1
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Sheydaafar Z, Dyre JC, Schrøder TB. Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Pseudoisomorphs for Harmonic-Bonded Molecules. J Phys Chem B 2024; 128:8054-8064. [PMID: 39110776 DOI: 10.1021/acs.jpcb.4c03982] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/23/2024]
Abstract
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been shown to exist in molecular models with flexible bonds [Olsen, A. E. J. Chem. Phys. 2016, 145, 241103]. We here present three force-based methods to trace out pseudoisomorphs based on a single configuration and test them on the asymmetric dumbbell and 10-bead Lennard-Jones chain models with bonds modeled as harmonic springs. The three methods are based on requiring that particle forces, center-of-mass forces, and torques, respectively, are invariant in reduced units. For each of the two investigated models we identify a method that works well for tracing out pseudoisomorphs, but these methods are not the same. Overall, we find that the more internal degrees of freedom there are in the molecule studied, the less they appear to affect the gross dynamical behavior. Moreover, the "internal" degrees of freedom (including rotation) do not significantly affect the scaling behavior of the dynamical/transport coefficients provided some 'quenching' is performed.
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Affiliation(s)
- Zahraa Sheydaafar
- 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
| | - Thomas B Schrøder
- 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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Sheydaafar Z, Dyre JC, Schrøder TB. Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Small Rigid Molecules. J Phys Chem B 2023; 127:3478-3487. [PMID: 37040433 DOI: 10.1021/acs.jpcb.3c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/13/2023]
Abstract
Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the direct-isomorph-check method. Recently a new method based on the scaling properties of forces was introduced and shown to work very well for atomic systems [T. B. Schrøder, Phys. Rev. Lett. 2022, 129, 245501]. A unique feature of this method is that it only requires a single equilibrium configuration for tracing out an isomorph. We here test generalizations of this method to molecular systems and compare to simulations of three simple molecular models: the asymmetric dumbbell model of two Lennard-Jones spheres, the symmetric inverse-power-law dumbbell model, and the Lewis-Wahnström o-terphenyl model. We introduce and test two force-based and one torque-based methods, all of which require just a single configuration for tracing out an isomorph. Overall, the method based on requiring invariant center-of-mass reduced forces works best.
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Affiliation(s)
- Zahraa Sheydaafar
- 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
| | - Thomas B Schrøder
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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3
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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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Saw S, Costigliola L, Dyre JC. Configurational temperature in active matter. I. Lines of invariant physics in the phase diagram of the Ornstein-Uhlenbeck model. Phys Rev E 2023; 107:024609. [PMID: 36932558 DOI: 10.1103/physreve.107.024609] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
This paper shows that the configurational temperature of liquid-state theory, T_{conf}, defines an energy scale, which can be used for adjusting model parameters of active Ornstein-Uhlenbeck particle (AOUP) models in order to achieve approximately invariant structure and dynamics upon a density change. The required parameter changes are calculated from the variation of a single configuration's T_{conf} for a uniform scaling of all particle coordinates. The resulting equations are justified theoretically for models involving a potential-energy function with hidden scale invariance. The validity of the procedure is illustrated by computer simulations of the Kob-Andersen binary Lennard-Jones AOUP model, showing the existence of lines of approximate invariance of the reduced-unit radial distribution function and time-dependent mean-square displacement.
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Affiliation(s)
- Shibu Saw
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Lorenzo Costigliola
- 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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5
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Jiang Y, Weeks ER, Bailey NP. Isomorphs in sheared binary Lennard-Jones glass: Transient response. Phys Rev E 2023; 107:014610. [PMID: 36797950 DOI: 10.1103/physreve.107.014610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2022] [Accepted: 01/06/2023] [Indexed: 01/31/2023]
Abstract
We have studied shear deformation of binary Lennard-Jones glasses to investigate the extent to which the transient part of the stress strain curves is invariant when the thermodynamic state point is varied along an isomorph. Shear deformations were carried out on glass samples of varying stability, determined by cooling rate, and at varying strain rates, at state points deep in the glass. Density changes up to and exceeding a factor of two were made. We investigated several different methods for generating isomorphs but none of the previously developed methods could generate sufficiently precise isomorphs given the large density changes and nonequilibrium situation. Instead, the temperatures for these higher densities were chosen to give state points isomorphic to the starting state point by requiring the steady-state flow stress for isomorphic state points to be invariant in reduced units. In contrast to the steady-state flow stress, we find that the peak stress on the stress strain curve is not invariant. The peak stress decreases by a few percent for each ten percent increase in density, although the differences decrease with increasing density. Analysis of strain profiles and nonaffine motion during the transient phase suggests that the root of the changes in peak stress is a varying tendency to form shear bands, with the largest tendency occurring at the lowest densities. We suggest that this reflects the effective steepness of the potential; a higher effective steepness gives a greater tendency to form shear bands.
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Affiliation(s)
- Yonglun Jiang
- Department of Physics, Emory University, 400 Dowman Drive, Atlanta, Georgia 30322, USA
| | - Eric R Weeks
- Department of Physics, Emory University, 400 Dowman Drive, Atlanta, Georgia 30322, USA
| | - 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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6
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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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7
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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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8
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Attia E, Dyre JC, Pedersen UR. Extreme case of density scaling: The Weeks-Chandler-Andersen system at low temperatures. Phys Rev E 2021; 103:062140. [PMID: 34271644 DOI: 10.1103/physreve.103.062140] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Accepted: 05/28/2021] [Indexed: 11/07/2022]
Abstract
This paper studies numerically the Weeks-Chandler-Andersen system, which is shown to obey hidden scale invariance with a density-scaling exponent that varies from below 5 to above 500. This unprecedented variation makes it advantageous to use the fourth-order Runge-Kutta algorithm for tracing out isomorphs. Good isomorph invariance of structure and dynamics is observed over more than three orders of magnitude temperature variation. For all state points studied, the virial potential-energy correlation coefficient and the density-scaling exponent are controlled mainly by the temperature. Based on the assumption of statistically independent pair interactions, a mean-field theory is developed that rationalizes this finding and provides an excellent fit to data at low temperatures.
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Affiliation(s)
- Eman Attia
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, 4000 Roskilde, Denmark
| | - Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, 4000 Roskilde, Denmark
| | - Ulf R Pedersen
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, 4000 Roskilde, Denmark
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9
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Singh AN, Dyre JC, Pedersen UR. Solid–liquid coexistence of neon, argon, krypton, and xenon studied by simulations. J Chem Phys 2021; 154:134501. [DOI: 10.1063/5.0045398] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Aditya N. Singh
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53703, USA
| | - 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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10
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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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11
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Lucco Castello F, Tolias P, Dyre JC. Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas. J Chem Phys 2021; 154:034501. [PMID: 33499616 DOI: 10.1063/5.0036226] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.
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Affiliation(s)
- F Lucco Castello
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - P Tolias
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - J C Dyre
- Glass and Time, IMFUFA, Roskilde University, Roskilde DK-4000, Denmark
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12
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Ingebrigtsen TS, Schrøder TB, Dyre JC. Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles. J Phys Chem B 2021; 125:317-327. [PMID: 33369412 DOI: 10.1021/acs.jpcb.0c09726] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Polydisperse systems of particles interacting by the purely repulsive exponential (EXP) pair potential are studied in regard to how structure and dynamics vary along isotherms, isochores, and isomorphs. The sizable size polydispersities of 23%, 29%, 35%, and 40%, as well as energy polydispersity 35%, were considered. For each system an isomorph was traced out covering about one decade in density. For all systems studied, the structure and dynamics vary significantly along the isotherms and isochores but are invariant to a good approximation along the isomorphs. We conclude that the single-component EXP system's hidden scale invariance (implying isomorph invariance of structure and dynamics) is maintained even when a sizable polydispersity is introduced into the system.
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Affiliation(s)
- Trond S Ingebrigtsen
- 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
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13
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Abstract
This paper generalizes isomorph theory to systems that are not in thermal equilibrium. The systems are assumed to be R-simple, i.e., to have a potential energy that as a function of all particle coordinates R obeys the hidden-scale-invariance condition U(Ra) < U(Rb) ⇒ U(λRa) < U(λRb). "Systemic isomorphs" are introduced as lines of constant excess entropy in the phase diagram defined by density and systemic temperature, which is the temperature of the equilibrium state point with the average potential energy equal to U(R). The dynamics is invariant along a systemic isomorph if there is a constant ratio between the systemic and the bath temperature. In thermal equilibrium, the systemic temperature is equal to the bath temperature and the original isomorph formalism is recovered. The new approach rationalizes within a consistent framework previously published observations of isomorph invariance in simulations involving nonlinear steady-state shear flows, zero-temperature plastic flows, and glass-state isomorphs. This paper relates briefly to granular media, physical aging, and active matter. Finally, we discuss the possibility that the energy unit defining the reduced quantities should be based on the systemic rather than the bath temperature.
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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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14
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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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15
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Bacher AK, Pedersen UR, Schrøder TB, Dyre JC. The EXP pair-potential system. IV. Isotherms, isochores, and isomorphs in the two crystalline phases. J Chem Phys 2020; 152:094505. [DOI: 10.1063/1.5144871] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] 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
| | - Ulf R. Pedersen
- 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
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16
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Kooij S, Lerner E. Characterizing nonaffinity upon decompression of soft-sphere packings. Phys Rev E 2019; 100:042609. [PMID: 31770889 DOI: 10.1103/physreve.100.042609] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2019] [Indexed: 06/10/2023]
Abstract
Athermal elastic moduli of soft-sphere packings are known to exhibit universal scaling properties near the unjamming point, most notably the vanishing of the shear-to-bulk moduli ratio G/B upon decompression. Interestingly, the smallness of G/B stems from the large nonaffinity of deformation-induced displacements under shear strains, compared to insignificant nonaffinity of displacements under compressive strains. In this work, we show using numerical simulations that the relative weights of the affine and nonaffine contributions to the bulk modulus, and their dependence on the proximity to the unjamming point, can differ qualitatively between different models that feature the same generic unjamming phenomenology. In canonical models of unjamming, we observe that the ratio of the nonaffine to total bulk moduli B_{na}/B approaches a constant upon decompression, while in other, less well-studied models, it vanishes. We show that the vanishing of B_{na}/B in noncanonical models stems from the emergence of an invariance of net (zero) forces on the constituent particles to compressive strains at the onset of unjamming. We provide a theoretical scaling analysis that fully explains our numerical observations, and allows us to predict the scaling behavior of B_{na}/B upon unjamming, given the functional form of the pairwise interaction potential.
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Affiliation(s)
- Stefan Kooij
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
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Bell IH, Messerly R, Thol M, Costigliola L, Dyre JC. Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid. J Phys Chem B 2019; 123:6345-6363. [PMID: 31241958 DOI: 10.1021/acs.jpcb.9b05808] [Citation(s) in RCA: 53] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Rosenfeld proposed two different scaling approaches to model the transport properties of fluids, separated by 22 years, one valid in the dilute gas, and another in the liquid phase. In this work, we demonstrate that these two limiting cases can be connected through the use of a novel approach to scaling transport properties and a bridging function. This approach, which is empirical and not derived from theory, is used to generate reference correlations for the transport properties of the Lennard-Jones 12-6 fluid of viscosity, thermal conductivity, and self-diffusion. This approach, with a very simple functional form, allows for the reproduction of the most accurate simulation data to within nearly their statistical uncertainty. The correlations are used to confirm that for the Lennard-Jones fluid the appropriately scaled transport properties are nearly monovariate functions of the excess entropy from low-density gases into the supercooled phase and up to extreme temperatures. This study represents the most comprehensive metastudy of the transport properties of the Lennard-Jones fluid to date.
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Affiliation(s)
- Ian H Bell
- Applied Chemicals and Materials Division , National Institute of Standards and Technology , Boulder , Colorado 80305 , United States
| | - Richard Messerly
- Applied Chemicals and Materials Division , National Institute of Standards and Technology , Boulder , Colorado 80305 , United States
| | - Monika Thol
- Thermodynamics , Ruhr-Universität Bochum , Universitätsstraße 150 , 44801 Bochum , Germany
| | - Lorenzo Costigliola
- DNRF Centre "Glass and Time," IMFUFA, Department of Science and Environment , Roskilde University , Postbox 260, DK-4000 Roskilde , Denmark
| | - Jeppe C Dyre
- DNRF Centre "Glass and Time," IMFUFA, Department of Science and Environment , Roskilde University , Postbox 260, DK-4000 Roskilde , Denmark
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Pedersen UR, Bacher AK, Schrøder TB, Dyre JC. The EXP pair-potential system. III. Thermodynamic phase diagram. J Chem Phys 2019; 150:174501. [PMID: 31067860 DOI: 10.1063/1.5094395] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper determines the thermodynamic phase diagram of the EXP system of particles interacting by the purely repulsive exponential pair potential. The solid phase is face-centered cubic (fcc) at low densities and pressures. At higher densities and pressures, the solid phase is body-centered cubic (bcc) with a re-entrant liquid phase at the highest pressures simulated. The investigation first identifies the phase diagram at zero temperature at which the following four crystal structures are considered: fcc, bcc, hexagonal close packed, and cubic diamond. There is a T = 0 phase transition at pressure 2.651 × 10-3 with the thermodynamically stable structure being fcc below and bcc above this pressure. The densities of the two crystal structures at the phase transition are 1.7469 × 10-2 (fcc) and 1.7471 × 10-2 (bcc). At finite temperatures, the fcc-bcc, fcc-liquid, and bcc-liquid coexistence lines are determined by numerical integration of the Clausius-Clapeyron equation and validated by interface-pinning simulations at selected state points. The bcc-fcc phase transition is a weak first-order transition. The liquid-fcc-bcc triple point, which is determined by the interface-pinning method, has temperature 5.9 × 10-5 and pressure 2.5 × 10-6; the triple-point densities are 1.556 × 10-3 (liquid), 1.583 × 10-3 (bcc), and 1.587 × 10-3 (fcc).
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Affiliation(s)
- Ulf R Pedersen
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Andreas K 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
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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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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
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