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)2470-004510.1103/PhysRevE.105.064703] 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, and 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.

Probing excitations and cooperatively rearranging regions in deeply supercooled liquids.

Upon approaching the glass transition, the relaxation of supercooled liquids is controlled by activated processes, which become dominant at temperatures below the so-called dynamical crossover predicted by Mode Coupling theory (MCT). Two of the main frameworks rationalising this behaviour are dynamic facilitation theory (DF) and the thermodynamic scenario which give equally good descriptions of the available data. Only particle-resolved data from liquids supercooled below the MCT crossover can reveal the microscopic mechanism of relaxation. By employing state-of-the-art GPU simulations and nano-particle resolved colloidal experiments, we identify the elementary units of relaxation in deeply supercooled liquids. Focusing on the excitations of DF and cooperatively rearranging regions (CRRs) implied by the thermodynamic scenario, we find that several predictions of both hold well below the MCT crossover: for the elementary excitations, their density follows a Boltzmann law, and their timescales converge at low temperatures. For CRRs, the decrease in bulk configurational entropy is accompanied by the increase of their fractal dimension. While the timescale of excitations remains microscopic, that of CRRs tracks a timescale associated with dynamic heterogeneity, [Formula: see text]. This timescale separation of excitations and CRRs opens the possibility of accumulation of excitations giving rise to cooperative behaviour leading to CRRs.

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 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, which 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 remains to be found, however.

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, where 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 mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, 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 molecules 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.

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.

Isomorphs in nanoconfined liquids.

We study in this paper the possible existence of Roskilde-simple liquids and their isomorphs in a rough-wall nanoconfinement. Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant in suitable nondimensionalized units. Two model liquids using molecular dynamics computer simulations are considered: the single-component Lennard-Jones (LJ) liquid and the Kob-Andersen binary LJ mixture, both of which in the bulk phases are known to have good isomorphs. Nanoconfinement is implemented by adopting a slit-pore geometry with fcc crystalline walls; this implies inhomogenous density profiles both parallel and perpendicular to the confining walls. Despite this fact and consistent with an earlier study [Ingebrigtsen et al., Phys. Rev. Lett., 2013, 111, 235901] we find that these two nanoconfined liquids have isomorphs to a good approximation. More specifically, we show good invariance along the isomorphs of inhomogenous density profiles, mean-square displacements, and higher-order structures probed using the topological cluster classification algorithm. Our study thus provides an alternative framework for understanding nanoconfined liquids.

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard-Jones Systems.

In the condensed liquid phase, both single- and multicomponent Lennard-Jones (LJ) systems obey the "hidden-scale-invariance" symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank-Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob-Andersen, Wahnström, NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF.

Single-parameter aging in a binary Lennard-Jones system.

This paper studies physical aging by computer simulations of a 2:1 Kob-Andersen binary Lennard-Jones mixture, a system that is less prone to crystallization than the standard 4:1 composition. Starting from thermal-equilibrium states, the time evolution of the following four quantities is monitored by following up and down jumps in temperature: potential energy, virial, average squared force, and the Laplacian of the potential energy. Despite the fact that significantly larger temperature jumps are studied here than in typical similar experiments, to a good approximation, all four quantities conform to the single-parameter-aging scenario derived and validated for small jumps in experiments [T. Hecksher, N. B. Olsen, and J. C. Dyre, J. Chem. Phys. 142, 241103 (2015)]. As a further confirmation of single-parameter aging with a common material time for the four different quantities monitored, their relaxing parts are found to be almost identical for all temperature jumps.

Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles.

Polydisperse systems of particles interacting by the purely repulsive exponential (EXP) pair potential are studied in regard to how structure and dynamics vary along isotherms, isochores, and isomorphs. The sizable size polydispersities of 23%, 29%, 35%, and 40%, as well as energy polydispersity 35%, were considered. For each system an isomorph was traced out covering about one decade in density. For all systems studied, the structure and dynamics vary significantly along the isotherms and isochores but are invariant to a good approximation along the isomorphs. We conclude that the single-component EXP system's hidden scale invariance (implying isomorph invariance of structure and dynamics) is maintained even when a sizable polydispersity is introduced into the system.

Excess-entropy scaling in supercooled binary mixtures.

Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for single-component quasiuniversality.

Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids.

Glass-forming liquids subjected to sufficiently strong shear universally exhibit striking nonlinear behavior; for example, a power-law decrease of the viscosity with increasing shear rate. This phenomenon has attracted considerable attention over the years from both fundamental and applicational viewpoints. However, the out-of-equilibrium and nonlinear nature of sheared fluids have made theoretical understanding of this phenomenon very challenging and thus slower to progress. We find here that the structural relaxation time as a function of the two-body excess entropy, calculated for the extensional axis of the shear flow, collapses onto the corresponding equilibrium curve for a wide range of pair potentials ranging from harsh repulsive to soft and finite. This two-body excess entropy collapse provides a powerful approach to predicting the dynamics of nonequilibrium liquids from their equilibrium counterparts. Furthermore, the two-body excess entropy scaling suggests that sheared dynamics is controlled purely by the liquid structure captured in the form of the two-body excess entropy along the extensional direction, shedding light on the perplexing mechanism behind shear thinning.

Effect of Energy Polydispersity on the Nature of Lennard-Jones Liquids.

In the companion paper [ Ingebrigtsen , T. S. ; Tanaka , H. J. Phys. Chem. B 2015 , 119 , 11052 ] the effect of size polydispersity on the nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, was studied. More specifically, it was shown that even highly size polydisperse LJ liquids are Roskilde-simple (RS) liquids. RS liquids are liquids with strong correlation between constant volume equilibrium fluctuations of virial and potential energy and are simpler than other types of liquids. Moreover, it was shown that size polydisperse LJ liquids have isomorphs to a good approximation. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless (reduced) units. In this paper, we study the effect of energy polydispersity on the nature of LJ liquids. We show that energy polydisperse LJ liquids are RS liquids. However, a tendency of particle segregation, which increases with the degree of polydispersity, leads to a loss of strong virial-potential energy correlation but is mitigated by increasing temperature and/or density. Isomorphs are a good approximation also for energy polydisperse LJ liquids, although particle-resolved quantities display a somewhat poorer scaling compared to the mean quantities along the isomorph.

Effect of Size Polydispersity on the Nature of Lennard-Jones Liquids.

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.

The impact range for smooth wall-liquid interactions in nanoconfined liquids.

Bulk and nanoconfined liquids have very different physics; for instance, nanoconfined liquids show stratification and position-dependent relaxation processes. A number of similarities between bulk and nanoconfined liquids have nevertheless been reported in computer simulations during the last decade. Inspired by these observations, we present results from molecular dynamics computer simulations of four nanoconfined liquids (the single-component Lennard-Jones liquid, the Kob-Andersen binary Lennard-Jones mixture, an asymmetric dumbbell model, and the Dzugutov liquid) demonstrating also a microscopic similarity between bulk and nanoconfined liquids. The results show that the interaction range for the wall-liquid and liquid-liquid interactions of the nanoconfined liquid is identical to that of the bulk liquid if the liquid is "Roskilde simple" in bulk as well as nanoconfinement, i.e., exhibits strong correlations between virial and potential-energy equilibrium fluctuations in the NVT ensemble. Under this condition, interactions beyond the first coordination shell may be ignored, in particular for the wall-liquid interactions. This is shown not to be the case for non-Roskilde-simple liquids.

Communication: The Rosenfeld-Tarazona expression for liquids' specific heat: a numerical investigation of eighteen systems.

We investigate the accuracy of the expression of Rosenfeld and Tarazona (RT) for the excess isochoric heat capacity, C(V)(ex)∝T(-2/5), for 18 model liquids. Previous investigations have reported no unifying features of breakdown for the RT expression. Here, liquids with different stoichiometric composition, molecular topology, chemical interactions, degree of undercooling, and environment are investigated. The RT expression is a better approximation for liquids with strong correlations between equilibrium fluctuations of virial and potential energy, i.e., "Roskilde-simple" liquids [T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, Phys. Rev. X 2, 011011 (2012)]. This observation holds even for molecular liquids under severe nanoscale confinement which does not follow from the original RT bulk hard-sphere fluid perturbation theory arguments. The density dependence of the specific heat is predicted from the isomorph theory for Roskilde-simple liquids, which in combination with the RT expression provides a complete description of the specific heat's density and temperature dependence.

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.

Predicting how nanoconfinement changes the relaxation time of a supercooled liquid.

The properties of nanoconfined fluids can be strikingly different from those of bulk liquids. A basic unanswered question is whether the equilibrium and dynamic consequences of confinement are related to each other in a simple way. We study this question by simulation of a liquid comprising asymmetric dumbbell-shaped molecules, which can be deeply supercooled without crystallizing. We find that the dimensionless structural relaxation times-spanning six decades as a function of temperature, density, and degree of confinement-collapse when plotted versus excess entropy. The data also collapse when plotted versus excess isochoric heat capacity, a behavior consistent with the existence of isomorphs in the bulk and confined states.

Communication: 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 = Const., (2) the density-scaling exponent is a function of density only, and (3) a Grüneisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has h(ρ) = ∑(n)C(n)ρ(n/3) in which the only non-zero terms are those appearing in the pair potential expanded as ν(r) = ∑(n)ν(n)r(-n). Molecular dynamics simulations of Lennard-Jones type systems confirm the theory.

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 (Gnan, N.; et al. J. Chem. Phys.2009, 131, 234504). A liquid has good isomorphs if and only if it is strongly correlating, i.e., if the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. Isomorphs were previously discussed with a focus on atomic systems. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of systems of small rigid molecules: the asymmetric dumbbell model, a symmetric inverse power-law dumbbell, and the Lewis-Wahnström o-terphenyl (OTP) model. For all model systems, the following quantities are found to a good approximation to be invariant along an isomorph: the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self-part of the intermediate scattering function, and the reduced molecular center-of-mass radial distribution function. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to an isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnström OTP model were found to be more approximative than those of the asymmetric dumbbell model; this is consistent with the OTP model being less strongly correlating. The asymmetric dumbbell and Lewis-Wahnström OTP models each have a "master isomorph"; i.e., the isomorphs have identical shape in the virial/potential energy phase diagram.

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 [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, J. Chem. Phys. 135, 104101 (2011); T. S. Ingebrigtsen, S. Toxvaerd, T. B. Schrøder, and J. C. Dyre, ibid. 135, 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 the 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-Wahnström o-terphenyl (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 Nosé-Hoover NVT dynamics. Since Nosé-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.