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Knudsen PA, Heyes DM, Niss K, Dini D, Bailey NP. Invariant dynamics in a united-atom model of an ionic liquid. J Chem Phys 2024; 160:034503. [PMID: 38230811 DOI: 10.1063/5.0177373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 12/11/2023] [Indexed: 01/18/2024] Open
Abstract
We study a united-atom model of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl)sulfonylamide to determine to what extent there exist curves in the phase diagram along which the microscopic dynamics are invariant when expressed in dimensionless, or reduced, form. The initial identification of these curves, termed isodynes, is made by noting that contours of reduced shear viscosity and reduced self-diffusion coefficient coincide to a good approximation. Choosing specifically the contours of reduced viscosity as nominal isodynes, further simulations were carried out for state points on these, and other aspects of dynamics were investigated to study their degree of invariance. These include the mean-squared displacement, shear-stress autocorrelation function, and various rotational correlation functions. These were invariant to a good approximation, with the main exception being rotations of the anion about its long axis. The dynamical features that are invariant have in common that they are aspects that would be relevant for a coarse-grained description of the system; specifically, removing the most microscopic degrees of freedom in principle leads to a simplification of the potential energy landscape, which allows for the existence of isodynes.
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Affiliation(s)
- Peter A Knudsen
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - David M Heyes
- Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Kristine Niss
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Daniele Dini
- Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Nicholas P Bailey
- "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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Dmitryuk NA, Mistryukova LA, Kryuchkov NP, Khrapak SA, Yurchenko SO. Diffusion mobility increases linearly on liquid binodals above triple point. Sci Rep 2023; 13:2815. [PMID: 36797382 PMCID: PMC9935557 DOI: 10.1038/s41598-022-26390-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Accepted: 12/14/2022] [Indexed: 02/18/2023] Open
Abstract
Self-diffusion in fluids has been thoroughly studied numerically, but even for simple liquids just a few scaling relationships are known. Relations between diffusion, excitation spectra, and character of the interparticle interactions remain poorly understood. Here, we show that diffusion mobility of particles in simple fluids increases linearly on the liquid branch of the liquid-gas binodal, from the triple point almost up to the critical point. With molecular dynamics simulations, we considered bulk systems of particles interacting via a generalised Lennard-Jones potential, as well as ethane. Using a two-oscillator model for the analysis of excitations, we observed that the mobility (inverse diffusion) coefficient on the liquid-gas binodal increases linearly above the triple point until the dispersion of high-frequency spectra has a solid-like (oscillating) shape. In terms of a separate mode analysis (of longitudinal and transverse modes), this corresponds to crossed modes in the intermediate range of wavenumbers q, between the hydrodynamic regime (small q) and the regime of individual particle motion (large q). The results should be interesting for a broad community in physics and chemistry of fluids, since self-diffusion is among the most fundamental transport phenomena, important for prospective chemical technologies, micro-, nanofluidics, and biotechnologies.
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Affiliation(s)
- Nikita A. Dmitryuk
- grid.61569.3d0000 0001 0405 5955Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, Moscow, Russia 105005
| | - Lucia A. Mistryukova
- grid.61569.3d0000 0001 0405 5955Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, Moscow, Russia 105005
| | - Nikita P. Kryuchkov
- grid.61569.3d0000 0001 0405 5955Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, Moscow, Russia 105005
| | - Sergey A. Khrapak
- grid.61569.3d0000 0001 0405 5955Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, Moscow, Russia 105005
| | - Stanislav O. Yurchenko
- grid.61569.3d0000 0001 0405 5955Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, Moscow, Russia 105005
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3
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Khrapak SA, Khrapak A. Freezing density scaling of fluid transport properties: Application to liquified noble gases. J Chem Phys 2022; 157:014501. [DOI: 10.1063/5.0096947] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A freezing density scaling of transport properties of the Lennard-Jones fluid is rationalized in terms of the Rosenfeld's excess entropy scaling and isomorph theory of Roskilde-simple systems. Then, it is demonstrated that the freezing density scaling operates reasonably well for viscosity and thermal conductivity coefficients of liquid argon, krypton, and xenon. Quasi-universality of the reduced transport coefficients at their minima and at freezing conditions is discussed. The magnitude of the thermal conductivity coefficient at the freezing point is shown to agree remarkably well with the prediction of the vibrational model of thermal transport in dense fluids.
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Affiliation(s)
- Sergey A. Khrapak
- Complex Plasma, FSBSI Joint Institute for High Temperatures of the Russian Academy of Sciences, Russia
| | - Alexey Khrapak
- Theoretical Department, Joint Institute for High Temperatures RAS, Russia
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5
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Khrapak SA, Khrapak AG. Freezing Temperature and Density Scaling of Transport Coefficients. J Phys Chem Lett 2022; 13:2674-2678. [PMID: 35302377 DOI: 10.1021/acs.jpclett.2c00408] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
It is demonstrated that the freezing density scaling of transport coefficients in fluids, similar to the freezing temperature scaling, originates from the quasi-universal excess entropy scaling approach proposed by Rosenfeld. The freezing density scaling has a considerably wider applicability domain on the phase diagram of Lennard-Jones and related systems. As an illustration of its predictive power, we show that it reproduces with an excellent accuracy the shear viscosity coefficients of saturated liquid argon, krypton, xenon, and methane.
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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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6
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Knudsen S, Todd BD, Dyre JC, Hansen JS. Generalized hydrodynamics of the Lennard-Jones liquid in view of hidden scale invariance. Phys Rev E 2021; 104:054126. [PMID: 34942805 DOI: 10.1103/physreve.104.054126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Accepted: 10/12/2021] [Indexed: 11/07/2022]
Abstract
In recent years lines along which structure and dynamics are invariant to a good approximation, so-called isomorphs, have been identified in the thermodynamic phase diagrams of several model liquids and solids. This paper reports computer simulation data of the transverse and longitudinal collective dynamics at different length scales along an isomorph of the Lennard-Jones system. Our findings are compared to corresponding results along an isotherm and an isochore. Confirming the theoretical prediction, the reduced-unit dynamics of the transverse momentum density is invariant to a good approximation along the isomorph on all time and length scales. Likewise, the wave-vector dependent shear-stress autocorrelation function is found to be isomorph invariant (with minor deviations at very short times). A similar invariance is not seen along the isotherm or the isochore. Using a spatially nonlocal hydrodynamic model for the transverse momentum-density time-autocorrelation function, the macroscopic shear viscosity and its wave dependence are determined, demonstrating that the shear viscosity is isomorphic invariant on all length scales studied. This analysis implies the existence of a length scale that is isomorph invariant in reduced units, i.e., which characterizes each isomorph. The transverse sound-wave velocity, the Maxwell relaxation time, and the rigidity shear modulus are also isomorph invariant. In contrast to the isomorph invariance of all aspects of the transverse dynamics, the reduced-unit dynamics of the mass density is not invariant on length scales longer than the interparticle distance. By fitting to a generalized hydrodynamic model, we extract values for the wave-vector-dependent thermal diffusion coefficient, sound attenuation coefficient, and adiabatic sound velocity. The isomorph variation of these quantities in reduced units on long length scales can be eliminated by scaling with the density-scaling exponent, a fundamental quantity in the isomorph theory framework; this is an empirical observation that remains to be explained theoretically.
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Affiliation(s)
- Solvej Knudsen
- "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.,Department of Mathematics, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Hawtorn, Victoria 3122, Australia
| | - B D Todd
- Department of Mathematics, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Hawtorn, Victoria 3122, Australia
| | - Jeppe C Dyre
- "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | - J S Hansen
- "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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7
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Khrapak SA, Khrapak AG. Transport properties of Lennard-Jones fluids: Freezing density scaling along isotherms. Phys Rev E 2021; 103:042122. [PMID: 34005910 DOI: 10.1103/physreve.103.042122] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2021] [Accepted: 03/30/2021] [Indexed: 11/07/2022]
Abstract
It is demonstrated that properly reduced transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of Lennard-Jones fluids along isotherms exhibit quasi-universal scaling on the density divided by its value at the freezing point. Moreover, this scaling is closely related to the density scaling of transport coefficients of hard-sphere fluids. The Stokes-Einstein relation without the hydrodynamic diameter is valid in the dense fluid regime. The lower density boundary of its validity can serve as a practical demarcation line between gaslike and liquidlike regimes.
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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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8
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Rahman M, Carter BMGD, Saw S, Douglass IM, Costigliola L, Ingebrigtsen TS, Schrøder TB, Pedersen UR, Dyre JC. Isomorph Invariance of Higher-Order Structural Measures in Four Lennard-Jones Systems. Molecules 2021; 26:molecules26061746. [PMID: 33804670 PMCID: PMC8003765 DOI: 10.3390/molecules26061746] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Revised: 03/07/2021] [Accepted: 03/09/2021] [Indexed: 11/16/2022] Open
Abstract
In the condensed liquid phase, both single- and multicomponent Lennard-Jones (LJ) systems obey the "hidden-scale-invariance" symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank-Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob-Andersen, Wahnström, NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF.
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Affiliation(s)
- Mahajabin Rahman
- Department of Physics, Emory University, Atlanta, GA 30322, USA;
| | | | - Shibu Saw
- “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark; (S.S.); (I.M.D.); (L.C.); (T.S.I.); (T.B.S.); (U.R.P.)
| | - Ian M. Douglass
- “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark; (S.S.); (I.M.D.); (L.C.); (T.S.I.); (T.B.S.); (U.R.P.)
| | - Lorenzo Costigliola
- “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark; (S.S.); (I.M.D.); (L.C.); (T.S.I.); (T.B.S.); (U.R.P.)
| | - Trond S. Ingebrigtsen
- “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark; (S.S.); (I.M.D.); (L.C.); (T.S.I.); (T.B.S.); (U.R.P.)
| | - Thomas B. Schrøder
- “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark; (S.S.); (I.M.D.); (L.C.); (T.S.I.); (T.B.S.); (U.R.P.)
| | - Ulf R. Pedersen
- “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark; (S.S.); (I.M.D.); (L.C.); (T.S.I.); (T.B.S.); (U.R.P.)
| | - Jeppe C. Dyre
- “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark; (S.S.); (I.M.D.); (L.C.); (T.S.I.); (T.B.S.); (U.R.P.)
- Correspondence:
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9
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Khrapak SA. Vibrational model of thermal conduction for fluids with soft interactions. Phys Rev E 2021; 103:013207. [PMID: 33601514 DOI: 10.1103/physreve.103.013207] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2020] [Accepted: 12/22/2020] [Indexed: 11/07/2022]
Abstract
A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is applied to quantify heat transfer in a dense Lennard-Jones liquid and a strongly coupled one-component plasma. Remarkable agreement with the available numerical results is documented. A similar picture does not apply to the momentum transfer and shear viscosity of liquids.
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Affiliation(s)
- Sergey A Khrapak
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia and Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 82234 Weßling, Germany
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10
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Bell IH, Dyre JC, Ingebrigtsen TS. Excess-entropy scaling in supercooled binary mixtures. Nat Commun 2020; 11:4300. [PMID: 32855393 PMCID: PMC7453028 DOI: 10.1038/s41467-020-17948-1] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2020] [Accepted: 07/22/2020] [Indexed: 11/09/2022] Open
Abstract
Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for single-component quasiuniversality.
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Affiliation(s)
- Ian H Bell
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO, 80305, USA
| | - Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, Roskilde, DK-4000, Denmark
| | - Trond S Ingebrigtsen
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, Roskilde, DK-4000, Denmark.
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11
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Meyer N, Xu H, Wax JF. The role of chemical order in the temperature and composition dependence of the viscosity of liquid alloys. J Chem Phys 2019; 150:174502. [PMID: 31067875 DOI: 10.1063/1.5092694] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The influence of the chemical order on the viscosity of liquid alloys is investigated by numerical simulation of molecular dynamics. The temperature and composition dependence is discussed in the case of two contrasting alloys: K-Cs and Li-Bi. These two mixtures have different chemical orders, the first one being random and the second one having strong heterocoordination tendencies. In the case of K-Cs, the behavior of the mixture vs temperature is similar to a pure system and its viscosity varies monotonically with the composition. It is not the case for Li-Bi due to its marked chemical order and the heterocoordination tendency is accompanied by a maximum of the viscosity of the mixture when the composition is changed. For the first time, estimates of the temperature dependence of the viscosity of three representative Li-Bi alloys are given.
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Affiliation(s)
- N Meyer
- Université de Lorraine, LCP-A2MC, F-57000 Metz, France
| | - H Xu
- Université de Lorraine, LCP-A2MC, F-57000 Metz, France
| | - J-F Wax
- Université de Lorraine, LCP-A2MC, F-57000 Metz, France
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12
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Khrapak SA, Khrapak AG, Kryuchkov NP, Yurchenko SO. Onset of transverse (shear) waves in strongly-coupled Yukawa fluids. J Chem Phys 2019; 150:104503. [PMID: 30876343 DOI: 10.1063/1.5088141] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A simple practical approach to describe transverse (shear) waves in strongly-coupled Yukawa fluids is presented. Theoretical dispersion curves, based on hydrodynamic consideration, are shown to compare favorably with existing numerical results for plasma-related systems in the long-wavelength regime. The existence of a minimum wave number below which shear waves cannot propagate and its magnitude are properly accounted in the approach. The relevance of the approach beyond plasma-related Yukawa fluids is demonstrated by using experimental data on transverse excitations in liquid metals Fe, Cu, and Zn, obtained from inelastic x-ray scattering. Some potentially important relations, scalings, and quasi-universalities are discussed. The results should be interesting for a broad community in chemical physics, materials physics, physics of fluids and glassy state, complex (dusty) plasmas, and soft matter.
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Affiliation(s)
- Sergey A Khrapak
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 82234 Weßling, Germany
| | - Alexey G Khrapak
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
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13
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Probing the link between residual entropy and viscosity of molecular fluids and model potentials. Proc Natl Acad Sci U S A 2019; 116:4070-4079. [PMID: 30770449 DOI: 10.1073/pnas.1815943116] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
This work investigates the link between residual entropy and viscosity based on wide-ranging, highly accurate experimental and simulation data. This link was originally postulated by Rosenfeld in 1977 [Rosenfeld Y (1977) Phys Rev A 15:2545-2549], and it is shown that this scaling results in an approximately monovariate relationship between residual entropy and reduced viscosity for a wide range of molecular fluids [argon, methane, [Formula: see text], [Formula: see text], refrigerant R-134a (1,1,1,2-tetrafluoroethane), refrigerant R-125 (pentafluoroethane), methanol, and water] and a range of model potentials (hard sphere, inverse power, Lennard-Jones, and Weeks-Chandler-Andersen). While the proposed "universal" correlation of Rosenfeld is shown to be far from universal, when used with the appropriate density scaling for molecular fluids, the viscosity of nonassociating molecular fluids can be mapped onto the model potentials. This mapping results in a length scale that is proportional to the cube root of experimentally measurable liquid volume values.
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14
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Costigliola L, Heyes DM, Schrøder TB, Dyre JC. Revisiting the Stokes-Einstein relation without a hydrodynamic diameter. J Chem Phys 2019; 150:021101. [PMID: 30646717 DOI: 10.1063/1.5080662] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present diffusion coefficient and shear viscosity data for the Lennard-Jones fluid along nine isochores above the critical density, each involving a temperature variation of roughly two orders of magnitude. The data are analyzed with respect to the Stokes-Einstein (SE) relation, which breaks down gradually at high temperatures. This is rationalized in terms of the fact that the reduced diffusion coefficient D ̃ and the reduced viscosity η ̃ are both constant along the system's lines of constant excess entropy (the isomorphs). As a consequence, D ̃ η ̃ is a function of T/T Ref(ρ) in which T is the temperature, ρ is the density, and T Ref(ρ) is the temperature as a function of the density along a reference isomorph. This allows one to successfully predict the viscosity from the diffusion coefficient in the studied region of the thermodynamic phase diagram.
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Affiliation(s)
- Lorenzo Costigliola
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - David M Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - 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
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15
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Abstract
This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.
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Affiliation(s)
- Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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16
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Meyer N, Wax JF, Xu H. Viscosity of Lennard-Jones mixtures: A systematic study and empirical law. J Chem Phys 2018; 148:234506. [PMID: 29935509 DOI: 10.1063/1.5034779] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A systematic study of the viscosity of the binary Lennard-Jones (LJ) mixtures is carried out by equilibrium molecular dynamics simulations via the Green-Kubo relation. The effects of mass, size, and energy-parameter asymmetries on the viscosity and the self-diffusion coefficients are examined separately, both in equimolar mixtures and by varying the molar fractions. The systems are mapped into an effective one-component model according to the van der Waals one-fluid (vdW1) model. Furthermore, using an empirical law for pure LJ liquids, similar to the one proposed recently for liquid sodium, it is shown that the viscosity of the mixtures studied here are well-predicted by the combination of vdW1 fluid and empirical law. The Stokes-Einstein relation in the mixtures has also been investigated. A possible simple extension of this relation, from pure liquids to mixtures, has been proposed and tested.
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Affiliation(s)
- N Meyer
- Laboratoire de Chimie et de Physique-A2MC, Institut Jean Barriol (FR-CNRS 2843), Université de Lorraine-Metz, 1, Boulevard Arago, 57078 Metz Cedex 3, France
| | - J-F Wax
- Laboratoire de Chimie et de Physique-A2MC, Institut Jean Barriol (FR-CNRS 2843), Université de Lorraine-Metz, 1, Boulevard Arago, 57078 Metz Cedex 3, France
| | - H Xu
- Laboratoire de Chimie et de Physique-A2MC, Institut Jean Barriol (FR-CNRS 2843), Université de Lorraine-Metz, 1, Boulevard Arago, 57078 Metz Cedex 3, France
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