358, United States
| | - Arnaud Chaix
- †UMR 5253 CNRS/UM/ENSCM, Institut Charles Gerhardt Montpellier, 8 rue de l'Ecole Normale, 34296 Montpellier, France
| | - Anne Galarneau
- †UMR 5253 CNRS/UM/ENSCM, Institut Charles Gerhardt Montpellier, 8 rue de l'Ecole Normale, 34296 Montpellier, France
| | - Philippe Gonzalez
- †UMR 5253 CNRS/UM/ENSCM, Institut Charles Gerhardt Montpellier, 8 rue de l'Ecole Normale, 34296 Montpellier, France
| | - Didier Cot
- §ENSCM/UM2/UMR 5635, Institut Européen des Membranes, Place Eugène Bataillon CC 047, 34095 Montpellier, France
| | - Michael J Sailor
- ‡Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093-0358, United States
| | - Jacques Jestin
- ∥Laboratoire Leon Brillouin, CEA-Saclay, 91191 Gif sur Yvette Cedex, France
| | - Jean-Marc Zanotti
- ∥Laboratoire Leon Brillouin, CEA-Saclay, 91191 Gif sur Yvette Cedex, France
| | - Frédérique Cunin
- †UMR 5253 CNRS/UM/ENSCM, Institut Charles Gerhardt Montpellier, 8 rue de l'Ecole Normale, 34296 Montpellier, France
| | - Benoit Coasne
- †UMR 5253 CNRS/UM/ENSCM, Institut Charles Gerhardt Montpellier, 8 rue de l'Ecole Normale, 34296 Montpellier, France
- ⊥MultiScale Materials Science for Energy and Environment, CNRS/MIT (UMI 3466), 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
- #Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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16
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Huber P. Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:103102. [PMID: 25679044 DOI: 10.1088/0953-8984/27/10/103102] [Citation(s) in RCA: 128] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bulk phenomenologies. The complexity of the confined molecular species is varied from simple building blocks, like noble gas atoms, normal alkanes and alcohols to liquid crystals, polymers, ionic liquids, proteins and water. Mostly, experiments with mesoporous solids of alumina, gold, carbon, silica, and silicon with pore diameters ranging from a few up to 50 nm are presented. The observed peculiarities of nanopore-confined condensed matter are also discussed with regard to applications. A particular emphasis is put on texture formation upon crystallisation in nanoporous media, a topic both of high fundamental interest and of increasing nanotechnological importance, e.g. for the synthesis of organic/inorganic hybrid materials by melt infiltration, the usage of nanoporous solids in crystal nucleation or in template-assisted electrochemical deposition of nano structures.
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Affiliation(s)
- Patrick Huber
- Hamburg University of Technology (TUHH), Institute of Materials Physics and Technology, Eißendorfer Str. 42, D-21073 Hamburg-Harburg (Germany
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Bruschi L, Mistura G, Nguyen PTM, Do DD, Nicholson D, Park SJ, Lee W. Adsorption in alumina pores open at one and at both ends. NANOSCALE 2015; 7:2587-2596. [PMID: 25578390 DOI: 10.1039/c4nr06469k] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We have studied adsorption in regular, self-ordered alumina pores open at both ends or only at one end. The straight, non-connected pores have diameters ranging from 22 to 83 nm, with a relative dispersion below 1% in the pore size. Adsorption isotherms measured in open pores with a torsional microbalance show pronounced hysteresis loops characterized by nearly vertical and parallel adsorption and desorption branches. Blocking one end of the pores with glue has a strong influence on adsorption, as expected from classical macroscopic arguments. However, the experimental measurements show an unexpectedly rich phenomenology dependent on the pore size. For large pores (Dp ≥ 67 nm), the isotherms for closed end pores present much narrower hysteresis loops whose adsorption and desorption boundaries envelop the desorption branches of the isotherms for the corresponding open pores of the same size. The loop for small closed end pores (Dp = 22 nm) is slightly wider than that for open pores while the adsorption branches coincide. For large pores, in contrast, the desorption branches of pores with the same Dp overlap regardless of the pore opening. These observations are in agreement with our grand canonical Monte Carlo (GCMC) simulations for a cylindrical pore model with constrictions, suggesting that the alumina pores could be modeled using a constricted pore model whose adsorption isotherm depends on the ratio of the constriction size to the pore size (Dc/Dp).
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Landers J, Gor GY, Neimark AV. Density functional theory methods for characterization of porous materials. Colloids Surf A Physicochem Eng Asp 2013. [DOI: 10.1016/j.colsurfa.2013.01.007] [Citation(s) in RCA: 768] [Impact Index Per Article: 69.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Morishige K. Effects of carbon coating and pore corrugation on capillary condensation of nitrogen in SBA-15 mesoporous silica. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2013; 29:11915-11923. [PMID: 23977846 DOI: 10.1021/la402365e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
To examine the origin of an ink-bottle-like structure in SBA-15 formed by carbon coating and the effects of pore corrugation on capillary condensation and evaporation of a vapor in the cylindrical pores, we measured the adsorption isotherms of nitrogen at 77 K on 10 kinds of SBA-15 samples before and after a carbon coating process by the exposure to acetylene at 1073 K, as well as desorption scanning curves and subloops on the untreated samples. These SBA-15 samples were synthesized under the different conditions of initial SiO2/P123 ratio and hydrothermal treatment. SBA-15 with relatively large microporosity tends to form easily constrictions inside the main channels by the carbon coating. This strongly suggests that the rough pore walls of SBA-15 may induce the incomplete wetting of carbon layers on the pore walls to form the constrictions inside the cylindrical pores. A comparison of two subloops implies that the pores of SBA-15 synthesized with a SiO2/P123 ratio of 75 consist of an assembly of connecting domains of different diameters; that is, the pores are highly corrugated. For SBA-15 synthesized with a SiO2/P123 ratio of 60, the amplitude of the pore corrugation is significantly decreased by the prolonged hydrothermal treatment at 373 K. On the other hand, for SBA-15 synthesized with a SiO2/P123 ratio of 45, the amplitude of the corrugation is negligibly small, although the cylindrical pores are interconnected through narrow necks with each other. It is found that the smaller the amplitude of the pore corrugation, the smaller the width of the hysteresis loop.
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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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Simulation study of hysteresis of argon adsorption in a conical pore and a constricted cylindrical pore. J Colloid Interface Sci 2013; 396:242-50. [DOI: 10.1016/j.jcis.2012.12.057] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2012] [Accepted: 12/25/2012] [Indexed: 11/19/2022]
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Gommes CJ. Three-dimensional reconstruction of liquid phases in disordered mesopores usingin situsmall-angle scattering. J Appl Crystallogr 2013. [DOI: 10.1107/s0021889813003816] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Small-angle scattering of X-rays (SAXS) or neutrons is one of the few experimental methods currently available for thein situanalysis of phenomena in mesoporous materials at the mesoscopic scale. In the case of disordered mesoporous materials, however, the main difficulty of the method lies in the data analysis. A stochastic model is presented, which enables one to reconstruct the three-dimensional nanostructure of liquids confined in disordered mesopores starting from small-angle scattering data. This so-called plurigaussian model is a multi-phase generalization of clipped Gaussian random field models. Its potential is illustrated through the synchrotron SAXS analysis of a gel permeated with a critical nitrobenzene/hexane solution that is progressively cooled below its consolute temperature. The reconstruction brings to light a wetting transition whereby the nanostructure of the pore-filling liquids passes from wetting layers that uniformly cover the solid phase of the gel to plugs that locally occlude the pores. Using the plurigaussian model, the dewetting phenomenon is analyzed quantitatively at the nanometre scale in terms of changing specific interface areas, contact angle and specific length of the triple line.
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Coasne B, Galarneau A, Pellenq RJM, Di Renzo F. Adsorption, intrusion and freezing in porous silica: the view from the nanoscale. Chem Soc Rev 2013; 42:4141-71. [PMID: 23348418 DOI: 10.1039/c2cs35384a] [Citation(s) in RCA: 115] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Benoit Coasne
- Institut Charles Gerhardt Montpellier, CNRS (UMR 5253), University Montpellier 2, ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier, France.
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Gor GY, Rasmussen CJ, Neimark AV. Capillary condensation hysteresis in overlapping spherical pores: a Monte Carlo simulation study. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2012; 28:12100-7. [PMID: 22823524 DOI: 10.1021/la302318j] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The mechanisms of hysteretic phase transformations in fluids confined to porous bodies depend on the size and shape of pores, as well as their connectivity. We present a Monte Carlo simulation study of capillary condensation and evaporation cycles in the course of Lennard-Jones fluid adsorption in the system of overlapping spherical pores. This model system mimics pore shape and connectivity in some mesoporous materials obtained by templating cubic surfactant mesophases or colloidal crystals. We show different mechanisms of capillary hysteresis depending on the size of the window between the pores. For the system with a small window, the hysteresis cycle is similar to that in a single spherical pore: capillary condensation takes place upon achieving the limit of stability of adsorption film and evaporation is triggered by cavitation. When the window is large enough, the capillary condensation shifts to a pressure higher than that of the isolated pore, and the possibility for the equilibrium mechanism of desorption is revealed. These finding may have important implications for practical problems of assessment of the pore size distributions in mesoporous materials with cagelike pore networks.
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Affiliation(s)
- Gennady Yu Gor
- Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, United States.
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Gommes CJ, Jiao Y, Torquato S. Microstructural degeneracy associated with a two-point correlation function and its information content. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051140. [PMID: 23004736 DOI: 10.1103/physreve.85.051140] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2012] [Indexed: 06/01/2023]
Abstract
A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the information content of any two-point correlation function, which makes our results broadly applicable to any field in which correlation functions are employed.
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Affiliation(s)
- C J Gommes
- Department of Chemical Engineering, University of Liège, Liège 4000, Belgium.
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