Excess Entropy Research Articles

Modeling Europium (II/III) ion solvation in the LiCl-KCl eutectic mixture with polarizable force fields

The solvation processes of Europium (II/III) ions within the molten salt eutectic mixture, 3LiCl-2KCl, are investigated over temperatures ranging from 673 K to 1173 K. New polarizable ion force fields are proposed to model Europium ions in a molten salt eutectic mixture with a goal of accurately capturing the underlying physics in the solutions. In contrast to rigid-ion models, the polarizable Drude model with an adjusted WBK (Wang-Buckingham) force field significantly improves predictions for diffusion coefficients, the average diffusion activation energy, and changes in excess ion chemical potential and partial molar entropy, producing good agreement with experimental measurements.

The Dynamic Diversity and Invariance of Ab Initio Water.

Comprehending water dynamics is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While ab initio molecular dynamics (AIMD) accurately portray water's structure, computing its dynamic properties over nanosecond time scales proves cost-prohibitive. This study employs machine learning potentials (MLPs) to accurately determine the dynamic properties of liquid water with ab initio accuracy. Our findings reveal diversity in the calculated diffusion coefficient (D) and viscosity of water (η) across different methodologies. Specifically, while the GGA, meta-GGA, and hybrid functional methods struggle to predict dynamic properties under ambient conditions, methods on the higher level of Jacob's ladder of DFT approximation perform significantly better. Intriguingly, we discovered that both D and η adhere to the established Stokes-Einstein (SE) relation for all of the ab initio water. The diversity observed across different methods can be attributed to distinct structural entropy, affirming the applicability of excess entropy scaling relations across all functionals. The correlation between D and η provides valuable insights for identifying the ideal temperature to accurately replicate the dynamic properties of liquid water. Furthermore, our findings can validate the rationale behind employing artificially high temperatures in the simulation of water via AIMD. These outcomes not only pave the path to designing better functionals for water but also underscore the significance of water's many-body characteristics.

MARTINI Coarse-Grained Force Field for Thermoplastic Starch Nanocomposites.

Thermoplastic starch (TPS) is an excellent film-forming material, and the addition of fillers, such as tetramethylammonium-montmorillonite (TMA-MMT) clay, has significantly expanded its use in packaging applications. We first used an all-atom (AA) simulation to predict several macroscopic (Young's modulus, glass transition temperature, density) and microscopic (conformation along 1-4 and 1-6 glycosidic linkages, composite morphology) properties of TPS melt and TPS-TMA-MMT composite. The interplay of polymer-surface (weakly repulsive), plasticizer-surface (attractive), and polymer-plasticizer (weakly attractive) interactions leads to conformational and dynamics properties distinct from those in systems with either attractive or repulsive polymer-surface interactions. A subset of AA properties was used to parametrize the MARTINI-2 coarse-grained (CG) force field (FF) for the melt and composite systems. The missing bonded parameters of amylose and amylopectin and the bead types for 1-4 and 1-6 linked α-D glucose were determined using two-body excess entropy, density, and bond and angle distributions in the AA TPS melt. This new MARTINI-2 CG model was also compared with the MARTINI-3 model for the TPS melt. However, the requirement of a polarizable water model necessitates the use of MARTINI-2 FF for the composite system. This liquid-liquid partitioning-based FF shows freezing and compaction of polymer chains near the clay surface, further accentuated by lowering of dispersive interactions between pairs of high-covalent-coordination ring units of TPS polymers and the montmorillonite sheet. A rescaling of the effective dispersive component of TPS-MMT cross interactions was used to optimize the MARTINI-2 FF for the composite system with structural (chain size distribution), thermodynamic (chain conformational entropy and density), and dynamic (self-diffusion coefficient) properties obtained from long AA simulations forming the constraints for optimization. The obtained CG FF parameters provided excellent estimates for several other properties of the melt and composite systems not used in parameter estimation, thus establishing the robustness of the developed model.

A Picture is Worth a Thousand Timesteps: Excess Entropy Scaling for Rapid Estimation of Diffusion Coefficients in Molecular-Dynamics Simulations of Fluids.

In molecular-dynamics simulations of fluids, the Einstein-Helfand (EH) and Green-Kubo (GK) relationships are frequently used to compute a variety of transport coefficients, including diffusion coefficients. These relationships are formally valid in the limit of infinite sampling time: The error in the estimate of a transport coefficient (relative to an infinitely long simulation) asymptotically approaches zero as more dynamics are simulated and recorded. In practice, of course, one can only simulate a finite number of particles for a finite amount of time. In this work, we show that in this pre-asymptotic regime, an approach for estimating diffusion coefficients based upon excess entropy scaling (EES) achieves a significantly lower error than either EH or GK relationships at fixed online sampling time. This approach requires access only to structural information at the level of the radial distribution function (RDF). We further demonstrate that the use of a recently developed RDF mollification scheme significantly reduces the amount of sampling time needed to converge to the long-time value of the diffusion coefficient. We also demonstrate favorable sample-to-sample variances in the diffusion coefficient estimate obtained using EES as compared to those obtained using EH and GK.

Response of Foldable Protein Conformations to Non-Physiological Perturbations: Interplay of Thermal Factors and Confinement.

Technological advances frequently interface biomolecules with nanomaterials at non-physiological conditions, necessitating response characterization of key processes. Similar encounters are expected in cellular contexts. We report in silico investigations of the response of diverse protein conformational states to lowering of temperature and imposition of spatial constraints. Conformational states are represented by folded form of the Albumin binding domain (ABD) protein, its compact denatured form, and structurally disordered nascent folding elements. Data from extensive simulations are evaluated to elicit structural, thermodynamic and dynamic responses of the states and their associated environment. Analyses reveal alterations to folding propensity with reduced thermal energy and confinement, with signatures of trend reversal in highly disordered states. Across temperatures, confinement has restrictive effects on volume and energetic fluctuations, leading to narrowing of differences in isothermal compressibility (κ) and heat capacities (Cp). While excess (over ideal gas) entropy of the hydration layer marks dependence on the conformational state at bulk, confinement triggers erasure of differences. These observations are largely consistent with timescales of protein-water hydrogen bonding dynamics. The results implicate multi-factorial associations within a simple bio-nano complex. We expect the current study to motivate investigations of more biologically relevant interfaces towards mechanistic understanding and potential applications.

Physicochemical and catalytic behavior of binary mixtures of n-alkyl imidazolium bromide ionic liquids with poly (ethylene glycol)-400: Application of flory statistical theory

In this work, Flory statistical theory is employed to predict the important physicochemical properties namely density, isothermal compressibility, internal pressure, coefficient of volume expansion, energy of vaporization, heat of vaporization, cohesive energy density, solubility parameter and polarity index for three binary mixtures of PEG-400 + [CnMim][Br], where n=4, 6, and 8 at different temperatures (T= 298.15 K, 308.15 K, and 318.15 K). Furthermore, the applicability of Flory statistical theory to predict certain physicochemical properties has been verified. Excess properties viz., excess enthalpy, excess Gibbs free energy, and excess entropy are also determined for these binary mixtures. The variation of energy of vaporization, heat of vaporization, solubility parameter and excess parameters are used to analyze the catalytic behavior and prevalent molecular interactions of these mixtures.

Use of third generation data for the pure elements to model the thermodynamics of binary alloy systems: Part 3 – The theoretical prediction of the Al–Si–Zn system

In a previous paper a method was developed to define Einstein temperatures for metastable phases of the elements and their relation to the so-called lattice stabilities used in the past, and also the variation of the Einstein temperature with composition to account for the composition dependence of the excess entropy. This approach was demonstrated successfully for the Al–Zn system. In this paper this approach is extended to cover the Al–Si and Si–Zn binary systems. The phase diagram for the Al–Si–Zn ternary system was then predicted from the thermodynamic description of the binary subsystems only without any ternary interaction parameters. Agreement with the experimental data is shown to be very good.

Linking excess entropy and acentric factor in spherical fluids.

Introduced by Pitzer in 1955, the acentric factor (ω) has been used to evaluate a molecule's deviation from the corresponding state principle. Pitzer devised ω based on a concept called perfect liquid (or centric fluid), a hypothetical species perfectly adhering to this principle. However, its physical significance remains unclear. This work attempts to clarify the centric fluid from an excess entropy perspective. We observe that the excess entropy per particle of centric fluids approximates -kB at their critical points, akin to the communal entropy of an ideal gas in classical cell theory. We devise an excess entropy dissection and apply it to model fluids (square-well, Lennard-Jones, Mie n-6, and the two-body abinitio models) to interpret this similarity. The dissection method identifies both centricity-independent and centricity-dependent entropic features. Regardless of the acentric factor, the attractive interaction contribution to the excess entropy peaks at the density where local density is most enhanced due to the competition between the local attraction and critical fluctuations. However, only in centric fluids does the entropic contribution from the local attractive potential become comparable to that of the hard sphere exclusion, making the centric fluid more structured than acentric ones. These findings elucidate the physical significance of the centric fluid as a system of particles where the repulsive and attractive contributions to the excess entropy become equal at its gas-liquid criticality. We expect these findings to offer a way to find suitable intermolecular potentials and assess the physical adequacy of equations of state.

Entropy of strongly coupled Yukawa fluids.

The entropy of strongly coupled Yukawa fluids is discussed from several perspectives. First, it is demonstrated that a vibrational paradigm of atomic dynamics in dense fluids can be used to obtain a simple and accurate estimate of the entropy without any adjustable parameters. Second, it is explained why a quasiuniversal value of the excess entropy of simple fluids at the freezing point should be expected, and it is demonstrated that a remaining very weak dependence of the freezing point entropy on the screening parameter in the Yukawa fluid can be described by a simple linear function. Third, a scaling of the excess entropy with the freezing temperature is examined, a modified form of the Rosenfeld-Tarazona scaling is put forward, and some consequences are briefly discussed. Fourth, the location of the Frenkel line on the phase diagram of Yukawa systems is discussed in terms of the excess entropy and compared with some predictions made in the literature. Fifth, the excess entropy scaling of the transport coefficients (self-diffusion, viscosity, and thermal conductivity) is reexamined using the contemporary datasets for the transport properties of Yukawa fluids. The results could be of particular interest in the context of complex (dusty) plasmas, colloidal suspensions, electrolytes, and other related systems with soft pairwise interactions.

The entropic origin of the enhancement of liquid diffusion close to a neutral confining surface.

It is known that, in the proximity of a neutral wall, liquids experience diffusion enhancement relative to their bulk diffusion, but the origin of this phenomenon is still unknown. We report a molecular dynamics simulation investigating the dynamics of a simple liquid in the proximity to a non-interacting smooth confining wall, which exhibits a strong diffusion enhancement within the liquid layers adjacent to the wall. We present an analysis of these results, demonstrating that the observed diffusion enhancement can be accounted for, with numerical accuracy, using the universal scaling law that relates the liquid diffusion rate to the excess entropy. These results show that the scaling law, which has so far only been used for the description of the bulk liquid diffusion, can be successfully used to describe the diffusion in liquids under nano-scale confinement.

Prediction of Sm- (Co, Cu, Fe, Zr) binary alloys’ thermodynamic parameters by improved miedema model

Abstract At present, the calculation results of the original Miedema mixing enthalpy model are still somewhat different from the experimental results. Therefore, it is necessary to improve the calculation accuracy of the Miedema model to promote the development of the Miedema model and its application in the design of samarium-cobalt permanent magnet alloys. To solve this problem, the enthalpies of mixing of Sm- (Co, Cu, Fe, Zr) binary alloys were calculated in this paper by using the modified model. The mixing enthalpy (DH), excess entropy (SE), excess Gibbs free energy (GE), component activity (α) and binary Gibbs free energy of Sm-Co, Sm-Fe were calculated. The results show that the improved Miedema model can better match the experimental values. Sm- (Co, Fe, Cu) binary alloys are easy to generate intermetallic compounds. And Sm-Zr is difficult to form intermetallic compounds. The DH, SE and GE of Sm- (Co, Fe) are negative, and there is a large negative deviation from Raoult's law for the activity of each component compared to the ideal solution. The Gibbs free energies for both SmCo5 and Sm2Co17 precipitation reactions are less than zero in the temperature range between 1550 and 1620 K. The Sm2Co17 phase is thermodynamically more stable than the SmCo5 phase.

Models to predict configurational adiabats of Lennard-Jones fluids and their transport coefficients.

A comparison is made between three simple approximate formulas for the configurational adiabat (i.e., constant excess entropy, sex) lines in a Lennard-Jones (LJ) fluid, one of which is an analytic formula based on a harmonic approximation, which was derived by Heyes et al. [J. Chem. Phys. 159, 224504 (2023)] (analytic isomorph line, AIL). Another is where the density is normalized by the freezing density at that temperature (freezing isomorph line, FIL). It is found that the AIL formula and the average of the freezing density and the melting density ("FMIL") are configurational adiabats at all densities essentially down to the liquid-vapor binodal. The FIL approximation departs from a configurational adiabat in the vicinity of the liquid-vapor binodal close to the freezing line. The self-diffusion coefficient, D, shear viscosity, ηs, and thermal conductivity, λ, in macroscopic reduced units are essentially constant along the AIL and FMIL at all fluid densities and temperatures, but departures from this trend are found along the FIL at high liquid state densities near the liquid-vapor binodal. This supports growing evidence that for simple model systems with no or few internal degrees of freedom, isodynes are lines of constant excess entropy. It is shown that for the LJ fluid, ηs and D can be predicted accurately by an essentially analytic procedure from the high temperature limiting inverse power fluid values (apart from at very low densities), and this is demonstrated quite well also for the experimental argon viscosity.

Equilibrium and non-equilibrium molecular dynamics simulation of thermo-osmosis: enhanced effects on polarised graphene surfaces

Thermo-osmotic flows, generated by applying a thermal gradient along a liquid-solid interface, could be harnessed to convert waste heat into electricity. While this phenomenon has been known for almost a century, there is a crucial need to gain a better understanding of the molecular origins of thermo-osmosis. In this paper, we start by detailing the multiple contributions to thermo-osmosis. We then showcase three approaches to computing the thermo-osmotic coefficient using molecular dynamics; a first method based on the computation of the interfacial enthalpy excess and Derjaguin's theoretical framework, a second approach based on the computation of the interfacial entropy excess using the so-called dry-surface method, and a novel non-equilibrium method to compute the thermo-osmotic coefficient in a periodic channel. We show that the three methods align with each other, in particular for smooth surfaces. In addition, for a polarised graphene-water interface, we observe large variations of thermo-osmotic responses, and multiple changes in flow direction with increasing surface charge. Overall, this study showcases the versatility of osmotic flows and calls for experimental investigation of thermo-osmotic behaviour in the vicinity of charged surfaces.

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Pseudoisomorphs for Harmonic-Bonded Molecules.

Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been shown to exist in molecular models with flexible bonds [Olsen, A. E. J. Chem. Phys. 2016, 145, 241103]. We here present three force-based methods to trace out pseudoisomorphs based on a single configuration and test them on the asymmetric dumbbell and 10-bead Lennard-Jones chain models with bonds modeled as harmonic springs. The three methods are based on requiring that particle forces, center-of-mass forces, and torques, respectively, are invariant in reduced units. For each of the two investigated models we identify a method that works well for tracing out pseudoisomorphs, but these methods are not the same. Overall, we find that the more internal degrees of freedom there are in the molecule studied, the less they appear to affect the gross dynamical behavior. Moreover, the "internal" degrees of freedom (including rotation) do not significantly affect the scaling behavior of the dynamical/transport coefficients provided some 'quenching' is performed.

Star Formation, Nebulae, and Active Galactic Nuclei in CLASH Brightest Cluster Galaxies. I. Dependence on Core Entropy of Intracluster Medium

We set the stage for reassessing how star formation, emission-line nebulae, and active galactic nuclei (AGNs) in brightest cluster galaxies (BCGs) depend on the thermodynamics of the intracluster medium (ICM). Our work is based on the 25 clusters observed in the CLASH program for which the aforementioned attributes in their BCGs can be well scrutinized, as has the thermodynamics of their ICM. Nine of these BCGs display complex UV morphologies tracing recent star formation, whereas the remaining 16 are characterized by a relatively compact central UV enhancement. Here, we show definitively that three of the latter BCGs also display star formation, whereas the diffuse UV of the remaining 13 is entirely consistent with old low-mass stars. The overall results support the previously established dependence of star formation and nebulae in BCGs on an “excess core entropy,” K 0, for the ICM: all 11 clusters with K 0 ≤ 24 keV cm2 (but only one of 14 clusters with K 0 ≥ 42 keV cm2) host star-forming BCGs that almost if not always possess nebulae. Instead of an entropy floor, we show that K 0 reflects the degree to which the radial entropy profile decreases inward within ∼100 kpc rather than (except perhaps at large K 0) actually flattening: clusters with lower ICM entropies and hence shorter cooling times at their cores preferentially host BCGs displaying star formation, nebulae, and more radio-luminous AGNs. Nearly all BCGs possess detectable AGNs, however, indicating multiple pathways for fuelling their AGNs.

Self-diffusion coefficient as a function of the thermodynamic factor.

Much effort has been put into developing theories for dense fluids; as a result of these efforts many theories work for a certain type of particle or in a certain concentration regime. Rosenfeld proposed a dependence of the self-diffusion coefficient on the excess entropy. Our proposal is similar to Rosenfeld's in that it also attempts to describe diffusion in terms of a thermodynamic function but, instead of the excess entropy, we use the thermodynamic factor or the excess chemical potential. Simulations were taken for hard spheres and our model was fitted with two free parameters. Simulations were then carried out for a Lennard-Jones gas and our model correctly described the new data with the value of the free parameters that we had obtained for hard spheres. This is a feature of our model that we wish to emphasize, since the usual situation is that parameters have to be readjusted for different interaction potentials. An experimental xenon self-diffusion data set was used as an example of where the model can be applied, especially in the high-density regime.

Line tension and line entropy associated with the monolayer/trilayer boundary of smectic liquid crystal at the air-water interface.

Molecularly thin films of the smectic liquid crystal 4'-octyl-4-biphenylcarbonitrile (8CB) at the air-water interface phase separate into regions with different numbers of layers, in analogy with freestanding smectic liquid crystalline films. This paper reports the line tension associated with the boundary of coexisting trilayer and monolayer phases of in Langmuir films of 8CB at the air-water interface as a function of temperature and humidity and infers information on the boundary profile between the coexisting phases. Two complementary techniques are used to characterize the 8CB thin films: surface pressure-area isotherm and Brewster angle microscopy (BAM). We determine the line tension by stretching isolated domains from their equilibrium circular shape and analyzing the free relaxation with a hydrodynamic model. Then, we interpret the line tension vs temperature data in terms of an excess line entropy for the domain boundary, which requires careful consideration of the thermodynamics of inhomogeneous monolayer systems.

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.

Thermophysical properties of Ni-Ti melts measured by electromagnetic levitation method using static magnetic field

The normal spectral emissivity, molar heat capacity at constant pressure, and thermal conductivity of Ni-Ti melts were measured during electromagnetic levitation under a static magnetic field. The emissivity and heat capacity of the Ni-Ti melts were measured under a 3 T static magnetic field. The temperature range for the emissivity measurements was 1240–1839 K, and the temperature range for the heat capacity measurements ranged was 1223–1851 K. The emissivity and heat capacity of the Ni-Ti melts, except for the Ni mole fractions (xNi) of 0 and 0.25, showed without temperature dependence within the experimental temperature range. Furthermore, the heat capacity was larger than the ideal solution over the whole range of compositions. The emissivity of the Ni-Ti melts was discussed based on the Drude model. The temperature dependence of thermodynamic functions, such as enthalpy of mixing, excess entropy, and excess Gibbs energy, were calculated using excess heat capacity. The thermal conductivity of Ni-Ti melts was measured under a static magnetic field of 10 T. The temperature range for the thermal conductivity measurements was 1177–1900 K. The thermal conductivities of the Ni-Ti melts increased with increasing temperature, exhibited a local minimum for xNi = 0.75, and were higher than those calculated using the Wiedemann–Franz laws. This difference in thermal conductivity was discussed by considering the contribution of atomic vibrations.

Effects of different alkyl chain lengths on excess properties of CO2-1-Butyl-1-methyl-pyrrolidinebis(trifluoromethanesulfonyl)imide, CO2-1-hexyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide, CO2-1-octyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide systems

The study investigates the solubility of carbon dioxide (CO2) in three ionic liquids [BMP][Tf2N] (1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide), [HMP][Tf2N] (1-hexyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide) and [OMP][Tf2N] (1-octyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide). The research is conducted over a temperature range of 303.15 to 363.15 K. The phase equilibria of the binary systems are predicted using the Peng-Robinson (PR) equation of state, the Wilson (WS) mixing rule and the UNIFAC activity coefficient model. The interaction parameter kij is regressed from the vapor-liquid equilibrium (VLE) experimental data. The study also calculates the excess Gibbs free energy (GE), excess enthalpy (HE), and excess entropy (SE) for these systems. The research results indicate that the length of the alkyl chain in the cation has a significant effect on the excess properties of the CO2-ionic liquid systems. As the alkyl chain length increases, the excess Gibbs free energy and excess enthalpy decrease, while the excess entropy increases. The CO2-[OMP][Tf2N] system exhibits stronger interactions between CO2 and the ionic liquid, indicating a higher capacity for CO2 absorption. The study results are helpful for optimization of CO2 capture processes and the broader comprehension of fluid phase equilibria in complex systems.