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David A Kofke - One of the best experts on this subject based on the ideXlab platform.
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cluster integrals and Virial Coefficients for realistic molecular models
Physical Review E, 2020Co-Authors: Richard J Wheatley, Andrew J Schultz, Navneeth Gokul, David A KofkeAbstract:We present a concise, general, and efficient procedure for calculating the cluster integrals that relate thermodynamic Virial Coefficients to molecular interactions. The approach encompasses nonpairwise intermolecular potentials generated from quantum chemistry or other sources; a simple extension permits efficient evaluation of temperature and other derivatives of the Virial Coefficients. We demonstrate with a polarizable model of water. We argue that cluster-integral methods are a potent yet underutilized instrument for the development and application of first-principles molecular models and methods.
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Virial Coefficients and equations of state for hard polyhedron fluids
Langmuir, 2017Co-Authors: Eric M Irrgang, Andrew J Schultz, David A Kofke, Michael Engel, Sharon C GlotzerAbstract:Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but no general scheme exists for predicting the effect of shape on thermodynamic properties, even in fluids of moderate density. Only the second Virial coefficient is known analytically for general convex shapes, so higher order equations of state have been elusive. Here we investigate high-precision state functions in the fluid phase of 14 representative polyhedra with different assembly behaviors. We discuss historic efforts in analytically approximating Virial Coefficients up to $B_4$ and numerically evaluating them to $B_8$ Using Virial Coefficients as inputs, we show the convergence properties for four equations of state for hard convex bodies. In particular, the exponential approximant of Barlow~\textit{et al.}~\cite{Barlow2012} is found to be useful up to the first ordering transition for most polyhedra. The convergence behavior we explore can guide choices in expending additional resources for improved estimates. Fl...
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fifth to eleventh Virial Coefficients of hard spheres
Physical Review E, 2014Co-Authors: Andrew J Schultz, David A KofkeAbstract:Virial Coefficients ${B}_{n}$ of three-dimensional hard spheres are reported for $n=5$ to 11, with precision exceeding that presently available in the literature. Calculations are performed using the recursive method due to Wheatley, and a binning approach is proposed to allow more flexibility in where computational effort is directed in the calculations. We highlight the difficulty as a general measure that quantifies performance of an algorithm that computes a stochastic average and show how it can be used as the basis for optimizing such calculations.
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Virial Coefficients of model alkanes
Journal of Chemical Physics, 2010Co-Authors: Andrew J Schultz, David A KofkeAbstract:We report the results from Mayer-sampling Monte Carlo calculations of the Virial Coefficients of the united-atom TraPPE-UA model of normal alkanes. For alkane chain lengths from n=2 to 20 (where n is the number of carbon atoms), results are given for the Virial Coefficients B2, B3, and B4; results for B5 are given for chains up to length n=12; and results for B6 are given for chains of length n=2, 3, and 4. In all cases, values are given for temperatures ranging from 200 K to 2000 K in 20–50 K increments. The values are used to calculate the equation of state for butane and the pressure-density behavior is compared to experimental data at 350 and 550 K. Critical points are calculated for all systems and compared to simulation data previously taken for the same molecular model, and to experiment. The comparison with temperature is very good (within 1.5% for all chain lengths up to n=12), while the critical density is underestimated by about 5%–15% and the critical pressure is given within about 10%. The co...
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fourth and fifth Virial Coefficients of polarizable water
Journal of Physical Chemistry B, 2009Co-Authors: Kenneth M Benjamin, Andrew J Schultz, David A KofkeAbstract:We report values of the Virial Coefficients B4 and B5 for the Gaussian charge polarizable model (GCPM) of water using the overlap-sampling implementation of Mayer sampling molecular simulation. These results supplement values for the lower-order Coefficients B2 and B3 reported previously, and in the present work, we provide more precise values of these Coefficients as well. The precision of all Virial Coefficients is such that the standard error in the calculated pressure is significantly less than 1% for most temperatures, with the exception of temperatures near the critical, where the error approaches 100% at the critical density, and supercritical, where the uncertainly in B5 introduces an error of about 5% in the pressure at the critical density. We examine these Coefficients in the context of the equation of state and molecular clustering. Comparisons are made to established molecular simulation data, quantum chemical calculations, and experimental data for real water. Over both sub- and supercritica...
Andrew J Schultz - One of the best experts on this subject based on the ideXlab platform.
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cluster integrals and Virial Coefficients for realistic molecular models
Physical Review E, 2020Co-Authors: Richard J Wheatley, Andrew J Schultz, Navneeth Gokul, David A KofkeAbstract:We present a concise, general, and efficient procedure for calculating the cluster integrals that relate thermodynamic Virial Coefficients to molecular interactions. The approach encompasses nonpairwise intermolecular potentials generated from quantum chemistry or other sources; a simple extension permits efficient evaluation of temperature and other derivatives of the Virial Coefficients. We demonstrate with a polarizable model of water. We argue that cluster-integral methods are a potent yet underutilized instrument for the development and application of first-principles molecular models and methods.
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Virial Coefficients and equations of state for hard polyhedron fluids
Langmuir, 2017Co-Authors: Eric M Irrgang, Andrew J Schultz, David A Kofke, Michael Engel, Sharon C GlotzerAbstract:Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but no general scheme exists for predicting the effect of shape on thermodynamic properties, even in fluids of moderate density. Only the second Virial coefficient is known analytically for general convex shapes, so higher order equations of state have been elusive. Here we investigate high-precision state functions in the fluid phase of 14 representative polyhedra with different assembly behaviors. We discuss historic efforts in analytically approximating Virial Coefficients up to $B_4$ and numerically evaluating them to $B_8$ Using Virial Coefficients as inputs, we show the convergence properties for four equations of state for hard convex bodies. In particular, the exponential approximant of Barlow~\textit{et al.}~\cite{Barlow2012} is found to be useful up to the first ordering transition for most polyhedra. The convergence behavior we explore can guide choices in expending additional resources for improved estimates. Fl...
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fifth to eleventh Virial Coefficients of hard spheres
Physical Review E, 2014Co-Authors: Andrew J Schultz, David A KofkeAbstract:Virial Coefficients ${B}_{n}$ of three-dimensional hard spheres are reported for $n=5$ to 11, with precision exceeding that presently available in the literature. Calculations are performed using the recursive method due to Wheatley, and a binning approach is proposed to allow more flexibility in where computational effort is directed in the calculations. We highlight the difficulty as a general measure that quantifies performance of an algorithm that computes a stochastic average and show how it can be used as the basis for optimizing such calculations.
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Virial Coefficients of model alkanes
Journal of Chemical Physics, 2010Co-Authors: Andrew J Schultz, David A KofkeAbstract:We report the results from Mayer-sampling Monte Carlo calculations of the Virial Coefficients of the united-atom TraPPE-UA model of normal alkanes. For alkane chain lengths from n=2 to 20 (where n is the number of carbon atoms), results are given for the Virial Coefficients B2, B3, and B4; results for B5 are given for chains up to length n=12; and results for B6 are given for chains of length n=2, 3, and 4. In all cases, values are given for temperatures ranging from 200 K to 2000 K in 20–50 K increments. The values are used to calculate the equation of state for butane and the pressure-density behavior is compared to experimental data at 350 and 550 K. Critical points are calculated for all systems and compared to simulation data previously taken for the same molecular model, and to experiment. The comparison with temperature is very good (within 1.5% for all chain lengths up to n=12), while the critical density is underestimated by about 5%–15% and the critical pressure is given within about 10%. The co...
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fourth and fifth Virial Coefficients of polarizable water
Journal of Physical Chemistry B, 2009Co-Authors: Kenneth M Benjamin, Andrew J Schultz, David A KofkeAbstract:We report values of the Virial Coefficients B4 and B5 for the Gaussian charge polarizable model (GCPM) of water using the overlap-sampling implementation of Mayer sampling molecular simulation. These results supplement values for the lower-order Coefficients B2 and B3 reported previously, and in the present work, we provide more precise values of these Coefficients as well. The precision of all Virial Coefficients is such that the standard error in the calculated pressure is significantly less than 1% for most temperatures, with the exception of temperatures near the critical, where the error approaches 100% at the critical density, and supercritical, where the uncertainly in B5 introduces an error of about 5% in the pressure at the critical density. We examine these Coefficients in the context of the equation of state and molecular clustering. Comparisons are made to established molecular simulation data, quantum chemical calculations, and experimental data for real water. Over both sub- and supercritica...
Yuan-yuan Duan - One of the best experts on this subject based on the ideXlab platform.
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prediction of the second cross Virial Coefficients of nonpolar binary mixtures
Fluid Phase Equilibria, 2005Co-Authors: Long Meng, Yuan-yuan DuanAbstract:Abstract The binary interaction parameter, kij, of 268 nonpolar mixtures were determined from the database of second cross Virial Coefficients containing 1728 experimental data points by fitting the second cross Virial Coefficients with a new correlation for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120] and classical mixing rules. Regularity distributions were found for both n-alkane/n-alkane binaries and fluorocarbon/fluorocarbon binaries. Correlations were developed following Tsonopoulos’ ideas [C. Tsonopoulos, Adv. Chem. Ser. 182 (1979) 143–162] with the quantity of binary compounds enlarged using Dymond's latest complication [J.H. Dymond, K.N. Marsh, R.C. Wilhoit, Virial Coefficients of Pure Gases and Mixtures, Subvolume B, Virial Coefficients of Mixtures, Series IV/21B, Landolt-Bornstein, 2002]. Correlations were also developed for inorganic/n-alkane binaries using new kij values. The predictions do not need any thermodynamic property parameters besides the carbon number. Comparisons with the existing correlations show that the present work is more accurate for nonpolar binary mixtures.
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Correlations for second and third Virial Coefficients of pure fluids
Fluid Phase Equilibria, 2004Co-Authors: Long Meng, Yuan-yuan DuanAbstract:Abstract A modified form of the well-known Tsonopoulos correlation for second Virial Coefficients was developed based on the corresponding-states principle. Comparisons with the new, high-quality experimental data and existing models show that the present correlation is more accurate, reliable and satisfactory for nonpolar compounds. The results also show that the present work is roughly equivalent to the Tsonopoulos and Weber correlations for second Virial Coefficients of polar fluids. The Weber correlation for the third Virial Coefficients was also improved since it did not well represent the experimental data of nonpolar gases. The new correlation gives a satisfactory fit for nonpolar compounds as the Orbey and Vera correlation did and can also accurately represent the literature data for the third Virial Coefficients of polar fluids, which was well represented by the Weber correlation. The two correlations for the second and third Virial Coefficients need the same additional parameters, such as the critical temperature, critical pressure, acentric factor and reduced dipole moment.
O D Crisalle - One of the best experts on this subject based on the ideXlab platform.
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on the behavior of the osmotic second Virial Coefficients of gases in aqueous solutions rigorous results accurate approximations and experimental evidence
Journal of Chemical Physics, 2019Co-Authors: Ariel A Chialvo, O D CrisalleAbstract:We present a novel molecular-based approach for the determination of the osmotic second Virial Coefficients of gaseous solutes in dilute binary solutions, according to a recently proposed molecular thermodynamic formalism of gas solubility [A. A. Chialvo, J. Chem. Phys. 148, 174502 (2018) and Fluid Phase Equilib. 472, 94 (2018)]. We discuss relevant solvation fundamentals and derive new expressions including (i) the relations among infinite-dilution solvation quantities leading to a novel self-consistent route to the calculation of the osmotic second Virial Coefficients, (ii) the new microstructural interpretation of the resulting osmotic second Virial Coefficients based on Kirkwood-Buff integrals, the unambiguous discrimination between short- and long-range contributions, and their limiting behavior as the solvent approaches its critical conditions, (iii) new rigorous expressions for the calculation of the osmotic second Virial Coefficients using standard reference thermodynamic data, and (iv) their underlying interdependence based on the constrained state variable invoked in the density expansion. We then invoke the proposed formalism to shed some light on the inaccuracies behind current calculations of osmotic second Virial Coefficients from molecular theory and simulation as well as macroscopic correlations. To advance the microscopic understanding and illustrate the functional relationship between the osmotic second Virial Coefficients, Henry’s law constant, and the solute-solvent intermolecular asymmetry as a source of solution non-ideality, we use data for the microstructural and thermodynamic behavior of infinitely dilute Lennard-Jones systems obtained self-consistently via integral equations calculations. The newly derived relationships leading to the proposed formalism offer novel routes for the accurate determination of osmotic second Virial Coefficients of any type of solutes in dilute solutions regardless of the type and nature of the intermolecular interactions. However, for illustration purposes in the current work, we dealt with aqueous solutions of simple gases to exploit the abundance of standard thermodynamic data for the orthobaric Henry’s law constant and solute distribution Coefficients, as well as the availability of results from molecular-based calculations and macroscopic correlations.We present a novel molecular-based approach for the determination of the osmotic second Virial Coefficients of gaseous solutes in dilute binary solutions, according to a recently proposed molecular thermodynamic formalism of gas solubility [A. A. Chialvo, J. Chem. Phys. 148, 174502 (2018) and Fluid Phase Equilib. 472, 94 (2018)]. We discuss relevant solvation fundamentals and derive new expressions including (i) the relations among infinite-dilution solvation quantities leading to a novel self-consistent route to the calculation of the osmotic second Virial Coefficients, (ii) the new microstructural interpretation of the resulting osmotic second Virial Coefficients based on Kirkwood-Buff integrals, the unambiguous discrimination between short- and long-range contributions, and their limiting behavior as the solvent approaches its critical conditions, (iii) new rigorous expressions for the calculation of the osmotic second Virial Coefficients using standard reference thermodynamic data, and (iv) their unde...
Long Meng - One of the best experts on this subject based on the ideXlab platform.
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prediction of the second cross Virial Coefficients of nonpolar binary mixtures
Fluid Phase Equilibria, 2005Co-Authors: Long Meng, Yuan-yuan DuanAbstract:Abstract The binary interaction parameter, kij, of 268 nonpolar mixtures were determined from the database of second cross Virial Coefficients containing 1728 experimental data points by fitting the second cross Virial Coefficients with a new correlation for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120] and classical mixing rules. Regularity distributions were found for both n-alkane/n-alkane binaries and fluorocarbon/fluorocarbon binaries. Correlations were developed following Tsonopoulos’ ideas [C. Tsonopoulos, Adv. Chem. Ser. 182 (1979) 143–162] with the quantity of binary compounds enlarged using Dymond's latest complication [J.H. Dymond, K.N. Marsh, R.C. Wilhoit, Virial Coefficients of Pure Gases and Mixtures, Subvolume B, Virial Coefficients of Mixtures, Series IV/21B, Landolt-Bornstein, 2002]. Correlations were also developed for inorganic/n-alkane binaries using new kij values. The predictions do not need any thermodynamic property parameters besides the carbon number. Comparisons with the existing correlations show that the present work is more accurate for nonpolar binary mixtures.
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Correlations for second and third Virial Coefficients of pure fluids
Fluid Phase Equilibria, 2004Co-Authors: Long Meng, Yuan-yuan DuanAbstract:Abstract A modified form of the well-known Tsonopoulos correlation for second Virial Coefficients was developed based on the corresponding-states principle. Comparisons with the new, high-quality experimental data and existing models show that the present correlation is more accurate, reliable and satisfactory for nonpolar compounds. The results also show that the present work is roughly equivalent to the Tsonopoulos and Weber correlations for second Virial Coefficients of polar fluids. The Weber correlation for the third Virial Coefficients was also improved since it did not well represent the experimental data of nonpolar gases. The new correlation gives a satisfactory fit for nonpolar compounds as the Orbey and Vera correlation did and can also accurately represent the literature data for the third Virial Coefficients of polar fluids, which was well represented by the Weber correlation. The two correlations for the second and third Virial Coefficients need the same additional parameters, such as the critical temperature, critical pressure, acentric factor and reduced dipole moment.
