1
|
van Westen T, Gross J. Double-Hard-Sphere perturbation theory: a perturbation theory that is less dependent on the value of the hard-sphere diameter. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2059410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart, Germany
| |
Collapse
|
2
|
van Westen T, Gross J. Accurate thermodynamics of simple fluids and chain fluids based on first-order perturbation theory and second virial coefficients: uv-theory. J Chem Phys 2021; 155:244501. [PMID: 34972377 DOI: 10.1063/5.0073572] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a simplification of our recently proposed uf-theory for describing the thermodynamics of simple fluids and fluids comprising short chain molecules. In its original form, the uf-theory interpolates the Helmholtz energy between a first-order f-expansion and first-order u-expansion as (effective) lower and upper bounds. We here replace the f-bound by a new, tighter (effective) lower bound. The resulting equation of state interpolates between a first-order u-expansion at high densities and another first-order u-expansion that is modified to recover the exact second virial coefficient at low densities. The theory merely requires the Helmholtz energy of the reference fluid, the first-order u-perturbation term, and the total perturbation contribution to the second virial coefficient as input. The revised theory-referred to as uv-theory-is thus simpler than the uf-theory but leads to similar accuracy, as we show for fluids with intermolecular pair interactions governed by a Mie potential. The uv-theory is thereby easier to extend to fluid mixtures and provides more flexibility in extending the model to non-spherical or chain-like molecules. The usefulness of the uv-theory for developing equation-of-state models of non-spherical molecules is here exemplified by developing an equation of state for Lennard-Jones dimers.
Collapse
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| |
Collapse
|
3
|
Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory. CONDENSED MATTER 2021. [DOI: 10.3390/condmat6030029] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to the Ornstein–Zernike equation in liquid state theory. The analytically solved Baxter’s adhesive hard sphere model is analyzed first by using coupling-parameter expansion. It was found that the expansion provides accurate approximations to solutions—including the liquid-vapor phase diagram—in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are obtained using analytical solutions within the mean spherical approximation for the hardcore Yukawa potential. However, numerical results indicate that the expansion converges in all regions in this model. Next, the convergence of the expansion is analyzed for the Lennard-Jones potential by using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two-phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. The results obtained for the generalized Lennard-Jones potential, with varying repulsive exponent, also compare well with the simulation data. Solution-spaces and the bifurcation of the solutions of the Ornstein–Zernike equation that are relevant to coupling-parameter expansion are also briefly discussed. All of these results taken together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.
Collapse
|
4
|
van Westen T. Algebraic second virial coefficient of the Mie m - 6 intermolecular potential based on perturbation theory. J Chem Phys 2021; 154:234502. [PMID: 34241261 DOI: 10.1063/5.0050659] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We propose several simple algebraic approximations for the second virial coefficient of fluids whose molecules interact by a generic Mie m - 6 intermolecular pair potential. In line with a perturbation theory, the parametric equations are formulated as the sum of a contribution due to a reference part of the intermolecular potential and a perturbation. Thereby, the equations provide a convenient (low-density) starting point for developing equation-of-state models of fluids or for developing similar approximations for the virial coefficient of (polymeric-)chain fluids. The choice of Barker and Henderson [J. Chem. Phys. 47, 4714 (1967)] and Weeks, Chandler, and Andersen [Phys. Rev. Lett. 25, 149 (1970); J. Chem. Phys. 54, 5237 (1971); and Phys. Rev. A 4, 1597 (1971)] for the reference part of the potential is considered. Our analytic approximations correctly recover the virial coefficient of the inverse-power potential of exponent m in the high-temperature limit and provide accurate estimates of the temperatures for which the virial coefficient equals zero or takes on its maximum value. Our description of the reference contribution to the second virial coefficient follows from an exact mapping onto the second virial coefficient of hard spheres; we propose a simple algebraic equation for the corresponding effective diameter of the hard spheres, which correctly recovers the low- and high-temperature scaling and limits of the reference fluid's second virial coefficient.
Collapse
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| |
Collapse
|
5
|
|
6
|
van Westen T, Gross J. Accurate first-order perturbation theory for fluids: uf-theory. J Chem Phys 2021; 154:041102. [PMID: 33514104 DOI: 10.1063/5.0031545] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We propose a new first-order perturbation theory that provides a near-quantitative description of the thermodynamics of simple fluids. The theory is based on the ansatz that the Helmholtz free energy is bounded below by a first-order Mayer-f expansion. Together with the rigorous upper bound provided by a first-order u-expansion, this brackets the actual free energy between an upper and (effective) lower bound that can both be calculated based on first-order perturbation theory. This is of great practical use. Here, the two bounds are combined into an interpolation scheme for the free energy. The scheme exploits the fact that a first-order Mayer-f perturbation theory is exact in the low-density limit, whereas the accuracy of a first-order u-expansion grows when density increases. This allows an interpolation between the lower "f"-bound at low densities and the upper "u" bound at higher liquid-like densities. The resulting theory is particularly well behaved. Using a density-dependent interpolating function of only two adjustable parameters, we obtain a very accurate representation of the full fluid-phase behavior of a Lennard-Jones fluid. The interpolating function is transferable to other intermolecular potential types, which is here shown for the Mie m-6 family of fluids. The extension to mixtures is simple and accurate without requiring any dependence of the interpolating function on the composition of the mixture.
Collapse
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| |
Collapse
|
7
|
Guérin H. First-order mean spherical approximation (FMSA) for the Buckingham Exp(αE, m) potential. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.112812] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
8
|
Gámez F, Rodríguez-Almeida LF, Trejos VM. Thermodynamics of two-dimensional molecular fluids: Discrete perturbation theory and Monte Carlo simulations. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2019.112293] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
|
9
|
Matyushov DV, Newton MD. Thermodynamics of Reactions Affected by Medium Reorganization. J Phys Chem B 2018; 122:12302-12311. [PMID: 30514079 DOI: 10.1021/acs.jpcb.8b08865] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.
Collapse
Affiliation(s)
- Dmitry V Matyushov
- Department of Physics and School of Molecular Sciences , Arizona State University , PO Box 871504, Tempe , Arizona 85287 , United States
| | - Marshall D Newton
- Brookhaven National Laboratory , Chemistry Department , Box 5000, Upton , New York 11973-5000 , United States
| |
Collapse
|
10
|
Sarhangi SM, Waskasi MM, Hashemianzadeh SM, Matyushov DV. Interfacial structural crossover and hydration thermodynamics of charged C 60 in water. Phys Chem Chem Phys 2018; 20:27069-27081. [PMID: 30328845 DOI: 10.1039/c8cp05422c] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Classical molecular dynamics simulations of the hydration thermodynamics, structure, and dynamics of water in hydration shells of charged buckminsterfullerenes are presented in this study. Charging of fullerenes leads to a structural transition in the hydration shell, accompanied by creation of a significant population of dangling O-H bonds pointing toward the solute. In contrast to the well accepted structure-function paradigm, this interfacial structural transition causes nearly no effect on either the dynamics of hydration water or on the solvation thermodynamics. Linear response to the solute charge is maintained despite significant structural changes in the hydration shell, and solvation thermodynamic potentials are nearly insensitive to the altering structure. Only solvation heat capacities, which are higher thermodynamic derivatives of the solvation free energy, indicate some sensitivity to the local hydration structure. We have separated the solvation thermodynamic potentials into direct solute-solvent interactions and restructuring of the hydration shell and analyzed the relative contributions of electrostatic and nonpolar interactions to the solvation thermodynamics.
Collapse
Affiliation(s)
- Setare Mostajabi Sarhangi
- Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science and Technology, Tehran 16846-13114, Iran
| | | | | | | |
Collapse
|
11
|
Trejos VM, Santos A, Gámez F. Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory. J Chem Phys 2018; 148:194505. [PMID: 30307191 DOI: 10.1063/1.5029375] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the two-dimensional square-well fluid in the Barker-Henderson framework. This equation of state is based on an approximate analytical radial distribution function for d-dimensional hard-sphere fluids (1 ≤ d ≤ 3) and is validated against existing and new simulation results. The so-obtained equation of state is implemented in a discrete perturbation theory able to account for general potential shapes. The prototypical Lennard-Jones and Yukawa fluids are tested in its two-dimensional version against available and new simulation data with semiquantitative agreement.
Collapse
Affiliation(s)
- Víctor M Trejos
- Instituto de Química, Universidad Nacional Autónoma de México, Apdo. Postal 70213, Coyoacán, 04510 Ciudad de México, Mexico
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 060006 Badajoz, Spain
| | - Francisco Gámez
- Department of Physical, Chemical and Natural Systems, Universidad Pablo de Olavide, 41013 Seville, Spain
| |
Collapse
|
12
|
Bacher AK, Schrøder TB, Dyre JC. The EXP pair-potential system. I. Fluid phase isotherms, isochores, and quasiuniversality. J Chem Phys 2018; 149:114501. [DOI: 10.1063/1.5043546] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andreas Kvist Bacher
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Thomas B. Schrøder
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C. Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| |
Collapse
|
13
|
Müller EA, Mejía A. Extension of the SAFT-VR Mie EoS To Model Homonuclear Rings and Its Parametrization Based on the Principle of Corresponding States. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2017; 33:11518-11529. [PMID: 28602088 DOI: 10.1021/acs.langmuir.7b00976] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The statistical associating fluid theory of variable range employing a Mie potential (SAFT-VR-Mie) proposed by Lafitte et al. (J. Chem Phys. 2013, 139, 154504) is one of the latest versions of the SAFT family. This particular version has been shown to have a remarkable capability to connect experimental determinations, theoretical calculations, and molecular simulations results. However, the theoretical development restricts the model to chains of beads connected in a linear fashion. In this work, the capabilities of the SAFT-VR Mie equation of state for modeling phase equilibria are extended for the case of planar ring compounds. This modification proposed replaces the Helmholtz energy of chain formation by an empirical contribution based on a parallelism to the second-order thermodynamic perturbation theory for hard sphere trimers. The proposed expression is given in terms of an extra parameter, χ, that depends on the number of beads, ms, and the geometry of the ring. The model is used to describe the phase equilibrium for planar ring compounds formed of Mie isotropic segments for the cases of ms equals to 3, 4, 5 (two configurations), and 7 (two configurations). The resulting molecular model is further parametrized, invoking a corresponding states principle resulting in sets of parameters that can be used indistinctively in theoretical calculations or in molecular simulations without any further refinements. The extent and performance of the methodology has been exemplified by predicting the phase equilibria and vapor pressure curves for aromatic hydrocarbons (benzene, hexafluorobenzene, toluene), heterocyclic molecules (2,5-dimethylfuran, sulfolane, tetrahydro-2H-pyran, tetrahydrofuran), and polycyclic aromatic hydrocarbons (naphthalene, pyrene, anthracene, pentacene, and coronene). An important aspect of the theory is that the parameters of the model can be used directly in molecular dynamics (MD) simulations to calculate equilibrium phase properties and interfacial tensions with an accuracy that rivals other coarse grained and united atom models, for example, liquid densities, are predicted, with a maximum absolute average deviation of 3% from both the theory and the MD simulations, while the interfacial tension is predicted, with a maximum absolute average of 8%. The extension to mixtures is exemplified by considering a binary system of hexane (chain fluid) and tetrahydro-2H-pyran (ring fluid).
Collapse
Affiliation(s)
- Erich A Müller
- Department of Chemical Engineering, Imperial College London , South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Andrés Mejía
- Departamento de Ingeniería Química, Universidad de Concepción POB 160 - C, Correo 3, Concepción, Chile
| |
Collapse
|
14
|
van Westen T, Gross J. A critical evaluation of perturbation theories by Monte Carlo simulation of the first four perturbation terms in a Helmholtz energy expansion for the Lennard-Jones fluid. J Chem Phys 2017; 147:014503. [DOI: 10.1063/1.4991008] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| |
Collapse
|
15
|
Wang LY, Gu F, Wang HJ, Sun ZL. Pressure Profile for an Associating Lennard-Jones Fluid Confined in a Spherical Cavity. J Phys Chem B 2017; 121:2142-2152. [PMID: 28191841 DOI: 10.1021/acs.jpcb.6b09861] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the pressure tensor of an associating Lennard-Jones (LJ) fluid confined in a spherical cavity of hard wall, where a high-order density correlation has been taken into account. To give the two-body association potential for calculating the pressure tensor, an angle-average of site-site attraction over all orientations of two particles is performed. Furthermore, the classical density functional theory is employed to obtain the density profile of the confined fluid, by which the normal and tangential pressure profiles are illustrated under various conditions to show the dependence of the pressure tensor on the association strength, number of associating sites, radius of cavity, and bulk density. As an application, the corresponding surface tension is calculated. It is shown that under a strong association interaction (both association strength and the number of associating sites are large), the pressure profiles are depleted from the wall of the cavity instead of the oscillatory behavior under a weak association interaction. Such a tendency is mainly determined by the competition between association interaction and excluded volume interaction. Therefore, the aggregation state and related properties of an associating LJ fluid within a confinement of nanoscale can be efficiently regulated by the association interaction.
Collapse
Affiliation(s)
| | | | | | - Zong-Li Sun
- Science and Technology College, North China Electric Power University , Baoding 071051, P. R. China
| |
Collapse
|
16
|
Desgranges C, Delhommelle J. Ginzburg-Landau free energy for molecular fluids: Determination and coarse-graining. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2016.12.052] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
17
|
Labík S, Malijevský A, Kolafa J. Virial coefficients of the additive hard-sphere binary mixtures up to the eighth. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1226441] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Stanislav Labík
- Department of Physical Chemistry, University of Chemistry and Technology, 166 28 Prague 6, Czech Republic
| | - Anatol Malijevský
- Department of Physical Chemistry, University of Chemistry and Technology, 166 28 Prague 6, Czech Republic
| | - Jiří Kolafa
- Department of Physical Chemistry, University of Chemistry and Technology, 166 28 Prague 6, Czech Republic
| |
Collapse
|
18
|
Dyre JC. Simple liquids' quasiuniversality and the hard-sphere paradigm. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:323001. [PMID: 27345623 DOI: 10.1088/0953-8984/28/32/323001] [Citation(s) in RCA: 72] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.
Collapse
Affiliation(s)
- Jeppe C Dyre
- "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| |
Collapse
|
19
|
Paricaud P. Extension of the BMCSL equation of state for hard spheres to the metastable disordered region: Application to the SAFT approach. J Chem Phys 2015; 143:044507. [PMID: 26233145 DOI: 10.1063/1.4927148] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A simple modification of the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is proposed for an application to the metastable disordered region. The new model has a positive pole at the jamming limit and can accurately describe the molecular simulation data of pure hard in the stable fluid region and along the metastable branch. The new model has also been applied to binary mixtures hard spheres, and an excellent description of the fluid and metastable branches can be obtained by adjusting the jamming packing fraction. The new model for hard sphere mixtures can be used as the repulsive term of equations of state for real fluids. In this case, the modified equations of state give very similar predictions of thermodynamic properties as the original models, and one can remove the multiple liquid density roots observed for some versions of the Statistical Associating Fluid Theory (SAFT) at low temperature without any modification of the dispersion term.
Collapse
Affiliation(s)
- P Paricaud
- Unité de Chimie et Procédés, ENSTA-ParisTech, Université Paris-Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau cedex, France
| |
Collapse
|
20
|
Ratkova EL, Palmer DS, Fedorov MV. Solvation thermodynamics of organic molecules by the molecular integral equation theory: approaching chemical accuracy. Chem Rev 2015; 115:6312-56. [PMID: 26073187 DOI: 10.1021/cr5000283] [Citation(s) in RCA: 135] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Ekaterina L Ratkova
- †G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya Street 1, Ivanovo 153045, Russia.,‡The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany
| | - David S Palmer
- ‡The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany.,§Department of Chemistry, University of Strathclyde, Thomas Graham Building, 295 Cathedral Street, Glasgow, Scotland G1 1XL, United Kingdom
| | - Maxim V Fedorov
- ‡The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany.,∥Department of Physics, Scottish Universities Physics Alliance (SUPA), University of Strathclyde, John Anderson Building, 107 Rottenrow East, Glasgow G4 0NG, United Kingdom
| |
Collapse
|
21
|
Guérin H. Unified SAFT-VR theory for simple and chain fluids formed of square-well, triangular-well, Sutherland and Mie segments. J Mol Liq 2015. [DOI: 10.1016/j.molliq.2015.01.001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
22
|
Zhao S, Liu Y, Chen X, Lu Y, Liu H, Hu Y. Unified Framework of Multiscale Density Functional Theories and Its Recent Applications. MESOSCALE MODELING IN CHEMICAL ENGINEERING PART II 2015. [DOI: 10.1016/bs.ache.2015.10.001] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
|
23
|
Ghobadi AF, Elliott JR. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces. J Chem Phys 2014; 141:024708. [DOI: 10.1063/1.4886398] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
|
24
|
Gámez F. Thermodynamic of fluids from a general equation of state: The molecular discrete perturbation theory. J Chem Phys 2014; 140:234504. [DOI: 10.1063/1.4882897] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
|
25
|
Zhou S. Convergence and low temperature adaptability analysis of the high temperature series expansion of the free energy. J Chem Phys 2014; 139:124111. [PMID: 24089754 DOI: 10.1063/1.4821762] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By appealing to the coupling parameter series expansion to calculate the first seven perturbation coefficients of the high temperature series expansion (HTSE) of the free energy, analysis of convergence and low temperature adaptability of the HTSE in calculating fluid thermodynamic properties is performed for the first time; the fluid thermodynamic properties considered include critical parameters, vapor-liquid coexistence curve, thermodynamic characteristic functions, chemical potential, pressure, and constant volume excess heat capacity. To proceed with the analysis, a well known square well model is used as sample; the well widths considered range over a wide interval, and the relevant temperatures amenable to simulation calculations (used as "exact" results to analyze the HTSE) can be both very high and very low. The main discoveries reached are summarized as follows: (1) The HTSE usually converges at the 4th-order truncation, but with decrease of the temperature considered, the lowest truncation order, which makes the HTSE to converge, tends to rise. As a conservative estimate, it is considered that the HTSE always converges for reduced temperature T* higher than 0.25, whereas for T* < 0.25 there appear signs indicating that the HTSE may diverge from the 7th-order truncation. (2) Within the temperature interval with T* ≥ 0.5, the HTSE converges approximately to the correct solution, and the HTSE can be reliably used to calculate the fluid thermodynamic properties, and within this temperature interval, the 4th-order truncation is enough; whereas for T* < 0.5, such as within the temperature interval with 0.275 ≤ T* ≤ 0.355, although the HTSE does converge, it does not converge to the correct solution, and the deviations between the HTSE calculations and MC simulations become an ever-prominent issue with the rising of the density, and the slopes of the thermodynamic properties over density are not satisfactorily represented. As a result, the HTSE is not suited for calculations for temperature interval T* < 0.5.
Collapse
Affiliation(s)
- Shiqi Zhou
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| |
Collapse
|
26
|
Forte E, Haslam AJ, Jackson G, Müller EA. Effective coarse-grained solid–fluid potentials and their application to model adsorption of fluids on heterogeneous surfaces. Phys Chem Chem Phys 2014; 16:19165-80. [PMID: 24872092 DOI: 10.1039/c4cp00670d] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
In the present contribution we emphasise the necessity of using an adequate averaging procedure to obtain effective fluid–surface potentials. A procedure to develop free-energy-averaged fluid–surface potentials retaining the important temperature dependence of the coarse-grained particle-surface interaction is described.
Collapse
Affiliation(s)
- Esther Forte
- Department of Chemical Engineering
- Imperial College London
- London SW7 2AZ, UK
- BP Centre for Petroleum and Surface Chemistry (BP-CPSC)
- Department of Chemistry
| | - Andrew J. Haslam
- Department of Chemical Engineering
- Imperial College London
- London SW7 2AZ, UK
- Qatar Carbonates and Carbon Storage Research Centre (QCCSRC)
- Imperial College London
| | - George Jackson
- Department of Chemical Engineering
- Imperial College London
- London SW7 2AZ, UK
| | - Erich A. Müller
- Department of Chemical Engineering
- Imperial College London
- London SW7 2AZ, UK
| |
Collapse
|
27
|
Ghobadi AF, Elliott JR. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. I. Homogeneous fluids. J Chem Phys 2013; 139:234104. [DOI: 10.1063/1.4838457] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
|
28
|
Dyre JC. Isomorphs, hidden scale invariance, and quasiuniversality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042139. [PMID: 24229147 DOI: 10.1103/physreve.88.042139] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Revised: 08/16/2013] [Indexed: 06/02/2023]
Abstract
This paper first establishes an approximate scaling property of the potential-energy function of a classical liquid with good isomorphs (a Roskilde-simple liquid). This "pseudohomogeneous" property makes explicit that-and in which sense-such a system has a hidden scale invariance. The second part of the paper gives a potential-energy formulation of the quasiuniversality of monatomic Roskilde-simple liquids, which was recently rationalized in terms of the existence of a quasiuniversal single-parameter family of reduced-coordinate constant-potential-energy hypersurfaces [J. C. Dyre, Phys. Rev. E 87, 022106 (2013)]. The new formulation involves a quasiuniversal reduced-coordinate potential-energy function. A few consequences of this are discussed.
Collapse
Affiliation(s)
- Jeppe C Dyre
- DNRF Center "Glass and Time,"IMFUFA, Dept. of Sciences, Roskilde University, P. O. Box 260, DK-4000 Roskilde, Denmark
| |
Collapse
|
29
|
Zhou S, Solana JR. The First Three Coefficients in the High Temperature Series Expansion of Free Energy for Simple Potential Models with Hard-Sphere Cores and Continuous Tails. J Phys Chem B 2013; 117:9305-13. [DOI: 10.1021/jp405406f] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Shiqi Zhou
- School of Physics and Electronics, Central South University, Changsha, Hunan, 410083, People’s
Republic of China
| | - J. R. Solana
- Departamento
de Física Aplicada, Universidad de Cantabria, 39005 Santander, España
| |
Collapse
|
30
|
Zhou S, Solana JR. Monte Carlo and theoretical calculations of the first four perturbation coefficients in the high temperature series expansion of the free energy for discrete and core-softened potential models. J Chem Phys 2013; 138:244115. [DOI: 10.1063/1.4811285] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
31
|
Shen G, Ji X, Lu X. A hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores. J Chem Phys 2013; 138:224706. [DOI: 10.1063/1.4808160] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
|
32
|
Hernandez DA, Domínguez H. Structural and thermodynamic behavior of alkane chains at the liquid/vapor interface. J Chem Phys 2013; 138:134702. [DOI: 10.1063/1.4798346] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
|
33
|
Gámez F, Benavides AL. Perturbation theory for non-spherical fluids based on discretization of the interactions. J Chem Phys 2013; 138:124901. [DOI: 10.1063/1.4794783] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
|
34
|
Bøhling L, Veldhorst AA, Ingebrigtsen TS, Bailey NP, Hansen JS, Toxvaerd S, Schrøder TB, Dyre JC. Do the repulsive and attractive pair forces play separate roles for the physics of liquids? JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:032101. [PMID: 23248158 DOI: 10.1088/0953-8984/25/3/032101] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
According to standard liquid-state theory repulsive and attractive pair forces play distinct roles for the physics of liquids. This paradigm is put into perspective here by demonstrating a continuous series of pair potentials that have virtually the same structure and dynamics, although only some of them have attractive forces of significance. Our findings reflect the fact that the motion of a given particle is determined by the total force on it, whereas the quantity usually discussed in liquid-state theory is the individual pair force.
Collapse
Affiliation(s)
- Lasse Bøhling
- DNRF Centre 'Glass and Time', IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | | | | | | | | | | | | | | |
Collapse
|
35
|
Improved analytical thermodynamic properties of the triangular-well fluid from perturbation theory. J Mol Liq 2012. [DOI: 10.1016/j.molliq.2012.03.014] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
36
|
Rodríguez-López T, del Río F. Thermodynamic properties of non-conformal soft-sphere fluids with effective hard-sphere diameters. Phys Chem Chem Phys 2012; 14:1440-8. [PMID: 22158949 DOI: 10.1039/c1cp22880c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
In this work we study a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids. This type of soft spheres is of interest because they represent quite accurately the effective intermolecular repulsion in fluid substances and also because they exhibit interesting properties. The thermodynamics of the soft-sphere fluids is obtained via an effective hard-sphere diameter approach that leads to a compact and accurate equation of state. The virial coefficients of soft spheres are shown to follow quite simple relationships that are incorporated into the equation of state. The approach followed exhibits the rescaling of the density that produces a unique equation for all systems and temperatures. The scaling is carried through to the level of the structure of the fluids.
Collapse
Affiliation(s)
- Tonalli Rodríguez-López
- Laboratorio de Termodinámica, Departamento de Física, Universidad Autónoma Metropolitana, Iztapalapa, México DF, Mexico.
| | | |
Collapse
|
37
|
Guérin H. Simple analytic equations of state for the generalized hard-core Mie(α, β) and Mie(α, β) fluids from perturbation theory. J Mol Liq 2011. [DOI: 10.1016/j.molliq.2011.09.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
38
|
Toxvaerd S, Dyre JC. Role of the first coordination shell in determining the equilibrium structure and dynamics of simple liquids. J Chem Phys 2011; 135:134501. [DOI: 10.1063/1.3643123] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
|
39
|
Benavides AL, Gámez F. Perturbation theory for multipolar discrete fluids. J Chem Phys 2011; 135:134511. [DOI: 10.1063/1.3646733] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
|
40
|
|
41
|
Ayadim A, Amokrane S. Binary Mixture of Nonadditive Hard Spheres Adsorbed in a Slit Pore: A Study of the Population Inversion by the Integral Equations Theory. J Phys Chem B 2010; 114:16824-31. [DOI: 10.1021/jp107157a] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- A. Ayadim
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010 Créteil Cedex, France
| | - S. Amokrane
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010 Créteil Cedex, France
| |
Collapse
|
42
|
Zhou S. Free energy density functional for adsorption of fluids in nanopores. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2010; 26:17037-17047. [PMID: 20954714 DOI: 10.1021/la102341a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena.
Collapse
Affiliation(s)
- Shiqi Zhou
- State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China.
| |
Collapse
|
43
|
Abstract
A local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) is proposed to provide a rapid route for obtaining thermodynamic and structural information for any thermodynamically stable or metastable state points in the bulk phase diagram without recourse to traditional thermodynamic integration, and extensive NVT-Monte Carlo simulations are performed on a recently proposed honeycomb potential in three dimensions to test the theory's reliability. The simulated quantities include radial distribution function (rdf) and excess internal energy, pressure, excess chemical potential, and excess Helmholtz free energy. It is demonstrated that (i) the theory reproduces the rdf very satisfactorily only if the bulk state does not enter deep into a two phases coexistence region; (ii) the excess internal energy is the only one of the four thermodynamic quantities investigated amenable to the most accurate prediction by the present theory, and the simulated pressure is somewhat overestimated by the theoretical calculations, but the deviation tends to vanish along with rising of the temperature; (iii) using the structural functions from the present local self-consistent OZ IET, a previously derived local expression, due to the present author, achieves even a higher accuracy in calculating for the excess chemical potential than the exact virial pressure formula for the pressure, and the resulting excess Helmholtz free energy is in surprisingly same with the simulation results due to offset of the errors. Based on the above observations, it is suggested that it may be a good procedure to integrate the theoretical excess internal energy along the isochors to get the excess Helmholtz free energy, which is then fitted to a polynomial to be used for calculation of all of other thermodynamic quantities in the framework of the OZ IET.
Collapse
Affiliation(s)
- Shiqi Zhou
- State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China.
| |
Collapse
|
44
|
Guérin H. A new simple analytic equation of state for square-well chain fluids with variable width, 1.1<λ<2, based on perturbation theory and an analytic representation of the hard-sphere radial distribution function gHS(r). J Mol Liq 2010. [DOI: 10.1016/j.molliq.2010.07.008] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
45
|
Zhou S. New free energy density functional and application to core-softened fluid. J Chem Phys 2010; 132:194112. [DOI: 10.1063/1.3435206] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
|
46
|
Amokrane S, Ayadim A, Malherbe J, Regnaut C. Comment on the contact values in asymmetric hard-sphere mixtures (Mol. Phys. 107, 685 (2009); Mol. Phys. 106, 607 (2008)). Mol Phys 2009. [DOI: 10.1080/00268970903362318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
47
|
Zhou S, Solana JR. Comprehensive investigation about the second order term of thermodynamic perturbation expansion. J Chem Phys 2009; 131:134106. [DOI: 10.1063/1.3242801] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
48
|
Zhou S. A new scheme for perturbation contribution in density functional theory and application to solvation force and critical fluctuations. J Chem Phys 2009; 131:134702. [DOI: 10.1063/1.3242717] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
|