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Jeppe C. Dyre - One of the best experts on this subject based on the ideXlab platform.
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Thermodynamics of condensed matter with strong Pressure-Energy correlations
The Journal of chemical physics, 2012Co-Authors: Trond S. Ingebrigtsen, Thomas B. Schrøder, Lasse Bøhling, Jeppe C. DyreAbstract:We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-Energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, $T=f(s)h(\rho)$. This implies that 1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by $h(\rho)/T={\rm Const.}$, 2) the density-scaling exponent is a function of density only, 3) a Gr{\"u}neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has $h(\rho)=\sum_nC_n\rho^{n/3}$ in which the only non-zero terms are those appearing in the pair potential expanded as $v(r)=\sum_n v_n r^{-n}$. Molecular dynamics simulations of Lennard-Jones type systems confirm the theory.
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Pressure-Energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems
The Journal of chemical physics, 2011Co-Authors: Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Jeppe C. DyreAbstract: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. v131, 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 to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse 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 potential Energy on isochores. It is shown that the new equation of state agrees well with simulations.
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Pressure-Energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams
The Journal of chemical physics, 2009Co-Authors: Nicoletta Gnan, Nicholas P. Bailey, Ulf R. Pedersen, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 state 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 coworkers. 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, as well as explains isochronal superposition for strongly correlating viscous liquids.
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Pressure-Energy correlations in liquids. I. Results from computer simulations
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 compa...
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Pressure Energy correlations in liquids i results from computer simulations
Journal of Chemical Physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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.
Thomas B. Schrøder - One of the best experts on this subject based on the ideXlab platform.
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Thermodynamics of condensed matter with strong Pressure-Energy correlations
The Journal of chemical physics, 2012Co-Authors: Trond S. Ingebrigtsen, Thomas B. Schrøder, Lasse Bøhling, Jeppe C. DyreAbstract:We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-Energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, $T=f(s)h(\rho)$. This implies that 1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by $h(\rho)/T={\rm Const.}$, 2) the density-scaling exponent is a function of density only, 3) a Gr{\"u}neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has $h(\rho)=\sum_nC_n\rho^{n/3}$ in which the only non-zero terms are those appearing in the pair potential expanded as $v(r)=\sum_n v_n r^{-n}$. Molecular dynamics simulations of Lennard-Jones type systems confirm the theory.
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Pressure-Energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems
The Journal of chemical physics, 2011Co-Authors: Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Jeppe C. DyreAbstract: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. v131, 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 to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse 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 potential Energy on isochores. It is shown that the new equation of state agrees well with simulations.
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Pressure-Energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams
The Journal of chemical physics, 2009Co-Authors: Nicoletta Gnan, Nicholas P. Bailey, Ulf R. Pedersen, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 state 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 coworkers. 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, as well as explains isochronal superposition for strongly correlating viscous liquids.
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Pressure-Energy correlations in liquids. I. Results from computer simulations
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 compa...
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Pressure Energy correlations in liquids i results from computer simulations
Journal of Chemical Physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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.
Nicholas P. Bailey - One of the best experts on this subject based on the ideXlab platform.
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Pressure-Energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems
The Journal of chemical physics, 2011Co-Authors: Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Jeppe C. DyreAbstract: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. v131, 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 to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse 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 potential Energy on isochores. It is shown that the new equation of state agrees well with simulations.
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Pressure-Energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams
The Journal of chemical physics, 2009Co-Authors: Nicoletta Gnan, Nicholas P. Bailey, Ulf R. Pedersen, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 state 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 coworkers. 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, as well as explains isochronal superposition for strongly correlating viscous liquids.
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Pressure-Energy correlations in liquids. I. Results from computer simulations
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 compa...
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Pressure Energy correlations in liquids i results from computer simulations
Journal of Chemical Physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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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Pressure-Energy correlations in liquids. II. Analysis and consequences
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract:We present a detailed analysis and discuss consequences of the strong correlations of the configurational parts of Pressure and Energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the previous paper [N. P. Bailey et al., J. Chem. Phys. 129, 184507 (2008)]. The analysis concentrates specifically on the single-component Lennard-Jones system. We demonstrate that the potential may be replaced, at fixed volume, by an effective power law but not simply because only short-distance encounters dominate the fluctuations. Indeed, contributions to the fluctuations are associated with the whole first peak of the radial distribution function, as we demonstrate by an eigenvector analysis of the spatially resolved covariance matrix. The reason the effective power law works so well depends crucially on going beyond single-pair effects and on the constraint of fixed volume. In particular, a better approximation to the potential includes a linear term, which contributes to the mean values of potential Energy and virial, but little to their fluctuations, for density fluctuations which conserve volume. We also study in detail the zero temperature limit of the (classical) crystalline phase, where the correlation coefficient becomes very close, but not equal, to unity, in more than one dimension; in one dimension the limiting value is exactly unity. In the second half of the paper we consider four consequences of strong Pressure-Energy correlations: (1) analyzing experimental data for supercritical argon we find 96% correlation; (2) we discuss the particular significance acquired by the correlations for viscous van der Waals liquids approaching the glass transition: For strongly correlating viscous liquids knowledge of just one of the eight frequency-dependent thermoviscoelastic response functions basically implies knowledge of them all; (3) we reinterpret aging simulations of ortho-terphenyl carried out by Mossa et al. [Eur. Phys. J. B 30, 351 (2002)], showing their conclusions follow from the strongly correlating property; and (4) we briefly discuss the presence of the correlations (after appropriate time averaging) in model biomembranes, showing that significant correlations may be present even in quite complex systems.
Ulf R. Pedersen - One of the best experts on this subject based on the ideXlab platform.
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Pressure-Energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems
The Journal of chemical physics, 2011Co-Authors: Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Jeppe C. DyreAbstract: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. v131, 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 to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse 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 potential Energy on isochores. It is shown that the new equation of state agrees well with simulations.
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Pressure-Energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams
The Journal of chemical physics, 2009Co-Authors: Nicoletta Gnan, Nicholas P. Bailey, Ulf R. Pedersen, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 state 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 coworkers. 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, as well as explains isochronal superposition for strongly correlating viscous liquids.
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Pressure-Energy correlations in liquids. I. Results from computer simulations
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 compa...
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Pressure Energy correlations in liquids i results from computer simulations
Journal of Chemical Physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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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Pressure-Energy correlations in liquids. II. Analysis and consequences
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract:We present a detailed analysis and discuss consequences of the strong correlations of the configurational parts of Pressure and Energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the previous paper [N. P. Bailey et al., J. Chem. Phys. 129, 184507 (2008)]. The analysis concentrates specifically on the single-component Lennard-Jones system. We demonstrate that the potential may be replaced, at fixed volume, by an effective power law but not simply because only short-distance encounters dominate the fluctuations. Indeed, contributions to the fluctuations are associated with the whole first peak of the radial distribution function, as we demonstrate by an eigenvector analysis of the spatially resolved covariance matrix. The reason the effective power law works so well depends crucially on going beyond single-pair effects and on the constraint of fixed volume. In particular, a better approximation to the potential includes a linear term, which contributes to the mean values of potential Energy and virial, but little to their fluctuations, for density fluctuations which conserve volume. We also study in detail the zero temperature limit of the (classical) crystalline phase, where the correlation coefficient becomes very close, but not equal, to unity, in more than one dimension; in one dimension the limiting value is exactly unity. In the second half of the paper we consider four consequences of strong Pressure-Energy correlations: (1) analyzing experimental data for supercritical argon we find 96% correlation; (2) we discuss the particular significance acquired by the correlations for viscous van der Waals liquids approaching the glass transition: For strongly correlating viscous liquids knowledge of just one of the eight frequency-dependent thermoviscoelastic response functions basically implies knowledge of them all; (3) we reinterpret aging simulations of ortho-terphenyl carried out by Mossa et al. [Eur. Phys. J. B 30, 351 (2002)], showing their conclusions follow from the strongly correlating property; and (4) we briefly discuss the presence of the correlations (after appropriate time averaging) in model biomembranes, showing that significant correlations may be present even in quite complex systems.
Nicoletta Gnan - One of the best experts on this subject based on the ideXlab platform.
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Pressure-Energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems
The Journal of chemical physics, 2011Co-Authors: Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Jeppe C. DyreAbstract: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. v131, 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 to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse 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 potential Energy on isochores. It is shown that the new equation of state agrees well with simulations.
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Pressure-Energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams
The Journal of chemical physics, 2009Co-Authors: Nicoletta Gnan, Nicholas P. Bailey, Ulf R. Pedersen, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 state 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 coworkers. 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, as well as explains isochronal superposition for strongly correlating viscous liquids.
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Pressure-Energy correlations in liquids. I. Results from computer simulations
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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 compa...
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Pressure Energy correlations in liquids i results from computer simulations
Journal of Chemical Physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract: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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Pressure-Energy correlations in liquids. II. Analysis and consequences
The Journal of chemical physics, 2008Co-Authors: Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, Jeppe C. DyreAbstract:We present a detailed analysis and discuss consequences of the strong correlations of the configurational parts of Pressure and Energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the previous paper [N. P. Bailey et al., J. Chem. Phys. 129, 184507 (2008)]. The analysis concentrates specifically on the single-component Lennard-Jones system. We demonstrate that the potential may be replaced, at fixed volume, by an effective power law but not simply because only short-distance encounters dominate the fluctuations. Indeed, contributions to the fluctuations are associated with the whole first peak of the radial distribution function, as we demonstrate by an eigenvector analysis of the spatially resolved covariance matrix. The reason the effective power law works so well depends crucially on going beyond single-pair effects and on the constraint of fixed volume. In particular, a better approximation to the potential includes a linear term, which contributes to the mean values of potential Energy and virial, but little to their fluctuations, for density fluctuations which conserve volume. We also study in detail the zero temperature limit of the (classical) crystalline phase, where the correlation coefficient becomes very close, but not equal, to unity, in more than one dimension; in one dimension the limiting value is exactly unity. In the second half of the paper we consider four consequences of strong Pressure-Energy correlations: (1) analyzing experimental data for supercritical argon we find 96% correlation; (2) we discuss the particular significance acquired by the correlations for viscous van der Waals liquids approaching the glass transition: For strongly correlating viscous liquids knowledge of just one of the eight frequency-dependent thermoviscoelastic response functions basically implies knowledge of them all; (3) we reinterpret aging simulations of ortho-terphenyl carried out by Mossa et al. [Eur. Phys. J. B 30, 351 (2002)], showing their conclusions follow from the strongly correlating property; and (4) we briefly discuss the presence of the correlations (after appropriate time averaging) in model biomembranes, showing that significant correlations may be present even in quite complex systems.