arXiv subjects

Jeppe C. Dyre

Publications and source records attributed to Jeppe C. Dyre.

At least 37 records · Page 2Linked to original sources

arXiv2023

Active-matter isomorphs in the size-polydisperse Ornstein-Uhlenbeck Lennard-Jones model

This paper studies size-polydisperse Lennard-Jones systems described by active Ornstein-Uhlenbeck particle dynamics. The focus is on the existence of isomorphs (curves of invariant structure and dynamics) in the model's three-dimensional phase diagram. Isomorphs are traced out from a single steady-state configuration by means of the configurational-temperature method. Good invariance of the reduced-unit radial distribution function and the mean-square displacement as a function of time is demonstrated for three uniform-distribution polydispersities, 12%, 23%, and 29%. Comparing to active-matter isomorphs generated by the analytical direct-isomorph-check method, the latter give somewhat poorer invariance of the structure, but better invariance of the dynamics. We conclude that both methods can be used to quickly get an overview of the phase diagram of polydisperse AOUP models involving a potential-energy function obeying the hidden-scale-invariance property required for isomorph theory to apply.

cond-mat.soft↗

arXiv2023

Scaling properties of liquid dynamics predicted from a single configuration: Small rigid molecules

Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the direct-isomorph-check method. Recently a new method based on the scaling properties of forces was introduced and shown to work very well for atomic systems [T. B. Schroder, Phys. Rev. Lett. 129, 245501 (2022)]. A unique feature of this method is that it only requires a single equilibrium configuration for tracing out an isomorph. We here test generalizations of this method to molecular systems and compare to simulations of three simple molecular models: the asymmetric dumbbell model of two Lennard-Jones spheres, the symmetric inverse-power-law dumbbell model, and the Lewis-Wahnström o-terphenyl model. We introduce and test two force-based and one torque-based methods, all of which require just a single configuration for tracing out an isomorph. Overall, the method based on requiring invariant center-of-mass reduced forces works best.

cond-mat.soft↗

arXiv2023

Hidden scale invariance in the Gay-Berne model. II. Smectic B phase

This paper complements a previous study of the isotropic and nematic phases of the Gay-Berne liquid-crystal model [Mehri et al., Phys. Rev. E 105, 064703 (2022)] with a study of its smectic B phase found at high density and low temperatures. We find also in this phase strong correlations between the virial and potential-energy thermal fluctuations, reflecting hidden scale invariance and implying the existence of isomorphs. The predicted approximate isomorph invariance of the physics is confirmed by simulations of the standard and orientational radial distribution functions, the mean-square displacement as a function of time, as well as the force, torque, velocity, angular velocity, and orientational time-autocorrelation functions. The regions of the Gay-Berne model that are relevant for liquid-crystal experiments can thus fully be simplified via the isomorph theory.

cond-mat.soft↗

arXiv2023

Even strong energy polydispersity does not affect the average structure and dynamics of simple liquids

Size-polydisperse liquids have become standard models for avoiding crystallization, thereby enabling studies of supercooled liquids and glasses formed, e.g., by colloidal systems. Purely \textit{energy} polydisperse liquids have been studied much less, but provide an interesting alternative. We here study numerically the difference in structure and dynamics obtained by introducing these two kinds of polydispersity into systems of particles interacting via the Lennard-Jones and EXP pair potentials. To a very good approximation, the average pair structure and dynamics are unchanged even for strong energy polydispersity, while this is not the case for size-polydisperse systems. When the system at extreme energy polydispersity undergoes a continuous phase separation into lower and higher particle-energy regions whose structure and dynamics are different from the average, the average structure and dynamics are still virtually the same as for the monodisperse system. Our findings are consistent with the fact that the distribution of forces on the individual particles do not change when energy polydispersity is introduced, while they do change in the case of size polydispersity. A theoretical explanation of our findings remains to be found, however.

cond-mat.soft↗

arXiv2023

Comparing zero-parameter theories for the WCA and harmonic-repulsive melting lines

The melting line of the Weeks-Chandler-Andersen (WCA) system was recently determined accurately and compared to the predictions of four analytical hard-sphere approximations [Attia et al., J. Chem. Phys. 157, 034502 (2022)]. Here, we study an alternative zero-parameter prediction based on the isomorph theory, the input of which relate to properties at a single reference state point on the melting line. The two central assumptions made are that the harmonic-repulsive potential approximates the WCA potential and that pair collisions are uncorrelated. The new approach gives excellent predictions at high temperatures, while the hard-sphere-theory based predictions are better at lower temperatures. Supplementing the WCA investigation, the face-centered-crystal to fluid coexistence line is determined for a system of harmonic-repulsive particles and compared to the zero-parameter theories. The results indicate that the excellent isomorph-theory predictions for the WCA potential at higher temperatures may be partly due to a cancellation of errors between the two above-mentioned assumptions.

cond-mat.stat-mech↗

arXiv2023

Configurational temperature in active matter. I. Lines of invariant physics in the phase diagram of the Ornstein-Uhlenbeck model

This paper shows that the configurational temperature of liquid-state theory, $\Tc$, defines an energy scale, which can be used for adjusting model parameters of active Ornstein-Uhlenbeck particle (AOUP) models in order to achieve approximately invariant structure and dynamics upon a density change. The required parameter changes are calculated from the variation of a single configuration's $\Tc$ for a uniform scaling of all particle coordinates. The resulting equations are justified theoretically for models involving a potential-energy function with hidden scale invariance. The validity of the procedure is illustrated by computer simulations of the Kob-Andersen binary Lennard-Jones AOUP model, demonstrating lines of approximate reduced-unit invariance of the radial distribution function and time-dependent mean-square displacement.

cond-mat.soft↗

arXiv2023

Configurational temperature in active matter. II. Quantifying the deviation from thermal equilibrium

This paper suggests using the configurational temperature $\Tc$ for quantifying how far an active-matter system is from thermal equilibrium. We measure this ``distance'' by the ratio of the systemic temperature $\Ts$ to $\Tc$, where $\Ts$ is the canonical-ensemble temperature for which the average potential energy is equal to that of the active-matter system. $\Tc$ is ``local'' in the sense that it is the average of a function, which only depends on how the potential energy varies in the vicinity of a given configuration; in contrast $\Ts$ is a global quantity. The quantity $\Ts/\Tc$ is straightforward to evaluate in a computer simulation; equilibrium simulations in conjunction with a single steady-state active-matter configuration are enough to determine $\Ts/\Tc$. We validate the suggestion that $\Ts/\Tc$ quantifies the deviation from thermal equilibrium by data for the radial distribution function of 3d Kob-Andersen and 2d Yukawa active-matter models with active Ornstein-Uhlenbeck and active Brownian Particle dynamics. Moreover, we show that $\Ts/\Tc$, structure, and dynamics of the homogeneous phase are all approximately invariant along the motility-induced phase separation (MIPS) boundary in the phase diagram of the 2d Yukawa model. The measure $\Ts/\Tc$ is not limited to active matter; it can be used for quantifying how far any system involving a potential-energy function, e.g., a driven Hamiltonian system, is from thermal equilibrium.

cond-mat.soft↗

arXiv2022

Isomorph invariance in the liquid and plastic-crystal phases of asymmetric-dumbbell models

We present a numerical study of the asymmetric dumbbell model consisting of ``molecules'' constructed as two different-sized Lennard-Jones spheres connected by a rigid bond. In terms of the largest (A) particle radius, we report data for the structure and dynamics of the liquid phase for the bond lengths 0.05, 0.1, 0.2, and 0.5, and analogous data for the plastic-crystal phase for the bond lengths 0.05, 0.1, 0.2, and 0.3. Structure is probed by means of the AA, AB, and BB radial distribution functions. Dynamics is probed via the A and B particle mean-square displacement as functions of time and via the rotational time-autocorrelation function. Consistent with the systems' strong virial potential-energy correlations, the structure and dynamics are found to be isomorph invariant to a good approximation in reduced units, while they generally vary considerably along isotherms of the same (20%) density variation. Even the rotational time-autocorrelation function, which due to the constant bond length is not predicted to be isomorph invariant, varies more along isotherms than along isomorphs. Our findings provide the first validation of isomorph-theory predictions for plastic crystals for which isomorph invariance, in fact, is found to apply better than in the liquid phase of asymmetric-dumbbell models.

cond-mat.soft↗

arXiv2022

Distance-as-time in physical aging

Although it has been known for half a century that the physical aging of glasses in experiments is described well by a linear thermal-history convolution integral over the so-called material time, the microscopic definition and interpretation of the material time remains a mystery. We propose that the material-time increase over a given time interval reflects the distance traveled by the system's particles. Different possible distance measures are discussed, starting from the standard mean-square displacement and its inherent-state version that excludes the vibrational contribution. The viewpoint adopted, which is inspired by and closely related to pioneering works of Cugliandolo and Kurchan of the 1990s, implies a "geometric reversibility" and a "unique-triangle property" characterizing the system's path in configuration space during aging. Both of these properties are inherited from equilibrium; they are confirmed by computer simulations of an aging binary Lennard-Jones system. Our simulations show that the slow particles control the material time. This motivates a "dynamic-rigidity-percolation" picture of physical aging. The numerical data show that the material time is dominated by the slowest particles' inherent mean-square displacement, which is conveniently quantified by the inherent harmonic mean-square displacement. This distance measure collapses data for potential-energy aging well in the sense that the normalized relaxation functions following different temperature jumps are almost the same function of the material time. Finally, the standard Tool-Narayanaswamy linear material-time convolution integral description of physical aging is derived from the assumption that when time is replaced by distance in the above sense, an aging system is described by the same expression as that of linear-response theory.

cond-mat.soft↗

arXiv2022

Single-parameter aging in the weakly nonlinear limit

Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for non-crystalline materials like polymers and inorganic glasses, both in production and during subsequent use. The Narayanaswamy theory from 1971 describes physical aging - an inherently nonlinear phenomenon - in terms of a linear convolution integral over the so-called material time $ξ$. The resulting "Tool-Narayanaswamy (TN) formalism" is generally recognized to provide an excellent description of physical aging for small, but still highly nonlinear temperature variations. The simplest version of the TN formalism is single-parameter aging according to which the clock rate $dξ/dt$ is an exponential function of the property monitored [T. Hecksher et al., J. Chem. Phys. 142, 241103 (2015)]. For temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation for property monitored, involving a system-specific function. The present paper shows analytically that the solution to this equation to first order in the temperature variation has a universal expression in terms of the zeroth-order solution, $R_0(t)$. Numerical data for a binary Lennard-Jones glass former probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging correctly from $R_0(t)$ (which by the fluctuation-dissipation theorem is the normalized equilibrium potential-energy time-autocorrelation function).

cond-mat.soft↗

arXiv2022

Hidden scale invariance in the Gay-Berne model

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity. There we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden-scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the reduced-unit time-autocorrelation functions of the mean-square displacement, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the particles and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.

cond-mat.soft↗

arXiv2022

Comparing four hard-sphere approximations for the low-temperature WCA melting line

By combining interface-pinning simulations with numerical integration of the Clausius-Clapeyron equation we determine accurately the melting-line coexistence pressure and fluid/crystal densities of the Weeks-Chandler-Andersen (WCA) system covering four decades of temperature. The data are used for comparing the melting-line predictions of the Boltzmann, Andersen-Weeks-Chandler, Barker-Henderson, and Stillinger hard-sphere approximations. The Andersen-Weeks-Chandler and the Barker-Henderson theories give the most accurate predictions, and they both work excellently in the zero-temperature limit for which analytical expressions are derived here.

cond-mat.stat-mech↗

arXiv2022

Rheological model for the alpha relaxation of glass-forming liquids and its comparison to data for DC704 and DC705

Dynamic shear-modulus data are presented for the two silicone oils DC704 and DC705 for frequencies between 1 mHz and 10 kHz at temperatures covering more than five decades of relaxation-time variation. The data are fitted to the alpha part of a phenomenological model previously shown to describe well the dynamic shear modulus of squalane, which has a large beta process [Hecksher \textit{et al.}, J. Chem. Phys. \textbf{146}, 154504 (2017)]; that model is characterized by additivity of the alpha and beta shear compliance and by a high-frequency decay of the alpha process in proportion to $ω^{-1/2}$ in which $ω$ is the angular frequency. The fits of the alpha part of this model to the DC704 and DC705 data are compared to fits by a Havriliak-Negami type model, the Barlow-Erginsav-Lamb model, and a Cole-Davidson type model. At all temperatures the best fit is obtained by the alpha part of the squalane model. This strengthens the conjecture that so-called $\sqrt{t}$-relaxation, leading to high-frequency decays proportional to $ω^{-1/2}$, is a general characteristic of the alpha relaxation of supercooled liquids [Dyre, Phys. Rev. E {\bf 74}, 021502 (2006); Nielsen \textit{et al.}, J. Chem. Phys. \textbf{130}, 154508 (2009); Pabst \textit{et al.}, J. Phys. Chem. Lett. \textbf{12}, 3685 (2021)].

cond-mat.soft↗

arXiv2022

Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time

The noncrystalline glassy state of matter plays a role in virtually all fields of materials science and offers complementary properties to those of the crystalline counterpart. The caveat of the glassy state is that it is out of equilibrium and therefore exhibits physical aging, i.e., material properties change over time. For half a century, the physical aging of glasses has been known to be described well by the material-time concept, although the existence of a material time has never been directly validated. We do this here by successfully predicting the aging of the molecular glass 4-vinyl-1,3-dioxolan-2-one from its linear relaxation behavior. This establishes the defining property of the material time. Via the fluctuation-dissipation theorem, our results imply that physical aging can be predicted from thermal-equilibrium fluctuation data, which is confirmed by computer simulations of a binary liquid mixture.

cond-mat.soft↗

arXiv2021

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 simulations 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 at all time and length scales. Likewise, the wave-vector dependent shear-stress autocorrelation function is found to be isomorph invariant. A similar invariance is not seen along the isotherm or the isochore. Using a spatially non-local 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 isomorph invariant on all length scales studied. This analysis implies the existence of a novel length scale which characterizes each isomorph. The transverse sound-wave velocity, the Maxwell relaxation time, and the rigidity shear modulus are also isomorph invariant. In contrast, the reduced-unit dynamics of the mass density is not invariant at length scales longer than the inter-particle 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 at long length scales can be eliminated by scaling with the density-scaling, a fundamental quantity in the isomorph theory framework, an empirical observation that remains to be explained theoretically.

cond-mat.soft↗

arXiv2021

Does mesoscopic elasticity control viscous slowing down in glassforming liquids?

The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase of the activation barrier $ΔE(T)$ with decreasing temperature $T$. A class of theoretical frameworks -- known as elastic models -- attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus $G_\infty(T)$. While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose that viscous slowing down is controlled by a mesoscopic elastic stiffness $κ(T)$, defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent states. First, we show that $κ(T)$ -- which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses -- increases more strongly with decreasing $T$ than the macroscopic inherent state shear modulus $G(T)$ in several computer liquids. Second, we show that the simple relation $ΔE(T)\proptoκ(T)$ holds remarkably well for some computer liquids, implying a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the $ΔE(T) \propto κ(T)$ relation holds, from those in which it does not, is that the latter feature highly granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. [Rest of abstract abridged]

cond-mat.soft↗

arXiv2021

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

This paper studies numerically the Weeks-Chandler-Andersen (WCA) 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 and densities.

cond-mat.soft↗

arXiv2021

Effectively one-dimensional phase diagram of CuZr liquids and glasses

This paper presents computer simulations of Cu$_x$Zr$_{100-x}$ $(x=36,50,64)$ in the liquid and glass phases. The simulations are based on the effective-medium theory (EMT) potentials. We find good invariance of both structure and dynamics in reduced units along the isomorphs of the systems. The state points studied involve a density variation of almost a factor of two and temperatures going from 1500 K to above 4000 K for the liquids and from 500 K to above 1500 K for the glasses. For comparison, results are presented also for similar temperature variations along isochores, showing little invariance. In general for a binary system the phase diagram has three axes: composition, temperature and pressure (or density). When isomorphs are present, there are effectively only two axes, and for a fixed composition just one. We conclude that the liquid and glass parts of the thermodynamic phase diagram of this metallic glass former at a fixed composition is effectively one-dimensional in the sense that many physical properties are invariant along the same curves, implying that in order to investigate the phase diagram, it is only necessary to go across these curves.

cond-mat.mtrl-sci↗