Excess entropy scaling of transport properties of Lennard-Jones chains

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.

Effect of the presence of pinned particles on the structural parameters of a liquid and correlation between structure and dynamics at the local level

Pinning particles at the equilibrium configuration of the liquid is expected not to affect the structure and any property that depends on the structure while slowing down the dynamics. This leads to a breakdown of the structure dynamics correlation. Here, we calculate two structural quantities: the pair excess entropy, S2, and the mean field caging potential, the inverse of which is our structural order parameter (SOP). We show that when the pinned particles are treated the same way as the mobile particles, both S2 and SOP of the mobile particles remain the same as those of the unpinned system, and the structure dynamics correlation decreases with an increase in pinning density, "c." However, when we treat the pinned particles as a different species, even if we consider that the structure does not change, the expression of S2 and SOP changes. The microscopic expressions show that the interaction between a pinned particle and a mobile particle affects S2 and SOP more than the interaction between two mobile particles. We show that a similar effect is also present in the calculation of the excess entropy and is the primary reason for the well-known vanishing of the configurational entropy at high temperatures. We further show that, contrary to the common belief, the pinning process does change the structure. When these two effects are considered, both S2 and SOP decrease with an increase in "c," and the correlation between the structural parameters and the dynamics continues even for higher values of "c."

A comparative study of the correlation between the structure and the dynamics for systems interacting via attractive and repulsive potentials

We present the study of the structure-dynamics correlation for systems interacting via attractive Lennard-Jones (LJ) and its repulsive counterpart, the Weeks-Chandler-Andersen (WCA) potentials. The structural order parameter (SOP) is related to the microscopic mean-field caging potential. At a particle level, the SOP shows a distribution. Although the two systems have similar pair structures, their average SOP differs. However, this difference alone is insufficient to explain the well known slowing down of the dynamics in the LJ system at low temperatures. The slowing down can be explained in terms of a stronger coupling between the SOP and the dynamics. To understand the origin of this system specific coupling, we study the difference in the microscopic structure between the hard and soft particles. We find that for the LJ system, the structural differences of the hard and soft particles are more significant and have a much stronger temperature dependence compared to the WCA system. Thus, the study suggests that attractive interaction creates more structurally different communities. This broader difference in the structural communities is probably responsible for stronger coupling between the structure and dynamics. Thus, the system specific structure-dynamics correlation, which also leads to a faster slowing down in the dynamics, appears to have a structural origin. A comparison of the predictive power of our SOP with the local energy and two body excess entropy in determining the dynamics shows that in the LJ system, the enthalpy plays a dominant role and in the WCA system, the entropy plays a dominant role, and our SOP can capture both these contributions.

Dynamic heterogeneity in polydisperse systems: A comparative study of the role of local structural order parameter and particle size

In polydisperse systems, describing the structure and any structural order parameter (SOP) is not trivial as it varies with the number of species we use to describe the system, M. Depending on the degree of polydispersity, there is an optimum value of M = M0 where we show that the mutual information of the system increases. However, surprisingly, the correlation between a recently proposed SOP and the dynamics is highest for M = 1. This effect increases with polydispersity. We find that the SOP at M = 1 is coupled with the particle size, σ, and this coupling increases with polydispersity and decreases with an increase in M. Careful analysis shows that at lower polydispersities, the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on σ. Since the coupling between the SOP and σ is higher for M = 1, it appears to be a better predictor of the dynamics. We also study the Vibrality, an order parameter independent of structural information. Compared to SOP, at high polydispersity, we find Vibrality to be a marginally better predictor of the dynamics. However, this high predictive power of Vibrality, which is not there at lower polydispersity, appears to be due to its stronger coupling with σ. Therefore, our study suggests that for systems with high polydispersity, the correlation of any order parameter and σ will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter.

Phase behavior of active and passive dumbbells

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

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.

Solvent-Evaporation Induced and Mechanistic Entropy-Enthalpy-Balance Controlled Polymer Patch Formation on Nanoparticle Surfaces

The formation of polymer-patch nanoparticles (PNPs) involves a condensation process of grafted chains on a nanoparticle (NP) surface, which is conventionally achieved via a fine-tuning of the solvent quality. However, such a critical solvent condition differs dramatically between polymers, and the formation mechanism of different patchy structures remains under debate. In this study, we demonstrate by a combined simulation and experimental study that such a surface-patterning process can be easily achieved via a simple solvent evaporation process, which creates a natural nonsolvent condition and is, in principle, adaptable for all polymers. More importantly, we find that patchy structures are controlled by a delicate balance between enthalpic interaction and the entropy penalty of grafted chains. A small variation of cohesive energy density can lead to a dramatic change in patch structure. This work offers a robust yet easy approach for the fabrication of PNPs and provides new insights into polymer segregation on spherical surfaces.

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.

Effective structure of a system with continuous polydispersity

In a system of N particles, with continuous size polydispersity, there exists an N(N - 1) number of partial structure factors, making it analytically less tractable. A common practice is to treat the system as an effective one component system, which is known to exhibit an artificial softening of the structure. The aim of this study is to describe the system in terms of M pseudospecies such that we can avoid this artificial softening but, at the same time, have a value of M ≪ N. We use potential energy and pair excess entropy to estimate an optimum number of species, M₀. We then define the maximum width of polydispersity, Δσ₀, that can be treated as a monodisperse system. We show that M₀ depends on the degree and type of polydispersity and also on the nature of the interaction potential, whereas Δσ₀ weakly depends on the type of polydispersity but shows a stronger dependence on the type of interaction potential. Systems with a softer interaction potential have a higher tolerance with respect to polydispersity. Interestingly, M₀ is independent of system size, making this study more relevant for bigger systems. Our study reveals that even 1% polydispersity cannot be treated as an effective monodisperse system. Thus, while studying the role of polydispersity by using the structure of an effective one component system, care must be taken in decoupling the role of polydispersity from that of the artificial softening of the structure.

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.

Universal Scaling Law for Colloidal Diffusion in Complex Media

Using video microscopy and simulations, we study the diffusion of probe particles in a wide range of complex backgrounds, both crystalline and disordered, in quasi-2D colloidal systems. The dimensionless diffusion coefficients D^{*} from different systems collapse to a single master curve when plotted as a function of the structural entropy of the backgrounds, confirming the universal relation between diffusion dynamics and the structure of the medium. A new scaling equation is proposed with consideration for the viscous friction from the solvent, which is absent in previous theoretical models. This new universal law quantitatively predicts the diffusion coefficients from different systems over several orders of magnitude of D^{*}, with a single common fitting parameter.

Probing the link between residual entropy and viscosity of molecular fluids and model potentials

This work investigates the link between residual entropy and viscosity based on wide-ranging, highly accurate experimental and simulation data. This link was originally postulated by Rosenfeld in 1977 [Rosenfeld Y (1977) Phys Rev A 15:2545-2549], and it is shown that this scaling results in an approximately monovariate relationship between residual entropy and reduced viscosity for a wide range of molecular fluids [argon, methane, [Formula: see text], [Formula: see text], refrigerant R-134a (1,1,1,2-tetrafluoroethane), refrigerant R-125 (pentafluoroethane), methanol, and water] and a range of model potentials (hard sphere, inverse power, Lennard-Jones, and Weeks-Chandler-Andersen). While the proposed "universal" correlation of Rosenfeld is shown to be far from universal, when used with the appropriate density scaling for molecular fluids, the viscosity of nonassociating molecular fluids can be mapped onto the model potentials. This mapping results in a length scale that is proportional to the cube root of experimentally measurable liquid volume values.

Entropy connects water structure and dynamics in protein hydration layer

The enzyme Candida Antarctica lipase B (CALB) serves here as a model for understanding connections among hydration layer dynamics, solvation shell structure, and protein surface structure. The structure and dynamics of water molecules in the hydration layer were characterized for regions of the CALB surface, divided around each α-helix, β-sheet, and loop structure. Heterogeneous hydration dynamics were observed around the surface of the enzyme, in line with spectroscopic observations of other proteins. Regional differences in the structure of the biomolecular hydration layer were found to be concomitant with variations in dynamics. In particular, it was seen that regions of higher density exhibit faster water dynamics. This is analogous to the behavior of bulk water, where dynamics (diffusion coefficients) are connected to water structure (density and tetrahedrality) by excess (or pair) entropy, detailed in the Rosenfeld scaling relationship. Additionally, effects of protein surface topology and hydrophobicity on water structure and dynamics were evaluated using multiregression analysis, showing that topology has a somewhat larger effect on hydration layer structure-dynamics. Concave and hydrophobic protein surfaces favor a less dense and more tetrahedral solvation layer, akin to a more ice-like structure, with slower dynamics. Results show that pairwise entropies of local hydration layers, calculated from regional radial distribution functions, scale logarithmically with local hydration dynamics. Thus, the Rosenfeld relationship describes the heterogeneous structure-dynamics of the hydration layer around the enzyme CALB. These findings raise the question of whether this may be a general principle for understanding the structure-dynamics of biomolecular solvation.

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

Scaling of the dynamics of flexible Lennard-Jones chains: Effects of harmonic bonds

The previous paper [A. A. Veldhorst et al., J. Chem. Phys. 141, 054904 (2014)] demonstrated that the isomorph theory explains the scaling properties of a liquid of flexible chains consisting of ten Lennard-Jones particles connected by rigid bonds. We here investigate the same model with harmonic bonds. The introduction of harmonic bonds almost completely destroys the correlations in the equilibrium fluctuations of the potential energy and the virial. According to the isomorph theory, if these correlations are strong a system has isomorphs, curves in the phase diagram along which structure, dynamics, and the excess entropy are invariant. The Lennard-Jones chain liquid with harmonic bonds does have curves in the phase diagram along which the structure and dynamics are invariant. The excess entropy is not invariant on these curves, which we refer to as "pseudoisomorphs." In particular, this means that Rosenfeld's excess-entropy scaling (the dynamics being a function of excess entropy only) does not apply for the Lennard-Jones chain with harmonic bonds.

Chain stiffness regulates entropy-templated perfect mixing at single-nanoparticle level

The mixing on a single-particle level of chemically incompatible nanoparticles is an outstanding challenge for many applications. Burgeoning research activity suggests that entropic templating is a potential strategy to address this issue. Herein, using systematic computer simulations of model nanoparticle systems, we show that the entropy-templated interfacial organization of nanoparticles significantly depends on the stiffness of tethered chains. Unexpectedly, the optimal chain stiffness can be identified wherein a system exhibits the most perfect mixing for a certain compression ratio. Our simulations demonstrate that entropic templating regulated by chain stiffness precisely reflects various entropic repulsion states that arise from typical conformation regimes of semiflexible chains. The physical mechanism of the chain stiffness effect is revealed by analyzing the entropic repulsion states of tethered chains and quantitatively estimating the resulting entropy penalties, which provides direct evidence that supports the key role of entropic transition in the entropic templating strategy, as suggested in experiments. Moreover, the model nanoparticle systems are found to evolve into binary nanoparticle superlattices by remixing at extremely high stiffness. The findings facilitate the wide application of the entropic templating strategy in creating interfacially reactive nanomaterials with ordered structures on the single-nanoparticle level as well as mechanomutable responses.

Transport properties and entropy-scaling laws for diffusion coefficients in liquid Fe0.9Ni0.1 up to 350 GPa

Transport properties and entropy-scaling laws for diffusion coefficients in liquid Fe_0.9Ni_0.1 alloy under high pressure conditions have been studied by molecular dynamics simulations based upon the Quantum Sutton and Chen potential.

Scaling of the dynamics of flexible Lennard-Jones chains

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of ρ(γ(S)), where ρ is density, T is temperature, and γ(S) is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as an empirical scaling parameter.

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.

Excess-entropy scaling for gas diffusivity in nanoporous materials

We present an efficient computational procedure for the rapid prediction of the self-diffusivity of gas molecules in nanoporous materials by a combination of the Knudsen model, Rosenfeld's excess-entropy scaling method, and a classical density functional theory (DFT). The self-diffusivity conforms to the Knudsen model at low density, and the effects of intermolecular interactions at higher densities are accounted for by Rosenfeld's excess-entropy scaling method. The classical DFT provides a convenient way to calculate the excess entropy used in the scaling analysis. The hybrid computational procedure has been calibrated with MD simulation for the adsorption of H2, He, Ne, and Ar gases in several nanoporous materials over a broad range of pressure. It predicts adsorption isotherms and different types of diffusion behavior in excellent agreement with the simulation results. Although the simulation of gas diffusion in nanoporous materials is extremely time-consuming, the new procedure is computationally very efficient because it uses only single molecular and thermodynamic parameters.