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Heyes DM, Dini D, Pieprzyk S, Brańka AC, Costigliola L. Models to predict configurational adiabats of Lennard-Jones fluids and their transport coefficients. J Chem Phys 2024; 161:084502. [PMID: 39193943 DOI: 10.1063/5.0225650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2024] [Accepted: 08/08/2024] [Indexed: 08/29/2024] Open
Abstract
A comparison is made between three simple approximate formulas for the configurational adiabat (i.e., constant excess entropy, sex) lines in a Lennard-Jones (LJ) fluid, one of which is an analytic formula based on a harmonic approximation, which was derived by Heyes et al. [J. Chem. Phys. 159, 224504 (2023)] (analytic isomorph line, AIL). Another is where the density is normalized by the freezing density at that temperature (freezing isomorph line, FIL). It is found that the AIL formula and the average of the freezing density and the melting density ("FMIL") are configurational adiabats at all densities essentially down to the liquid-vapor binodal. The FIL approximation departs from a configurational adiabat in the vicinity of the liquid-vapor binodal close to the freezing line. The self-diffusion coefficient, D, shear viscosity, ηs, and thermal conductivity, λ, in macroscopic reduced units are essentially constant along the AIL and FMIL at all fluid densities and temperatures, but departures from this trend are found along the FIL at high liquid state densities near the liquid-vapor binodal. This supports growing evidence that for simple model systems with no or few internal degrees of freedom, isodynes are lines of constant excess entropy. It is shown that for the LJ fluid, ηs and D can be predicted accurately by an essentially analytic procedure from the high temperature limiting inverse power fluid values (apart from at very low densities), and this is demonstrated quite well also for the experimental argon viscosity.
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Affiliation(s)
- D M Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - S Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - L Costigliola
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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2
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Khrapak SA, Khrapak AG. Freezing density scaling of transport coefficients in the Weeks-Chandler-Andersen fluid. J Chem Phys 2024; 160:134504. [PMID: 38557849 DOI: 10.1063/5.0199310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 03/13/2024] [Indexed: 04/04/2024] Open
Abstract
It is shown that the transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of the Weeks-Chandler-Andersen (WCA) fluid along isotherms exhibit a freezing density scaling (FDS). The functional form of this FDS is essentially the same or closely related to those in the Lennard-Jones fluid, hard-sphere fluid, and some liquefied noble gases. This proves that this FDS represents a quasi-universal corresponding state principle for simple classical fluids with steep interactions. Some related aspects, such as a Stokes-Einstein relation without a hydrodynamic diameter and gas-to-liquid dynamical crossover, are briefly discussed. Simple fitting formulas for the transport coefficients of the dense WCA fluid are suggested.
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Affiliation(s)
- S A Khrapak
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
| | - A G Khrapak
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
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Heyes DM, Dini D, Pieprzyk S, Brańka AC. Departures from perfect isomorph behavior in Lennard-Jones fluids and solids. J Chem Phys 2023; 158:134502. [PMID: 37031156 DOI: 10.1063/5.0143651] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2023] Open
Abstract
Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼ T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant.
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Affiliation(s)
- D. M. Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D. Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - S. Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - A. C. Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
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4
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Attia E, Dyre JC, Pedersen UR. Comparing four hard-sphere approximations for the low-temperature WCA melting line. J Chem Phys 2022; 157:034502. [DOI: 10.1063/5.0097593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By combining interface-pinning simulations with numerical integration of the Clausius–Clapeyron equation, we accurately determine the melting-line coexistence pressure and fluid/crystal densities of the Weeks–Chandler–Andersen system, covering four decades of temperature. The data are used for comparing the melting-line predictions of the Boltzmann, Andersen–Weeks–Chandler, Barker–Henderson, and Stillinger hard-sphere approximations. The Andersen–Weeks–Chandler and Barker–Henderson theories give the most accurate predictions, and they both work excellently in the zero-temperature limit for which analytical expressions are derived here.
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Affiliation(s)
- Eman Attia
- 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
| | - Ulf R. Pedersen
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Primitive noble gases sampled from ocean island basalts cannot be from the Earth's core. Nat Commun 2022; 13:3770. [PMID: 35773267 PMCID: PMC9247082 DOI: 10.1038/s41467-022-31588-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Accepted: 06/23/2022] [Indexed: 11/09/2022] Open
Abstract
Noble gas isotopes in plumes require a source of primitive volatiles largely isolated in the Earth for 4.5 Gyrs. Among the proposed reservoirs, the core is gaining interest in the absence of robust geochemical and geophysical evidence for a mantle source. This is supported by partitioning data showing that sufficient He and Ne could have been incorporated into the core to source plumes today. Here we perform ab initio calculations on the partitioning of He, Ne, Ar, Kr and Xe between liquid iron and silicate melt under core forming conditions. For He our results are consistent with previous studies allowing for substantial amounts of He in the core. In contrast, the partition coefficient for Ne is three orders of magnitude lower than He. This very low partition coefficient would result in a 3He/22Ne ratio of ~103 in the core, far higher than observed in ocean island basalts (OIBs). We conclude that the core is not the source of noble gases in OIBs.
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Hedayati A, Feyzi F. CO2-binding organic liquids for high pressure CO2 absorption: Statistical mixture design approach and thermodynamic modeling of CO2 solubility using LJ-Global TPT2 EoS. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.116396] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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Fai TG, Taylor JM, Virga EG, Zheng X, Palffy-Muhoray P. Leaky cell model of hard spheres. J Chem Phys 2021; 154:104505. [PMID: 33722050 DOI: 10.1063/5.0037442] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan-Starling and Percus-Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials.
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Affiliation(s)
- Thomas G Fai
- Department of Mathematics and Volen Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Jamie M Taylor
- Basque Center for Applied Mathematics (BCAM), Bilbao, Bizkaia, Spain
| | | | - Xiaoyu Zheng
- Department of Mathematical Sciences, Kent State University, Kent, Ohio, 44242, USA
| | - Peter Palffy-Muhoray
- Department of Mathematical Sciences, Kent State University, Kent, Ohio, 44242, USA
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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.
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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
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Mirzaeinia A, Feyzi F. A perturbed-chain equation of state based on Wertheim TPT for the fully flexible LJ chains in the fluid and solid phases. J Chem Phys 2020; 152:134502. [PMID: 32268737 DOI: 10.1063/1.5134511] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
In the framework of thermodynamic perturbation theory (TPT), a new perturbed-chain equation of state (EOS) is presented for a fully flexible Lennard-Jones (LJ) chain system. The EOS is the sum of repulsive and perturbation contributions. The reference term of the EOS is derived based on first- and second-order TPT of Wertheim for the chains interacting with each other through the Weeks-Chandler-Anderson potential model. In order to derive the perturbation term, we have used the radial distribution function of the hard-chain system with a chain range of m = 2-10 and packing fraction range of η = 0.10-0.72, which cover the entire density range from vapor to solid phases. The performance of the EOS is tested against simulation data of the compressibility factor, residual internal energy, and phase equilibrium. A close agreement was observed across all cases. The EOS has three pure component parameters and is able to describe the global vapor-liquid-solid phase diagram of the LJ chain.
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Affiliation(s)
- Ali Mirzaeinia
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
| | - Farzaneh Feyzi
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
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Abolala M, Peyvandi K, Varaminian F, Hashemianzadeh SM. Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation. Mol Phys 2020. [DOI: 10.1080/00268976.2019.1582813] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Mostafa Abolala
- Gas Hydrate Research Laboratory, Faculty of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
| | - Kiana Peyvandi
- Gas Hydrate Research Laboratory, Faculty of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
| | - Farshad Varaminian
- Gas Hydrate Research Laboratory, Faculty of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
| | - Seyed Majid Hashemianzadeh
- Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science and Technology, Tehran, Iran
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11
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Maffioli L, Clisby N, Frascoli F, Todd BD. Computation of the equilibrium three-particle entropy for dense atomic fluids by molecular dynamics simulation. J Chem Phys 2019; 151:164102. [PMID: 31675868 DOI: 10.1063/1.5124715] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
We have computed the two- and three-particle contribution to the entropy of a Weeks-Chandler-Andersen fluid via molecular dynamics simulations. The three-particle correlation function and entropy were computed with a new method which simplified the calculation. Results are qualitatively similar to Lennard-Jones systems. We observed a numerical instability in the three-particle contribution. This phenomenon has been previously detected when the traditional method is used; thus, it is likely to be intrinsic in the computation. While the effect of statistical fluctuations can be removed through an extrapolation procedure, the discretization error due to the finite bin size is more difficult to characterize. With a correct choice of the bin size, a good estimate of the three-particle entropy contribution can be achieved at any state, even close to the freezing point. We observed that, despite the fact that the magnitude of the three-particle contribution increases significantly compared to that of the two-particle contribution as freezing is approached, the error induced from overestimation of the excess entropy by the two- and three-body terms exceeds that induced by approximating the excess entropy with the two body term alone.
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Affiliation(s)
- Luca Maffioli
- Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Nathan Clisby
- Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - Federico Frascoli
- Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| | - B D Todd
- Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
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12
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Shevkunov SV. Water Vapor Nucleation on a Surface with Nanoscopic Grooves. 2. Features of Thermodynamic Behavior. COLLOID JOURNAL 2019. [DOI: 10.1134/s1061933x19030141] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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13
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Mirzaeinia A, Feyzi F, Hashemianzadeh SM. Equations of state for the fully flexible WCA chains in the fluid and solid phases based on Wertheims-TPT2. J Chem Phys 2018; 148:104502. [PMID: 29544293 DOI: 10.1063/1.5018789] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
Based on Wertheim's second order thermodynamic perturbation theory (TPT2), equations of state (EOSs) are presented for the fluid and solid phases of tangent, freely jointed spheres. It is considered that the spheres interact with each other through the Weeks-Chandler-Anderson (WCA) potential. The developed TPT2 EOS is the sum of a monomeric reference term and a perturbation contribution due to bonding. MC NVT simulations are performed to determine the structural properties of the reference system in the reduced temperature range of 0.6 ≤ T* ≤ 4.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. Mathematical functions are fitted to the simulation results of the reference system and employed in the framework of Wertheim's theory to develop TPT2 EOSs for the fluid and solid phases. The extended EOSs are compared to the MC NPT simulation results of the compressibility factor and internal energy of the fully flexible chain systems. Simulations are performed for the WCA chain system for chain lengths of up to 15 at T* = 1.0, 1.5, 2.0, 3.0. Across all the reduced temperatures, the agreement between the results of the TPT2 EOS and MC simulations is remarkable. Overall Average Absolute Relative Percent Deviation at T* = 1.0 for the compressibility factor in the entire chain lengths we covered is 0.51 and 0.77 for the solid and fluid phases, respectively. Similar features are observed in the case of residual internal energy.
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Affiliation(s)
- Ali Mirzaeinia
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
| | - Farzaneh Feyzi
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
| | - Seyed Majid Hashemianzadeh
- Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science and Technology, Tehran 16846-13114, Iran
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