Using flat-histogram Monte Carlo methods, we investigate the adsorptive behavior of the square-we... more Using flat-histogram Monte Carlo methods, we investigate the adsorptive behavior of the square-well fluid in two simple slit-pore-like models intended to capture fundamental characteristics of flexible adsorbent materials. Both models require as input thermodynamic information about the flexible adsorbent material itself. An important component of this work involves formulating the flexible pore models in the appropriate thermodynamic (statistical mechanical) ensembles, namely, the osmotic ensemble and a variant of the grand-canonical ensemble. Two-dimensional probability distributions, which are calculated using flat-histogram methods, provide the information necessary to determine adsorption thermodynamics. For example, we are able to determine precisely adsorption isotherms, (equilibrium) phase transition conditions, limits of stability, and free energies for a number of different flexible adsorbent materials, distinguishable as different inputs into the models. While the models used in this work are relatively simple from a geometric perspective, they yield non-trivial adsorptive behavior, including adsorption-desorption hysteresis solely due to material flexibility and so-called “breathing” of the adsorbent. The observed effects can in turn be tied to the inherent properties of the bare adsorbent. Some of the effects are expected on physical grounds while others arise from a subtle balance of thermodynamic and mechanical driving forces. In addition, the computational strategy presented here can be easily applied to more complex models for flexible adsorbents.
Computational screening of adsorbent materials often uses the Henry’s law constant (KH) (at a par... more Computational screening of adsorbent materials often uses the Henry’s law constant (KH) (at a particular temperature) as a first discriminator metric due to its relative ease of calculation. The isosteric heat of adsorption in the limit of zero pressure (qst∞) is often calculated along with the Henry’s law constant, and both properties are informative metrics of adsorbent material performance at low-pressure conditions. In this article, we introduce a method for extrapolating KH as a function of temperature, using series-expansion coefficients that are easily computed at the same time as KH itself; the extrapolation function also yields qst∞. The extrapolation is highly accurate over a wide range of temperatures when the basis temperature is sufficiently high, for a wide range of adsorbent materials and adsorbate gases. Various results suggest that the extrapolation is accurate when the extrapolation range in inverse-temperature space is limited to |β − β0| < 0.5 mol/kJ. Application of the extrapolation to a large set of materials is shown to be successful provided that KH is not extremely large and/or the extrapolation coefficients converge satisfactorily. The extrapolation is also able to predict qst∞ for a system that shows an unusually large temperature dependence. The work provides a robust method for predicting KH and qst∞ over a wide range of industrially relevant temperatures with minimal effort beyond that necessary to compute those properties at a single temperature, which facilitates the addition of practical operating (or processing) conditions to computational screening exercises.
In this work, a flexible metal-org. framework (MOF) (nickname BPene), [Ni'(L)Ni(CN)4]n (L=1,2... more In this work, a flexible metal-org. framework (MOF) (nickname BPene), [Ni'(L)Ni(CN)4]n (L=1,2-bis(4-pyridyl)-ethylene) that shows reversible structural transitions between low porosity and high porosity phases during the adsorption and desorption of CO2 has been synthesized and analyzed. Pore size distribution detn. has also been conducted. Time resolved, in-situ studies including single-crystal and powder X-ray and neutron diffraction, SANS, and Ultra-small-Angle X-ray Scattering (USAXS) techniques will be developed to study the sorption processes of CO2 and other relevant gases using the flexible MOFs.
1Materials Science and Engineering Division, National Institute of Standards and Technology, Gait... more 1Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA. 2Theiss Research, La Jolla, 92037, CA, USA. 3NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA. 4Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA. 5Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA.
The Standard Reference Simulation Website is an ongoing project whose aim is to provide well-docu... more The Standard Reference Simulation Website is an ongoing project whose aim is to provide well-documented simulation results for a variety of systems and from various simulation techniques. The data include raw canonical potential energy, macrostate probability distributions, metadata explaining the simulation parameters and constraints, and thermophysical properties generated by processing the raw simulation output, including pressure, phase coexistence properties, self-diffusivity, and excess entropy. Thermodynamic properties and reference energy calculations are given on the website in tabular form. Data are generated from well-proven molecular simulation software with repeated simulation runs to prove repeatability and provide error estimates so that the data can serve as Standard Reference Data (http://www.nist.gov/srd/upload/SRDAct-2.pdf).
The NIST Registry of Adsorbent Materials is a free, web-based catalog of adsorbent materials and ... more The NIST Registry of Adsorbent Materials is a free, web-based catalog of adsorbent materials and metadata describing those adsorbent materials. Each adsorbent material in the registry is assigned a registry ID to 1) allow unique identification adsorbents independent of arbitrary naming schemes (e.g., HKUST-1, CuBTC, Basolate C300® are the same material and have the same registry ID) and 2) enable cross referencing information about each material from outside databases and material registries. The registry ID is based on a cryptographic hash, to prevent ID collisions as the registry grows in content. This web application also includes a mechanism for users to provide feedback regarding entries in the registry, to facilitate growth and correction of the database contents. Current feedback options, available through the "User Feedback" menu item are 1) general comments, 2) revision of a database entry (e.g., addition of an external data resource about a specific material), 3)...
Journal of Research of the National Institute of Standards and Technology, 2021
Sorption isotherms collected from tables in the seminal dissertation, “The Thermodynamics and Hys... more Sorption isotherms collected from tables in the seminal dissertation, “The Thermodynamics and Hysteresis of Adsorption” by A. J. Brown, have been digitized and made publicly available, along with supporting software scripts that facilitates usage of the data. The isotherms include laboratory measurements of xenon, krypton, and carbon dioxide adsorption (and, when possible, desorption) isotherms on a single sample of Vycor glass1, at various temperatures including subcritical conditions for xenon and krypton. The highlight of this dataset is the collection of “scanning” isotherms for xenon on Vycor at 131 K. The scanning isotherms examine numerous trajectories through the adsorption-desorption hysteresis region, such as primary adsorption and desorption scanning isotherms that terminate at the hysteresis boundary, secondary scanning isotherms made by selective reversals that return to the boundary, and closed scanning loops. This dataset was originally used to test the independent do...
Simplified fluid-substrate interaction models derived from the Lennard-Jones potential are widely... more Simplified fluid-substrate interaction models derived from the Lennard-Jones potential are widely used in the simulation of gas physisorption phenomena. In this paper, we reinterpret the well known Steele 10-4-3 potential for a gas molecule interacting with a planar surface, and use the resultant scheme to derive new potentials for cylindrical and spherical pore geometries. These new potentials correctly recover the Steele result in the limit of infinite pore radius, a useful improvement over existing models. We demonstrate the new cylindrical Steele 10-4-3 potential in calculations of argon adsorption via fluid density functional theory. This potential yields markedly different adsorption behavior than existing cylindrical potentials, which follow from small but significant differences in both the strength and the shape of the fluid-surface interaction. These differences cannot be fully reconciled simply by reparameterizing (scaling) the existing models; the new potential is more realistic in design, and is especially to be preferred in studies where comparison with planar substrates is made. Finally, we discuss extensions of this approach to more complicated pore geometries, yielding a family of Steele-like potentials that all satisfy the correct planar limit.
Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural p... more Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural properties of on-lattice hard-sphere fluids. Our purpose in this work is to provide reference data for on-lattice density functional theories [D. W. Siderius and L. D. Gelb, Langmuir 25, 1296 (2009)] and related perturbation theories. In this model, hard spheres are located at sites on a finely discretized cubic lattice where the spacing between lattice sites is between one-tenth and one-third the hard-sphere diameter. We calculate exactly the second, third, and fourth virial coefficients as functions of the lattice spacing. Via Monte Carlo simulation, we measure the excess chemical potential as a function of density for several lattice spacings. These results are then parametrized with a convenient functional form and can immediately be used in on-lattice density functional theories. Of particular interest is to identify those lattice spacings that yield properties similar to those of the off-lattice fluid. We find that the properties of the on-lattice fluid are strongly dependent on lattice spacing, generally approaching those of the off-lattice fluid with increasing lattice resolution, but not smoothly. These observations are consistent with results for larger lattice spacings [A. Z. Panagiotopoulos, J. Chem. Phys. 123, 104504 (2005)]. Certain lattice spacings are found to yield fluid properties in particularly good agreement with the off-lattice fluid. We also find that the agreement of many different on- and off-lattice hard-sphere fluid properties is predicted quite well by that of the virial coefficients, suggesting that they may be used to identify favorable lattice spacings. The direct correlation function at a few lattice spacings and a single density is obtained from simulation. The on-lattice fluid is structurally anisotropic, exhibiting spherical asymmetry in correlation functions. Interestingly, the anisotropies are properly captured in the Percus-Yevick-based calculation of the direct correlation function. Lastly, we speculate on the possibility of obtaining a theoretical equation of state of the on-lattice hard-sphere fluid computed in the Percus-Yevick approximation.
We consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding ... more We consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding to those states sampled during a MD simulation in which the application of periodic boundary conditions imposes a constraint on the momentum of the center of mass. As noted by Shirts et al. [J. Chem. Phys. 125, 164102 (2006)] for an isolated system, we find that the principle of equipartition is not satisfied within such simulations, i.e., the total kinetic energy of the system is not shared equally among all the translational degrees of freedom. Nevertheless, we derive two different versions of Tolman&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s generalized equipartition theorem, one appropriate for the canonical ensemble and the other relevant to the microcanonical ensemble. In both cases, the breakdown of the principle of equipartition immediately follows from Tolman&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s result. The translational degrees of freedom are, however, still equivalent, being coupled to the same bulk property in an identical manner. We also show that the temperature of an isolated system is not directly proportional to the average of the total kinetic energy (in contrast to the direct proportionality that arises between the temperature of the external bath and the kinetic energy within the canonical ensemble). Consequently, the system temperature does not appear within Tolman&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s generalized equipartition theorem for the microcanonical ensemble (unlike the immediate appearance of the temperature of the external bath within the canonical ensemble). Both of these results serve to highlight the flaws in the argument put forth by Hertz [Ann. Phys. 33, 225 (1910); 33, 537 (1910)] for defining the entropy of an isolated system via the integral of the phase space volume. Only the Boltzmann-Planck entropy definition, which connects entropy to the integral of the phase space density, leads to the correct description of the properties of a finite, isolated system. We demonstrate that the use of the integral of the phase space volume leads to unphysical results, indicating that the property of adiabatic invariance has little to do with the behavior of small systems.
Using flat-histogram Monte Carlo methods, we investigate the adsorptive behavior of the square-we... more Using flat-histogram Monte Carlo methods, we investigate the adsorptive behavior of the square-well fluid in two simple slit-pore-like models intended to capture fundamental characteristics of flexible adsorbent materials. Both models require as input thermodynamic information about the flexible adsorbent material itself. An important component of this work involves formulating the flexible pore models in the appropriate thermodynamic (statistical mechanical) ensembles, namely, the osmotic ensemble and a variant of the grand-canonical ensemble. Two-dimensional probability distributions, which are calculated using flat-histogram methods, provide the information necessary to determine adsorption thermodynamics. For example, we are able to determine precisely adsorption isotherms, (equilibrium) phase transition conditions, limits of stability, and free energies for a number of different flexible adsorbent materials, distinguishable as different inputs into the models. While the models used in this work are relatively simple from a geometric perspective, they yield non-trivial adsorptive behavior, including adsorption-desorption hysteresis solely due to material flexibility and so-called “breathing” of the adsorbent. The observed effects can in turn be tied to the inherent properties of the bare adsorbent. Some of the effects are expected on physical grounds while others arise from a subtle balance of thermodynamic and mechanical driving forces. In addition, the computational strategy presented here can be easily applied to more complex models for flexible adsorbents.
Computational screening of adsorbent materials often uses the Henry’s law constant (KH) (at a par... more Computational screening of adsorbent materials often uses the Henry’s law constant (KH) (at a particular temperature) as a first discriminator metric due to its relative ease of calculation. The isosteric heat of adsorption in the limit of zero pressure (qst∞) is often calculated along with the Henry’s law constant, and both properties are informative metrics of adsorbent material performance at low-pressure conditions. In this article, we introduce a method for extrapolating KH as a function of temperature, using series-expansion coefficients that are easily computed at the same time as KH itself; the extrapolation function also yields qst∞. The extrapolation is highly accurate over a wide range of temperatures when the basis temperature is sufficiently high, for a wide range of adsorbent materials and adsorbate gases. Various results suggest that the extrapolation is accurate when the extrapolation range in inverse-temperature space is limited to |β − β0| < 0.5 mol/kJ. Application of the extrapolation to a large set of materials is shown to be successful provided that KH is not extremely large and/or the extrapolation coefficients converge satisfactorily. The extrapolation is also able to predict qst∞ for a system that shows an unusually large temperature dependence. The work provides a robust method for predicting KH and qst∞ over a wide range of industrially relevant temperatures with minimal effort beyond that necessary to compute those properties at a single temperature, which facilitates the addition of practical operating (or processing) conditions to computational screening exercises.
In this work, a flexible metal-org. framework (MOF) (nickname BPene), [Ni'(L)Ni(CN)4]n (L=1,2... more In this work, a flexible metal-org. framework (MOF) (nickname BPene), [Ni'(L)Ni(CN)4]n (L=1,2-bis(4-pyridyl)-ethylene) that shows reversible structural transitions between low porosity and high porosity phases during the adsorption and desorption of CO2 has been synthesized and analyzed. Pore size distribution detn. has also been conducted. Time resolved, in-situ studies including single-crystal and powder X-ray and neutron diffraction, SANS, and Ultra-small-Angle X-ray Scattering (USAXS) techniques will be developed to study the sorption processes of CO2 and other relevant gases using the flexible MOFs.
1Materials Science and Engineering Division, National Institute of Standards and Technology, Gait... more 1Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA. 2Theiss Research, La Jolla, 92037, CA, USA. 3NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA. 4Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA. 5Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA.
The Standard Reference Simulation Website is an ongoing project whose aim is to provide well-docu... more The Standard Reference Simulation Website is an ongoing project whose aim is to provide well-documented simulation results for a variety of systems and from various simulation techniques. The data include raw canonical potential energy, macrostate probability distributions, metadata explaining the simulation parameters and constraints, and thermophysical properties generated by processing the raw simulation output, including pressure, phase coexistence properties, self-diffusivity, and excess entropy. Thermodynamic properties and reference energy calculations are given on the website in tabular form. Data are generated from well-proven molecular simulation software with repeated simulation runs to prove repeatability and provide error estimates so that the data can serve as Standard Reference Data (http://www.nist.gov/srd/upload/SRDAct-2.pdf).
The NIST Registry of Adsorbent Materials is a free, web-based catalog of adsorbent materials and ... more The NIST Registry of Adsorbent Materials is a free, web-based catalog of adsorbent materials and metadata describing those adsorbent materials. Each adsorbent material in the registry is assigned a registry ID to 1) allow unique identification adsorbents independent of arbitrary naming schemes (e.g., HKUST-1, CuBTC, Basolate C300® are the same material and have the same registry ID) and 2) enable cross referencing information about each material from outside databases and material registries. The registry ID is based on a cryptographic hash, to prevent ID collisions as the registry grows in content. This web application also includes a mechanism for users to provide feedback regarding entries in the registry, to facilitate growth and correction of the database contents. Current feedback options, available through the "User Feedback" menu item are 1) general comments, 2) revision of a database entry (e.g., addition of an external data resource about a specific material), 3)...
Journal of Research of the National Institute of Standards and Technology, 2021
Sorption isotherms collected from tables in the seminal dissertation, “The Thermodynamics and Hys... more Sorption isotherms collected from tables in the seminal dissertation, “The Thermodynamics and Hysteresis of Adsorption” by A. J. Brown, have been digitized and made publicly available, along with supporting software scripts that facilitates usage of the data. The isotherms include laboratory measurements of xenon, krypton, and carbon dioxide adsorption (and, when possible, desorption) isotherms on a single sample of Vycor glass1, at various temperatures including subcritical conditions for xenon and krypton. The highlight of this dataset is the collection of “scanning” isotherms for xenon on Vycor at 131 K. The scanning isotherms examine numerous trajectories through the adsorption-desorption hysteresis region, such as primary adsorption and desorption scanning isotherms that terminate at the hysteresis boundary, secondary scanning isotherms made by selective reversals that return to the boundary, and closed scanning loops. This dataset was originally used to test the independent do...
Simplified fluid-substrate interaction models derived from the Lennard-Jones potential are widely... more Simplified fluid-substrate interaction models derived from the Lennard-Jones potential are widely used in the simulation of gas physisorption phenomena. In this paper, we reinterpret the well known Steele 10-4-3 potential for a gas molecule interacting with a planar surface, and use the resultant scheme to derive new potentials for cylindrical and spherical pore geometries. These new potentials correctly recover the Steele result in the limit of infinite pore radius, a useful improvement over existing models. We demonstrate the new cylindrical Steele 10-4-3 potential in calculations of argon adsorption via fluid density functional theory. This potential yields markedly different adsorption behavior than existing cylindrical potentials, which follow from small but significant differences in both the strength and the shape of the fluid-surface interaction. These differences cannot be fully reconciled simply by reparameterizing (scaling) the existing models; the new potential is more realistic in design, and is especially to be preferred in studies where comparison with planar substrates is made. Finally, we discuss extensions of this approach to more complicated pore geometries, yielding a family of Steele-like potentials that all satisfy the correct planar limit.
Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural p... more Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural properties of on-lattice hard-sphere fluids. Our purpose in this work is to provide reference data for on-lattice density functional theories [D. W. Siderius and L. D. Gelb, Langmuir 25, 1296 (2009)] and related perturbation theories. In this model, hard spheres are located at sites on a finely discretized cubic lattice where the spacing between lattice sites is between one-tenth and one-third the hard-sphere diameter. We calculate exactly the second, third, and fourth virial coefficients as functions of the lattice spacing. Via Monte Carlo simulation, we measure the excess chemical potential as a function of density for several lattice spacings. These results are then parametrized with a convenient functional form and can immediately be used in on-lattice density functional theories. Of particular interest is to identify those lattice spacings that yield properties similar to those of the off-lattice fluid. We find that the properties of the on-lattice fluid are strongly dependent on lattice spacing, generally approaching those of the off-lattice fluid with increasing lattice resolution, but not smoothly. These observations are consistent with results for larger lattice spacings [A. Z. Panagiotopoulos, J. Chem. Phys. 123, 104504 (2005)]. Certain lattice spacings are found to yield fluid properties in particularly good agreement with the off-lattice fluid. We also find that the agreement of many different on- and off-lattice hard-sphere fluid properties is predicted quite well by that of the virial coefficients, suggesting that they may be used to identify favorable lattice spacings. The direct correlation function at a few lattice spacings and a single density is obtained from simulation. The on-lattice fluid is structurally anisotropic, exhibiting spherical asymmetry in correlation functions. Interestingly, the anisotropies are properly captured in the Percus-Yevick-based calculation of the direct correlation function. Lastly, we speculate on the possibility of obtaining a theoretical equation of state of the on-lattice hard-sphere fluid computed in the Percus-Yevick approximation.
We consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding ... more We consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding to those states sampled during a MD simulation in which the application of periodic boundary conditions imposes a constraint on the momentum of the center of mass. As noted by Shirts et al. [J. Chem. Phys. 125, 164102 (2006)] for an isolated system, we find that the principle of equipartition is not satisfied within such simulations, i.e., the total kinetic energy of the system is not shared equally among all the translational degrees of freedom. Nevertheless, we derive two different versions of Tolman&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s generalized equipartition theorem, one appropriate for the canonical ensemble and the other relevant to the microcanonical ensemble. In both cases, the breakdown of the principle of equipartition immediately follows from Tolman&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s result. The translational degrees of freedom are, however, still equivalent, being coupled to the same bulk property in an identical manner. We also show that the temperature of an isolated system is not directly proportional to the average of the total kinetic energy (in contrast to the direct proportionality that arises between the temperature of the external bath and the kinetic energy within the canonical ensemble). Consequently, the system temperature does not appear within Tolman&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s generalized equipartition theorem for the microcanonical ensemble (unlike the immediate appearance of the temperature of the external bath within the canonical ensemble). Both of these results serve to highlight the flaws in the argument put forth by Hertz [Ann. Phys. 33, 225 (1910); 33, 537 (1910)] for defining the entropy of an isolated system via the integral of the phase space volume. Only the Boltzmann-Planck entropy definition, which connects entropy to the integral of the phase space density, leads to the correct description of the properties of a finite, isolated system. We demonstrate that the use of the integral of the phase space volume leads to unphysical results, indicating that the property of adiabatic invariance has little to do with the behavior of small systems.
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