6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

/pdf/quantum-mechanical-continuum-solvation-models-3edv963g14.pdf

Quantum mechanical continuum solvation models.

https://dc.engconfintl.org/cgi/viewcontent.cgi?article=1032&context=superalloys_ii

A critical review of high entropy alloys and related concepts

A modified SAFT equation of state is developed by applying the perturbation theory of Barker and Henderson to a hard-chain reference fluid. With conventional one-fluid mixing rules, the equation of state is applicable to mixtures of small spherical molecules such as gases, nonspherical solvents, and chainlike polymers. The three pure-component parameters required for nonassociating molecules were identified for 78 substances by correlating vapor pressures and liquid volumes. The equation of state gives good fits to these properties and agrees well with caloric properties. When applied to vapor−liquid equilibria of mixtures, the equation of state shows substantial predictive capabilities and good precision for correlating mixtures. Comparisons to the SAFT version of Huang and Radosz reveal a clear improvement of the proposed model. A brief comparison with the Peng−Robinson model is also given for vapor−liquid equilibria of binary systems, confirming the good performance of the suggested equation of state. ...

Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules

An equation of state for associating liquids is presented as a sum of three Helmholtz energy terms: Lennard-Lones (LJ) segment (temperature-dependent hard sphere + dispersion), chain (increment due to chain formation), and association (increment due to association). This equation of state has been developed by extending Wertheim’s theory obtained from a resummed cluster expansion. Pure component molecules are characterized by segment diameter, segment-segment interaction energy, for example, Lennard-Jones u and E, and chain length expressed as the number of segments. There are also two association parameters, the association energy and volume, characteristic of each site-site pair. The agreement with molecular simulation data is shown to be excellent at all the stages of development for associating spheres, mixtures of associating spheres, and nonassociating chains. The model has been shown to reproduce experimental phase equilibrium data for a few selected real pure compounds.

New reference equation of state for associating liquids

https://scholars.cityu.edu.hk/files/27103119/High_entropy_alloy_challenges_and_prospects.pdf

High-entropy alloy: challenges and prospects

An equation of state is proposed for the mixture of hard spheres based on an averaging process over the two results of the solution of the Percus–Yevick integral equation for the mixture of hard spheres. Compressibility and other equilibrium properties of the binary mixtures of hard spheres are calculated and they are compared with the related machine‐calculated (Monte Carlo and molecular dynamics) data. The comparison shows excellent agreement between the proposed equation of state and the machine‐calculated data.

Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres

The corresponding states principle—a review of current theory and practice

A new method for the calculation of thermodynamic properties of simple fluid mixtures constitutes an extension of the approach defined earlier as the “van der Waals” conformal solution theory. This extension is made possible by advances in the analytical representation of the thermodynamic properties of a mixture of hard spheres which permit the properties to be calculated directly, without the use of a reference fluid. A new hard-sphere excess function, defined as a property of the mixture less the value of this property for the hard-sphere mixture, is obtained by a new conformal solution theory using a single pure fluid as a reference substance. Although the reference substance properties could be experimentally measured values, this work obtains them from an analytical form of the Barker-Henderson perturbation theory.This new method improves prediction of the effects of large molecular size differences on the excess properties of the mixture. It uses the reference fluid to account for most of the temperature dependence of the cut-off parameter needed to define the molecular diameters in the direct hard-sphere mixture calculations and the calculations need only the high temperature limit of the cut-off parameters, even far below the critical temperature. The new method extends the original vdW conformal solution method to lower temperatures and provides an opening for inclusion of three-body interactions.Conventional excess mixing functions for several binary liquid mixtures calculated by the new method are compared with the predictions of other theories and with both experimental and Monte Carlo data.

Statistical thermodynamics of mixtures. A new version for the theory of conformal solution

Use of molecular shape factors in vapor-liquid equilibrium calculations with the corresponding states principle

A new ideal K value is defined which does not depend on the Lewis and Randall ideal solution rule but is derived only from composition dependent pseudo criticals and the corresponding states principle. Properties of the liquid and vapor mixtures are evaluated from either experimentally measured properties of closely related pure substances or from generalized tables of thermodynamic properties. A derivation of an improved pseudocritical expression applicable to liquids which may be approximated by simple spherical molecules is presented. The derivation illustrates the assumptions involved and points the way for a possible extension of the technique to more complex molecules.

There are some advantages to this approach. It does not require the troublesome extrapolation of liquid properties into regions where no liquid can exist, a fact which is characteristic of K value calculations from the ideal solution rule. It is especially useful for systems in which an equation of state is not available for all of the components present. It avoids the difficulties in defining combination rules for complicated equations of state. Even for systems including very complex or moderately polar molecules it provides a base for subsequent empirical modification. This base follows the correct isotherm of In K vs. In P up to the actual critical of the system without the difficulties associated with defining a convergence pressure or evaluating the extremely large activity coefficient corrections to the ideal solution rule in the critical region. For mixtures of simple molecules the calculated ideal K value is within about 10% of the experimental value in both the low pressure and in the critical region. The entire calculation may be expressed completely analytically for use on a digital computer and may be coupled with an equilibrium flash calculation so that the ideal K values may be determined from a given overall composition, temperature, and pressure.

Thomas W. Leland

Papers

Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres

The corresponding states principle—a review of current theory and practice

Statistical thermodynamics of mixtures. A new version for the theory of conformal solution

Use of molecular shape factors in vapor-liquid equilibrium calculations with the corresponding states principle

Prediction of vapor‐liquid equilibria from the corresponding states principle