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Koperwas K, Grzybowski A, Paluch M. Virial-potential-energy correlation and its relation to density scaling for quasireal model systems. Phys Rev E 2021; 102:062140. [PMID: 33466035 DOI: 10.1103/physreve.102.062140] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 11/18/2020] [Indexed: 11/07/2022]
Abstract
In this paper, we examine the virial- and the potential-energy correlation for quasireal model systems. This correlation constitutes the framework of the theory of the isomorph in the liquid phase diagram commonly examined using simple liquids. Interestingly, our results show that for the systems characterized by structural anisotropy and flexible bonds, the instantaneous values of total virial and total potential energy are entirely uncorrelated. It is due to the presence of the intramolecular interactions because the contributions to the virial and potential energy resulting from the intermolecular interactions still exhibit strong linear dependence. Interestingly, in contrast to the results reported for simple liquids, the slope of the mentioned linear dependence is different than the values of the density scaling exponent. However, our findings show that for quasireal materials, the slope of dependence between the virial and potential energy (resulting from the intermolecular interactions) strongly depends on the interval of intermolecular distances that are taken into account. Consequently, the value of the slope of the discussed relationship, which enables satisfactory density scaling, can be obtained. Interestingly, this conclusion is supported by the results obtained for analogous systems without intermolecular attraction, for which the value the slope of the virial-potential-energy correlation is independent of considered intermolecular distances, directly corresponds to the exponent of the intermolecular repulsion, and finally leads to accurate density scaling.
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Affiliation(s)
- K Koperwas
- University of Silesia in Katowice, Institute of Physics, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland and Silesian Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
| | - A Grzybowski
- University of Silesia in Katowice, Institute of Physics, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland and Silesian Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
| | - M Paluch
- University of Silesia in Katowice, Institute of Physics, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland and Silesian Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
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2
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Fragiadakis D, Roland C. Intermolecular distance and density scaling of dynamics in molecular liquids. J Chem Phys 2019; 150:204501. [DOI: 10.1063/1.5098455] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- D. Fragiadakis
- Naval Research Laboratory, Chemistry Division, Washington, District of Columbia 20375-5342, USA
| | - C.M. Roland
- Naval Research Laboratory, Chemistry Division, Washington, District of Columbia 20375-5342, USA
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Niss K, Hecksher T. Perspective: Searching for simplicity rather than universality in glass-forming liquids. J Chem Phys 2018; 149:230901. [PMID: 30579292 DOI: 10.1063/1.5048093] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This article gives an overview of experimental results on dynamics in bulk glass-forming molecular liquids. Rather than looking for phenomenology that is universal, in the sense that it is seen in all liquids, the focus is on identifying the basic characteristics, or "stylized facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner.
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Affiliation(s)
- Kristine Niss
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Tina Hecksher
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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4
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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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Abstract
This paper derives and discusses the configuration-space Langevin equation describing a physically aging R-simple system and the corresponding Smoluchowski equation. Externally controlled thermodynamic variables like temperature, density, and pressure enter the description via the single parameter Ts/T, in which T is the bath temperature and Ts is the "systemic" temperature defined at any time t as the thermodynamic equilibrium temperature of the state point with density ρ(t) and potential energy U(t). In equilibrium, Ts ≅ T with fluctuations that vanish in the thermodynamic limit. In contrast to Tool's fictive temperature and other effective temperatures in glass science, the systemic temperature is defined for any configuration with a well-defined density, even if it is not close to equilibrium. Density and systemic temperature define an aging phase diagram, in which the aging system traces out a curve. Predictions are discussed for aging following various density-temperature and pressure-temperature jumps from one equilibrium state to another, as well as for a few other scenarios. The proposed theory implies that R-simple glass-forming liquids are characterized by the dynamic Prigogine-Defay ratio being equal to unity.
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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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6
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Predicting the Flory-Huggins χ Parameter for Polymers with Stiffness Mismatch from Molecular Dynamics Simulations. Polymers (Basel) 2016; 8:polym8060241. [PMID: 30979334 PMCID: PMC6432250 DOI: 10.3390/polym8060241] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Revised: 06/13/2016] [Accepted: 06/16/2016] [Indexed: 11/16/2022] Open
Abstract
The Flory–Huggins χ parameter describes the excess free energy of mixing and governs phase behavior for polymer blends and block copolymers. For chemically-distinct nonpolar polymers, the value of χ is dominated by the mismatch in cohesive energy densities of the monomers. For blends of chemically-similar polymers, the entropic portion of χ, arising from non-ideal local packing, becomes more significant. Using polymer field theory, Fredrickson et al. predicted that a difference in backbone stiffness can result in a positive χ for chains consisting of chemically-identical monomers. To quantitatively investigate this phenomenon, we perform molecular dynamic (MD) simulations for bead-spring chains, which differ only in stiffness. From the simulations, we apply a novel thermodynamic integration to extract χ as low as 10-4 per monomer for blends with stiffness mismatch. To compare with experiments, we introduce a standardized effective monomer to map real polymers onto our bead-spring chains. The predicted χ agrees well with experimental values for a wide variety of pairs of chemically-similar polymers.
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7
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Ninarello AS, Gnan N, Sciortino F. Observable-dependence of the effective temperature in off-equilibrium diatomic molecular liquids. J Chem Phys 2014; 141:194507. [PMID: 25416898 DOI: 10.1063/1.4901526] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We discuss the observable-dependence of the effective temperature Teff, defined via the fluctuation-dissipation relation, of an out-of-equilibrium system composed by homonuclear dumbbell molecules. Teff is calculated by evaluating the fluctuation and the response for two observables associated, respectively, to translational and to rotational degrees of freedom, following a sudden temperature quench. We repeat our calculations for different dumbbell elongations ζ. At high elongations (ζ > 0.4), we find the same Teff for the two observables. At low elongations (ζ ⩽ 0.4), only for very deep quenches Teff coincides. The observable-dependence of Teff for low elongations and shallow quenches stresses the importance of a strong coupling between orientational and translational variables for a consistent definition of the effective temperature in glassy systems.
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Affiliation(s)
| | - Nicoletta Gnan
- CNR-ISC Uos "Sapienza," Piazzale A. Moro 2, 00186 Roma, Italy
| | - Francesco Sciortino
- Dipartimento di Fisica, "Sapienza" Università di Roma, Piazzale A. Moro 2, 00186 Roma, Italy
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Abstract
Recent developments show that many liquids and solids have an approximate "hidden" scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments.
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Affiliation(s)
- Jeppe C Dyre
- DNRF Center "Glass and Time", IMFUFA, Department of Sciences, Roskilde University , P.O. Box 260, DK-4000 Roskilde, Denmark
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9
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Pieprzyk S, Heyes DM, Brańka AC. Thermodynamic properties and entropy scaling law for diffusivity in soft spheres. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012106. [PMID: 25122250 DOI: 10.1103/physreve.90.012106] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2014] [Indexed: 06/03/2023]
Abstract
The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8.
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Affiliation(s)
- S Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
| | - D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
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10
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Mirigian S, Schweizer KS. Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. II. Thermal liquids. J Chem Phys 2014; 140:194507. [DOI: 10.1063/1.4874843] [Citation(s) in RCA: 125] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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11
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Hansen JS. Generalized extended Navier-Stokes theory: multiscale spin relaxation in molecular fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032101. [PMID: 24125208 DOI: 10.1103/physreve.88.032101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2013] [Indexed: 06/02/2023]
Abstract
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent on the state point.
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Affiliation(s)
- J S Hansen
- DNRF Centre "Glass and Time," IMFUFA Department of Nature, Systems and Models Roskilde University, DK-4000 Denmark
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12
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Klieber C, Hecksher T, Pezeril T, Torchinsky DH, Dyre JC, Nelson KA. Mechanical spectra of glass-forming liquids. II. Gigahertz-frequency longitudinal and shear acoustic dynamics in glycerol and DC704 studied by time-domain Brillouin scattering. J Chem Phys 2013; 138:12A544. [DOI: 10.1063/1.4789948] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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13
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Gujrati PD, Aung PP. Nonequilibrium thermodynamics. III. Generalization of Maxwell, Clausius-Clapeyron, and response-function relations, and the Prigogine-Defay ratio for systems in internal equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041129. [PMID: 22680441 DOI: 10.1103/physreve.85.041129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2011] [Revised: 08/01/2011] [Indexed: 06/01/2023]
Abstract
We follow the consequences of internal equilibrium in nonequilibrium systems that has been introduced recently [Gujrati, Phys. Rev. E 81, 051130 (2010) and Gujrati, Phys. Rev. E 85, 041128 (2012).] to obtain the generalization of the Maxwell relation and the Clausius-Clapeyron relation that are normally given for equilibrium systems. The use of Jacobians allows for a more compact way to address the generalized Maxwell relations in the presence of internal variables. The Clausius-Clapeyron relation in the subspace of observables shows not only the nonequilibrium modification but also the modification due to internal variables that play a dominant role in glasses to which we apply the above relations. Real systems do not directly turn into glasses (GL) that are frozen structures from the supercooled liquid state L; there is an intermediate state (gL) where the internal variables are not frozen. A system possesses several kinds of glass transitions, some conventional (L→gL; gL→GL) in which the state changes continuously and the transition mimics a continuous or second-order transition, and some apparent (L→gL; L→GL) in which the free energies are discontinuous so that the transition appears as a zeroth-order transition, as discussed in the text. We evaluate the Prigogine-Defay ratio Π in the subspace of the observables at these transitions. We find that it is normally different from 1, except at the conventional transition L→gL, where Π=1.
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Affiliation(s)
- P D Gujrati
- Department of Physics, Department of Polymer Science, University of Akron, Akron, Ohio 44325, USA.
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14
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Ingebrigtsen TS, Toxvaerd S, Schrøder TB, Dyre JC. NVU dynamics. II. Comparing to four other dynamics. J Chem Phys 2012; 135:104102. [PMID: 21932871 DOI: 10.1063/1.3623586] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, "NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface," J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1∕N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nosé-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.
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Affiliation(s)
- Trond S Ingebrigtsen
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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Ingebrigtsen TS, Toxvaerd S, Heilmann OJ, Schrøder TB, Dyre JC. NVUdynamics. I. Geodesic motion on the constant-potential-energy hypersurface. J Chem Phys 2011; 135:104101. [DOI: 10.1063/1.3623585] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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16
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Schrøder TB, Gnan N, Pedersen UR, Bailey NP, Dyre JC. Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems. J Chem Phys 2011; 134:164505. [PMID: 21528971 DOI: 10.1063/1.3582900] [Citation(s) in RCA: 90] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.
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Affiliation(s)
- Thomas B Schrøder
- DNRF Center Glass and Time, IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark.
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17
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Chopra R, Truskett TM, Errington JR. Excess entropy scaling of dynamic quantities for fluids of dumbbell-shaped particles. J Chem Phys 2011; 133:104506. [PMID: 20849177 DOI: 10.1063/1.3477767] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
We use molecular simulation to study the ability of entropy scaling relationships to describe the kinetic properties of two Lennard-Jones dumbbell models. We begin by examining the excess entropy, the key quantity used to correlate dynamic properties within entropy scaling strategies. We compute the thermodynamic excess entropy as well as contributions to the two-body excess entropy stemming from translational and orientational intermolecular correlations. Our results indicate that the total two-body contribution accounts for more than 70% of the thermodynamic excess entropy at all state conditions explored. For the two dumbbell models studied here, the orientational component of the two-body excess entropy dominates at moderate and high fluid densities. We next investigate the relationships between kinetic properties and various contributions to the excess entropy. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate-scattering function. We find that the thermodynamic excess entropy provides the best metric for describing kinetic properties. For each of the dynamic properties considered, reduced data collapse onto a common curve when expressed as a function of the thermodynamic excess entropy. The likelihood of a two-body contribution to the excess entropy serving as a reliable scaling variable is linked to the extent to which it correlates with the thermodynamic excess entropy. The total two-body term contributes significantly to the excess entropy, and therefore this quantity generally serves as a suitable scaling variable.
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Affiliation(s)
- Ravi Chopra
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA.
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18
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Chopra R, Truskett TM, Errington JR. On the Use of Excess Entropy Scaling To Describe Single-Molecule and Collective Dynamic Properties of Hydrocarbon Isomer Fluids. J Phys Chem B 2010; 114:16487-93. [DOI: 10.1021/jp107878u] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ravi Chopra
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Thomas M. Truskett
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States, and Department of Chemical Engineering and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
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Pedersen UR, Schrøder TB, Dyre JC. Repulsive reference potential reproducing the dynamics of a liquid with attractions. PHYSICAL REVIEW LETTERS 2010; 105:157801. [PMID: 21230939 DOI: 10.1103/physrevlett.105.157801] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2010] [Indexed: 05/30/2023]
Abstract
A well-known result of liquid state theory is that the structure of dense fluids is mainly determined by their repulsive forces. The Weeks-Chandler-Andersen potential, which cuts intermolecular potentials at their minima, is therefore often used as a reference. However, this cannot reproduce the viscous dynamics of the Kob-Andersen binary Lennard-Jones liquid [Berthier and Tarjus, Phys. Rev. Lett. 103, 170601 (2009)]. This paper shows that repulsive inverse-power-law potentials provide a reference for this liquid that reproduces its structure, dynamics, and isochoric heat capacity.
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Affiliation(s)
- Ulf R Pedersen
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA.
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Pedersen UR, Peters GH, Schrøder TB, Dyre JC. Correlated volume-energy fluctuations of phospholipid membranes: a simulation study. J Phys Chem B 2010; 114:2124-30. [PMID: 20095587 PMCID: PMC2820308 DOI: 10.1021/jp9086865] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
This paper reports all-atom computer simulations of five phospholipid membranes (DMPC, DPPC, DMPG, DMPS, and DMPSH) with focus on the thermal equilibrium fluctuations of volume, energy, area, thickness, and chain order. At constant temperature and pressure, volume and energy exhibit strong correlations of their slow fluctuations (defined by averaging over 0.5 ns). These quantities, on the other hand, do not correlate significantly with area, thickness, or chain order. The correlations are mainly reported for the fluid phase, but we also give some results for the ordered (gel) phase of two membranes, showing a similar picture. The cause of the observed strong correlations is identified by splitting volume and energy into contributions from tails, heads, and water, and showing that the slow volume-energy fluctuations derive from van der Waals interactions of the tail region; they are thus analogous to the similar strong correlations recently observed in computer simulations of the Lennard-Jones and other simple van der Waals type liquids (U. R. Pedersen et al., Phys. Rev. Lett. 2008, 100, 015701). The strong correlations reported here confirm one crucial assumption of a recent theory for nerve signal propagation proposed by Heimburg and Jackson (T. Heimburg and A. D. Jackson, Proc. Natl. Acad. Sci. 2005, 102, 9790-9795).
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Affiliation(s)
- Ulf R Pedersen
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
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21
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Papathanassiou AN, Sakellis I. Correlation of the scaling exponent γ of the diffusivity-density function in viscous liquids with their elastic properties. J Chem Phys 2010; 132:154503. [DOI: 10.1063/1.3382645] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Gnan N, Maggi C, Schrøder TB, Dyre JC. Predicting the effective temperature of a glass. PHYSICAL REVIEW LETTERS 2010; 104:125902. [PMID: 20366549 DOI: 10.1103/physrevlett.104.125902] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2009] [Indexed: 05/29/2023]
Abstract
We explain the findings by Di Leonardo et al. [Phys. Rev. Lett. 84, 6054 (2000)10.1103/PhysRevLett.84.6054] that the effective temperature of a Lennard-Jones glass depends only on the final density in the volume and/or temperature jump that produces the glass. This is not only a property of the Lennard-Jones liquid, but a feature of all strongly correlating liquids. For such liquids data from a single quench simulation provide enough information to predict the effective temperature of any glass produced by jumping from an equilibrium state. This prediction is validated by simulations of the Kob-Andersen binary Lennard-Jones liquid and shown not to apply for the nonstrongly correlating monatomic Lennard-Jones Gaussian liquid.
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Affiliation(s)
- Nicoletta Gnan
- DNRF Center Glass and Time, IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark.
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Gnan N, Schrøder TB, Pedersen UR, Bailey NP, Dyre JC. Pressure-energy correlations in liquids. IV. "Isomorphs" in liquid phase diagrams. J Chem Phys 2010; 131:234504. [PMID: 20025332 DOI: 10.1063/1.3265957] [Citation(s) in RCA: 223] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the phase diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and co-workers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, and it explains isochronal superposition for strongly correlating viscous liquids.
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Affiliation(s)
- Nicoletta Gnan
- DNRF Center Glass and Time, IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark.
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Schrøder TB, Bailey NP, Pedersen UR, Gnan N, Dyre JC. Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance. J Chem Phys 2009; 131:234503. [DOI: 10.1063/1.3265955] [Citation(s) in RCA: 95] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas B. Schrøder
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Nicholas P. Bailey
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Ulf R. Pedersen
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Nicoletta Gnan
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C. Dyre
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Schrøder TB, Pedersen UR, Bailey NP, Toxvaerd S, Dyre JC. Hidden scale invariance in molecular van der Waals liquids: a simulation study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041502. [PMID: 19905311 DOI: 10.1103/physreve.80.041502] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2008] [Revised: 07/27/2009] [Indexed: 05/28/2023]
Abstract
Results from molecular dynamics simulations of two viscous molecular model liquids--the Lewis-Wahnström model of orthoterphenyl and an asymmetric dumbbell model--are reported. We demonstrate that the liquids have a "hidden" approximate scale invariance: equilibrium potential energy fluctuations are accurately described by inverse power-law (IPL) potentials, the radial distribution functions are accurately reproduced by the IPL's, and the radial distribution functions obey the IPL predicted scaling properties to a good approximation. IPL scaling of the dynamics also applies--with the scaling exponent predicted by the equilibrium fluctuations. In contrast, the equation of state does not obey the IPL scaling. We argue that our results are general for van der Waals liquids, but do not apply, e.g., for hydrogen-bonded liquids.
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Affiliation(s)
- Thomas B Schrøder
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Post Box 260, DK-4000 Roskilde, Denmark
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Mauro JC, Gupta PK, Loucks RJ. Composition dependence of glass transition temperature and fragility. II. A topological model of alkali borate liquids. J Chem Phys 2009; 130:234503. [DOI: 10.1063/1.3152432] [Citation(s) in RCA: 197] [Impact Index Per Article: 13.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Papathanassiou AN. Density scaling of the diffusion coefficient at various pressures in viscous liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:032501. [PMID: 19391997 DOI: 10.1103/physreve.79.032501] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2008] [Indexed: 05/27/2023]
Abstract
Fundamental thermodynamics and an earlier elastic solid-state point defect model [P. Varotsos and K. Alexopoulos, Phys. Rev. B 15, 4111 (1977); Phys. Rev. B 18, 2683 (1978)] are employed to formulate an analytical second-order polynomial function describing the density scaling of the diffusion coefficient in viscous liquids. The function parameters are merely determined by the scaling exponent, which is directly connected with the Grüneisen constant. Density scaling diffusion coefficient isotherms obtained at different pressures collapse on a unique master curve, in agreement with recent computer simulation results of Lennard-Jones viscous liquids [D. Coslovich and C. M. Roland, J. Phys. Chem. 112, 1329 (2008)].
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Affiliation(s)
- A N Papathanassiou
- Department of Physics, Solid State Physics Section, University of Athens, Panepistimiopolis, 157 84 Zografos, Greece.
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Ribeiro MCC, Scopigno T, Ruocco G. Prigogine−Defay Ratio for an Ionic Glass-Former: Molecular Dynamics Simulations. J Phys Chem B 2009; 113:3099-104. [DOI: 10.1021/jp810934e] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Mauro C. C. Ribeiro
- Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, C.P. 26077, 05513-970, São Paulo, SP, Brazil, and Istituto Nazionale per la Física della Materia (INFM-CNR) and Dipartimento di Fisica, “Sapienza” Universitá di Roma, 00185 Roma, Italy
| | - Tullio Scopigno
- Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, C.P. 26077, 05513-970, São Paulo, SP, Brazil, and Istituto Nazionale per la Física della Materia (INFM-CNR) and Dipartimento di Fisica, “Sapienza” Universitá di Roma, 00185 Roma, Italy
| | - Giancarlo Ruocco
- Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, C.P. 26077, 05513-970, São Paulo, SP, Brazil, and Istituto Nazionale per la Física della Materia (INFM-CNR) and Dipartimento di Fisica, “Sapienza” Universitá di Roma, 00185 Roma, Italy
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Bailey NP, Pedersen UR, Gnan N, Schrøder TB, Dyre JC. Pressure-energy correlations in liquids. I. Results from computer simulations. J Chem Phys 2009; 129:184507. [PMID: 19045414 DOI: 10.1063/1.2982247] [Citation(s) in RCA: 186] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that a number of model liquids at fixed volume exhibit strong correlations between equilibrium fluctuations of the configurational parts of (instantaneous) pressure and energy. We present detailed results for 13 systems, showing in which systems these correlations are significant. These include Lennard-Jones liquids (both single- and two-component) and several other simple liquids, neither hydrogen-bonding liquids such as methanol and water, nor the Dzugutov liquid, which has significant contributions to pressure at the second nearest neighbor distance. The pressure-energy correlations, which for the Lennard-Jones case are shown to also be present in the crystal and glass phases, reflect an effective inverse power-law potential dominating fluctuations, even at zero and slightly negative pressure. An exception to the inverse power-law explanation is a liquid with hard-sphere repulsion and a square-well attractive part, where a strong correlation is observed, but only after time averaging. The companion paper [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)] gives a thorough analysis of the correlations, with a focus on the Lennard-Jones liquid, and a discussion of some experimental and theoretical consequences.
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Affiliation(s)
- Nicholas P Bailey
- DNRF Center Glass and Time, IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark.
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Toxvaerd S, Heilmann OJ, Ingebrigtsen T, Schro̸der TB, Dyre JC. Time-reversible molecular dynamics algorithms with bond constraints. J Chem Phys 2009; 131:064102. [DOI: 10.1063/1.3194785] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Bailey NP, Pedersen UR, Gnan N, Schrøder TB, Dyre JC. Pressure-energy correlations in liquids. II. Analysis and consequences. J Chem Phys 2008; 129:184508. [DOI: 10.1063/1.2982249] [Citation(s) in RCA: 154] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Pick RM. The Prigogine–Defay ratio and the microscopic theory of supercooled liquids. J Chem Phys 2008; 129:124115. [DOI: 10.1063/1.2969899] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Christensen T, Dyre JC. Solution of the spherically symmetric linear thermoviscoelastic problem in the inertia-free limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021501. [PMID: 18850835 DOI: 10.1103/physreve.78.021501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2008] [Revised: 05/17/2008] [Indexed: 05/26/2023]
Abstract
The coupling between mechanical and thermal properties due to thermal expansion complicates the problem of measuring frequency-dependent thermoviscoelastic properties, in particular for highly viscous liquids. A simplification arises if there is spherical symmetry where--as detailed in the present paper--the thermoviscoelastic problem may be solved analytically in the inertia-free limit, i.e., the limit where the sample is much smaller than the wavelength of sound waves at the frequencies of interest. As for the one-dimensional thermoviscoelastic problem [Christensen et al., Phys. Rev. E 75, 041502 (2007)], the solution is conveniently formulated in terms of the so-called transfer matrix, which directly links to the boundary conditions that can be experimentally controlled. Once the transfer matrix has been calculated, it is fairly easy to deduce the equations describing various experimentally relevant special cases (boundary conditions that are adiabatic, isothermal, isochoric, etc.). In most situations the relevant frequency-dependent specific heat is the longitudinal specific heat, a quantity that is in between the isochoric and isobaric frequency-dependent specific heats.
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Affiliation(s)
- Tage Christensen
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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