Perspective: Excess-entropy scaling

Understanding dynamics in coarse-grained models. IV. Connection of fine-grained and coarse-grained dynamics with the Stokes-Einstein and Stokes-Einstein-Debye relations

Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.

Role of anisotropy in understanding the molecular grounds for density scaling in dynamics of glass-forming liquids

Molecular Dynamics (MD) simulations of glass-forming liquids play a pivotal role in uncovering the molecular nature of the liquid vitrification process. In particular, much focus was given to elucidating the interplay between the character of intermolecular potential and molecular dynamics behaviour. This has been tried to achieve by simulating the spherical particles interacting via isotropic potential. However, when simulation and experimental data are analysed in the same way by using the density scaling approaches, serious inconsistency is revealed between them. Similar scaling exponent values are determined by analysing the relaxation times and pVT data obtained from computer simulations. In contrast, these values differ significantly when the same analysis is carried out in the case of experimental data. As discussed thoroughly herein, the coherence between results of simulation and experiment can be achieved if anisotropy of intermolecular interactions is introduced to MD simulations. In practice, it has been realized in two different ways: (1) by using the anisotropic potential of the Gay-Berne type or (2) by replacing the spherical particles with quasi-real polyatomic anisotropic molecules interacting through isotropic Lenard-Jones potential. In particular, the last strategy has the potential to be used to explore the relationship between molecular architecture and molecular dynamics behaviour. Finally, we hope that the results presented in this review will also encourage others to explore how 'anisotropy' affects remaining aspects related to liquid-glass transition, like heterogeneity, glass transition temperature, glass forming ability, etc.

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.

Freezing density scaling of transport coefficients in the Weeks-Chandler-Andersen fluid

It is shown that the transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of the Weeks-Chandler-Andersen (WCA) fluid along isotherms exhibit a freezing density scaling (FDS). The functional form of this FDS is essentially the same or closely related to those in the Lennard-Jones fluid, hard-sphere fluid, and some liquefied noble gases. This proves that this FDS represents a quasi-universal corresponding state principle for simple classical fluids with steep interactions. Some related aspects, such as a Stokes-Einstein relation without a hydrodynamic diameter and gas-to-liquid dynamical crossover, are briefly discussed. Simple fitting formulas for the transport coefficients of the dense WCA fluid are suggested.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Influence of repulsion on entropy scaling and density scaling of monatomic fluids

Entropy scaling is applied to the shear viscosity, self-diffusion coefficient, and thermal conductivity of simple monatomic fluids. An extensive molecular dynamics simulation series is performed to obtain these transport properties and the residual entropy of three potential model classes with variable repulsive exponents: n, 6 Mie (n = 9, 12, 15, and 18), Buckingham's exponential-six (α = 12, 14, 18, and 30), and Tang-Toennies (αT = 4.051, 4.275, and 4.600). A wide range of liquid and supercritical gas- and liquid-like states is covered with a total of 1120 state points. Comparisons to equations of state, literature data, and transport property correlations are made. Although the absolute transport property values within a given potential model class may strongly depend on the repulsive exponent, it is found that the repulsive steepness plays a negligible role when entropy scaling is applied. Hence, the plus-scaled transport properties of n, 6 Mie, exponential-six, and Tang-Toennies fluids lie basically on one master curve, which closely corresponds with entropy scaling correlations for the Lennard-Jones fluid. This trend is confirmed by literature data of n, 6 Mie, and exponential-six fluids. Furthermore, entropy scaling holds for state points where the Pearson correlation coefficient R is well below 0.9. The condition R > 0.9 for strongly correlating liquids is thus not necessary for the successful application of entropy scaling, pointing out that isomorph theory may be a part of a more general framework that is behind the success of entropy scaling. Density scaling reveals a strong influence of the repulsive exponent on this particular approach.

Entropy approximations for simple fluids

Liquid state entropy formulas based on configurational probability distributions are examined for Lennard-Jones fluids across a range temperatures and densities. These formulas are based on expansions of the entropy in a series of n-body distribution functions. We focus on two special cases. One, which we term the "perfect gas" series, starts with the entropy of an ideal gas; the other, which we term the "dense liquid" series, removes a many-body contribution from the ideal gas entropy and reallocates it among the subsequent n-body terms. We show that the perfect gas series is most accurate at low density, while the dense liquid series is most accurate at high density. We propose empirical interpolation methods that are capable of connecting the two series and giving consistent predictions in most situations.

Atomic diffusion in liquid gallium and gallium-nickel alloys probed by quasielastic neutron scattering and molecular dynamic simulations

The atomic mobility in liquid pure gallium and a gallium-nickel alloy with 2 at% of nickel is studied experimentally by incoherent quasielastic neutron scattering. The integral diffusion coefficients for all-atom diffusion are derived from the experimental data at different temperatures. DFT-basedab-initiomolecular dynamics (MD) is used to find numerically the diffusion coefficient of liquid gallium at different temperatures, and numerical theory results well agree with the experimental findings at temperatures below 500 K. Machine learning force fields derived fromab-initiomolecular dynamics (AIMD) overestimate within a small 6% error the diffusion coefficient of pure gallium within the genuine AIMD. However, they better agree with experiment for pure gallium and enable the numerical finding of the diffusion coefficient of nickel in the considered melted alloy along with the diffusion coefficient of gallium and integral diffusion coefficient, that agrees with the corresponding experimental values within the error bars. The temperature dependence of the gallium diffusion coefficientDGa(T)follows the Arrhenius law experimentally for all studied temperatures and below 500 K also in the numerical simulations. However,DGa(T)can be well described alternatively by an Einstein-Stokes dependence with the metallic liquid viscosity following the Arrhenius law, especially for the MD simulation results at all studied temperatures. Moreover, a novel variant of the excess entropy scaling theory rationalized our findings for gallium diffusion. Obtained values of the Arrhenius activation energies are profoundly different in the competing theoretical descriptions, which is explained by different temperature-dependent prefactors in the corresponding theories. The diffusion coefficient of gallium is significantly reduced (at the same temperature) in a melted alloy with natural nickel, even at a tiny 2 at% concentration of nickel, as compared with its pure gallium value. This highly surprising behavior contradicts the existing excess entropy scaling theories and opens a venue for further research.

Invariant dynamics in a united-atom model of an ionic liquid

We study a united-atom model of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl)sulfonylamide to determine to what extent there exist curves in the phase diagram along which the microscopic dynamics are invariant when expressed in dimensionless, or reduced, form. The initial identification of these curves, termed isodynes, is made by noting that contours of reduced shear viscosity and reduced self-diffusion coefficient coincide to a good approximation. Choosing specifically the contours of reduced viscosity as nominal isodynes, further simulations were carried out for state points on these, and other aspects of dynamics were investigated to study their degree of invariance. These include the mean-squared displacement, shear-stress autocorrelation function, and various rotational correlation functions. These were invariant to a good approximation, with the main exception being rotations of the anion about its long axis. The dynamical features that are invariant have in common that they are aspects that would be relevant for a coarse-grained description of the system; specifically, removing the most microscopic degrees of freedom in principle leads to a simplification of the potential energy landscape, which allows for the existence of isodynes.

Simulation and Data-Driven Modeling of the Transport Properties of the Mie Fluid

This work reports the computation and modeling of the self-diffusivity (D*), shear viscosity (η*), and thermal conductivity (κ*) of the Mie fluid. The transport properties were computed using equilibrium molecular dynamics simulations for the Mie fluid with repulsive exponents (λr) ranging from 7 to 34 and at a fixed attractive exponent (λa) of 6 over the whole fluid density (ρ*) range and over a wide temperature (T*) range. The computed database consists of 17,212, 14,288, and 13,099 data points for self-diffusivity, shear viscosity, and thermal conductivity, respectively. The database is successfully validated against published simulation data. The above-mentioned transport properties are correlated using artificial neural networks (ANNs). Two modeling approaches were tested: a semiempirical formulation based on entropy scaling and an empirical formulation based on density and temperature as input variables. For the former, it was found that a unique formulation based on entropy scaling does not yield satisfactory results over the entire density range due to a divergent and incorrect scaling of the transport properties at low densities. For the latter empirical modeling approach, it was found that regularizing the data, e.g., modeling ρ*D* instead of D*, ln η* instead of η*, and ln κ* instead of κ*, as well as using the inverse of the temperature as an input feature, helps to ease the interpolation efforts of the artificial neural networks. The trained ANNs can model seen and unseen data over a wide range of density and temperature. Ultimately, the ANNs can be used alongside equations of state to regress effective force field parameters from volumetric and transport data.

Reassessing the transport properties of fluids: A symbolic regression approach

The viscosity and thermal conductivity coefficients of the Lennard-Jones fluid are extracted through symbolic regression (SR) techniques from data derived from simulations at the atomic scale. This data-oriented approach provides closed form relations that achieve fine accuracy when compared to well-established theoretical, empirical, or approximate equations, fully transparent, with small complexity and high interpretability. The novelty is further outlined by suggesting analytical expressions for estimating fluid transport properties across the whole phase space, from a dilute gas to a dense liquid, by considering only two macroscopic properties (density and temperature). In such expressions, the underlying physical mechanisms are reflected, while, at the same time, it can be a computationally efficient alternative to costly in time and size first principle and/or molecular dynamics simulations.

Thermodynamic Insights into Variation in Thermomechanical and Physical Properties of Isotactic Polypropylene: Effect of Shear and Cooling Rates

In order to elucidate the effect of shear and cooling process on structural, thermomechanical, and physical properties of polymer melt, excess entropy, a thermodynamic quantity is calculated from radial distribution function generated from equilibrated parts of the molecular simulation trajectories. The structural properties are calculated, which includes the density of polypropylene melt, end to end distance, radius of gyration of the polypropylene polymer chain, and monomer-monomer radial distribution function. Non-equilibrium molecular dynamics simulation was employed to investigate the role of the applied shear rate on the properties of polypropylene. Furthermore, a range of cooling rates were employed to cool the melt. Thermomechanical properties, such as Young's modulus, and physical properties, such as glass transition temperature, were determined for different cases. Results showed that slow cooling and high shear substantially improved the Young's modulus and glass transition temperature of the i-PP. Furthermore, a two-body contribution to the excess entropy was used to elucidate the structure-property relationships in the polymer melt as well as the glassy state and the dependence of shear and cooling rate on these properties. We have used the Rosenfeld excess entropy-viscosity relationship to calculate the viscous behavior of the polymer under a steady shear condition.

Universal Relation between Entropy and Kinetics

Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle configurations. It is universal and applicable to steady states arbitrarily far from thermodynamic equilibrium. Applying the general relation to diffusive dynamics yields a relation between the entropy and the (normal or anomalous) diffusion coefficient. The relation can be used to obtain useful bounds for the late-time diffusion coefficient from the calculated steady-state entropy or, conversely, to estimate the entropy based on measured diffusion coefficients. We demonstrate the validity and usefulness of the relation through several examples and discuss its broad range of applications, in particular, for systems far from equilibrium.

Entropy Scaling of Molecular Dynamics in a Prototypical Anisotropic Model near the Glass Transition

Dynamics and thermodynamics of molecular systems in the vicinity of the boundary between thermodynamically nonequilibrium glassy and metastable supercooled liquid states are still incompletely explored and their theoretical and simulation models are imperfect despite many previous efforts. Among them, the role of total system entropy, configurational entropy, and excess entropy in the temperature-pressure or temperature-density dependence of global molecular dynamics (MD) timescale relevant to the glass transition is an essential topic intensively studied for over half of a century. By exploiting a well-known simple ellipsoidal model recently successfully applied to simulate the supercooled liquid state and the glass transition, we gain a new insight into the different views on the relationship between entropy and relaxation dynamics of glass formers, showing the molecular grounds for the entropy scaling of global MD timescale. Our simulations in the anisotropic model of supercooled liquid, which involves only translational and rotational degrees of freedom, give evidence that the total system entropy is sufficient to scale global MD timescale. It complies with the scaling effect on relaxation dynamics exerted by the configurational entropy defined as the total entropy diminished by vibrational contributions, which was earlier discovered for measurement data collected near the glass transition. Moreover, we argue that such a scaling behavior is not possible to achieve by using the excess entropy that is in excess of the ideal gas entropy, which is contrary to the results earlier suggested within the framework of simple isotropic models of supercooled liquids. Thus, our findings also warn against an excessive reliance on isotropic models in theoretical interpretations of molecular phenomena, despite their simplicity and popularity, because they may reflect improperly various physicochemical properties of glass formers.

Detecting Liquid-Liquid Phase Separations Using Molecular Dynamics Simulations and Spectral Clustering

A stringent test of the accuracy of empirical force fields is reproducing the phase diagram of bulk phases and mixtures. Exploring the phase diagram of mixtures requires the detection of phase boundaries and critical points. In contrast to most solid-liquid transitions, in which a global order parameter (average density) can be used to discriminate between two phases, some demixing transitions entail relatively subtle changes in the local environment of each molecule. In such cases, finite sampling errors and finite-size effects make the identification of trends in local order parameters extremely challenging. Here we analyze one such example, namely a methanol/hexane mixture, and compute several local and global structural properties. We simulate the system at various temperatures and study the structural changes associated with demixing. We show that despite a seemingly continuous transformation between mixed and demixed states, the topological properties of the H-bond network change abruptly as the system crosses the demixing line. In particular, by using spectral clustering, we show that the distribution of cluster sizes develops a fat tail (as expected from percolation theory) in the vicinity of the critical point. We illustrate a simple criterion to identify this behavior, which results from the emergence of large system-spanning clusters from a collection of aggregates. We further tested the spectral clustering analysis on a Lennard-Jones system as a standard example of a system with no H-bonds, and also, in this case, we were able to detect the demixing transition.

Departures from perfect isomorph behavior in Lennard-Jones fluids and solids

Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼ T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant.

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.

Entropy-Driven Liquid Electrolytes for Lithium Batteries

Developing liquid electrolytes with higher kinetics and enhanced interphase stability is one of the key challenges for lithium batteries. However, the poor solubility of lithium salts in solvents sets constraints that compromises the electrolyte properties. Here, it is shown that introducing multiple salts to form a high-entropy solution, alters the solvation structure, which can be used to raise the solubility of specific salts and stabilize electrode-electrolyte interphases. The prepared high-entropy electrolytes significantly enhance the cycling and rate performance of lithium batteries. For lithium-metal anodes the reversibility exceeds 99%, which extends the cycle life of batteries even under aggressive cycling conditions. For commercial batteries, combining a graphite anode with a LiNi0.8 Co0.1 Mn0.1 O2 cathode, more than 1000 charge-discharge cycles are achieved while maintaining a capacity retention of more than 90%. These performance improvements with respect to regular electrolytes are rationalized by the unique features of the solvation structure in high-entropy electrolytes. The weaker solvation interaction induced by the higher disorder results in improved lithium-ion kinetics, and the altered solvation composition leads to stabilized interphases. Finally, the high-entropy, induced by the presence of multiple salts, enables a decrease in melting temperature of the electrolytes and thus enables lower battery operation temperatures without changing the solvents.

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.

Diffusion mobility increases linearly on liquid binodals above triple point

Self-diffusion in fluids has been thoroughly studied numerically, but even for simple liquids just a few scaling relationships are known. Relations between diffusion, excitation spectra, and character of the interparticle interactions remain poorly understood. Here, we show that diffusion mobility of particles in simple fluids increases linearly on the liquid branch of the liquid-gas binodal, from the triple point almost up to the critical point. With molecular dynamics simulations, we considered bulk systems of particles interacting via a generalised Lennard-Jones potential, as well as ethane. Using a two-oscillator model for the analysis of excitations, we observed that the mobility (inverse diffusion) coefficient on the liquid-gas binodal increases linearly above the triple point until the dispersion of high-frequency spectra has a solid-like (oscillating) shape. In terms of a separate mode analysis (of longitudinal and transverse modes), this corresponds to crossed modes in the intermediate range of wavenumbers q, between the hydrodynamic regime (small q) and the regime of individual particle motion (large q). The results should be interesting for a broad community in physics and chemistry of fluids, since self-diffusion is among the most fundamental transport phenomena, important for prospective chemical technologies, micro-, nanofluidics, and biotechnologies.

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

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

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, T_{conf}, 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 T_{conf} 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, showing the existence of lines of approximate invariance of the reduced-unit radial distribution function and time-dependent mean-square displacement.

High entropy liquid electrolytes for lithium batteries

High-entropy alloys/compounds have large configurational entropy by introducing multiple components, showing improved functional properties that exceed those of conventional materials. However, how increasing entropy impacts the thermodynamic/kinetic properties in liquids that are ambiguous. Here we show this strategy in liquid electrolytes for rechargeable lithium batteries, demonstrating the substantial impact of raising the entropy of electrolytes by introducing multiple salts. Unlike all liquid electrolytes so far reported, the participation of several anionic groups in this electrolyte induces a larger diversity in solvation structures, unexpectedly decreasing solvation strengths between lithium ions and solvents/anions, facilitating lithium-ion diffusivity and the formation of stable interphase passivation layers. In comparison to the single-salt electrolytes, a low-concentration dimethyl ether electrolyte with four salts shows an enhanced cycling stability and rate capability. These findings, rationalized by the fundamental relationship between entropy-dominated solvation structures and ion transport, bring forward high-entropy electrolytes as a composition-rich and unexplored space for lithium batteries and beyond.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Entropy scaling of viscosity for molecular models of molten salts

Entropy scaling relates dynamic and thermodynamic properties by reducing the viscosity to a function of only the residual entropy. Molecular simulations are used to investigate the entropy scaling of the viscosity of three models of sodium chloride and five monovalent salts. Even though the correlation between the potential energy and the virial is weak, entropy scaling applies at liquid densities for all models and salts investigated. At lower densities, entropy scaling breaks down due to the formation of ion pairs and chains. Entropy scaling can be used to develop more extendable correlations for the dynamic properties of molten salts.

Isomorphs in sheared binary Lennard-Jones glass: Transient response

We have studied shear deformation of binary Lennard-Jones glasses to investigate the extent to which the transient part of the stress strain curves is invariant when the thermodynamic state point is varied along an isomorph. Shear deformations were carried out on glass samples of varying stability, determined by cooling rate, and at varying strain rates, at state points deep in the glass. Density changes up to and exceeding a factor of two were made. We investigated several different methods for generating isomorphs but none of the previously developed methods could generate sufficiently precise isomorphs given the large density changes and nonequilibrium situation. Instead, the temperatures for these higher densities were chosen to give state points isomorphic to the starting state point by requiring the steady-state flow stress for isomorphic state points to be invariant in reduced units. In contrast to the steady-state flow stress, we find that the peak stress on the stress strain curve is not invariant. The peak stress decreases by a few percent for each ten percent increase in density, although the differences decrease with increasing density. Analysis of strain profiles and nonaffine motion during the transient phase suggests that the root of the changes in peak stress is a varying tendency to form shear bands, with the largest tendency occurring at the lowest densities. We suggest that this reflects the effective steepness of the potential; a higher effective steepness gives a greater tendency to form shear bands.

Predicting Scaling Properties from a Single Fluid Configuration

Time-dependent dynamical properties of a fluid cannot be estimated directly from a single configuration without performing a simulation. Here, however, we present a method that predicts the scaling properties of both structure and dynamics from a single configuration. The method is demonstrated to work well for the Lennard-Jones fluid as well as the viscous Kob-Andersen Lennard-Jones mixture, both in and out of equilibrium. The method is conceptually simple and easy to implement and, thus, should become a standard tool in the study of scaling properties of fluids and liquids.

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 accurately determine the melting-line coexistence pressure and fluid/crystal densities of the Weeks–Chandler–Andersen 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 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.

Connecting Entropy Scaling and Density Scaling

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

First-principles study of the specific heat of glass at the glass transition with a case study on glycerol

The standard method to determine the transition temperature (T_g) of glasses is the jump in the specific heat,ΔCp. Despite its importance, standard theory for this jump is lacking. The difficulties include lack of proper treatment of the specific heat of liquids, hysteresis, and the timescale issue. The first part of this paper provides a non-empirical method for calculating the specific heat in the glass transition. The method consists of molecular dynamics (MD) simulations based on density-functional theory (DFT) and thermodynamics methods. Calculation of the total energy, which is the heart of DFT, is the most general method for obtaining specific heat for any state of matters. The influence of energy dissipation processes on specific heat is treated by adiabatic MD simulations. The problems of hysteresis and the timescale are alleviated by restricting the scope of calculations to equilibrium states only. The second part of this paper demonstrates the validity and usefulness of the methods by applying to the specific-heat jump of glycerol. By decomposingΔCpinto contributions of the structural, phonon, and thermal expansion energies, an appropriate interpretation for the specific-heat jump has been established: the major contribution toΔCpis the change in the structural energy. From this, a neat energy diagram about the glass transition is obtained. An outcome of this study is verification of the empirical relationship between the fragility and the specific-heat jump. These two quantities scale to the ratiok=Tg/ΔTg, whereΔTgis the width of the transition, through which the two quantities are interrelated.

Excess Entropy Scaling in Active-Matter Systems

Active-matter systems feature discrete particles that can convert stored or ambient free energy into motion. To realize the engineering potential of active matter, there is a strong need for predictive and theoretically grounded techniques for describing transport in these systems. In this work, we perform molecular-dynamics (MD) simulations of a model active-matter system, in which we vary the total fraction of active particles (0.01 ≤ ϕ ≤ 0.5) as well as the degree of activity of the active particles. These simulations reveal a fascinating array of transport phenomena, including activity-enhanced diffusion coefficients. By adapting an existing result for binary (inactive) fluids, we demonstrate the existence of an excess entropy scaling relation in an active system. This relationship is well supported by our MD results and establishes a new connection between transport (dynamics) and structure (statics) in active matter, a promising step for predictive and generalizable models of other transport phenomena in such systems.

Freezing density scaling of fluid transport properties: Application to liquified noble gases

A freezing density scaling of transport properties of the Lennard-Jones fluid is rationalized in terms of the Rosenfeld's excess entropy scaling and isomorph theory of Roskilde-simple systems. Then, it is demonstrated that the freezing density scaling operates reasonably well for viscosity and thermal conductivity coefficients of liquid argon, krypton, and xenon. Quasi-universality of the reduced transport coefficients at their minima and at freezing conditions is discussed. The magnitude of the thermal conductivity coefficient at the freezing point is shown to agree remarkably well with the prediction of the vibrational model of thermal transport in dense fluids.

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.

Connection between water's dynamical and structural properties: Insights from ab initio simulations

SignificanceFirst-principles calculations, which explicitly account for the electronic structure of matter, can shed light on the molecular structure and dynamics of water in its supercooled state. In this work, we use density functional theory, which relies on a functional to describe electronic exchange and correlations, to evaluate which functional best describes the temperature evolution of bulk water transport coefficients. We also assess the validity of the Stokes-Einstein relation for all the functionals in the temperature range studied, and explore the link between structure and dynamics. Based on these results, we show how transport coefficients can be computed from structural descriptors, which require shorter simulation times to converge, and we point toward strategies to develop better functionals.

Roughness Volumes: An Improved RoughMob Concept for Predicting the Increase of Molecular Mobility upon Coarse-Graining

The reduced number of degrees of freedom in a coarse-grained molecular model compared to its parent atomistic model not only makes it possible to simulate larger systems for longer time scales but also results in an artificial mobility increase. The RoughMob method [Meinel, M. K. and Müller-Plathe, F. J. Chem. Theory Comput. 2020, 16, 1411.] linked the acceleration factor of the dynamics to the loss of geometric information upon coarse-graining. Our hypothesis is that coarse-graining a multiatom molecule or group into a single spherical bead smooths the molecular surface and, thus, leads to reduced intermolecular friction. A key parameter is the molecular roughness difference, which is calculated via a numerical comparison of the molecular surfaces of both the atomistic and coarse-grained models. Augmenting the RoughMob method, we add the concept of the region where the roughness acts. This information is contained in four so-called roughness volumes. For 17 systems of homogeneous hydrocarbon fluids, simple one-bead coarse-grained models are derived by the structure-based iterative Boltzmann inversion. They include 13 different homogeneous aliphatic and aromatic molecules and two different mapping schemes. We present a simple way to correlate the roughness volumes to the acceleration factor. The resulting relation is able to a priori predict the acceleration factors for an extended size and shape range of hydrocarbon molecules, with different mapping schemes and different densities.

Freezing Temperature and Density Scaling of Transport Coefficients

It is demonstrated that the freezing density scaling of transport coefficients in fluids, similar to the freezing temperature scaling, originates from the quasi-universal excess entropy scaling approach proposed by Rosenfeld. The freezing density scaling has a considerably wider applicability domain on the phase diagram of Lennard-Jones and related systems. As an illustration of its predictive power, we show that it reproduces with an excellent accuracy the shear viscosity coefficients of saturated liquid argon, krypton, xenon, and methane.