1
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Kolesnikov AL, Möllmer J. Temperature Evolution of Sorbonorit-4 Methane-Induced Deformation through the Eyes of Classical Density Functional Theory. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:4122-4131. [PMID: 38348950 DOI: 10.1021/acs.langmuir.3c03063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/28/2024]
Abstract
Activated carbons are widely used industrial adsorbents due to their attractive sorption properties. Although extensive research on activated carbon has been carried out for several centuries, some aspects of the adsorption-induced deformation of activated carbon remain unclear. The puzzling temperature dependence of the methane-induced deformation of activated carbon is investigated in the present work. Several experimental studies have shown that an increase in temperature leads to a reversal of the sign of adsorption strain at low pressures, i.e., the contraction turns into an expansion. Here we suggest a possible explanation for this effect by applying classical density functional theory to the adsorption isotherms of nitrogen, carbon dioxide, and methane as well as to methane-induced deformation isotherms. Our calculations show that the adsorption stress generated in the smallest pores predominates at higher temperatures and leads to material swelling. Lowering the temperature, on the other hand, leads to a predominance of larger pores and compression of the activated carbon material. We also investigated the possibility of determining the pore size distribution from methane-induced deformation and adsorption data and the predictive capabilities of our theoretical approach.
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Affiliation(s)
- Andrei L Kolesnikov
- Institut für Nichtklassische Chemie e.V., Permoserstr. 15, 04318 Leipzig, Germany
- Otto H. York Department Chemical and Materials Engineering, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102, United States
| | - Jens Möllmer
- Institut für Nichtklassische Chemie e.V., Permoserstr. 15, 04318 Leipzig, Germany
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2
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Hua L, Shomali A, Zhang C, Coasne B, Derome D, Carmeliet J. Anisotropic Deformation in a Polymer Slab Subjected to Fluid Adsorption. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:4382-4391. [PMID: 38349330 DOI: 10.1021/acs.langmuir.3c03677] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/28/2024]
Abstract
Nanoporous adsorbents can mechanically swell or shrink once upon the accumulation of guest fluid molecules at their internal surfaces or in their cavities. Existing theories in this field attribute such sorption-induced swelling to a tensile force, while shrinkage is always associated with a contractive force. In this study, however, we propose that the sorption-induced deformation of a porous architecture is not solely dictated by the stress conditions but can also be largely influenced by its mechanical anisotropy. In more detail, the sorption-induced deformation of a polymeric slab is investigated using a hybrid molecular dynamics and Monte Carlo algorithm. When subjected to water loading, the slab is found to swell along its normal direction and display an overall positive volumetric strain. Moreover, the surface roughness is enhanced as a response to the surface energy decrease induced by the water covering the slab external surface. Unexpectedly, the in-plane deformation of the slab material seems to be highly constrained, so that it is far below its normal counterpart. This anisotropy is enhanced when the slab thickness decreases. With a thickness of around 1.35 nm, an in-plane shrinkage is observed throughout the entire hygroscopic range. A theoretical analysis based on a poromechanical model suggests that the anisotropic mechanical properties, which are common for a slab material, are the essence of the constrained in-plane swelling or even shrinkage under the isotropic sorption-induced tensile forces. This study, unveiling overlooked mechanisms of sorption-induced shrinkage in mechanically anisotropic materials, provides new insights into this field.
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Affiliation(s)
- Lingji Hua
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland
| | - Ali Shomali
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland
| | - Chi Zhang
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland
| | - Benoit Coasne
- Univ. Grenoble Alpes, CNRS, LIPhy, Grenoble F-38000, France
- Institut Laue-Langevin, Grenoble F-38042, France
| | - Dominique Derome
- Department of Civil and Building Engineering, Université de Sherbrooke, Sherbrooke J1K 2R1 Québec, Canada
| | - Jan Carmeliet
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland
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3
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Zou J, Fan C, Zhang J, Liu X, Zhou W, Huang L, Xu H. Effect of Adsorbent Properties on Adsorption-Induced Deformation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:14813-14822. [PMID: 34910489 DOI: 10.1021/acs.langmuir.1c02512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Adsorption-induced adsorbent deformation is of fundamental importance to geoscientists and engineers. To gain insight into the deformation behaviors of different materials, we presented grand canonical Monte Carlo (GCMC) simulations of methane adsorption-induced deformation in slit pores. Adsorption isotherms and deformation behaviors of the pores were obtained for adsorbents with variations in solid density and affinity. The results showed that the adsorption-induced deformation depends on adsorbate loading, pore width, solid density, and affinity. The deformation at a given adsorption loading could be comparable between different solid densities or affinities because solid density or affinity is related to the solvation pressure as the driving force behind the deformation and also the resistance of the deformation. The interaction of these two effects controls the deformation behavior. We expect that our results will help to understand the adsorption-induced deformation in solids with heterogeneous properties and estimate deformation using the gas adsorption data.
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Affiliation(s)
- Jie Zou
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu 610059, China
- College of Energy, Chengdu University of Technology, Chengdu, Sichuan 610059, China
| | - Chunyan Fan
- WA School of Mines: Minerals, Energy and Chemical Engineering, Curtin University, Bentley 6102, Australia
| | - Junfang Zhang
- CSIRO Energy, 26 Dick Perry Ave, Kensington, WA 6151, Australia
| | - Xiu Liu
- WA School of Mines: Minerals, Energy and Chemical Engineering, Curtin University, Bentley 6102, Australia
| | - Wen Zhou
- College of Energy, Chengdu University of Technology, Chengdu, Sichuan 610059, China
| | - Liang Huang
- College of Energy, Chengdu University of Technology, Chengdu, Sichuan 610059, China
| | - Hao Xu
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu 610059, China
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4
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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: 6] [Impact Index Per Article: 2.0] [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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5
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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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6
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Ludescher L, Morak R, Braxmeier S, Balzer C, Putz F, Busch S, Hüsing N, Reichenauer G, Gor GY, Paris O. Adsorption-induced deformation of hierarchical organised carbon materials with ordered, non-convex mesoporosity. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1894362] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Affiliation(s)
- Lukas Ludescher
- Institute of Physics, Montanuniversität Leoben, Leoben, Austria
| | - Roland Morak
- Institute of Physics, Montanuniversität Leoben, Leoben, Austria
| | | | | | - Florian Putz
- Chemistry and Physics of Materials, Paris Lodron University Salzburg, Salzburg, Austria
| | - Sebastian Busch
- German Engineering Materials Science Centre (GEMS) at Heinz Maier-Leibnitz Zentrum (MLZ), Helmholtz-Zentrum Geesthacht GmbH, Garching bei München, Germany
| | - Nicola Hüsing
- Chemistry and Physics of Materials, Paris Lodron University Salzburg, Salzburg, Austria
| | | | - Gennady Y. Gor
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ, USA
| | - Oskar Paris
- Institute of Physics, Montanuniversität Leoben, Leoben, Austria
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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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Krause S, Hosono N, Kitagawa S. Chemistry of Soft Porous Crystals: Structural Dynamics and Gas Adsorption Properties. Angew Chem Int Ed Engl 2020; 59:15325-15341. [DOI: 10.1002/anie.202004535] [Citation(s) in RCA: 128] [Impact Index Per Article: 32.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Indexed: 01/08/2023]
Affiliation(s)
- Simon Krause
- Stratingh Institute for Chemistry University of Groningen Nijenborgh 4 9747 AG Groningen The Netherlands
| | - Nobuhiko Hosono
- Department of Advanced Materials Science Graduate School of Frontier Sciences The University of Tokyo, Kashiwa Chiba 277-8561 Japan
| | - Susumu Kitagawa
- Institute for Integrated Cell-Material Sciences Institute for Advanced Study Kyoto University, Ushinomiya, Yoshida, Sakyo-ku Kyoto 606-8501 Japan
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9
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Krause S, Hosono N, Kitagawa S. Die Chemie verformbarer poröser Kristalle – Strukturdynamik und Gasadsorptionseigenschaften. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.202004535] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Simon Krause
- Stratingh Institute for Chemistry University of Groningen Nijenborgh 4 9747 AG Groningen Niederlande
| | - Nobuhiko Hosono
- Department of Advanced Materials Science Graduate School of Frontier Sciences The University of Tokyo, Kashiwa Chiba 277-8561 Japan
| | - Susumu Kitagawa
- Institute for Integrated Cell-Material Sciences Institute for Advanced Study Kyoto University, Ushinomiya, Yoshida, Sakyo-ku Kyoto 606-8501 Japan
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10
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Emelianova A, Maximov MA, Gor GY. Solvation pressure in spherical mesopores: Macroscopic theory and molecular simulations. AIChE J 2020. [DOI: 10.1002/aic.16542] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Alina Emelianova
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology University Heights Newark New Jersey USA
| | - Max A. Maximov
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology University Heights Newark New Jersey USA
| | - Gennady Y. Gor
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology University Heights Newark New Jersey USA
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11
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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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12
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Abstract
AbstractCapillary condensation within the pore space formed by a hexagonal arrangement of carbon nanorods is investigated using a thermodynamic model. Numerical solution of the corresponding non-linear differential equations predicts two characteristic equilibrium phase transitions corresponding to liquid-bridge formation between adjacent rods, and the subsequent filling of the entire pore space with liquid adsorbate at higher relative pressure, respectively. These separate transitions are predicted for a wide range of porosities, as demonstrated for two non-polar fluids, nitrogen and n-pentane, employing experimentally determined reference isotherms to model the fluid–solid interactions. The theoretical predictions are compared to experimental data for nitrogen and n-pentane adsorption in an ordered mesoporous CMK-3 type material, with the necessary structural parameters obtained from small-angle X-ray scattering. Although the experimental adsorption isotherms do not unambiguously show two separate transitions due to a high degree of structural disorder of the mesopore space, their general trends are consistent with the theoretical predictions for both adsorbates.
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13
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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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14
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Chen M, Coasne B, Guyer R, Derome D, Carmeliet J. Molecular Simulation of Sorption-Induced Deformation in Atomistic Nanoporous Materials. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:7751-7758. [PMID: 31117732 DOI: 10.1021/acs.langmuir.9b00859] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
An atomistic slit pore model is built to study the sorption-induced deformation of nanoporous materials with the help of molecular simulation. Both sorption and strain isotherms are determined to probe the anisotropic deformation behavior induced upon molecular adsorption. A detailed analysis shows that the driving microscopic mechanisms at different sorption stages are different. At high relative pressure, as expected from the classical macroscopic picture, the pore deformation is governed by the Laplace pressure as the pore gets filled with liquid because of capillary condensation. In such situation, the strain in normal and longitudinal directions can be predicted from the stiffness modulus in the corresponding direction. At low pressure, when liquid films are adsorbed at the pore surfaces and separated by the vapor phase, the strain is driven by the attractive solid-fluid forces and in-plane pressure within the film, and the deformation is confined in the direction parallel to the film-solid interface. Because of the interplay of the two factors, the strain changes from shrinkage to expansion upon increase of pressure. Analysis of isosteric heat of adsorption shows that the contribution arising from the deformation is small compared to the sorption contribution, which indicates that the influence of deformation on the sorption process is limited.
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Affiliation(s)
- Mingyang Chen
- Chair of Building Physics, Department of Mechanical and Process Engineering , ETH Zurich , HIB E13 Stefano-Franscini-Platz 1 , 8093 Zurich , Switzerland
| | - Benoit Coasne
- Univ. Grenoble Alpes, CNRS, LIPhy , 140 Avenue de la physique , 38000 Grenoble , France
| | - Robert Guyer
- Department of Physics , University of Nevada , 1664 N. Virginia Street , 89557 Reno , Nevada , United States
| | - Dominique Derome
- Laboratory for Multiscale Studies in Building Physics-Swiss Federal Laboratories for Materials Science and Technology , Ueberlandstrasse 129 , 8600 Duebendorf , Switzerland
| | - Jan Carmeliet
- Chair of Building Physics, Department of Mechanical and Process Engineering , ETH Zurich , HIB E13 Stefano-Franscini-Platz 1 , 8093 Zurich , Switzerland
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15
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Balzer C, Waag AM, Putz F, Huesing N, Paris O, Gor GY, Neimark AV, Reichenauer G. Mechanical Characterization of Hierarchical Structured Porous Silica by in Situ Dilatometry Measurements during Gas Adsorption. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:2948-2956. [PMID: 30667221 PMCID: PMC6393851 DOI: 10.1021/acs.langmuir.8b03242] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2018] [Revised: 12/12/2018] [Indexed: 06/02/2023]
Abstract
Mechanical properties of hierarchically structured nanoporous materials are determined by the solid phase stiffness and the pore network morphology. We analyze the mechanical stiffness of hierarchically structured silica monoliths synthesized via a sol-gel process, which possess a macroporous scaffold built of interconnected struts with hexagonally ordered cylindrical mesopores. We consider samples with and without microporosity within the mesopore walls and analyze them on the macroscopic level as well as on the microscopic level of the mesopores. Untreated as-prepared samples still containing some organic components and the respective calcined and sintered counterparts of varying microporosity are investigated. To determine Young's moduli on the level of the macroscopic monoliths, we apply ultrasonic run time measurements, while Young's moduli of the mesopore walls are obtained by analysis of the in situ strain isotherms during N2 adsorption at 77 K. For the latter, we extended our previously reported theoretical approach for this type of materials by incorporating the micropore effects, which are clearly not negligible in the calcined and most of the sintered samples. The comparison of the macro- and microscopic Young's moduli reveals that both properties follow essentially the same trends, that is, calcination and sintering increase the mechanical stiffness on both levels. Consequently, stiffening of the monolithic samples can be primarily attributed to stiffening of the backbone material which is consistent with the fact that the morphology on the mesopore level is mainly preserved with the post-treatments applied.
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Affiliation(s)
- Christian Balzer
- Bavarian
Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Würzburg, Germany
| | - Anna M. Waag
- Bavarian
Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Würzburg, Germany
| | - Florian Putz
- Materials
Chemistry, Paris Lodron University Salzburg, Jakob-Haringer Str. 2a, 5020 Salzburg, Austria
| | - Nicola Huesing
- Materials
Chemistry, Paris Lodron University Salzburg, Jakob-Haringer Str. 2a, 5020 Salzburg, Austria
| | - Oskar Paris
- Institute
of Physics, Montanuniversität Leoben, Franz-Josef-Str. 18, 8700 Leoben, Austria
| | - Gennady Y. Gor
- Otto
H. York Department of Chemical and Materials Engineering, New Jersey
Institute of Technology, University Heights, Newark, New Jersey 07102, United States
| | - Alexander V. Neimark
- Department
of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey University, 98 Brett Road, Piscataway, New Jersey 08854, United States
| | - Gudrun Reichenauer
- Bavarian
Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Würzburg, Germany
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16
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Galukhin A, Bolmatenkov D, Emelianova A, Zharov I, Gor GY. Porous Structure of Silica Colloidal Crystals. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:2230-2235. [PMID: 30636422 DOI: 10.1021/acs.langmuir.8b03476] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We prepared silica colloidal crystals with different pore sizes using isothermal heating evaporation-induced self-assembly in quantities suitable for nitrogen porosimetry and studied their porous structure. We observed pores of two types in agreement with the description of silica colloidal crystals as face-centered cubic packed structures containing octahedral and tetrahedral voids. We calculated the sizes of these pores using the Derjaguin-Broekhoff-de Boer theory of capillary condensation for spherical pores. We also described the pore geometry mathematically and showed that the octahedral pore radii measured experimentally matches closely the radii of the spheres of the same volume. In the case of the tetrahedral pores, the proposed approach underestimated the pore radius by ca. 40%. Overall, this simple geometrical description provides a good representation of the porous system in silica colloidal crystals.
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Affiliation(s)
- Andrey Galukhin
- Alexander Butlerov Institute of Chemistry , Kazan Federal University , Kremlevskaya Str. 18 , 420008 Kazan , Russian Federation
| | - Dmitrii Bolmatenkov
- Alexander Butlerov Institute of Chemistry , Kazan Federal University , Kremlevskaya Str. 18 , 420008 Kazan , Russian Federation
| | - Alina Emelianova
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology , University Heights , Newark , New Jersey 07102 , United States
| | - Ilya Zharov
- Alexander Butlerov Institute of Chemistry , Kazan Federal University , Kremlevskaya Str. 18 , 420008 Kazan , Russian Federation
- Department of Chemistry , University of Utah , 315 S 1400 E , Salt Lake City , Utah 84112 , United States
- Department of Materials Science & Engineering , University of Utah , 122 Central Campus Dr. , Salt Lake City , Utah 84112 , United States
| | - Gennady Y Gor
- Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology , University Heights , Newark , New Jersey 07102 , United States
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17
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Schappert K, Pelster R. Requirements to Determine the Average Pore Size of Nanoporous Media Using Ultrasound. ACS OMEGA 2018; 3:18906-18910. [PMID: 31458452 PMCID: PMC6643813 DOI: 10.1021/acsomega.8b03091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/05/2018] [Accepted: 12/18/2018] [Indexed: 06/10/2023]
Abstract
Liquids in nanoporous media are exposed to an adsorption-induced pressure, a consequence of the interaction with the pore surface. The smaller the pore diameter, d P, the higher the pressure at saturation and thus the bulk modulus of the confined liquid. Therefore, it has been proposed to use ultrasonic measurements on saturated nanoporous media for the determination of the average pore size. Here, we discuss the requirements for such an analysis. Although predictions for the size-dependent pore pressure and the liquid's modulus, K iso(d P), are based on isothermal simulations, an experimentalist studying the propagation of ultrasonic waves determines adiabatic moduli, K ad(d P). We show that the quantity relating adiabatic and isothermal moduli, the heat capacity ratio γ = c p/c v = K ad/K iso, exhibits a strong pressure dependence for many bulk liquids. In nanopores, this translates into a size-dependent γ(d P), provided the confinement does not alter the heat capacity ratio. Disregarding this effect in the analysis of ultrasonic data would yield an underestimate of the isothermal modulus and thus an overestimate of the average pore size. For a correct analysis, an experimentalist thus needs to know the size dependence of three quantities: the isothermal modulus, adsorption-induced pressure, and heat capacity ratio.
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Affiliation(s)
- Klaus Schappert
- FR Physik, Universität
des Saarlandes, 66123 Saarbrücken, Germany
| | - Rolf Pelster
- FR Physik, Universität
des Saarlandes, 66123 Saarbrücken, Germany
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18
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Kolesnikov AL, Georgi N, Budkov YA, Möllmer J, Hofmann J, Adolphs J, Gläser R. Effects of Enhanced Flexibility and Pore Size Distribution on Adsorption-Induced Deformation of Mesoporous Materials. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:7575-7584. [PMID: 29792800 DOI: 10.1021/acs.langmuir.8b00591] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Here, we present a new model of adsorption-induced deformation of mesoporous solids. The model is based on a simplified version of local density functional theory in the framework of solvation free energy. Instead of density, which is treated as constant here, we used film thickness and pore radius as order parameters. This allows us to obtain a self-consistent system of equations describing simultaneously the processes of gas adsorption and adsorbent deformation, as well as conditions for capillary condensation and evaporation. In the limit of infinitely rigid pore walls, when the film becomes several monolayers thick, the model reduces to the well-known Derjaguin-Broekhoff-de Boer theory for pores with cylindrical geometry. We have investigated the effects of enhanced flexibility of the solid as well as the influence of pore size distribution on the adsorption/deformation process. The formulation of the theory allows to determine the average pore size and its width from the desorption branch of the strain isotherm only. The model reproduces the nonmonotonic behavior of the strain isotherm at low relative pressure. Furthermore, we discuss the effect of rigidity of the adsorbent on the pore size distribution, showing qualitatively different results of the adsorption isotherms for rigid and highly flexible materials, in particular, the shift of evaporation pressure to lower values and the absence of a limiting value of the loading at high relative pressure. We also discuss the results of the theory with respect to experimental data obtained from the literature.
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Affiliation(s)
- A L Kolesnikov
- Institut für Nichtklassische Chemie e.V. , Permoserstr. 15 , 04318 Leipzig , Germany
- Porotec GmbH , Niederhofheimer Str. 55A , 65719 Hofheim am Taunus , Germany
| | - N Georgi
- GMBU , Erich-Neuß-Weg 5 , 06120 Halle (Saale) , Germany
| | - Yu A Budkov
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences , Akademicheskaya Street 1 , 153045 Ivanovo , Russia
- Tikhonov Moscow Institute of Electronics and Mathematics, School of Applied Mathematics , National Research University Higher School of Economics , 34 Tallinskaya Ulitsa , 123458 Moscow , Russia
| | - J Möllmer
- Institut für Nichtklassische Chemie e.V. , Permoserstr. 15 , 04318 Leipzig , Germany
| | - J Hofmann
- Institut für Nichtklassische Chemie e.V. , Permoserstr. 15 , 04318 Leipzig , Germany
| | - J Adolphs
- Porotec GmbH , Niederhofheimer Str. 55A , 65719 Hofheim am Taunus , Germany
| | - R Gläser
- Institut für Nichtklassische Chemie e.V. , Permoserstr. 15 , 04318 Leipzig , Germany
- Institut für Technische Chemie , Universität Leipzig , 04103 Leipzig , Germany
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19
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Motahari A, Hu N, Vahid A, Omrani A, Rostami AA, Schaefer DW. Multilevel Morphology of Complex Nanoporous Materials. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:6719-6726. [PMID: 29757656 DOI: 10.1021/acs.langmuir.8b00970] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This work exploits gas adsorption and small-angle X-ray scattering (SAXS) to determine the morphology of complex nanoporous materials. We resolve multiple classes of porosity including previously undetected large-scale texture that significantly compromises the canonical interpretation of gas adsorption. Specifically, a UVM-7 class mesoporous silica was synthesized that has morphological features on three length scales: macropores due to packing of 150 nm globules, 1.9 nm radius spherical mesopores inside the globules, and >7 nm pockets on and between the globules. The total and external surface areas, as well as the mesopore volume, were determined using gas adsorption (αs-plot) and SAXS. A new approach was applied to the SAXS data using multilevel fitting to determine the surface areas on multiple length scales. The SAXS analysis code is applicable to any two-phase system and is freely available to the public. The total surface area determined by SAXS was 12% greater than that obtained by gas adsorption. The macropore interfacial area, however, is only 30% of the external surface area determined by the αs-plot. The overestimation of the external surface area by the αs-plot method is attributed to capillary condensation in nanoscale surface irregularities. The discrepancy is resolved assuming that the macropore-globule interfaces harbor fractally distributed nooks and crannies, which lead to gas adsorption at pressures above the mesopore filling pressure.
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Affiliation(s)
- Ahmad Motahari
- Department of Chemical and Environmental Engineering , University of Cincinnati , Cincinnati , Ohio 45221-0012 , United States
- Department of Physical Chemistry, Faculty of Chemistry , University of Mazandaran , P.O. Box 453, Babolsar 47416-13534 , Iran
| | - Naiping Hu
- Department of Chemical and Environmental Engineering , University of Cincinnati , Cincinnati , Ohio 45221-0012 , United States
| | - Amir Vahid
- Research Institute of Petroleum Industry , Tehran 1485733111 , Iran
| | - Abdollah Omrani
- Department of Physical Chemistry, Faculty of Chemistry , University of Mazandaran , P.O. Box 453, Babolsar 47416-13534 , Iran
| | - Abbas Ali Rostami
- Department of Physical Chemistry, Faculty of Chemistry , University of Mazandaran , P.O. Box 453, Babolsar 47416-13534 , Iran
| | - Dale W Schaefer
- Department of Chemical and Environmental Engineering , University of Cincinnati , Cincinnati , Ohio 45221-0012 , United States
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20
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Hlushak S. Heat of adsorption, adsorption stress, and optimal storage of methane in slit and cylindrical carbon pores predicted by classical density functional theory. Phys Chem Chem Phys 2018; 20:872-888. [PMID: 29239426 DOI: 10.1039/c7cp06591d] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Temperature, pressure and pore-size dependences of the heat of adsorption, adsorption stress, and adsorption capacity of methane in simple models of slit and cylindrical carbon pores are studied using classical density functional theory (CDFT) and grand-canonical Monte-Carlo (MC) simulation. Studied properties depend nontrivially on the bulk pressure and the size of the pores. Heat of adsorption increases with loading, but only for sufficiently narrow pores. While the increase is advantageous for gas storage applications, it is less significant for cylindrical pores than for slits. Adsorption stress and the average adsorbed fluid density show oscillatory dependence on the pore size and increase with bulk pressure. Slit pores exhibit larger amplitude of oscillations of the normal adsorption stress with pore size increase than cylindrical pores. However, the increase of the magnitude of the adsorption stress with bulk pressure increase is more significant for cylindrical than for slit pores. Adsorption stress appears to be negative for a wide range of pore sizes and external conditions. The pore size dependence of the average delivered density of the gas is analyzed and the optimal pore sizes for storage applications are estimated. The optimal width of slit pore appears to be almost independent of storage pressure at room temperature and pressures above 10 bar. Similarly to the case of slit pores, the optimal radius of cylindrical pores does not exhibit much dependence on the storage pressure above 15 bar. Both optimal width and optimal radii of slit and cylindrical pores increase as the temperature decreases. A comparison of the results of CDFT theory and MC simulations reveals subtle but important differences in the underlying fluid models employed by the approaches. The differences in the high-pressure behaviour between the hard-sphere 2-Yukawa and Lennard-Jones models of methane, employed by the CDFT and MC approaches, respectively, result in an overestimation of the heat of adsorption by the CDFT theory at higher loadings. However, both adsorption stress and adsorption capacity appear to be much less sensitive to the differences between the models and demonstrate excellent agreement between the theory and the computer experiment.
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Affiliation(s)
- Stepan Hlushak
- Institute for Condensed Matter Physics, Svientsitskoho 1, 79011, Lviv, Ukraine.
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21
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Morak R, Braxmeier S, Ludescher L, Putz F, Busch S, Hüsing N, Reichenauer G, Paris O. Quantifying adsorption-induced deformation of nanoporous materials on different length scales. J Appl Crystallogr 2017; 50:1404-1410. [PMID: 29021735 PMCID: PMC5627682 DOI: 10.1107/s1600576717012274] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Accepted: 08/24/2017] [Indexed: 11/11/2022] Open
Abstract
A new in situ setup combining small-angle neutron scattering (SANS) and dilatometry was used to measure water-adsorption-induced deformation of a monolithic silica sample with hierarchical porosity. The sample exhibits a disordered framework consisting of macropores and struts containing two-dimensional hexagonally ordered cylindrical mesopores. The use of an H2O/D2O water mixture with zero scattering length density as an adsorptive allows a quantitative determination of the pore lattice strain from the shift of the corresponding diffraction peak. This radial strut deformation is compared with the simultaneously measured macroscopic length change of the sample with dilatometry, and differences between the two quantities are discussed on the basis of the deformation mechanisms effective at the different length scales. It is demonstrated that the SANS data also provide a facile way to quantitatively determine the adsorption isotherm of the material by evaluating the incoherent scattering contribution of H2O at large scattering vectors.
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Affiliation(s)
- Roland Morak
- Institute of Physics, Montanuniversität Leoben, Franz-Josef Strasse 18, Leoben, 8700, Austria
| | - Stephan Braxmeier
- Bavarian Center for Applied Energy Research, Magdalene-Schoch-Strasse 3, Würzburg, 97074, Germany
| | - Lukas Ludescher
- Institute of Physics, Montanuniversität Leoben, Franz-Josef Strasse 18, Leoben, 8700, Austria
| | - Florian Putz
- Chemistry and Physics of Materials, Paris Lodron Universität Salzburg, Jakob-Haringer-Strasse 2a, Salzburg, 5020, Austria
| | - Sebastian Busch
- German Engineering Materials Science Centre (GEMS) at Heinz Maier-Leibnitz Zentrum (MLZ), Helmholtz-Zentrum Geesthacht GmbH, Lichtenbergstrasse 1, Garching bei München, 85747, Germany
| | - Nicola Hüsing
- Chemistry and Physics of Materials, Paris Lodron Universität Salzburg, Jakob-Haringer-Strasse 2a, Salzburg, 5020, Austria
| | - Gudrung Reichenauer
- Bavarian Center for Applied Energy Research, Magdalene-Schoch-Strasse 3, Würzburg, 97074, Germany
| | - Oskar Paris
- Institute of Physics, Montanuniversität Leoben, Franz-Josef Strasse 18, Leoben, 8700, Austria
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22
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Balzer C, Waag AM, Gehret S, Reichenauer G, Putz F, Hüsing N, Paris O, Bernstein N, Gor GY, Neimark AV. Adsorption-Induced Deformation of Hierarchically Structured Mesoporous Silica-Effect of Pore-Level Anisotropy. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2017; 33:5592-5602. [PMID: 28547995 PMCID: PMC5484557 DOI: 10.1021/acs.langmuir.7b00468] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2017] [Revised: 04/27/2017] [Indexed: 06/01/2023]
Abstract
The goal of this work is to understand adsorption-induced deformation of hierarchically structured porous silica exhibiting well-defined cylindrical mesopores. For this purpose, we performed an in situ dilatometry measurement on a calcined and sintered monolithic silica sample during the adsorption of N2 at 77 K. To analyze the experimental data, we extended the adsorption stress model to account for the anisotropy of cylindrical mesopores, i.e., we explicitly derived the adsorption stress tensor components in the axial and radial direction of the pore. For quantitative predictions of stresses and strains, we applied the theoretical framework of Derjaguin, Broekhoff, and de Boer for adsorption in mesopores and two mechanical models of silica rods with axially aligned pore channels: an idealized cylindrical tube model, which can be described analytically, and an ordered hexagonal array of cylindrical mesopores, whose mechanical response to adsorption stress was evaluated by 3D finite element calculations. The adsorption-induced strains predicted by both mechanical models are in good quantitative agreement making the cylindrical tube the preferable model for adsorption-induced strains due to its simple analytical nature. The theoretical results are compared with the in situ dilatometry data on a hierarchically structured silica monolith composed by a network of mesoporous struts of MCM-41 type morphology. Analyzing the experimental adsorption and strain data with the proposed theoretical framework, we find the adsorption-induced deformation of the monolithic sample being reasonably described by a superposition of axial and radial strains calculated on the mesopore level. The structural and mechanical parameters obtained from the model are in good agreement with expectations from independent measurements and literature, respectively.
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Affiliation(s)
- Christian Balzer
- Bavarian
Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Wuerzburg, Germany
| | - Anna M. Waag
- Bavarian
Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Wuerzburg, Germany
| | - Stefan Gehret
- Bavarian
Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Wuerzburg, Germany
| | - Gudrun Reichenauer
- Bavarian
Center for Applied Energy Research, Magdalene-Schoch-Str. 3, 97074 Wuerzburg, Germany
| | - Florian Putz
- Materials
Chemistry, Paris Lodron University Salzburg, Jakob-Haringer Str. 2a, 5020 Salzburg, Austria
| | - Nicola Hüsing
- Materials
Chemistry, Paris Lodron University Salzburg, Jakob-Haringer Str. 2a, 5020 Salzburg, Austria
| | - Oskar Paris
- Institute
of Physics, Montanuniversitaet Leoben, Franz-Josef-Str. 18, 8700 Leoben, Austria
| | - Noam Bernstein
- Center
for Materials Physics and Technology, U.S.
Naval Research Laboratory, Washington, D.C. 20375, United States
| | - Gennady Y. Gor
- Otto
H. York Department of Chemical, Biological, and Pharmaceutical Engineering, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102, United States
| | - Alexander V. Neimark
- Department
of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854, United States
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23
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Schappert K, Pelster R. Experimental method for the determination of adsorption-induced changes of pressure and surface stress in nanopores. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:06LT01. [PMID: 27991423 DOI: 10.1088/1361-648x/aa4e7d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The change of surface stress is an important quantity characterising the behaviour of nanoporous systems, however, it is difficult to assess experimentally. In this letter we develop and demonstrate an experimental method for the determination of adsorption-induced changes of the surface stress in nanoporous materials. With the aid of ultrasonic measurements we determine the dependence of the adsorbate's longitudinal modulus [Formula: see text] on the adsorption-induced normal pressure, [Formula: see text], which is exerted by the adsorbate on the porous matrix. From this dependence we deduce the normal pressure at saturation, [Formula: see text], and thereby changes of the surface stress [Formula: see text] at the interface between the solid matrix and the liquid adsorbate. For the model system of argon in nanoporous glass (pore radius [Formula: see text] nm) the ultrasonic method reveals a value for [Formula: see text] that is in very good agreement with the theoretical value known for the argon-silica interface. The disclosure of this experimental method and its application on other systems will enable a better understanding of the behaviour of adsorbates in nanoporous materials.
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Affiliation(s)
- Klaus Schappert
- FR Physik, Universität des Saarlandes, Campus E2 6, 66123 Saarbrücken, Germany
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24
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Schappert K, Reiplinger N, Pelster R. Correlation between the Sorption-Induced Deformation of Nanoporous Glass and the Continuous Freezing of Adsorbed Argon. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:7741-7746. [PMID: 27398774 DOI: 10.1021/acs.langmuir.6b01533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this article we study the dependence of the sorption-induced deformation of nanoporous glass on the liquid-solid phase transition of adsorbed argon. During cooling we observe a continuous reduction of the expansion of the porous glass matrix caused by the adsorbate. The contraction is attended by a likewise continuous change of the adsorbed argon's phase state from liquid to solid. This simultaneous behavior evidences that the liquid-solid phase transition leads to a reduction of the pressure the adsorbate exerts on the pore walls. Furthermore, the study shows that small temperature changes can temporarily cause strong deformations of the porous material that decay in long time intervals of up to 1 week. We expect that our observations for the model system of argon and porous glass can be generalized to other systems. Consequently, this study will have implications when considering porous materials for applications, e.g., as a medium for storage.
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Affiliation(s)
- Klaus Schappert
- FR 7.2 Experimentalphysik, Universität des Saarlandes , 66123 Saarbrücken, Germany
| | - Nicolas Reiplinger
- FR 7.2 Experimentalphysik, Universität des Saarlandes , 66123 Saarbrücken, Germany
| | - Rolf Pelster
- FR 7.2 Experimentalphysik, Universität des Saarlandes , 66123 Saarbrücken, Germany
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25
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Jeanmairet G, Levy N, Levesque M, Borgis D. Molecular density functional theory of water including density-polarization coupling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:244005. [PMID: 27116250 DOI: 10.1088/0953-8984/28/24/244005] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.
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Affiliation(s)
- Guillaume Jeanmairet
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, Stuttgart 70569, Germany
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26
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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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27
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Gor GY, Bernstein N. Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress. Phys Chem Chem Phys 2016; 18:9788-98. [PMID: 27001041 DOI: 10.1039/c6cp00051g] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Adsorption-induced deformation has to be described in terms of the change of the surface stress Δfand not the surface energy Δγ. The former explains both expansion and contraction.
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Affiliation(s)
- Gennady Y. Gor
- NRC Research Associate
- Resident at Center for Materials Physics and Technology
- Naval Research Laboratory
- Washington
- USA
| | - Noam Bernstein
- Center for Materials Physics and Technology
- Naval Research Laboratory
- Washington
- USA
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28
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Liu Y. Development of 3-dimensional time-dependent density functional theory and its application to gas diffusion in nanoporous materials. Phys Chem Chem Phys 2016; 18:13158-63. [DOI: 10.1039/c6cp01610c] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
An entropy scaling based TDDFT has been proposed and applied to diffusion in a nanoporous material.
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Affiliation(s)
- Yu Liu
- State Key Laboratory of Chemical Engineering and Department of Chemical Engineering
- East China University of Science and Technology
- Shanghai 200237
- China
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29
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Balzer C, Braxmeier S, Neimark AV, Reichenauer G. Deformation of Microporous Carbon during Adsorption of Nitrogen, Argon, Carbon Dioxide, and Water Studied by in Situ Dilatometry. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:12512-12519. [PMID: 26506409 DOI: 10.1021/acs.langmuir.5b03184] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Adsorption-induced deformation of a monolithic, synthetic carbon of clearly distinguishable micro- and mesoporosity was analyzed by in situ dilatometry with N2 (77 K), Ar (77 K), CO2 (273 K), and H2O (298 K). A characteristic nonmonotonic shape of the strain isotherm showing contraction of the sample at initial micropore adsorption followed by expansion toward completion of micropore filling was found for all adsorbates. However, the extent of contraction and expansion varied significantly with the adsorbate type. The deformation differences observed were compared with the density ratio of the adsorbates within the micropores and the respective unconfined fluids. In particular, CO2 caused the least contraction of the sample, while in parallel adsorbed CO2 molecules were predicted to be considerably compacted inside carbon micropores compared to bulk liquid CO2. On the contrary, the packing of H2O molecules within carbon micropores is less dense than in the bulk liquid and adsorption of H2O produced the most pronounced contraction. N2 and Ar, both exhibiting essentially the same densities in adsorbed and bulk liquid phase, induced very similar deformation of the sample. These findings support theoretical predictions, which correlate adsorption-induced deformation and packing of molecules adsorbed in micropores. Additionally for the first time, we demonstrated with the N2 strain isotherm the existence of two nonmonotonic stages of subsequent contraction and expansion in the regions of micropore and mesopore filling. This characteristic behavior is expected for any micro- and mesoporous material.
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Affiliation(s)
- Christian Balzer
- Bavarian Center for Applied Energy Research, Am Galgenberg 87, 97074 Wuerzburg, Germany
| | - Stephan Braxmeier
- Bavarian Center for Applied Energy Research, Am Galgenberg 87, 97074 Wuerzburg, Germany
| | - Alexander V Neimark
- Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey , 98 Brett Road, Piscataway, New Jersey 08854, United States
| | - Gudrun Reichenauer
- Bavarian Center for Applied Energy Research, Am Galgenberg 87, 97074 Wuerzburg, Germany
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30
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Guyer RA, Kim HA. Theoretical model for fluid-solid coupling in porous materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042406. [PMID: 25974507 DOI: 10.1103/physreve.91.042406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Indexed: 06/04/2023]
Abstract
This paper introduces a unifying theory for describing complex behavior for porous materials. The key ingredients are the stored energy in solid-fluid interaction as well as the solid-solid and fluid-fluid interactions. A finite element formulation is employed which naturally accounts for the pore-pore network effects and is easily applicable to most pore geometries such as cellular solids and foams. The interactions, built in at the finite element level, give rise to the mechanical response of the macroscopic material unit. Through numerical studies, we show that there is strong coupling between fluid and solid that induces complex mechanical response, i.e., hysteresis and anisotropy. It is demonstrated that hysteresis arises directly from the fluid-solid coupling. We term this type of hysteresis emergent hysteresis.
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Affiliation(s)
- Robert A Guyer
- Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
- Department of Physics, University of Nevada, Reno, Nevada 89577, USA
| | - H Alicia Kim
- Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom
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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: 130] [Impact Index Per Article: 14.4] [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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Schappert K, Pelster R. Unexpected sorption-induced deformation of nanoporous glass: evidence for spatial rearrangement of adsorbed argon. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:14004-14013. [PMID: 25358117 DOI: 10.1021/la502974w] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Sorption of substances in pores generally results in a deformation of the porous matrix. The clarification of this effect is of particular importance for the recovery of methane and the geological storage of CO2. As a model system, we study the macroscopic deformation of nanoporous Vycor glass during the sorption of argon using capacitative measurements of the length change of the sample. Upon desorption we observe an unpredicted sharp contraction and re-expansion peak, which contains information on the draining mechanism of the porous sample. We have modified the theoretical model by Gor and Neimark1 to predict the sorption-induced deformation of (partly) filled porous samples. In this analysis, the contraction is attributed to a metastable or nonequilibrium configuration where a thin surface layer on the pore walls coexists with capillary bridges. Alternatively, pore blocking and cavitation during the draining of the polydisperse pore network can be at the origin of the deformation peak. The results are a substantial step toward a correlation between the spatial configuration of adsorbate, its interaction with the host material, and the resulting deformation.
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Affiliation(s)
- Klaus Schappert
- FR 7.2 Experimentalphysik, Universität des Saarlandes , 66123 Saarbrücken, Germany
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Gor GY. Adsorption stress changes the elasticity of liquid argon confined in a nanopore. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:13564-13569. [PMID: 25346060 DOI: 10.1021/la503877q] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Knowledge of the elastic properties of a fluid is crucial for predicting its flow under high pressure, particularly in porous media. However, when a fluid is confined to a nanopore, many of its thermodynamic properties change as compared to bulk. Here we study the effect of confinement on the bulk modulus of liquid argon adsorbed in mesopores using classical density functional theory. We show that, at pressures lower than the saturation pressure, high adsorption stress in the pore causes the lowering of the fluid bulk modulus, a phenomenon which was recently observed experimentally [ Schappert, K.; Pelster, R. Europhys. Lett. 2014 , 105 , 5600 ]. Furthermore, we find that the pore size has a strong effect on the fluid bulk modulus, so that even at saturation, the elastic properties of nanoconfined fluid differ from the bulk values. We show that this difference is also due to the adsorption stress. Our results provide a basis for a new method for characterization of porous materials and have implications for modeling fluids in nanoporous geological formations, such as coal or shale.
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Affiliation(s)
- Gennady Y Gor
- Department of Civil and Environmental Engineering, Princeton University , Princeton, New Jersey 08544, United States
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Sergiievskyi VP, Jeanmairet G, Levesque M, Borgis D. Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections. J Phys Chem Lett 2014; 5:1935-1942. [PMID: 26273876 DOI: 10.1021/jz500428s] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.
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Affiliation(s)
- Volodymyr P Sergiievskyi
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Guillaume Jeanmairet
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Maximilien Levesque
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Daniel Borgis
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
- ‡Maison de la Simulation, CNRS USR 3441, CEA Saclay, 91191 Gif-sur-Yvette, France
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Jeanmairet G, Levesque M, Borgis D. Molecular density functional theory of water describing hydrophobicity at short and long length scales. J Chem Phys 2013; 139:154101. [DOI: 10.1063/1.4824737] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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Gor GY, Paris O, Prass J, Russo PA, Ribeiro Carrott MML, Neimark AV. Adsorption of n-pentane on mesoporous silica and adsorbent deformation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2013; 29:8601-8608. [PMID: 23758155 DOI: 10.1021/la401513n] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Development of quantitative theory of adsorption-induced deformation is important, e.g., for enhanced coalbed methane recovery by CO2 injection. It is also promising for the interpretation of experimental measurements of elastic properties of porous solids. We study deformation of mesoporous silica by n-pentane adsorption. The shape of experimental strain isotherms for this system differs from the shape predicted by thermodynamic theory of adsorption-induced deformation. We show that this difference can be attributed to the difference of disjoining pressure isotherm, responsible for the solid-fluid interactions. We suggest the disjoining pressure isotherm suitable for n-pentane adsorption on silica and derive the parameters for this isotherm from experimental data of n-pentane adsorption on nonporous silica. We use this isotherm in the formalism of macroscopic theory of adsorption-induced deformation of mesoporous materials, thus extending this theory for the case of weak solid-fluid interactions. We employ the extended theory to calculate solvation pressure and strain isotherms for SBA-15 and MCM-41 silica and compare it with experimental data obtained from small-angle X-ray scattering. Theoretical predictions for MCM-41 are in good agreement with the experiment, but for SBA-15 they are only qualitative. This deviation suggests that the elastic modulus of SBA-15 may change during pore filling.
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Affiliation(s)
- Gennady Yu Gor
- Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey 08544, USA.
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Jeanmairet G, Levesque M, Vuilleumier R, Borgis D. Molecular Density Functional Theory of Water. J Phys Chem Lett 2013; 4:619-624. [PMID: 26281876 DOI: 10.1021/jz301956b] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Three-dimensional implementations of liquid-state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular density functional theory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short-range. The approach is shown to provide the correct 3-D microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two to three orders of magnitude lower than with explicit simulations.
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Affiliation(s)
- Guillaume Jeanmairet
- †Pôle de Physico-Chimie Théorique, École Normale Supérieure, UMR 8640 CNRS-ENS-UPMC, 24, rue Lhomond, 75005 Paris, France
| | - Maximilien Levesque
- †Pôle de Physico-Chimie Théorique, École Normale Supérieure, UMR 8640 CNRS-ENS-UPMC, 24, rue Lhomond, 75005 Paris, France
- ‡Université Pierre et Marie Curie, UMR 7195 PECSA, CNRS-UPMC-ESPCI, 75005 Paris, France
| | - Rodolphe Vuilleumier
- †Pôle de Physico-Chimie Théorique, École Normale Supérieure, UMR 8640 CNRS-ENS-UPMC, 24, rue Lhomond, 75005 Paris, France
| | - Daniel Borgis
- †Pôle de Physico-Chimie Théorique, École Normale Supérieure, UMR 8640 CNRS-ENS-UPMC, 24, rue Lhomond, 75005 Paris, France
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Nguyen VT, Do D, Nicholson D. Solid deformation induced by the adsorption of methane and methanol under sub- and supercritical conditions. J Colloid Interface Sci 2012; 388:209-18. [DOI: 10.1016/j.jcis.2012.08.021] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2012] [Revised: 08/09/2012] [Accepted: 08/09/2012] [Indexed: 10/27/2022]
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Triguero C, Coudert FX, Boutin A, Fuchs AH, Neimark AV. Understanding adsorption-induced structural transitions in metal-organic frameworks: from the unit cell to the crystal. J Chem Phys 2012. [PMID: 23163384 DOI: 10.1021/jz4013849] [Citation(s) in RCA: 94] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/23/2023] Open
Abstract
Breathing transitions represent recently discovered adsorption-induced structural transformations between large-pore and narrow-pore conformations in bi-stable metal-organic frameworks such as MIL-53. We present a multiscale physical mechanism of the dynamics of breathing transitions. We show that due to interplay between host framework elasticity and guest molecule adsorption, these transformations on the crystal level occur via layer-by-layer shear. We construct a simple Hamiltonian that describes the physics of host-host and host-guest interactions on the level of unit cells and reduces to one effective dimension due to the long-range elastic cell-cell interactions. We then use this Hamiltonian in Monte Carlo simulations of adsorption-desorption cycles to study how the behavior of unit cells is linked to the transition mechanism at the crystal level through three key physical parameters: the transition energy barrier, the cell-cell elastic coupling, and the system size.
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Affiliation(s)
- Carles Triguero
- CNRS & Chimie ParisTech, 11 rue Pierre et Marie Curie, 75005 Paris, France
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Wilke A, Weber J. Mesoporous Polymer Networks-Ultraporous DVB Resins by Hard-Templating of Close-Packed Silica Spheres. Macromol Rapid Commun 2012; 33:785-90. [DOI: 10.1002/marc.201100862] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2011] [Revised: 01/17/2012] [Indexed: 11/06/2022]
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