arXiv subjects

Jeppe C. Dyre

Publications and source records attributed to Jeppe C. Dyre.

At least 109 records · Page 6Linked to original sources

arXiv2012

Do the repulsive and attractive pair forces play separate roles for the physics of liquids?

According to standard liquid-state theory repulsive and attractive pair forces play distinct roles for the physics of liquids. This paradigm is put into perspective here by demonstrating a continuous series of pair potentials that have virtually the same structure and dynamics, although only some of them have attractive forces of significance. Our findings reflect the fact that the motion of a given particle is determined by the total force on it, whereas the quantity usually discussed in liquid-state theory is the individual pair force.

cond-mat.soft↗

arXiv2012

NVU dynamics. III. Simulating molecules at constant potential energy

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [Ingebrigtsen et al., J. Chem. Phys. 135, 104101 (2011); ibid, 104102 (2011)], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algorithm has the same desirable properties as the Verlet algorithm for Newtonian NVE dynamics, i.e., it is time-reversible and symplectic. Additionally, it was concluded that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit. In this paper, the NVU algorithm for atomic systems is extended to be able to simulate geodesic motion of molecules at constant potential energy. We derive an algorithm for simulating rigid bonds and test this algorithm on three different systems: an asymmetric dumbbell model, Lewis-Wahnstrom OTP, and rigid SPC/E water. The rigid bonds introduce additional constraints beyond that of constant potential energy for atomic systems. The rigid-bond NVU algorithm conserves potential energy, bond lengths, and step length for indefinitely long runs. The quantities probed in simulations give results identical to those of Nose-Hoover NVT dynamics. Since Nose-Hoover NVT dynamics is known to give results equivalent to those of NVE dynamics, the latter results show that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit also for molecular systems.

cond-mat.soft↗

arXiv2012

"Cooling by heating" - demonstrating the significance of the longitudinal specific heat

Heating a solid sphere at the surface induces mechanical stresses inside the sphere. If a finite amount of heat is supplied, the stresses gradually disappear as temperature becomes homogeneous throughout the sphere. We show that before this happens, there is a temporary lowering of pressure and density in the interior of the sphere, inducing a transient lowering of the temperature here. For ordinary solids this effect is small because c_p is almost equal to c_V. For fluent liquids the effect is negligible because their dynamic shear modulus vanishes. For a liquid at its glass transition, however, the effect is generally considerably larger than in solids. This paper presents analytical solutions of the relevant coupled thermoviscoelastic equations. In general, there is a difference between the isobaric specific heat, c_p, measured at constant isotropic pressure and the longitudinal specific heat, c_l, pertaining to mechanical boundary conditions that confine the associated expansion to be longitudinal. In the exact treatment of heat propagation the heat diffusion constant contains c_l rather than c_p. We show that the key parameter controlling the magnitude of the "cooling-by-heating" effect is the relative difference between these two specific heats. For a typical glass-forming liquid, when temperature at the surface is increased by 1 K, a lowering of the temperature in the sphere center of order 5 mK is expected if the experiment is performed at the glass transition. The cooling-by-heating effect is confirmed by measurements on a 19 mm diameter glucose sphere at the glass transition.

cond-mat.soft↗

arXiv2012

The instantaneous shear modulus in the shoving model

We point out that the instantaneous shear modulus of the shoving model for the non-Arrhenius temperature dependence of viscous liquids' relaxation time is the experimentally accessible high-frequency plateau modulus, not the idealized instantaneous affine shear modulus that cannot be measured. Data for a large selection of metallic glasses are compared to three different versions of the shoving model. The original shear-modulus based version shows a slight correlation to the Poisson ratio, which is eliminated by the energy-landscape formulation of the model in which the bulk modulus plays a minor role.

cond-mat.soft↗

arXiv2012

Identical temperature dependence of the time scales of several linear-response functions of two glass-forming liquids

The frequency-dependent dielectric constant, shear and adiabatic bulk moduli, longitudinal thermal expansion coefficient, and longitudinal specific heat have been measured for two van der Waals glass-forming liquids, tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl-4-ether. Within the experimental uncertainties the loss-peak frequencies of the measured response functions have identical temperature dependence over a range of temperatures, for which the Maxwell relaxation time varies more than nine orders of magnitude. The time scales are ordered from fastest to slowest as follows: Shear modulus, adiabatic bulk modulus, dielectric constant, longitudinal thermal expansion coefficient, longitudinal specific heat. The ordering is discussed in light of the recent conjecture that van der Waals liquids are strongly correlating, i.e., approximate single-parameter liquids.

cond-mat.soft↗

arXiv2012

Thermodynamics of condensed matter with strong pressure-energy correlations

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, $T=f(s)h(ρ)$. This implies that 1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by $h(ρ)/T={\rm Const.}$, 2) the density-scaling exponent is a function of density only, 3) a Gr{ü}neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has $h(ρ)=\sum_nC_nρ^{n/3}$ 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.

cond-mat.soft↗

arXiv2012

What constitutes a simple liquid?

Simple liquids are traditionally defined as many-body systems of classical particles interacting via radially symmetric pair potentials. We suggest that a simple liquid should be defined instead by the property of having strong correlation between virial and potential energy equilibrium fluctuations in the NVT ensemble. There is considerable overlap between the two definitions, but also some notable differences. For instance, in the new definition simplicity is not a property of the intermolecular potential only because a liquid is usually only strongly correlating in part of its phase diagram. Moreover, according to the new definition not all simple liquids are atomic (i.e., with radially symmetric pair potentials) and not all atomic liquids are simple. The main part of the paper motivates the new definition of liquid simplicity by presenting evidence that a liquid is strongly correlating if and only if its intermolecular interactions may be ignored beyond the first coordination shell (FCS). This is demonstrated by NVT simulations of structure and dynamics of 15 atomic and molecular model liquids with a shifted-forces cutoff placed at the first minimum of the radial distribution function. No proof is given that the chemical characterization follows from the strong correlation property, but it is shown to be consistent with the existence of isomorphs in strongly correlating liquids' phase diagram. Finally, we note that the FCS characterization of simple liquids calls into question the basis for standard perturbation theory, according to which the repulsive and attractive forces play fundamentally different roles for the physics of liquids.

cond-mat.soft↗

arXiv2012

Measuring the dynamic thermal expansivity of molecular liquids near the glass transition

Based on previous works on polymers by Bauer et al. [Phys, Rev. B (2000)], this paper describes a capacitative method for measuring the dynamical expansion coefficient of a viscous liquid. Data are presented for the glass-forming liquid tetramethyl tetraphenyl trisiloxane (DC704) in the ultraviscous regime. Compared to the method of Bauer et al. the dynamical range has been extended by making time-domain experiments and by making very small and fast temperature steps. The modelling of the experiment presented in this paper includes the situation where the capacitor is not full because the liquid contracts when cooling from room temperature down to around the glass-transition temperature, which is relevant when measuring on a molecular liquid rather than polymer.

cond-mat.soft↗

arXiv2011

Beyond power-law density scaling: Theory, Simulation, and Experiment

Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. Many liquids have been shown to obey power-law density scaling, according to which the relaxation time is a function of density to some power over temperature. We show that power-law density scaling breaks down for larger density variations than usually studied. This is demonstrated by simulations of the Kob-Andersen binary Lennard-Jones mixture and two molecular models, as well as by experimental results for two van der Waals liquids. A more general form of density scaling is derived, which is consistent with results for all the systems studied. An analytical expression for the scaling function for liquids of particles interacting via generalized Lennard-Jones potentials is derived and shown to agree very well with simulations. This effectively reduces the problem of understanding the viscous slowing down from being a quest for a function of two variables to a search for a single-variable function.

cond-mat.soft↗

arXiv2011

Isomorphs in the phase diagram of a model liquid without inverse power law repulsion

It is demonstrated by molecular dynamics simulations that liquids interacting via the Buckingham potential are strongly correlating, i.e., have regions of their phase diagram where constant-volume equilibrium fluctuations in the virial and potential energy are strongly correlated. A binary Buckingham liquid is cooled to a viscous phase and shown to have isomorphs, which are curves in the phase diagram along which structure and dynamics in appropriate units are invariant to a good approximation. To test this, the radial distribution function, and both the incoherent and coherent intermediate scattering function are calculated. The results are shown to reflect a hidden scale invariance; despite its exponential repulsion the Buckingham potential is well approximated by an inverse power-law plus a linear term in the region of the first peak of the radial distribution function. As a consequence the dynamics of the viscous Buckingham liquid is mimicked by a corresponding model with purely repulsive inverse-power-law interactions. The results presented here closely resemble earlier results for Lennard-Jones type liquids, demonstrating that the existence of strong correlations and isomorphs does not depend critically on the mathematical form of the repulsion being an inverse power law.

cond-mat.soft↗

arXiv2011

Simplistic Coulomb forces in molecular dynamics: Comparing the Wolf and shifted-force approximations

This paper compares the Wolf method to the shifted forces (SF) method for efficient computer simulation of isotropic systems interacting via Coulomb forces, taking results from the Ewald summation method as representing the true behavior. We find that for the Hansen-McDonald molten salt model the SF approximation overall reproduces the structural and dynamical properties as accurately as does the Wolf method. It is shown that the optimal Wolf damping parameter depends on the property in focus, and that neither the potential energy nor the radial distribution function are useful measures for the convergence of theWolf method to the Ewald summation method. The SF approximation is also tested for the SPC/Fw model of liquid water at room temperature, showing good agreement with both the Wolf and the particle mesh Ewald methods; this confirms previous findings [Fennell & Gezelter, J. Chem. Phys. {\bf 124}, 234104 (2006)]. Beside its conceptualsimplicity the SF approximation implies a speed-up of a factor 2 to 3 compared to the Wolf method (which is in turn much faster than the Ewald method).

cond-mat.mes-hall↗

arXiv2011

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.

cond-mat.soft↗

arXiv2011

NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface

An algorithm is derived for computer simulation of geodesics on the constant potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant potential energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, simulations show that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.

cond-mat.soft↗

arXiv2011

NVU dynamics. II. Comparing to four other dynamics

In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here simulations of this 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 Gaussian Lennard-Jones 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 then 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 section 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 Nose-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make their single-particle diffusion constants identical to those of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.

cond-mat.soft↗

arXiv2011

Role of the first coordination shell in determining the equilibrium structure and dynamics of simple liquids

The traditional view that the physical properties of a simple liquid are determined primarily by its repulsive forces was recently challenged by Berthier and Tarjus, who showed that in some cases ignoring the attractions leads to large errors in the dynamics [L. Berthier and G. Tarjus, Phys. Rev. Lett. 103, 170601 (2009); J. Chem. Phys. 134, 214503 (2011)]. We present simulations of the standard Lennard-Jones liquid at several condensed-fluid state points, including a fairly low density state and a very high density state, as well as simulations of the Kob-Andersen binary Lennard-Jones mixture at several temperatures. By varying the range of the forces, results for the thermodynamics, dynamics, and structure show that the determining factor for getting the correct statics and dynamics is not whether or not the attractive forces {\it per se} are included in the simulations. What matters is whether or not interactions are included from all particles within the first coordination shell (FCS) - the attractive forces can thus be ignored, but only at extremely high densities. The recognition of the importance of a local shell in condensed fluids goes back to van der Waals; our results confirm this idea and thereby the basic picture of the old hole- and cell theories for simple condensed fluids.

cond-mat.soft↗

arXiv2011

Do all liquids become strongly correlating at high pressure?

We present molecular dynamics simulations studying the influence of pressure on the correlation between the constant-volume thermal equilibrium fluctuations of virial W and potential energy U, focusing on liquids that are not strongly correlating at low pressure, i.e., do not have a WU correlation coefficient above 0.9. The systems studied are the two hydrogen-bonded liquids GROMOS methanol and TIT5P water, the ionic liquid defined by a united-atom model of the 1-butyl-3-methyl-imidazolium nitrate and, for reference, the standard single-component Lennard-Jones liquid. The simulations were performed for pressures varying from 0 GPa to 10 GPa. For all systems studied we find that the virial / potential energy correlation increases with increasing pressure. This suggests that if crystallization is avoided, all liquids become strongly correlating at sufficiently high pressure.

cond-mat.soft↗

arXiv2011

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

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.

cond-mat.soft↗

arXiv2011

Shifted forces in molecular dynamics

Simulations involving the Lennard-Jones potential usually employ a cut-off at $r=2.5σ$. This paper investigates the possibility of reducing the cut-off. Two different cut-off implementations are compared, the standard shifted potential cut-off and the less commonly used shifted forces cut-off. The first has correct forces below the cut-off, whereas the shifted forces cut-off modifies Newton's equations at all distances. The latter is nevertheless superior; we find that for most purposes realistic simulations may be obtained using a shifted-forces cut-off at $r=1.5σ$, even though the pair force is here 30 times larger than at $r=2.5σ$.

cond-mat.soft↗