Density-scaling Exponent Research Articles

The breakdown of the direct relation between the density scaling exponent of rotational dynamics and the intermolecular interaction potential for molecular systems with purely repulsive intermolecular forces

The breakdown of the direct relation between the density scaling exponent of rotational dynamics and the intermolecular interaction potential for molecular systems with purely repulsive intermolecular forces

The breakdown of the direct relation between the density scaling exponent and the intermolecular interaction potential for molecular systems with purely repulsive intermolecular forces

In this work, we question the generally accepted statement that the character of intermolecular interactions can be directly determined from the scaling exponent. We show that the scaling exponent evidently differs on the molecular architecture for pure inverse power law systems. Since these systems are characterized by a well-defined dependency between the intermolecular virial and potential energy, the results contradict theoretical predictions and previous reports. Moreover, we suggest that the recently proposed “molecular force” method also returns the value that varies from the one scaling the dynamics. Finally, the obtained result allows us to conclude that the value of the density scaling exponent for real liquids depends on intramolecular interactions.

Predicting the Density-Scaling Exponent of a Glass-Forming Liquid from Complex Dielectric Permittivity Measurements.

One of the challenging problems related to the liquid-glass transition phenomenon is establishing a link between the character of intermolecular interactions and the behavior of molecular dynamics. Introducing the density scaling concept, according to which dynamic quantities, e.g., viscosity or structural relaxation time (τ_{α}) measured at different thermodynamic conditions are expressed as a single universal curve if plotted against ρ^{γ}/T, led to significant progress in solving this problem since the scaling exponent γ defines the steepness of the repulsive part of the intermolecular potential. Herein, we found that relaxation dynamics of van der Waals and H-bonding glass formers, for which the Kirkwood factor (g_{K}) is an isomorph-invariant quantity, satisfy an alternative scaling, logτ_{α} vs T(Δϵ_{s}T)^{-γ}. As a result, the exponent γ is determined from the temperature and pressure evolutions of τ_{α} and dielectric relaxation strength Δϵ-both obtained in a single dielectric experiment, which makes the γ coefficient to be accessed in the future for an extensive database of glass-forming liquids.

The origin of the density scaling exponent for polyatomic molecules and the estimation of its value from the liquid structure.

In this article, we unravel the problem of interpreting the density scaling exponent for the polyatomic molecules representing the real van der Waals liquids. Our studies show that the density scaling exponent is a weighted average of the exponents of the repulsive terms of all interatomic interactions that occur between molecules, where the potential energy of a given interaction represents its weight. It implies that potential energy is a key quantity required to calculate the density scaling exponent value for real molecules. Finally, we use the well-known method for potential energy estimation and show that the density scaling exponent could be successfully predicted from the liquid structure for fair representatives of the real systems.

Connecting entropy scaling and density scaling.

It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches. The residual entropy and the effective hardness of interaction (itself a derivative at constant residual entropy) are studied for the Lennard-Jones monomer and dimer as well as a range of rigid molecular models for carbon dioxide. It is observed that the density scaling exponent appears to be related to the two-body interactions in the dilute-gas limit.

Lines of invariant physics in the isotropic phase of the discotic Gay-Berne model

The Gay-Berne model is studied numerically with a choice of parameters allowing for the formation of a discotic liquid crystal at low temperatures. We show that the model has strong virial potential-energy correlations in the isotropic phase at high temperatures, i.e., it obeys the criterion for the existence of isomorphs, which are curves of approximately invariant structure and dynamics. These properties are demonstrated to be approximately invariant in reduced units along the isomorph studied. The isomorph is described well by the constant density-scaling exponent 11.5, a number that is significantly larger than the density-scaling exponents of various Lennard-Jones models that are always below 6.

Generalized hydrodynamics of the Lennard-Jones liquid in view of hidden scale invariance.

In recent years lines along which structure and dynamics are invariant to a good approximation, so-called isomorphs, have been identified in the thermodynamic phase diagrams of several model liquids and solids. This paper reports computer simulation data of the transverse and longitudinal collective dynamics at different length scales along an isomorph of the Lennard-Jones system. Our findings are compared to corresponding results along an isotherm and an isochore. Confirming the theoretical prediction, the reduced-unit dynamics of the transverse momentum density is invariant to a good approximation along the isomorph on all time and length scales. Likewise, the wave-vector dependent shear-stress autocorrelation function is found to be isomorph invariant (with minor deviations at very short times). A similar invariance is not seen along the isotherm or the isochore. Using a spatially nonlocal hydrodynamic model for the transverse momentum-density time-autocorrelation function, the macroscopic shear viscosity and its wave dependence are determined, demonstrating that the shear viscosity is isomorphic invariant on all length scales studied. This analysis implies the existence of a length scale that is isomorph invariant in reduced units, i.e., which characterizes each isomorph. The transverse sound-wave velocity, the Maxwell relaxation time, and the rigidity shear modulus are also isomorph invariant. In contrast to the isomorph invariance of all aspects of the transverse dynamics, the reduced-unit dynamics of the mass density is not invariant on length scales longer than the interparticle distance. By fitting to a generalized hydrodynamic model, we extract values for the wave-vector-dependent thermal diffusion coefficient, sound attenuation coefficient, and adiabatic sound velocity. The isomorph variation of these quantities in reduced units on long length scales can be eliminated by scaling with the density-scaling exponent, a fundamental quantity in the isomorph theory framework; this is an empirical observation that remains to be explained theoretically.

Extreme case of density scaling: The Weeks-Chandler-Andersen system at low temperatures

This paper studies numerically the Weeks-Chandler-Andersen system, which is shown to obey hidden scale invariance with a density-scaling exponent that varies from below 5 to above 500. This unprecedented variation makes it advantageous to use the fourth-order Runge-Kutta algorithm for tracing out isomorphs. Good isomorph invariance of structure and dynamics is observed over more than three orders of magnitude temperature variation. For all state points studied, the virial potential-energy correlation coefficient and the density-scaling exponent are controlled mainly by the temperature. Based on the assumption of statistically independent pair interactions, a mean-field theory is developed that rationalizes this finding and provides an excellent fit to data at low temperatures.

Virial-potential-energy correlation and its relation to density scaling for quasireal model systems.

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.

Density scaling of generalized Lennard-Jones fluids in different dimensions

Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d=1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.

On the 2015 St. Patrick's Storm Turbulent State of the Ionosphere: Hints From the Swarm Mission

AbstractThe scaling features of electron density fluctuations during the St. Patrick's magnetic storm (17 March 2015) are analyzed to try to characterize the possible turbulent nature of the ionosphere during the development of the geomagnetic storm. The electron density values recorded by two of the three satellites of Swarm constellation during a period of 7 days (16–22 March 2015) around the storm peak are analyzed at middle‐ and high‐latitude regions in both hemispheres. The analysis reveals interesting patterns in the scaling properties of electron density fluctuations and a possible explanation for the occurrence of high values of the Rate of change Of the electron Density Index (RODI). Indeed, the obtained results seem to suggest that very high values of RODI, which describes the structuring of the plasma within a fixed time and is used as an ionospheric disturbance index, are correlated with the antipersistent character of electron density fluctuations and with the values around 5/3 of the power spectral density scaling exponent. These features are independent of the different phases of the analyzed geomagnetic storm and seem to support the idea of a fluid and/or magnetohydrodynamic turbulence as the main responsible of the high values of RODI recorded at high latitudes in the auroral and polar cap regions.

Exploring the connection between the density-scaling exponent and the intermolecular potential for liquids on the basis of computer simulations of quasireal model systems.

In this paper, based on the molecular dynamics simulations of quasireal model systems, we propose a method for determination of the effective intermolecular potential for real materials. We show that in contrast to the simple liquids, the effective intermolecular potential for the studied systems depends on the thermodynamic conditions. Nevertheless, the previously established relationship for simple liquids between the exponent of the inverse power law approximation of intermolecular potential and the density-scaling exponent is still preserved when small enough intermolecular distances are considered. However, our studies show that molecules approach each other at these very short distances relatively rarely. Consequently, only sparse interactions between extremely close molecules determine the value of the scaling exponent and then strongly influence the connection between dynamics and thermodynamics of the whole system.

The complex behavior of the "simplest" liquid: Breakdown of density scaling in tetramethyl tetraphenyl trisiloxane.

Dielectric relaxation measurements, in combination with density determinations, on tetramethyl tetraphenyl trisiloxane (DC704) over an unusually broad range of temperatures and pressures revealed a state-point dependency in its density scaling exponent. This is the first unambiguous experimental demonstration of a breakdown of density scaling in a nonassociated glass-forming material, and unanticipated for DC704, among the "simplest" of liquids, having a constant breadth of the relaxation dispersion and a Prigogine-Defay ratio near unity characteristic of approximate single-parameter systems. We speculate that the anomalous behavior has origins in the large value of its scaling exponent and relative flexibility of the chemical structure.

Hidden scale invariance at high pressures in gold and five other face-centered-cubic metal crystals

Recent density functional theory simulations showed that metals have a hitherto overlooked symmetry termed "hidden scale invariance" [Hummel et al., Phys. Rev. B 92, 174116 (2015)PRBMDO1098-012110.1103/PhysRevB.92.174116]. This scaling property implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics are invariant to a good approximation when given in properly reduced units. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. This paper investigates consequences and implications of the isomorph theory in six metallic crystals: Au, Ni, Cu, Pd, Ag, and Pt. The data are obtained from molecular dynamics simulations employing many-body effective medium theory (EMT) to model the atomic interactions realistically. We test the predictions from isomorph theory for structure and dynamics by means of the radial distribution and the velocity autocorrelation functions, as well as the prediction of instantaneous equilibration after a jump between two isomorphic state points. Many properties of crystals tend to be dominated by defects, and many of the properties associated with these defects are expected to be isomorph invariant as well. This is investigated in this paper for the case of vacancy diffusion. In regard to the perfect crystal properties, we find the predicted invariance of structure and also, though less perfectly, of dynamics. We show results on the variation of the density-scaling exponent γ, which can be related to the Grüneisen parameter, for all six metals. We consider large density changes up to a factor of two, corresponding to very high pressures. Unlike systems modeled using the Lennard-Jones potential where the density-scaling exponent γ is almost constant, this quantity varies substantially when using the EMT potential and is also strongly material dependent.

The effect of molecular architecture on the physical properties of supercooled liquids studied by MD simulations: Density scaling and its relation to the equation of state.

Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement results obtained for real materials. One of the examples is an intriguing problem within the density scaling idea that has attracted attention in recent decades due to its hallmarks of universality, i.e., the fact that the difference between the density scaling exponent and the exponent of the equation of state is observed for real materials, whereas it has not been reported for the model system. In this paper, we use new model molecules of simple but anisotropic architecture to study the effect of molecular anisotropy on the dynamic and thermodynamic properties of the system. We identify the applicable range of intermolecular interactions for a given physical process, and then we explain the reason for observed differences between the behavior of the model and real systems. It demonstrates that the new model systems open broad perspectives for simulation and theoretical research, for example, into unifying concepts in the glass transition physics.

Isochronal superposition and density scaling of the α-relaxation from pico- to millisecond.

The relaxation dynamics in two van der Waals bonded liquids and one hydrogen-bonding molecular liquid are studied as a function of pressure and temperature by incoherent neutron scattering using simultaneous dielectric spectroscopy. The dynamics are studied in a range of alpha relaxation times from pico- to milliseconds, primarily in the equilibrium liquid state. In this range, we find that isochronal superposition and density scaling work not only for the two van der Waals liquids but also for the hydrogen-bonding liquid, though the density scaling exponent is much smaller for the latter. Density scaling and isochronal superposition are seen to break down for intra-molecular dynamics when it is separated in time from the alpha relaxation, in close agreement with previous observations from molecular dynamics simulations.

Vitrification and Density Scaling of Polyurea at Pressures up to 6 GPa

Elastomeric polyurea is an important polymer for impact mitigation, but viscoelasticity, nonlinearity, pressure-effects, and the onset of the glass transition complicate analyses of experimental measurements. Consequently, development efforts rely on modeling, which in turn requires accurate potential functions. To address this issue, we measured the glass transition, Tg, of polyurea at pressures up to 6 GPa in a diamond anvil cell. In this method, Tg is determined as the lowest temperature at which the pressure is hydrostatic. From the pressure dependence of Tg, in combination with equation of state measurements at pressures up to 1 GPa, the density scaling exponent for the polyurea was obtained. The value 2.39 ± 0.06 is in accord with previous determinations based on lower pressure experiments; thus, density scaling remains valid for density changes as large as 50%. The scaling exponent reflects the steepness of the intermolecular repulsive potential and should serve as a guide to the choice of potentia...

Density-scaling exponents and virial potential-energy correlation coefficients for the (2n, n) Lennard-Jones system

This paper investigates the relation between the density-scaling exponent $$\gamma $$ and the virial potential-energy correlation coefficient R at several thermodynamic state points in three dimensions for the generalized (2n, n) Lennard-Jones (LJ) system for $$n=4, 9, 12, 18$$ , as well as for the standard $$n=6$$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $$\gamma \cong 3nR/d$$ in d dimensions. This result is discussed in light of the approximate “extended inverse power law” description of generalized LJ potentials (Bailey N P et al. 2008 J. Chem. Phys. 129 184508). In the plot of $$\gamma $$ versus R there is in all cases a transition around $$R\approx 0.9$$ , above which $$\gamma $$ starts to decrease as R approaches unity. This is consistent with the fact that $$\gamma \rightarrow 2n/d$$ for $$R\rightarrow 1$$ , a limit that is approached at high densities and/or high temperatures at which the repulsive $$r^{-2n}$$ term dominates the physics. The paper presents numerical data for the density-scaling exponent $$\gamma $$ and the virial potential-energy correlation coefficient R for generalized (2n, n) Lennard-Jones (LJ) systems. An unanticipated linear relation is observed between R and a properly scaled version of $$\gamma $$ .

Simplicity of condensed matter at its core: generic definition of a Roskilde-simple system.

The isomorph theory is reformulated by defining Roskilde-simple systems by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a different density. If the potential energy as a function of all particle coordinates is denoted by U(R), this requirement translates into U(Ra) < U(Rb) ⇒ U(λRa) < U(λRb). Isomorphs remain curves in the thermodynamic phase diagram along which structure, dynamics, and excess entropy are invariant, implying that the phase diagram is effectively one-dimensional with respect to many reduced-unit properties. In contrast to the original formulation of the isomorph theory, however, the density-scaling exponent is not exclusively a function of density and the isochoric heat capacity is not an exact isomorph invariant. A prediction is given for the latter quantity's variation along the isomorphs. Molecular dynamics simulations of the Lennard-Jones and Lennard-Jones Gaussian systems validate the new approach.

Estimating the density-scaling exponent of a monatomic liquid from its pair potential

This paper investigates two conjectures for calculating the density dependence of the density-scaling exponent γ of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for γ directly in terms of the pair potential. The second conjecture is a refined version of this involving the most likely nearest-neighbor distance determined from the pair-correlation function. The conjectures are tested by simulations of three systems, one of which is the standard Lennard-Jones liquid. While both expressions give qualitatively correct results, the second is more accurate.