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Evolution of adsorption isotherm and isosteric heat from sub-triple to super-critical points. ADSORPTION 2021. [DOI: 10.1007/s10450-020-00294-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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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: 19] [Impact Index Per Article: 3.2] [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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Cimino RT, Kowalczyk P, Ravikovitch PI, Neimark AV. Determination of Isosteric Heat of Adsorption by Quenched Solid Density Functional Theory. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2017; 33:1769-1779. [PMID: 28135415 DOI: 10.1021/acs.langmuir.6b04119] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The heat of adsorption is one of the most important parameters characterizing energetic heterogeneity of the adsorbent surface. Heats of adsorption are either determined directly by calorimetry or calculated from adsorption isotherms measured at different temperatures using the thermodynamic Clausius-Clapeyron equation. Here, we present a method for calculating the isosteric heat of adsorption that requires as input only a single adsorption isotherm measured at one temperature. The proposed method is implemented with either nonlocal (NLDFT) or quenched solid (QSDFT) density functional theory models of adsorption that are currently widely used for calculating pore size distributions in various micro- and mesoporous solids. The pore size distribution determined from the same experimental isotherm is used for predicting the isosteric heat. The QSDFT method has advantages of taking into account two factors contributing to the structural heterogeneity of adsorbents: the molecular level roughness of the surface and the pore size distribution. The method is illustrated with examples of low temperature nitrogen and argon adsorption on selected samples of carbons of different degree of graphitization and MCM-41 mesoporous silicas of different pore size. The isosteric heat predictions from the NLDFT and QSDFT methods are compared against relevant experiments and the results of Monte Carlo (MC) simulations, with good agreement found in the cases where the surface model adequately reflects the pore surface roughness. Analyses with the QSDFT method show that the isosteric heat of adsorption significantly depends of the molecular level roughness of the adsorbent surface, which is ignored in NLDFT and MC models. The proposed QSDFT method with further verification can be used for calculating the isosteric heat as an additional parameter characterizing the adsorbent surface in parallel with routine calculations of the pore size distribution from a single adsorption isotherm.
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Affiliation(s)
- Richard T Cimino
- Department of Chemical and Biochemical Engineering, Rutgers University , Piscataway, New Jersey 08854, United States
| | - Piotr Kowalczyk
- School of Engineering and Information Technology, Murdoch University , Perth WA 6150, Australia
| | - Peter I Ravikovitch
- ExxonMobil Research and Engineering Company, Annandale, New Jersey 08801, United States
| | - Alexander V Neimark
- Department of Chemical and Biochemical Engineering, Rutgers University , Piscataway, New Jersey 08854, United States
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Hart KE, Abbott LJ, McKeown NB, Colina CM. Toward Effective CO2/CH4 Separations by Sulfur-Containing PIMs via Predictive Molecular Simulations. Macromolecules 2013. [DOI: 10.1021/ma400334b] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Kyle E. Hart
- Department of Materials Science
and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Lauren J. Abbott
- Department of Materials Science
and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Neil B. McKeown
- School of Chemistry, Cardiff University, Cardiff, CF10 3AT, U.K
| | - Coray M. Colina
- Department of Materials Science
and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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Wang Y, Do D, Herrera L, Nicholson D. On the condensation/evaporation pressures and isosteric heats for argon adsorption in pores of different cross-sections. Colloids Surf A Physicochem Eng Asp 2013. [DOI: 10.1016/j.colsurfa.2012.12.033] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Hart KE, Abbott LJ, Colina CM. Analysis of force fields and BET theory for polymers of intrinsic microporosity. MOLECULAR SIMULATION 2013. [DOI: 10.1080/08927022.2012.733945] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Liu Z, Horikawa T, Do DD, Nicholson D. Packing effects on argon and methanol adsorption inside graphitic cylindrical and slit pores: A GCMC simulation study. J Colloid Interface Sci 2012; 368:474-87. [PMID: 22082798 DOI: 10.1016/j.jcis.2011.10.046] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Revised: 10/13/2011] [Accepted: 10/14/2011] [Indexed: 11/30/2022]
Affiliation(s)
- Zhongjun Liu
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
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Do DD, Nicholson D, Fan C. Development of equations for differential and integral enthalpy change of adsorption for simulation studies. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2011; 27:14290-9. [PMID: 22013949 DOI: 10.1021/la203531j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We present equations to calculate the differential and integral enthalpy changes of adsorption for their use in Monte Carlo simulation. Adsorption of a system of N molecules, subject to an external potential energy, is viewed as one of transferring these molecules from a reference gas phase (state 1) to the adsorption system (state 2) at the same temperature and equilibrium pressure (same chemical potential). The excess amount adsorbed is the difference between N and the hypothetical amount of gas occupying the accessible volume of the system at the same density as the reference gas. The enthalpy change is a state function, which is defined as the difference between the enthalpies of state 2 and state 1, and the isosteric heat is defined as the negative of the derivative of this enthalpy change with respect to the excess amount of adsorption. It is suitable to determine how the system behaves for a differential increment in the excess phase adsorbed under subcritical conditions. For supercritical conditions, use of the integral enthalpy of adsorption per particle is recommended since the isosteric heat becomes infinite at the maximum excess concentration. With these unambiguous definitions we derive equations which are applicable for a general case of adsorption and demonstrate how they can be used in a Monte Carlo simulation. We apply the new equations to argon adsorption at various temperatures on a graphite surface to illustrate the need to use the correct equation to describe isosteric heat of adsorption.
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Affiliation(s)
- D D Do
- School of Chemical Engineering, University of Queensland, St. Lucia, Queensland 4072, Australia.
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Razak MA, Nguyen VT, Herrera LF, Do DD, Nicholson D. Microscopic analysis of adsorption in slit-like pores: layer fluctuations of particle number, layer isosteric heat and histogram of particle number. MOLECULAR SIMULATION 2011. [DOI: 10.1080/08927022.2011.586349] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Liu Z, Do D, Nicholson D. Effects of confinement on the molar enthalpy of argon adsorption in graphitic cylindrical pores: A grand canonical Monte Carlo (GCMC) simulation study. J Colloid Interface Sci 2011; 361:278-87. [DOI: 10.1016/j.jcis.2011.05.072] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2011] [Revised: 05/23/2011] [Accepted: 05/24/2011] [Indexed: 11/30/2022]
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Fan C, Do DD, Nicholson D. New Monte Carlo Simulation of Adsorption of Gases on Surfaces and in Pores: A Concept of Multibins. J Phys Chem B 2011; 115:10509-17. [DOI: 10.1021/jp205497s] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Chunyan Fan
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
| | - D. D. Do
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
| | - D. Nicholson
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
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Wang Y, Do D, Nicholson D. Study of heat of adsorption across the capillary condensation in cylindrical pores. Colloids Surf A Physicochem Eng Asp 2011. [DOI: 10.1016/j.colsurfa.2011.02.016] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Herrera LF, Fan C, Do DD, Nicholson D. Novel Method To Determine Accessible Volume, Area, and Pore Size Distribution of Activated Carbon. Ind Eng Chem Res 2011. [DOI: 10.1021/ie102169u] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- L. F. Herrera
- School of Chemical Engineering University of Queensland St. Lucia, Qld 4072 AUSTRALIA
| | - Chunyan Fan
- School of Chemical Engineering University of Queensland St. Lucia, Qld 4072 AUSTRALIA
| | - D. D. Do
- School of Chemical Engineering University of Queensland St. Lucia, Qld 4072 AUSTRALIA
| | - D. Nicholson
- School of Chemical Engineering University of Queensland St. Lucia, Qld 4072 AUSTRALIA
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Palmer JC, Moore JD, Roussel TJ, Brennan JK, Gubbins KE. Adsorptive behavior of CO2, CH4 and their mixtures in carbon nanospace: a molecular simulation study. Phys Chem Chem Phys 2011; 13:3985-96. [DOI: 10.1039/c0cp02281k] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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Gumma S, Talu O. Net adsorption: a thermodynamic framework for supercritical gas adsorption and storage in porous solids. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2010; 26:17013-17023. [PMID: 20886890 DOI: 10.1021/la102186q] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
The thermodynamic treatment of adsorption phenomena is based on the Gibbs dividing surface, which is conceptually clear for a flat surface. On a flat surface, the primary extensive property is the area of the solid. As applications became more significant, necessitating microporous solids, early researchers such as McBain and Coolidge implemented the Gibbs definition by invoking a reference state for microporous solids. The mass of solid is used as a primary extensive property because surface area loses its physical meaning for microporous solids. A reference state is used to fix the hypothetical hyperdividing surface typically using helium as a probe molecule, resulting in the commonly used excess adsorption; experimentalists measure this reference state for each new sample. Molecular simulations, however, provide absolute adsorption. Theoreticians perform helium simulations to convert absolute to excess adsorption, mimicking experiments for comparison. This current structure of adsorption thermodynamics is rigorous (if the conditions for reference state helium measurements are completely disclosed) but laborious. In addition, many studies show that helium, or any other probe molecule for that matter, does adsorb, albeit to a small extent. We propose a novel thermodynamic framework, net adsorption, which completely circumvents the use of probe molecules to fix the reference state for each microporous sample. Using net adsorption, experimentalists calibrate their apparatus only once without any sample in the system. Theoreticians can directly calculate net adsorption; no additional simulations with a probe gas are necessary. Net adsorption also provides a direct indication of the density enhancement achieved (by using an adsorbent) over simple compression for gas (e.g., hydrogen) storage applications.
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Affiliation(s)
- Sasidhar Gumma
- Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India
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Fan C, Do DD, Li Z, Nicholson D. Computer simulation of argon adsorption on graphite surface from subcritical to supercritical conditions: the behavior of differential and integral molar enthalpies of adsorption. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2010; 26:15852-15864. [PMID: 20860399 DOI: 10.1021/la1024857] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We investigate in detail the computer simulation of argon adsorption on a graphite surface over a very wide range of temperature, from below the triple point to well above the critical point. Adsorption over such a wide temperature range has not been reported previously in the form of adsorption isotherms and enthalpy change during adsorption. The adsorption isotherms can be classified broadly into four categories: below the triple point, the isotherms show stepwise character (a strict layering mechanism) with 2D condensation; type II (according to the IUPAC classification) is followed by isotherms at temperatures above the triple point and below the critical point and a sharp spike is seen for isotherms in the neighborhood of the critical point; and finally the typical behavior of a maximum is observed for isotherms above the critical point. For the isosteric heat, the heat curve (plotted against loading) remains finite for subcritical conditions but is infinite (singularity) at the maximum in excess loading for supercritical adsorption. For the latter case, a better representation of the energy change is the use of the integral molecular enthalpy because this does not exhibit a singularity as in the case of isosteric heat. We compare the differential and integral molecular enthalpies for the subcritical and supercritical adsorptions.
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Affiliation(s)
- Chunyan Fan
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
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Liu Z, Do D, Nicholson D, Xi Z. Effects of Surface Curvature and Surface Strength on Argon Adsorption in Carbon Nanotubes at Temperatures below the Triple Point. ADSORPT SCI TECHNOL 2010. [DOI: 10.1260/0263-6174.28.7.561] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022] Open
Affiliation(s)
- Zhongjun Liu
- College of Materials and Metallurgy, Northeastern University, Shenyang 110004, P. R. China
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
| | - D.D. Do
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
| | - D. Nicholson
- School of Chemical Engineering, University of Queensland, St. Lucia, Qld 4072, Australia
| | - Zhengping Xi
- State Key Laboratory of Porous Metal Materials, Xi'an 710016, P. R. China
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Do DD, Herrera L, Fan C, Wongkoblap A, Nicholson D. The role of accessibility in the characterization of porous solids and their adsorption properties. ADSORPTION 2009. [DOI: 10.1007/s10450-009-9203-8] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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