Perspective: Excess-entropy scaling

Gas–liquid crossover in the Lennard-Jones system

It is demonstrated that the crossover between gas- and liquid-like regions on the phase diagram of the Lennard-Jones system occurs at a fixed value of the density divided by its value at the freezing point, ρ/ ρfr ≃ 0.35. This definition is consistent with other definitions proposed recently. As a result, a very simple practical expression for the gas-to-liquid crossover line emerges.

Pressing matter: why are ionic liquids so viscous?

Room temperature ionic liquids are considered to have huge potential for practical applications such as batteries. However, their high viscosity presents a significant challenge to their use changing from niche to ubiquitous. The modelling and prediction of viscosity in ionic liquids is the subject of an ongoing debate involving two competing hypotheses: molecular and local mechanisms versus collective and long-range mechanisms. To distinguish between these two theories, we compared an ionic liquid with its uncharged, isoelectronic, isostructural molecular mimic. We measured the viscosity of the molecular mimic at high pressure to emulate the high densities in ionic liquids, which result from the Coulomb interactions in the latter. We were thus able to reveal that the relative contributions of coulombic compaction and the charge network interactions are of similar magnitude. We therefore suggest that the optimisation of the viscosity in room temperature ionic liquids must follow a dual approach.

Medium-range atomic correlation in simple liquids. I. Distinction from short-range order

Physical properties of liquids and glasses are controlled not only by the short-range order (SRO) in the nearest-neighbor atoms but also by the medium-range order (MRO) observed for atoms beyond the nearest neighbors. In this article the nature of the MRO as the descriptor of point-to-set atomic correlation is discussed focusing on simple liquids, such as metallic liquids. Through the results of x-ray diffraction and simulation with classical potentials we show that the third peak of the pair-distribution function, which describes the MRO, shows a distinct change in temperature dependence at the glass transition, whereas the first peak, which represents the SRO, changes smoothly through the glass transition. The result suggests that the glass transition is induced by the freezing of the MRO rather than that of the SRO, implying a major role of the MRO on the viscosity of supercooled liquid.

Structure-dynamics relationships in cryogenically deformed bulk metallic glass

The atomistic mechanisms occurring during the processes of aging and rejuvenation in glassy materials involve very small structural rearrangements that are extremely difficult to capture experimentally. Here we use in-situ X-ray diffraction to investigate the structural rearrangements during annealing from 77 K up to the crystallization temperature in Cu₄₄Zr₄₄Al₈Hf₂Co₂ bulk metallic glass rejuvenated by high pressure torsion performed at cryogenic temperatures and at room temperature. Using a measure of the configurational entropy calculated from the X-ray pair correlation function, the structural footprint of the deformation-induced rejuvenation in bulk metallic glass is revealed. With synchrotron radiation, temperature and time resolutions comparable to calorimetric experiments are possible. This opens hitherto unavailable experimental possibilities allowing to unambiguously correlate changes in atomic configuration and structure to calorimetrically observed signals and can attribute those to changes of the dynamic and vibrational relaxations (α-, β- and γ-transition) in glassy materials. The results suggest that the structural footprint of the β-transition is related to entropic relaxation with characteristics of a first-order transition. Dynamic mechanical analysis data shows that in the range of the β-transition, non-reversible structural rearrangements are preferentially activated. The low-temperature γ-transition is mostly triggering reversible deformations and shows a change of slope in the entropic footprint suggesting second-order characteristics.

Understanding of the atomic-scale mechanisms of rejuvenation of bulk metallic glass still remains unclear. Here, using configurational entropy derived from X-ray experiments, authors show a clear picture of the relaxation process during annealing of a metallic glass.

Bridge functions of classical one-component plasmas

In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.

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.

Atomic transport properties of liquid iron at conditions of planetary cores

Atomic transport properties of liquid iron are important for understanding the core dynamics and magnetic field generation of terrestrial planets. Depending on the sizes of planets and their thermal histories, planetary cores may be subject to quite different pressures (P) and temperatures (T). However, previous studies on the topic mainly focus on the P-T range associated with the Earth's outer core; a systematic study covering conditions from small planets to massive exoplanets is lacking. Here, we calculate the self-diffusion coefficient D and viscosity η of liquid iron via ab initio molecular dynamics from 7.0 to 25 g/cm³ and 1800 to 25 000 K. We find that D and η are intimately related and can be fitted together using a generalized free volume model. The resulting expressions are simpler than those from previous studies where D and η were treated separately. Moreover, the new expressions are in accordance with the quasi-universal atomic excess entropy (S_ex) scaling law for strongly coupled liquids, with normalized diffusivity D^⋆ = 0.621 exp(0.842S_ex) and viscosity η^⋆ = 0.171 exp(-0.843S_ex). We determine D and η along two thermal profiles of great geophysical importance: the iron melting curve and the isentropic line anchored at the ambient melting point. The variations of D and η along these thermal profiles can be explained by the atomic excess entropy scaling law, demonstrating the dynamic invariance of the system under uniform time and space rescaling. Accordingly, scale invariance may serve as an underlying mechanism to unify planetary dynamos of different sizes.

Excess entropy and Stokes-Einstein relation in simple fluids

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy s_{ex} can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately s_{ex}≲-2. In addition, we demonstrate that the line separating gaslike and liquidlike fluid behaviours on the phase diagram is roughly characterized by s_{ex}≃-1.

Excess entropy scaling law: A potential energy landscape view

The relationship between excess entropy and diffusion is revisited by means of large-scale computer simulation combined to supervised learning approach to determine the excess entropy for the Lennard-Jones potential. Results reveal a strong correlation with the properties of the potential energy landscape (PEL). In particular the exponential law holding in the liquid is seen to be linked with the landscape-influenced regime of the PEL whereas the fluidlike power-law corresponds to the free diffusion regime.

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.

Quantifying dynamical and structural invariance in a simple molten salt model

Recent experimental results for the structure in the ionic liquid PYR₁₄ ⁺TFSI^- have shown invariance in the main structure factor peak along curves of equal electrical conductivity [Hansen et al., Phys. Chem. Chem. Phys. 22, 14169 (2020)]. The charge peak decreases slightly with increasing temperature at fixed conductivity, however. For simple liquids, curves with invariant dynamics and structure, known as isomorphs, can be identified as configurational adiabats. While liquids with strong-Coulomb interactions do not have good isomorphs, ionic liquids could be an intermediate case with approximate isomorphs along which some aspects of structure and dynamics are invariant. We study a simple molten salt model using molecular dynamics simulations to test this hypothesis. Simple measures of structure and dynamics are investigated along with one transport property, the shear viscosity. We find that there is a substantial degree of invariance of the self-intermediate scattering function, the mean square displacement, and the viscosity along configurational adiabats over a wide range of densities for the three adiabats simulated. The density range studied is more than a factor of two and extends from the strong-Coulomb regime at low densities to the weak-Coulomb regime at high densities. The structure is not invariant over the full range of density, but in the weak-Coulomb regime, we see behavior similar to that seen experimentally over density changes of order 15%. In view of the limited structural invariance but substantial dynamical invariance, we designate the configurational adiabats as isodynes.

Core-softened water-alcohol mixtures: the solute-size effects

Water is the most anomalous material on Earth, with a long list of thermodynamic, dynamic and structural behaviors that deviate from what is expected. Recent studies have indicated that these anomalies may be related to a competition between two liquids, which means that water has a potential liquid-liquid phase transition (LLPT) that ends at a liquid-liquid critical point (LLCP). In a recent study [J. Mol. Liq., 2020, 320, 114420], using molecular dynamics simulations and a core-softened potential approach, we have shown that adding a simple solute such as methanol can "kill" the density-anomalous behavior as the LLCP is suppressed by spontaneous crystallization in a hexagonal close packing (HCP) crystal near the LLPT. Now, we extend this work to realize how longer-chain alcohols will affect the complex behavior of water-alcohol mixtures in the supercooled regime. Besides core-softened (CS) methanol, ethanol and 1-propanol were added to a system of identical particles that interact through the continuous shouldered well (CSW) potential. We observed that the density anomaly gradually decreases its extension in phase diagrams until it disappears with the growth of the non-polar chain and the alcohol concentration, different from the liquid-liquid phase transition (and the LLCP), which remained present in all analyzed mixtures, according to Nature, 2001, 409, 692. For our model, the longer non-polar chains and higher concentrations gradually impact the competition between the scales in the CS potential, leading to a gradual disappearing of the anomalies until the TMD total disappearance is observed when the first coordination shell structure is also affected: short-range ordering is favored, leading to less competition between short- and long-range ordering and, consequently, to the extinction of anomalies. Also, the non-polar chain size and concentration have an effect on the solid phases, favoring the hexagonal close packed (HCP) solid and the amorphous solid phase over the body-centered cubic (BCC) crystal. These findings help to elucidate the behavior of water solutions in the supercooled regime and indicate that the LLCP can be observed in systems without density-anomalous behavior.

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.

Dynamic Crossover in Fluids: From Hard Spheres to Molecules

We propose a simple and generic definition of a demarcation reconciling structural and dynamic frameworks when combined with the entropy scaling framework. This crossover line between gas- and liquid-like behaviors is defined as the curve for which an individual property, the contribution to viscosity due to molecules' translation, is exactly equal to a collective property, the contribution to viscosity due to molecular interactions. Such a definition is shown to be consistent with the one based on the minima of the kinematic viscosity. For the hard sphere, this is shown to be an exact solution. For Lennard-Jones spheres and dimers and for some simple real fluids, this relation holds very well. This crossover line passes nearby the critical point, and for all studied fluids, it is well captured by the critical excess entropy curve for atomic fluids, emphasizing the link between transport properties and local structure.

Understanding simple liquids through statistical and deep learning approaches

Statistical and deep learning-based methods are employed to obtain insights into the quasi-universal properties of simple liquids. In the first part, a statistical model is employed to provide a probabilistic explanation for the similarity in the structure of simple liquids interacting with different pair potential forms, collectively known as simple liquids. The methodology works by sampling the radial distribution function and the number of interacting particles within the cutoff distance, and it produces the probability density function of the net force. We show that matching the probability distribution of the net force can be a direct route to parameterize simple liquid pair potentials with a similar structure, as the net force is the main component of the Newtonian equations of motion. The statistical model is assessed and validated against various cases. In the second part, we exploit DeepILST [A. Moradzadeh and N. R. Aluru, J. Phys. Chem. Lett. 10, 1242-1250 (2019)], a data-driven and deep-learning assisted framework to parameterize the standard 12-6 Lennard-Jones (LJ) pair potential, to find structurally equivalent/isomorphic LJ liquids that identify constant order parameter [τ=∫₀ ^ξ_cf gξ-1ξ²dξ, where gξ and ξ(=rρ¹³) are the reduced radial distribution function and radial distance, respectively] systems in the space of non-dimensional temperature and density of the LJ liquids. We also investigate the consistency of DeepILST in reproducibility of radial distribution functions of various quasi-universal potentials, e.g., exponential, inverse-power-law, and Yukawa pair potentials, quantified based on the radial distribution functions and Kullback-Leibler errors. Our results provide insights into the quasi-universality of simple liquids using the statistical and deep learning methods.

Experimental test of a predicted dynamics-structure-thermodynamics connection in molecularly complex glass-forming liquids

Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different "order parameters" including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local-nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply supercooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.

Transport properties of Lennard-Jones fluids: Freezing density scaling along isotherms

It is demonstrated that properly reduced transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of Lennard-Jones fluids along isotherms exhibit quasi-universal scaling on the density divided by its value at the freezing point. Moreover, this scaling is closely related to the density scaling of transport coefficients of hard-sphere fluids. The Stokes-Einstein relation without the hydrodynamic diameter is valid in the dense fluid regime. The lower density boundary of its validity can serve as a practical demarcation line between gaslike and liquidlike regimes.

Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory

This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO₂ in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. The first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO₂ is the C-C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO₂ model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.

Targeted modifications in ionic liquids - from understanding to design

Ionic liquids are extremely versatile and continue to find new applications in academia as well as industry. This versatility is rooted in the manifold of possible ion types, ion combinations, and ion variations. However, to fully exploit this versatility, it is imperative to understand how the properties of ionic liquids arise from their constituents. In this work, we discuss targeted modifications as a powerful tool to provide understanding and to enable design. A 'targeted modification' is a deliberate change in the structure of an ionic liquid. This includes chemical changes in an experiment as well as changes to the parameterisation in a computer simulation. In any case, such a change must be purposeful to isolate what is of interest, studying, as far as is possible, only one concept at a time. The concepts can then be used as design elements. However, it is often found that several design elements interact with each other - sometimes synergistically, and other times antagonistically. Targeted modifications are a systematic way of navigating these overlaps. We hope this paper shows that understanding ionic liquids requires experimentalists and theoreticians to join forces and provides a tool to tackle the difficult transition from understanding to design.

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.

Unveiling the strong dependence of the α-relaxation dispersion on mixing thermodynamics in binary glass-forming liquids

Structural α-relaxation dispersion in binary molecular glass forming mixtures with distinct mixing enthalpy ΔHmix was investigated using enthalpic and dielectric relaxation measurements across the entire composition range. This study focused on the dependence of the relaxation dispersion on the mixing thermodynamics by determining the non-exponential exponent β, and its composition dependence. The β values determined by the enthalpic and dielectric relaxations agree well. Remarkably, it is found that the systems with positive enthalpy of mixing (exothermic, ΔHmix >0) have positive deviations in the composition dependence of β from the linear averaging of the two β values of the pure components, while negative deviations are observed for the systems with negative enthalpy of mixing (endothermic, ΔHmix <0). Furthermore, the relation between the non-exponential behaviors and entropy of mixing is discussed, revealing that the positive or negative deviation of β in its composition dependence on mixing is accompanied by the same sign of the excess entropy of mixing relative to the ideal one.

Diffusion of colloidal particles in model porous media

Using video microscopy and simulations, we study the long-time diffusion of colloidal tracers in a wide range of model porous media composed of frozen colloidal matrices with different structures. We found that the diffusion coefficient of a tracer can be quantitatively determined by the structures of porous media. In particular, a universal scaling relation exists between the dimensionless diffusion coefficient of the tracer and the structural entropy of the system. This universal scaling relation is an extension of the scaling law previously discovered for the diffusion of colloidal particles in fluctuating media.

Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics

We demonstrate that the time evolution of the van Hove dynamical pair correlation function is governed by adiabatic forces that arise from the free energy and by superadiabatic forces that are induced by the flow of the van Hove function. The superadiabatic forces consist of drag, viscous, and structural contributions, as occur in active Brownian particles, in liquids under shear and in lane forming mixtures. For hard sphere liquids, we present a power functional theory that predicts these universal force fields in quantitative agreement with our Brownian dynamics simulation results.

Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas

It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.

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.

Structure of the Lennard-Jones liquid estimated from a single simulation

Combining the recent Piskulich-Thompson approach [Z. A. Piskulich and W. H. Thompson, J. Chem. Phys. 152, 011102 (2020)JCPSA60021-960610.1063/1.5135932] with isomorph theory, from a single simulation the structure of a single-component Lennard-Jones (LJ) system is obtained at an arbitrary state point in almost the whole liquid region of the temperature-density phase diagram. The LJ system exhibits two temperature ranges where the van't Hoff assumption that energetic and entropic forces are temperature independent is valid to a good approximation. A method to evaluate the structure at an arbitrary state point along an isochore from the knowledge of structures at two temperatures on the isochore is also discussed. We argue that, in general, the structure of any hidden scale-invariant system obeying the van't Hoff assumption in the whole range of temperatures can be determined in the whole liquid region of the phase diagram from a single simulation.

Vibrational model of thermal conduction for fluids with soft interactions

A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is applied to quantify heat transfer in a dense Lennard-Jones liquid and a strongly coupled one-component plasma. Remarkable agreement with the available numerical results is documented. A similar picture does not apply to the momentum transfer and shear viscosity of liquids.

Fragile Glasses Associated with a Dramatic Drop of Entropy under Supercooling

We perform kinetic Monte Carlo simulations of a distinguishable-particle lattice model of structural glasses with random particle interactions. By varying the interaction distribution and the average particle hopping energy barrier, we obtain an extraordinarily wide range of kinetic fragility. A stretching exponent, characterizing structural relaxation, is found to decrease with the kinetic fragility in agreement with experiments. The most fragile glasses are those exhibiting low hopping barriers and, more importantly, dramatic drops of entropies upon cooling toward the glass transition temperatures. The entropy drops reduce possible kinetic pathways and lead to dramatic slowdowns in the dynamics. In addition, the kinetic fragility is shown to correlate with a thermodynamic fragility.

Role of local order in anomalous ion diffusion: Interrogation through tetrahedral entropy of aqueous solvation shells

Small rigid ions perturb the water structure around them significantly. At constant viscosity, alkali cations (Li⁺, Na⁺, and so on) exhibit an anomalous non-monotonic dependence of diffusivity on ion-size, in stark violation of the Stokes-Einstein expression. Although this is a well-known problem, we find that an entropic view of the problem can be developed, which provides valuable insight. The local entropy experienced by the solute ion is relevant here, which leads to the connection with local viscosity, discussed earlier by many. Due to the strong interactions with ions, the translational and rotational entropy of solvation water decreases sharply; however, an opposite effect comes from the disruption of the tetrahedral network structure of water near the charges. We compute the tetrahedral order of water molecules (q_tet) around the ion and suitably defined tetrahedral entropy [S(q_tet)] that is a contribution to the excess entropy of the system. Our results reveal that although the structural properties of the second shell become nearly identical to the bulk, S(q_tet) of the second shell is found to play an important role in giving rise to the non-monotonic ion-size dependence. The detailed study of the static and dynamic fluctuations in q_tet and the number of hydration water molecules provides interesting insights into correlation between the structure and dynamics; the smallest static fluctuation of q_tet for the first hydration shell water molecules of Li⁺ is indicative of the iceberg picture. The study of fluctuation properties of q_tet and the coordination number also reveals the role of the second hydration layer and could explain the anomalous behavior of the Rb⁺ ion.

Entropy Scaling of Viscosity - II: Predictive Scheme for Normal Alkanes

In this work, a residual entropy value 6/10 of the way between the critical point and a value of -2/3 of Boltzmann's constant is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the experimental data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on experimentally accessible values. This collapse is shown to be valid to a residual entropy half way between the critical point and the triple point, beyond which the macroscopically-scaled viscosity has a super-exponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramolecular degrees of freedom. A study of the transport and thermodynamic properties at the triple point rounds out the analysis.

Isomorph theory beyond thermal equilibrium

This paper generalizes isomorph theory to systems that are not in thermal equilibrium. The systems are assumed to be R-simple, i.e., to have a potential energy that as a function of all particle coordinates R obeys the hidden-scale-invariance condition U(R_a) < U(R_b) ⇒ U(λR_a) < U(λR_b). "Systemic isomorphs" are introduced as lines of constant excess entropy in the phase diagram defined by density and systemic temperature, which is the temperature of the equilibrium state point with the average potential energy equal to U(R). The dynamics is invariant along a systemic isomorph if there is a constant ratio between the systemic and the bath temperature. In thermal equilibrium, the systemic temperature is equal to the bath temperature and the original isomorph formalism is recovered. The new approach rationalizes within a consistent framework previously published observations of isomorph invariance in simulations involving nonlinear steady-state shear flows, zero-temperature plastic flows, and glass-state isomorphs. This paper relates briefly to granular media, physical aging, and active matter. Finally, we discuss the possibility that the energy unit defining the reduced quantities should be based on the systemic rather than the bath temperature.

Thermodynamic or density scaling of the thermal conductivity of liquids

Thermodynamic or density scaling is applied to thermal conductivity (λ) data from the literature for the model Lennard-Jones (12-6) fluid; the noble gases neon to xenon; nitrogen, ethene, and carbon dioxide as examples of linear molecules; the quasi-spherical molecules methane and carbon tetrachloride; the flexible chain molecules n-hexane and n-octane; the planar toluene and m-xylene; the cyclic methylcyclohexane; the polar R132a and chlorobenzene; and ammonia and methanol as H-bonded fluids. Only data expressed as Rosenfeld reduced properties could be scaled successfully. Two different methods were used to obtain the scaling parameter γ, one based on polynomial fits to the group (TV^γ) and the other based on the Avramov equation. The two methods agree well, except for λ of CCl₄. γ for the thermal conductivity is similar to those for the viscosity and self-diffusion coefficient for the smaller molecules. It is significantly larger for the Lennard-Jones fluid, possibly due to a different dependence on packing fraction, and much larger for polyatomic molecules where heat transfer through internal modes may have an additional effect. Methanol and ammonia, where energy can be transmitted through intermolecular hydrogen bonding, could not be scaled. This work is intended as a practical attempt to examine thermodynamic scaling of the thermal conductivity of real fluids. The divergence of the scaling parameters for different properties is unexpected, suggesting that refinement of theory is required to rationalize this result. For the Lennard-Jones fluid, the Ohtori-Iishi version of the Stokes-Einstein-Sutherland relation applies at high densities in the liquid and supercritical region.

Coarse-graining strategy for modeling effective, highly diffusive fluids with reduced polydispersity: A dynamical study

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of application, we chose the bidisperse Lennard-Jones-like mixture, discovered by Kob and Andersen [Phys. Rev. Lett. 73, 1376 (1994)], possessing a slow dynamics due to the fluid's multi-component character with its apparently unconventional choice for the pair potential of the type-A-type-B arrangement. We further established in a so-formed coarse-grained and temperature-independent monodisperse system an equilibrium structure with a radial distribution function resembling its mixture counterpart. This one-component system further possesses similar dynamic features such as glass transition temperature and critical exponents while subjected to Newtonian mechanics. This strategy may finally lead to the manufacturing of new nanoparticle/colloidal fluids by experimentally modeling only the outcoming effective pair potential(s) and no other macroscopic quantity.

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.

Thermodynamics-Structure-Dynamics Correlations and Nonuniversal Effects in the Elastically Collective Activated Hopping Theory of Glass-Forming Liquids

We employ the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated dynamics in combination with crystal-avoiding simulations to study four inter-related questions for metastable monodisperse hard sphere fluids. The first is how significantly improved integral equation theory structural input (Modified-Verlet (MV) closure) changes the dynamical predictions of ECNLE theory. The main consequence is a modest enhancement of the importance of the collective elastic barrier relative to its local cage contribution, which increases the alpha relaxation time and fragility relative to prior results based on the Percus-Yevick closure. Second, ECNLE-MV theory predictions for the alpha time and self-diffusion constant in the metastable regime are quantitatively compared to our new simulations. The small adjustment of a numerical prefactor that enters the collective elastic barrier leads to quantitative agreement over three decades. Third, using the more accurate MV structural input, ECNLE theory is shown to predict thermodynamics-structure-dynamics "correlations" based on various long and short wavelength scalar properties all related to static two-point collective density fluctuations. The logarithm of the alpha relaxation time scales as a power law with these scalar metrics with an exponent that is significantly lower in the less dense noncooperative activated regime compared to the very dense highly cooperative regime. However, the discovered correlation of activated relaxation with a thermodynamic property (dimensionless compressibility) is not causal in ECNLE theory, but rather reflects a strong connection between the local structural quantities that quantify kinetic constraints in the theory with the amplitude of long wavelength density fluctuations. Fourth, the consequences of chemically specific nonuniversalities associated with the onset condition and relative importance of collective elasticity are studied. The predicted thermodynamics-structure-dynamics correlations are found to be robust, albeit with nontrivial shifts of the onset condition.

An entropy scaling demarcation of gas- and liquid-like fluid behaviors

In this work, we propose a generic and simple definition of a line separating gas-like and liquid-like fluid behaviors from the standpoint of shear viscosity. This definition is valid even for fluids such as the hard sphere and the inverse power law that exhibit a unique fluid phase. We argue that this line is defined by the location of the minimum of the macroscopically scaled viscosity when plotted as a function of the excess entropy, which differs from the popular Widom lines. For hard sphere, Lennard-Jones, and inverse-power-law fluids, such a line is located at an excess entropy approximately equal to -2/3 times Boltzmann's constant and corresponds to points in the thermodynamic phase diagram for which the kinetic contribution to viscosity is approximately half of the total viscosity. For flexible Lennard-Jones chains, the excess entropy at the minimum is a linear function of the chain length. This definition opens a straightforward route to classify the dynamical behavior of fluids from a single thermodynamic quantity obtainable from high-accuracy thermodynamic models.

Scaling of relaxation and excess entropy in plastically deformed amorphous solids

When stressed sufficiently, solid materials yield and deform plastically via reorganization of microscopic constituents. Indeed, it is possible to alter the microstructure of materials by judicious application of stress, an empirical process utilized in practice to enhance the mechanical properties of metals. Understanding the interdependence of plastic flow and microscopic structure in these nonequilibrium states, however, remains a major challenge. Here, we experimentally investigate this relationship, between the relaxation dynamics and microscopic structure of disordered colloidal solids during plastic deformation. We apply oscillatory shear to solid colloidal monolayers and study their particle trajectories as a function of shear rate in the plastic regime. Under these circumstances, the strain rate, the relaxation rate associated with plastic flow, and the sample microscopic structure oscillate together, but with different phases. Interestingly, the experiments reveal that the relaxation rate associated with plastic flow at time t is correlated with the strain rate and sample microscopic structure measured at earlier and later times, respectively. The relaxation rate, in this nonstationary condition, exhibits power-law, shear-thinning behavior and scales exponentially with sample excess entropy. Thus, measurement of sample static structure (excess entropy) provides insight about both strain rate and constituent rearrangement dynamics in the sample at earlier times.