Entropy Scaling of Viscosity - I: A Case Study of Propane

Viscosity and Thermal Conductivity Models of 151 Common Fluids Based on Residual Entropy Scaling and Cubic Equations of State

A residual entropy scaling (RES) approach combined with the cubic equation of state (EoS) was developed to calculate the viscosity and thermal conductivity of 151 common fluids. These pure fluids are all the pure fluids available in the NIST's REFPROP 10.0 database. Seven cubic EoS were studied, while only four yielded good and similar results; these are Peng-Robinson (PR), Soave-Redlich-Kwong (SRK), Patel-Teja-Valderrama (PTV), and Yang-Frotscher-Richter (YFR) EoS. The parameters of a pure fluid in this cubic EoS + RES approach were fitted using experimental data if they are available in the NIST ThermoData Engine database 10.1, otherwise, using the calculations of REFPROP 10.0. This approach is applicable in the entire temperature and pressure ranges for thermal conductivity and at pressures lower than 60 MPa for viscosity. Using this approach, the average absolute value of the relative deviation (AARD) of all of the analyzable experimental values from model calculations was approximately 3.1% and 3.6% for viscosity and thermal conductivity, respectively. This result is not too bad compared to 2.7% and 2.5% obtained by the state-of-the-art viscosity and thermal conductivity models in REFPROP 10.0. The key advantage of this approach is that it has a much simpler equation form and can be easily extended to more fluids. The developed approach has been implemented in the OilMixProp 1.0 software package, and this work will be a basis for the future development of more than 600 pure fluids.

Entropy Scaling of Viscosity IV-Application to 124 Industrially Important Fluids

In our previous work [Yang X.J. Chem. Eng. Data2021, 66, 1385-1398], a residual entropy scaling (RES) approach was developed to link viscosity to residual entropy using a 4-term power function for 39 refrigerants. In further research [Yang X.Int. J. Thermophys.2022, 43, 183], this RES approach was extended to 124 pure fluids containing fluids from light gases (hydrogen and helium) to dense fluids (e.g., heavy hydrocarbons) and fluids with strong association force (e.g., water). In these previous research studies, the model was developed by manual optimization of the power function. The average absolute relative deviation (AARD) of experimental data from the RES model is approximately 3.36%, which is higher than the 2.74% obtained with the various models in REFPROP 10.0. In the present work, the power function was optimized by iteratively fitting the global (fluid-independent power terms) and local parameters (fluid-specific and group-specific parameters) and screening the experimental data. The resulting equation has only three terms instead of four. Most notably, the AARD of the new RES model is reduced down to 2.76%; this is very close to the various multiparameter models in REFPROP 10.0, while the average relative deviation (ARD) amounts to 0.03%, which is smaller than REFPROP 10.0's 0.7%. A Python package is provided for the use of the developped model.

Linking Thermal Conductivity to Equations of State Using the Residual Entropy Scaling Theory

In recent years, the application of the residual entropy scaling (RES) method for modeling transport properties has become increasingly prominent. Based on Yang et al. (Ind. Eng. Chem. Res. 2021, 60, 13052) in modeling the thermal conductivity of refrigerants, we present here an RES model that extends Yang et al.'s approach to a wider range of pure fluids and their mixtures. All fluids available in the REFPROP 10.0 software, i.e., those with reference equations of state (EoS), were studied. A total of 71,554 experimental data of 125 pure fluids and 16,702 experimental data of 164 mixtures were collected from approximately 647 references, mainly based on the NIST ThermoData Engine (TDE) database 10.1. As a result, over 68.2% (corresponding to the standard deviation of a normal distribution) of the well-screened experimental data agree with the developed RES model within 3.1% and 4.6% for pure fluids and mixtures, respectively. Comparative analysis against the various models implemented in the REFPROP 10.0 (one of the state-of-the-art software packages for thermophysical property calculations) reveals that our RES model demonstrates analogous statistical agreement with experimental data yet with much fewer parameters. Regarding the average absolute value of the relative deviation (AARD) from experimental values to model predictions, the developed RES model shows a smaller or equal AARD for 74 pure fluids out of 125 and 76 mixtures out of 164. Besides, a detailed examination of the impact of the critical enhancement term on mixture calculations was conducted. To use our model easily, a software package written in Python is provided in the Supporting Information.

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 ab initio 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.

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.

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.

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.

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.

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.

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.

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

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

Thermodynamic or density scaling of the thermal conductivity of liquids

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

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.