Ternary Interaction Term Research Articles

Study of excess free energy of mixing and heat of mixing of liquid ternary Al–Li–Zn alloy by assessing the thermodynamic properties of sub-binary alloys

The exponential temperature-dependent interaction parameters of the Redlich-Kister (R–K) polynomial for the binary sub-systems of the liquid Al–Li–Zn ternary alloy were optimized using available literature data. The ternary interaction terms of the Redlich-Kister-Maggianu (R–K–M) polynomial were then optimized in order to determine the excess Gibbs free energy of mixing (GMxs) and the enthalpy of mixing (HM) of the system. These functions for the liquid ternary alloys were also computed at temperatures of 973 K, 1273 K and 1573 K. The calculated inverted miscibility gap that appeared in GMxs while using the linear temperature-dependent interaction parameters was suppressed in this work by the assumption of the interaction parameters to be exponential temperature dependent. The enthalpy of mixing of the alloy so calculated was found to be in good agreement with the available experimental data.

Thermodynamic Modeling and Validation of the Temperature Influence in Ternary Phase Polymer Systems.

The effect of the temperature, as a process variable in the fabrication of polymeric membranes by the non-solvent induced phase separation (NIPS) technique, has been scarcely studied. In the present work, we studied the influence of temperature, working at 293, 313 and 333 K, on the experimental binodal curves of four ternary systems composed of PVDF and PES as the polymers, DMAc and NMP as the solvents and water as the non-solvent. The increase of the temperature caused an increase on the solubility gap of the ternary system, as expected. The shift of the binodal curve with the temperature was more evident in PVDF systems than in PES systems indicating the influence of the rubbery or glassy state of the polymer on the thermodynamics of phase separation. As a novelty, the present work has introduced the temperature influence on the Flory–Huggins model to fit the experimental cloud points. Binary interaction parameters were calculated as a function of the temperature: (i) non-solvent/solvent (g12) expressions with UNIFAC-Dortmund methodology and (ii) non-solvent/polymer (χ13) and solvent/polymer (χ23) using Hansen solubility parameters. Additionally, the effect of the ternary interaction term was not negligible in the model. Estimated ternary interaction parameters (χ123) presented a linear relation with temperature and negative values, indicating that the solubility of the polymers in mixtures of solvent/non-solvent was higher than expected for single binary interaction. Finally, PES ternary systems exhibited higher influence of the ternary interaction parameter than PVDF systems.

Comments on the correlation of vapor–liquid equilibrium (VLE) data in azeotropic ternary systems

The analysis has been carried out of the possible theoretical types of ternary systems regarding the distillation boundaries, for systems involving up to three binary azeotropes and one ternary azeotrope. The study reveals that there are some of these theoretical behaviors that classical activity coefficient models such as NRTL cannot predict. The objective of the present work is to show these limitations, analyze their causes and suggest possible solutions. The addition of one ternary interaction term to the Gibbs energy of excess function removes many of the limitations of classical models expanding the number and type of systems that could be correlated with the models and, what is more important, markedly improving the correlation capability of the model.

Equivalence of the McAllister and Heric Equations for Correlating the Liquid Viscosity of Multicomponent Mixtures

This paper demonstrates the equivalence between two equations for correlating liquid kinematic viscosities, the Heric and McAllister equations. For ternary and multicomponent mixtures, the only difference is in the ternary interaction term. If this term is constant, both equations correlate the viscosity data identically. This approach can prove the equivalence of the Nissan and Grunberg equation and the Frenkel equation to correlate the dynamic viscosity of liquid mixtures. Examples are included for binary and ternary mixtures.

High-Throughput Determination of Quantitative Structure−Property Relationships Using a Resonant Multisensor System: Solvent Resistance of Bisphenol A Polycarbonate Copolymers

Polymers are important materials for sensor, microfluidic, and other demanding applications. High-throughput screening methodology has been applied for the evaluation of the solvent resistance of a family of polycarbonate copolymers prepared from the reaction of bisphenol A (BPA), hydroquinone (HQ), and resorcinol (RS) in different solvents of practical importance, such as chloroform, tetrahydrofuran (THF), and methyl ethyl ketone (MEK). We employed a 24-channel acoustic-wave sensor system that provided previously unavailable capabilities for parallel evaluation of polymer solvent resistance. This high-throughput polymer evaluation approach assisted in construction of detailed solvent-resistance maps of polycarbonate copolymers and in determination of quantitative structure-property relationships. The best absolute solvent resistance of all studied copolymers was achieved in MEK, followed by chloroform and THF. A D-optimal mixture design was employed to explore the relationship between the copolymer compositions and their solvent resistance. The applied special cubic model for each solvent took into account the primary mixture terms such as BPA, HQ, and RS; binary interaction terms such as BPA-HQ, BPA-RS, and HQ-RS; and a ternary interaction term BPA-HQ-RS. A combination of the normal distribution of the model residuals and the very high values of adjusted R2 (0.97-0.99) demonstrated a good quality of the model. At a HQ concentration of 40 mol %, the solvent resistance was the highest for all tested solvents, and different concentrations of BPA (40 and 60 mol %) and RS (0 and 20 mol %) did not affect the solvent resistance. Without HQ, solvent resistance was decreasing with an increase of RS and decrease of BPA. Overall, with an increase of HQ concentration from 0 to 40 mol %, the solvent resistance of BPA-HQ-RS copolymers was improved by up to 3 times in THF, by 21 times in chloroform, and by 32 times in MEK.

Surface tension prediction of high-temperature melts

In this paper the artificial neural network (ANN) was applied to predict the surface tension of pure liquid metals and Butler’s original treatment in conjunction with the CALPHAD (CALculation of PHAse Diagram) technique was extended to predict surface tensions of binary, ternary and multi-component high-temperature melts: liquid alloys, molten salt mixtures and molten mattes. The model parameter β in Butler’s equation was discussed for different high-temperature melts. In addition, the geometric models and general solution model were used for predicting surface tensions of multi-component systems from those of sub-binary systems. The importance of the ternary interaction term in geometric models and general solution model for ternary systems far away from regular solutions is emphasized.

Calculation of ternary mixing properties of melts and minerals from the bounding binaries

Among the several methods that have been used to predict thermodynamic properties of ternary alloys and oxides from three binary data, we used the models proposed by Kohler(1), Toop(2), and Muggianu (3) in order to evaluate the possibility of the application of these methods to geologically important systems, such as zeolites, clay minerals and silicate glasses. These models can represent the ternary excess Gibbs energy of the NaCl-KCl-H 2O and Ca-Mg-Fe 2+ garnet (Ca 3Al 2Si 3O 12 - Mg 3Al 2Si 3O 12 - Fe 3Al 2Si 3O 12) systems relatively well without a ternary correction term. The deviation from the reference data increases in the central region of the composition triangle. Toop's model with constant mole fractions of NaCl and Mg best simulated the ternary systems among the models. The path independent Muggianu model was applied to diopside (CaMgSi 2O 6) -jadeite (NaAlSi 2O 6) - acmite (NaFe 3+Si 2O 6) ternary as an example. Although there exists intrinsic uncertainty in calculation without the ternary interaction term, these models, especially, Muggianu and Kohler can be good approximation methods for prediction of the ternary excess properties of the natural mineral solid solutions, devoid of ternary experimental thermodynamic data.

Ionic Interactions in Aqueous Mixtures of NaCl with Guanidinium Chloride: Osmotic Coefficients, Densities, Speeds of Sound, Surface Tensions, Viscosities, and the Derived Properties

The isopiestic osmotic coefficients, densities, and speeds of sound of aqueous mixtures of NaCl with guanidinium chloride (GnCl) have been measured at different ionic strengths with varying compositions at 298.15 K with a view to determine the ionic interactions. The excess free energy, ΔmGE, volume, ΔmVE, and compressibility of mixing, ΔmKE, of the NaCl−GnCl mixtures at constant ionic strength show interesting features with changing ionic strength fractions of the electrolytes. These excess properties of mixing with both negative and positive signs can be attributed to the mixing of hydrophilic and hydrophobic ions. It is shown that the binary and ternary interaction terms play an important role in the accurate representation of the osmotic coefficients, activity coefficients, volumes, and compressibilities of the mixtures. Measurements on the surface tension and viscosity of the NaCl−GnCl mixtures have also been reported. A simple equation incorporating like charge interactions has been employed to corr...

Experimental determination and computation of the liquid miscibility gap in the system CaO-MgO-SiO2-TiO2

Coexisting liquids in the CaO-MgO-SiO2-TiO2 system were synthesized and quenched at ambient pressure in air from 1600 °C using a Rh-Pt resistance furnace and from 1800 to 2000 °C using a laser heated air levitation setup. Compositions of quenched glasses determined by electron microprobe analysis are reproduced in detail by weighted extrapolations of binary Margules-type excess functions. Using a generalized Kohler method, the authors illustrate the correlation between the degree of binary excess polynomials and their extrapolation behavior to higher-order systems. The presented extrapolation approach avoids additional ternary parameters in the CaO-SiO2-TiO2 and MgO-SiO2-TiO2 systems and affords a reasonable extrapolation outside of the compositional region of stable liquid immiscibility. In contrast, ternary excess parameters had to be added to binary interaction terms in the CaO-MgO-TiO2 and CaO-MgO-SiO2 systems to reproduce the solvus and liquidus phase relations reported in the literature. The excess entropy terms of the liquid were minimized in order to avoid unjustified stable miscibility gaps of the melt up to at least 3000 °C. The reliability of the authors’ polynomial approximation for the excess Gibbs energy of the melt is reduced only when ternary interaction terms are added to binary terms in the melt. However, the proposed method permits a valuable approximation of the highly complex excess Gibbs energy at solvus compositions in the system CaO-MgO-SiO2-TiO2 with a minimum number of excess terms.

A computer calculation of the ternary MoPdRh phase diagram

Thermodynamic coefficients for the phases in the binary MoPd, PdRh and MoRh systems were derived by the assessment of the available experimental data using the binary Lukas optimization program. The resulting coefficients were first successfully utilised in reestablishing the binaries. The coefficients thus obtained in the binary computation were combined with ternary descriptions to compute ternary isothermal sections. Although no ternary interaction term was involved in the construction of the isotherms, the section calculated at 1373 K is found to be consistent with the experimentally established isothermal section at the same temperature. The location of three-phase field ( bcc+hcp+fcc) and phase boundaries in both isotherms are matching reasonably well. Combining only binary coefficients of these phases, it is possible to construct reasonable isothermal sections at different temperatures. Following this conclusion, isothermal sections ranging from 1373 to 2673 K of the ternary MoPdRh system were calculated.

A computer assessment of the ternary Ru-Rh-Pd system

Abstract Thermodynamic coefficients of the phases in the binary Ru-Rh, Pd-Rh and Ru-Pd systems were derived by assessment of the available experimental data using the binary Lukas optimization program. The resulting coefficients were first successfully utilised in re-establishing the binaries. The coefficients thus established in the binary computation were combined with binary descriptions to compute ternary isothermal sections. Although no ternary interaction term was involved in the construction of the isotherms, the calculation at 1973 K is found to be consistent with the experimentally established isothermal section at the same temperature. The location of three-phase fields (liquid + hcp + fcc) and phase boundaries in both isotherms are matching reasonably well and these show that that ternary interactions of the components in these phases are less strong. Combining only binary coefficients of these phases it is possible to construct reasonable isothermal sections at different temperatures. Following this conclusion, isothermal sections ranging from 973 to 2473 K of the ternary Ru-Rh-Pd system were calculated.

Representation of excess thermodynamic properties of ternary systems using interaction parameters

A ternary function has been developed based on the Maclaurin infinite series, which is expressed in the neighborhood of each of the pure components of the system. Each of the series is subjected to various boundary conditions. The ternary function is based on the summation of these series. In the process of converting the terms of these infinite series to the corresponding infinite dilution constants and interaction parameters, the ternary function also distinguishes between the binary and ternary interaction parameters of the system. The truncation of the infinite series pertaining to the binary and ternary interaction terms is adjusted by a suitable technique which is described in the text. The function is thermodynamically consistent and capable of interpreting properties of the ternary system.

A new solution model for predicting ternary thermodynamic properties

A new symmetric model for predicting ternary thermodynamic properties from its three binary properties is presented. In comparison with other current models, this new model contains a stronger ternary interaction terms. It is expected that this model will be suitable for the systems, in which the ternary interaction can not be neglected. This model is also easy to compute as R function method is used.

The effect of specific interactions on the sorption equilibrium in the polymer/mixed solvent system

AbstractUsing the theory of association equilibria, equations are derived for preferential and total sorption into the coil for a ternary system containing inert liquid A, self‐associating liquid B and polymer C, capable of specific interactions with component B. Due to strong interactions, the assumption of random mixing is not valid for this system. In preceding work differences between experiment and prediction based on the classical Flory‐Huggins equation were formally described by the introduction of a ternary interaction term. For this particular system the ternary term may be interpreted as a consequence of the decrease in the entropy of mixing, caused by strong association of component B. On the contrary, if this component is bound to the polymer at the same time, the ternary term decreases. The equations derived in the paper lead to a reasonable fit with experimental data of the system benzene (A)/alcohol(B)/poly(methyl methacrylate)(C).

Thermodynamic modeling of binary and ternary metallic solutions

A model is proposed for describing heat of mixing behavior in binary and ternary metallic solutions. The binary model, which has the form, ΔH M =α1 X 2 X B +α2 X A X 2 −α3 X 2 X 2 , whereX A andX B are mole fractions of componentsA andB and α1, α2, and α3 are constants, is applied to the heat of mixing values for 84 solid and liquid systems and the results are compared with the subregular model. The ternary model, which is composed of the sum of the binary equations and a ternary interaction term of the form α ABC X A X B X C , was applied to the Bi−Cd−Pb, Cd−Pb−Sn, and Cd−Pb−Sb systems. There was excellent agreement both as to the shapes of the isoenthalpy of mixing curves and as to the heat of mixing values in the ternary systems when the model was used to predict the experimental values.