On the Use of Excess Entropy Scaling To Describe Single-Molecule and Collective Dynamic Properties of Hydrocarbon Isomer Fluids

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.

Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

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.

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.

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.

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.

Residual entropy model for predicting the viscosities of dense fluid mixtures

In this work, we have investigated the mono-variant relationship between the reduced viscosity and residual entropy in pure fluids and in binary mixtures of hydrocarbons and hydrocarbons with dissolved carbon dioxide. The mixtures considered were octane + dodecane, decane + carbon dioxide, and 1,3-dimethylbenzene (m-xylene) + carbon dioxide. The reduced viscosity was calculated according to the definition of Bell, while the residual entropy was calculated from accurate multi-parameter Helmholtz-energy equations of state and, for mixtures, the multi-fluid Helmholtz energy approximation. The mono-variant dependence of reduced viscosity upon residual molar entropy was observed for the pure fluids investigated, and by incorporating two scaling factors (one for reduced viscosity and the other for residual molar entropy), the data were represented by a single universal curve. To apply this method to mixtures, the scaling factors were determined from a mole-fraction weighted sum of the pure-component values. This simple model was found to work well for the systems investigated. The average absolute relative deviation (AARD) was observed to be between 1% and 2% for pure components and a mixture of similar hydrocarbons. Larger deviations, with AARDs of up to 15%, were observed for the asymmetric mixtures, but this compares favorably with other methods for predicting the viscosity of such systems. We conclude that the residual-entropy concept can be used to estimate the viscosity of mixtures of similar molecules with high reliability and that it offers a useful engineering approximation even for asymmetric mixtures.

Temperature and pressure dependence of the alpha relaxation in ortho-terphenyl

Molecular dynamics (MD) simulations of ortho-terphenyl using an all-atom model with the optimized potentials for liquid simulations (OPLS) force field were performed both in the high temperature Arrhenian region and at lower temperatures that include the onset of the super-Arrhenian region. From the MD simulations, the internal energy of both the equilibrium liquid and crystal was determined from 300 K to 600 K and at pressures from 0.1 MPa to 1 GPa. The translational and rotational diffusivities were also determined at these temperatures and pressures for the equilibrium liquid. It is shown that within a small offset, the excess internal energy Ū_x from the MD simulations is consistent with the experimentally determined excess internal energy reported earlier [Caruthers and Medvedev, Phys. Rev. Mater. 2, 055604, (2018)]. The MD mobility data {including extremely long-time 1 atm simulations from the study by Eastwood et al. [J. Phys. Chem. B 117, 12898, (2013)]} were combined with experimental data to form a unified dataset, where it was shown that in both the high temperature Arrhenian region and the lower temperature super-Arrhenian region, the mobility is a linear function of 1/Ū_x(T,p), albeit with different proportionality constants. The transition between the Arrhenian and super-Arrhenian regions is relatively sharp at a critical internal energy Ū_x ^α. The 1/Ū_x(T,p) model is able to describe the mobility data over nearly 16 orders-of-magnitude. Other excess thermodynamic properties such as excess enthalpy and excess entropy (i.e., the Adam-Gibbs model) are unable to unify the pressure dependence of the mobility.

Protein Solvent Shell Structure Provides Rapid Analysis of Hydration Dynamics

The solvation layer surrounding a protein is clearly an intrinsic part of protein structure-dynamics-function, and our understanding of how the hydration dynamics influences protein function is emerging. We have recently reported simulations indicating a correlation between regional hydration dynamics and the structure of the solvation layer around different regions of the enzyme Candida antarctica lipase B, wherein the radial distribution function (RDF) was used to calculate the pairwise entropy, providing a link between dynamics (diffusion) and thermodynamics (excess entropy) known as Rosenfeld scaling. Regions with higher RDF values/peaks in the hydration layer (the first peak, within 6 Å of the protein surface) have faster diffusion in the hydration layer. The finding thus hinted at a handle for rapid evaluation of hydration dynamics at different regions on the protein surface in molecular dynamics simulations. Such an approach may move the analysis of hydration dynamics from a specialized venture to routine analysis, enabling an informatics approach to evaluate the role of hydration dynamics in biomolecular function. This paper first confirms that the correlation between regional diffusive dynamics and hydration layer structure (via water center of mass around protein side-chain atom RDF) is observed as a general relationship across a set of proteins. Second, it seeks to devise an approach for rapid analysis of hydration dynamics, determining the minimum amount of information and computational effort required to get a reliable value of hydration dynamics from structural data in MD simulations based on the protein-water RDF. A linear regression model using the integral of the hydration layer in the water-protein RDF was found to provide statistically equivalent apparent diffusion coefficients at the 95% confidence level for a set of 92 regions within five different proteins. In summary, RDF analysis of 10 ns of data after simulation convergence is sufficient to accurately map regions of fast and slow hydration dynamics around a protein surface. Additionally, it is anticipated that a quick look at protein-water RDFs, comparing peak heights, will be useful to provide a qualitative ranking of regions of faster and slower hydration dynamics at the protein surface for rapid analysis when investigating the role of solvent dynamics in protein function.

Perspective: Excess-entropy scaling

This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.

Flat-Histogram Monte Carlo as an Efficient Tool To Evaluate Adsorption Processes Involving Rigid and Deformable Molecules

Monte Carlo simulations are the foundational technique for predicting thermodynamic properties of open systems where the process of interest involves the exchange of particles. Thus, they have been used extensively to computationally evaluate the adsorption properties of nanoporous materials and are critical for the in silico identification of promising materials for a variety of gas storage and chemical separation applications. In this work we demonstrate that a well-known biasing technique, known as "flat-histogram" sampling, can be combined with temperature extrapolation of the free energy landscape to efficiently provide significantly more useful thermodynamic information than standard open ensemble MC simulations. Namely, we can accurately compute the isosteric heat of adsorption and number of particles adsorbed for various adsorbates over an extremely wide range of temperatures and pressures from a set of simulations at just one temperature. We extend this derivation of the temperature extrapolation to adsorbates with intramolecular degrees of freedom when Rosenbluth sampling is employed. Consequently, the working capacity and isosteric heat can be computed for any given combined temperature/pressure swing adsorption process for a large range of operating conditions with both rigid and deformable adsorbates. Continuous thermodynamic properties can be computed with this technique at very moderate computational cost, thereby providing a strong case for its application to the in silico identification of promising nanoporous adsorbents.

Temperature extrapolation of multicomponent grand canonical free energy landscapes

We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.

Role of entropy in the thermodynamic evolution of the time scale of molecular dynamics near the glass transition

In this paper, we investigate how changes in the system entropy influence the characteristic time scale of the system molecular dynamics near the glass transition. Independently of any model of thermodynamic evolution of the time scale, against some previous suppositions, we show that the system entropy S is not sufficient to govern the time scale defined by structural relaxation time τ. In the density scaling regime, we argue that the decoupling between τ and S is a consequence of different values of the scaling exponents γ and γ(S) in the density scaling laws, τ=f(ρ(γ)/T) and S=h(ρ(γ(S))/T), where ρ and T denote density and temperature, respectively. It implies that the proper relation between τ and S requires supplementing with a density factor, u(ρ), i.e., τ=g(u(ρ)w(S)). This meaningful finding additionally demonstrates that the density scaling idea can be successfully used to separate physically relevant contributions to the time scale of molecular dynamics near the glass transition. The relation reported by us between τ and S constitutes a general pattern based on nonconfigurational quantities for describing the thermodynamic evolution of the characteristic time scale of molecular dynamics near the glass transition in the density scaling regime, which is a promising alternative to the approaches based as the Adam-Gibbs model on the configurational entropy that is difficult to evaluate in the entire thermodynamic space. As an example, we revise the Avramov entropic model of the dependence τ(T,ρ), giving evidence that its entropic basis has to be extended by the density dependence of the maximal energy barrier for structural relaxation. We also discuss the excess entropy S(ex), the density scaling of which is found to mimic the density scaling of the total system entropy S.

Hidden scale invariance in condensed matter

Recent developments show that many liquids and solids have an approximate "hidden" scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments.

Excess entropy scaling for the segmental and global dynamics of polyethylene melts

The range of validity of the Rosenfeld and Dzugutov excess entropy scaling laws is analyzed for unentangled linear polyethylene chains.

Systematic coarse-graining of potential energy landscapes and dynamics in liquids

Recent efforts have shown that the dynamic properties of a wide class of liquids can be mapped onto semi-universal scaling laws and constitutive relations that are motivated by thermodynamic analyses of much simpler models. In particular, it has been found that many systems exhibit dynamics whose behavior in state space closely follows that of soft-sphere particles interacting through an inverse power repulsion. In the present work, we show that a recently developed coarse-graining theory provides a natural way to understand how arbitrary liquids can be mapped onto effective soft-sphere models and hence how one might potentially be able to extract underlying dynamical scaling laws. The theory is based on the relative entropy, an information metric that quantifies how well a soft-sphere approximation to a liquid's multidimensional potential energy landscape performs. We show that optimization of the relative entropy not only enables one to extract effective soft-sphere potentials that suggest an inherent scaling of thermodynamic and dynamic properties in temperature-density space, but that also has rather interesting connections to excess entropy based theories of liquid dynamics. We apply the approach to a binary mixture of Lennard-Jones particles, and show that it gives effective soft-sphere scaling laws that well-describe the behavior of the diffusion constants. Our results suggest that the relative entropy formalism may be useful for "perturbative" type theories of dynamics, offering a general strategy for systematically connecting complex energy landscapes to simpler reference ones with better understood dynamic behavior.

Isomorphs in model molecular liquids

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

Communication: Generalizing Rosenfeld's excess-entropy scaling to predict long-time diffusivity in dense fluids of Brownian particles: from hard to ultrasoft interactions

Computer simulations are used to test whether a recently introduced generalization of Rosenfeld's excess-entropy scaling method for estimating transport coefficients in systems obeying molecular dynamics can be extended to predict long-time diffusivities in fluids of particles undergoing Brownian dynamics in the absence of interparticle hydrodynamic forces. Model fluids with inverse-power-law, Gaussian-core, and Hertzian pair interactions are considered. Within the generalized Rosenfeld scaling method, long-time diffusivities of ultrasoft Gaussian-core and Hertzian particle fluids, which display anomalous trends with increasing density, are predicted (to within 20%) based on knowledge of interparticle interactions, excess entropy, and scaling behavior of simpler inverse-power-law fluids.