Thermodynamic Functions Of Mixing Research Articles

Thermodynamic Assessment of the Pyrazinamide Dissolution Process in Some Organic Solvents.

Pyrazinamide is a first line drug used for the treatment of tuberculosis, a pathology that caused the death of more than 1.3 million people in the world during 2022, according to WHO, being a drug of current interest due to its relevance in pharmaceutical and medical sciences. In this context, solubility is one of the most important physicochemical parameters in the development and/or optimization of new pharmaceutical forms, so the present work aims to present a thermodynamic study of the solubility of pyrazinamide in nine organic solvents of pharmaceutical interest. Using the shake-flask method and UV/Vis spectrophotometry, the solubility of this drug was determined at 9 temperatures; the maximum solubility was obtained in dimethyl sulfoxide at 318.15 K (x2=0.0816±0.004) and the minimum in cyclohexane at 283.15 K (1.73±0.05×10-5). From the apparent solubility data, the thermodynamic functions of solution and mixing were calculated, indicating an endothermic process. In addition, the solubility parameter of pyrazinamide was calculated using the Hoftyzer-van Krevelen (32.90 MPa1/2) and Bustamante (28.14 MPa1/2) methods. The maximum solubility was reached in dimethyl sulfoxide and the minimum in cyclohexane. As for the thermodynamic functions, the entropy drives the solution process in all cases. In relation to the solubility parameter, it can be analyzed that the mathematical models offer approximations; however, the experimental data are still primordial at the time of inferring any process.

Thermodynamic Properties of the Glass-Forming Ternary (Fe, Co, Ni, Cu)–Ti–Zr Liquid Alloys II. Temperature–Concentration Dependence of Thermodynamic Mixing Functions and Chemical Ordering in Liquid Alloys

Thermodynamic Properties of the Glass-Forming Ternary (Fe, Co, Ni, Cu)–Ti–Zr Liquid Alloys II. Temperature–Concentration Dependence of Thermodynamic Mixing Functions and Chemical Ordering in Liquid Alloys

Thermodynamics of Formation and Liquid-Vapor Phase Transitions of Antimony Alloys with Selenium and Sulfur.

The authors conducted liquid solution studies of antimony with selenium and sulfur in order to provide information on the thermodynamic functions of the formation of these alloys. The studies are based on the vapor pressure values of the components, comprising the double partial systems of antimony with antimony chalcogenides (Sb2Se3 and Sb2S3) and antimony chalcogenides with chalcogens (Se and S). We calculated the thermodynamic functions of mixing (graphical dependencies) and evaporation (tabular data) based on the partial vapor pressure values of components, which are represented by temperature-concentration dependencies. Based on the partial pressure values of melt components, we calculated the boundaries of liquid and vapor coexistence fields at atmospheric pressure (101.3 kPa) and in a vacuum (0.9 kPa). We established the absence of the stratification region on the Sb2S3-S diagram due to the fact that, on state diagrams, the stratification region is indicated at temperatures above 530 °C, while the boiling point of liquid sulfur at an atmospheric pressure corresponds to 429 °C. Based on the position of the field boundaries (L + V) on the state diagrams, the separation of antimony alloys with selenium and sulfur via distillation into elements at atmospheric pressure is difficult due to the high boiling points of antimony-based alloys in a vacuum: Sb2Se3-Se melts require some number of condensate re-evaporation cycles.

Solid-liquid phase equilibrium and thermodynamic properties analysis of Bazedoxifene acetate in fifteen kinds of mono-solvents

Crystallization is widely used for the isolation and purification of active pharmaceutical ingredients (APIs) in the final manufacturing stage. Bazedoxifene (BZD) acetate, classified as a third-generation selective estrogen receptor modulator, is employed in the treatment of postmenopausal osteoporosis. This work reports the equilibrium solubility data of BZD acetate in fifteen different mono-solvents, including methanol, ethanol, n-propanol, i-propanol, n-butanol, ethyl formate, methyl acetate, ethyl acetate, acetone, 2-butanone, cyclohexanone, tetrahydrofuran (THF), 2-methyltetrahydrofurane (2-MeTHF), 1,4-dioxane and acetonitrile (ACN), within the temperature range “T = 283.15–323.15 K” under p = 0.1 MPa. The solubilities of BZD acetate in various solvents increase with increasing temperature. Among the alcoholic solvents, the solubility order is as follows: methanol > ethanol > n-propanol > n-butanol > i-propanol. In esters solvent, the solubility of BZD acetate decreases in the following order: methyl acetate > ethyl acetate > ethyl formate. For ketones solvent, the solubility decreases in the following order: cyclohexanone > acetone > 2-butanone. The maximum value of BZD acetate solubility was 0.011 mol·mol−1 in tetrahydrofuran at T = 323.15 K, but the least data was found in ethyl formate at 283.15 K. Four thermodynamic models, i.e., the Yaws model, modified Apelblat model, λh model, and Wilson model were applied to fit the solubility data of BZD acetate in different solvents. Among them, the Wilson model represents the most accurate fitting outcomes. Finally, the thermodynamic functions of mixing (including enthalpy, entropy, and Gibbs energy) were calculated, and the results indicate a mixing process that is both spontaneous and driven by entropy. The solubility data, correlated models, and derived thermodynamic functions present essential thermodynamic fundamentals for the industrial production of BZD acetate crystallization, facilitating efficient separation and purification.

Solubility measurement, correlation and thermodynamic properties of 9H-thioxanthen-9-one in twelve mono organic solvents from 292.15 K to 335.95 K

The 9H-thioxanthen-9-one (TX) solubilities in twelve pure organic solvents were measured from 292.15 K to 335.95 K with the synthetic method at normal pressure. It was found that the TX solubilities increased with temperature. The measured solubilities of TX are well correlated by modified Apelblat equation, λh equation, Wilson equation and non-random two liquid (NRTL) equation, and the Wilson equation provides the best fitting results. The mixing thermodynamic functions including the mixing Gibbs free energy, mixing enthalpy and mixing entropy are calculated using the activity coefficients obtained from the Wilson equation model. The results suggest that the solubility behavior of TX may be determined mainly by the enthalpy, whereas the intermolecular interactions, especially the hydrogen bonds, between the TX and solvent molecules play important roles for the solubilities of TX.

Solubility measurement and correlation of 2-chlorothioxanthone (CTX) in twelve mono organic solvents

• Solubility of 2-chlorothioxanthone in twelve pure solvents was determined. • Solubility was correlated by Apelblat, λh , Wilson and NRTL model. • Thermodynamic properties of mixing process were also discussed. 2-Chlorothioxanthone (CTX) is one of the most widely used commercial photoinitiators for pharmaceutical preparations as well as for preparations of synthetic resins. The solubility of CTX in twelve pure organic solvents was measured using the gravimetric method from 287.55 to 335.95 K at normal pressure. The results shows that the solubility of CTX in all the solvents increases as temperature rising. The melting point and fusion enthalpy of CTX were measured with differential scanning calorimeter. The experimental solubility data were correlated with four thermodynamic models, including modified Apelblat equation, λh equation, Wilson equation and NRTL equation. The best correlation results were found with modified Apelblat equation and NRTL equation. The mixing thermodynamic functions (Gibbs free energy, enthalpy and entropy) were calculated based on the Wilson equation. The results showed that the entire mixing process is spontaneous.

New criteria for predicting compositions with high glass-forming ability in Zr–Co–Al alloys

We show that the widespread parameters PHS, PHSS and δ related with mixing enthalpy, mismatch entropy, configurational entropy and atom size difference do not provide proper prediction of the bulk metal glasses (BMGs) compositions with high glass-forming ability in Zr-Co-Al system. A new computational approach has been developed for the accurate determination of BMGs compositions having a maximum critical diameter (Dmax). Using new parameters ΘCo-Zr(xCo), ΘAl-Zr(xAl), the range of Co-Zr-Al compositions with the best GFA was determined and Zr55Co29Al16 composition with maximum Dmax was identified. The thermodynamic mixing functions (∆Gmix, ∆Hmix) for the glass-forming Zr-Co-Al system were calculated for the first time. The results obtained reveal a relationship between thermodynamic and geometric factors and open up prospects for the development of reliable theoretical methods for new metallic glasses discovery.

Solubility study of m-aminobenzoic acid form III in different mono-solvents by thermodynamic analysis and molecular simulation

The solid–liquid equilibrium behavior of m–aminobenzoic acid (m–ABA) form III in eleven mono–solvents (methanol, ethanol, n–propanol, isopropanol, n–butanol, methyl acetate, propyl acetate, butyl acetate, acetone, butanone and water) was investigated in the temperature from 283.15 K to 323.15 K. Solubility data were successfully described and correlated by four thermodynamic models, and all calculated ARD% values are lower than 5%. The thermodynamic functions of mixing were calculated and analyzed based on the NRTL model, and the results show that the mixing process is spontaneous and entropy–driving. The characteristics of m–ABA form III both in solution and solid phases were studied. Molecular electrostatic potential surface has been employed to present the overall charge distribution and estimate intermolecular interactions between the form III and solvents. Hirshfeld surface analysis has been applied to visualize various molecular interactions. Besides, the effect of selected solvent properties on the dissolution behavior of m–ABA form III was examined. Finally, molecular simulations have been further applied to disclose the interactions between solute and solvent molecules. This work has guiding significance for the design and optimization of the m–ABA crystallization process.

Interaction of Components in Glass-Forming Melts of Iron and Nickel with Titanium, Zirconium, and Hafnium II. Temperature–Concentration Dependence of Thermodynamic Mixing Functions of Liquid Alloys

Interaction of Components in Glass-Forming Melts of Iron and Nickel with Titanium, Zirconium, and Hafnium II. Temperature–Concentration Dependence of Thermodynamic Mixing Functions of Liquid Alloys

THERMODYNAMIC MIXING FUNCTIONS OF A MULTICOMPONENT LIQUID METAL AND SLAG

The work proposes a thermodynamic model of a multicomponent condensed phase applicable to metal and slag melts. The integral and partial thermodynamic mixing functions: Gibbs energy, enthalpy, entropy, heat capacity have been obtained using configurational statistical sum. Methods for estimating of model parameters using available data on activity coefficients and heats of mixing, Wagner interaction parameters have been suggested. Using binary Fe-Mn system as an example, the high accuracy of the calculation of the mixing thermodynamic functions of the metal phase in the entire concentration range has been shown. Mixing heat capacity has been shown to comply 3rd law of thermodynamics. Suggested thermodynamic model is already being used in steelmaking control system «Master» at metallurgical plant «Zaporizhstal», and in heat projecting and control system «DesigningMelt» at XuanSteel metallurgical works (PRC).

Mixing enthalpy of the Co–Ti–Hf liquid alloys and regularities of the function change in the row of the ternary (Co, Ni, Cu)–Ti–Hf glass-forming melts

The partial molar mixing enthalpies of titanium and hafnium in liquid Co–Ti–Hf alloys were studied at 1900 K by high-temperature isoperibolic calorimetry along xCo/xHf = 3 and xCo/xHf = 3 sections. The partial mixing enthalpies of undercooled liquid titanium and hafnium in liquid alloys and the integral mixing enthalpy are negative over the studied composition range. The thermodynamic mixing functions of liquid (Co, Ni, Cu)–Ti–Hf alloys were modeled in the framework of the associate solution model. Regularities in the change of thermodynamic mixing functions in liquid glass-forming (Co, Ni, Cu)–Ti–Hf alloys are discussed considering donor–acceptor interaction of the components in the melts.

Thermodynamic mixing functions of the Fe–Ni–Zr liquid alloys

The mixing enthalpies of liquid Fe–Ni–Zr alloys were studied at 1873 K by means of a high-temperature isoperibolic calorimeter. The study was performed along the section xFe/xNi = 1/1 at xZr = 0–0.45. The limiting partial enthalpy of mixing of undercooled liquid zirconium in liquid Fe50Ni50 (at.%) alloy is (–139 ± 6) kJ⋅mol−1. The integral mixing enthalpy are negative over the investigated composition range. For the integral mixing enthalpy, an analytical expression was obtained by the least square fit of the experimental results and relevant literature data using the Redlich–Kister–Muggianu polynomial. The mixing thermodynamic functions of the Fe–Ni–Zr liquid alloys were modelled in the framework of the associate solution model.

Solubility of Sulfamethazine in the Binary Mixture of Acetonitrile + Methanol from 278.15 to 318.15 K: Measurement, Dissolution Thermodynamics, Preferential Solvation, and Correlation

Solubility of sulfamethazine (SMT) in acetonitrile (MeCN) + methanol (MeOH) cosolvents was determined at nine temperatures between 278.15 and 318.15 K. From the solubility data expressed in molar fraction, the thermodynamic functions of solution, transfer and mixing were calculated using the Gibbs and van ’t Hoff equations; on the other hand, the solubility data were modeled according to the Wilson models and NRTL. The solubility of SMT is thermo-dependent and is influenced by the solubility parameter of the cosolvent mixtures. In this case, the maximum solubility was achieved in the cosolvent mixture at 318.15 K and the minimum in pure MeOH at 278.15 K. According to the thermodynamic functions, the SMT solution process is endothermic in addition to being favored by the entropic factor, and as for the preferential solvation parameter, SMT tends to be preferentially solvated by MeOH in all cosolvent systems; however, , so the results are not conclusive. Finally, according to mean relative deviations (MRD%), the two models could be very useful tools for calculating the solubility of SMT in cosolvent mixtures and temperatures different from those reported in this research.

Thermodynamic analysis and molecular dynamic simulation of the solubility of 2,2-Bis(hydroxymethyl)propionic acid in 12 monosolvents

The solubility of 2,2-Bis(hydroxymethyl)propionic acid (DMPA) in 12 mono solvents (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, methyl ethanoate, ethyl acetate, butyl acetate, N, N-dimethylformamide, water, and acetone) was determined by the gravimetric method at temperatures ranging from 288.15 to 328.15 K under atmospheric pressure (0.1 MPa). Solubility data were correlated by the Apelblat model, λh equation, and van’t Hoff model, and the Apelblat equation achieved the best fitting performance. Furthermore, the mixing thermodynamic functions were derived by NRTL model, which showed that the dissolution was a spontaneous and entropy-driven mixing process in solvents. Besides, the contributions of multiple physicochemical properties of solvents to the solubility of DMPA were evaluated. The results indicated that polarity and summation of the hydrogen bond acceptor propensities played crucial roles in determining DMPA solubility among all solvents. Molecular dynamic simulations were further employed to investigate solvent effect on the solubility of DMPA. Radial distribution function (RDF) analyses showed that the rank of solute-solvent interactions can be well correlated with solubility order of DMPA in the solvents. Moreover, the rank of solvation free energy of DMPA in different solutions is consistent with the order of solubility very well.

MODELING THE PHASE DIAGRAM OF THE Tl9TbTe6–Tl4PbTe3–Tl9BiTe6 SYSTEM

The analytical multi 3D model of phase diagram of the Tl9TbTe6–Tl8Pb2Te6–Tl9BiTe6 system was obtained as temperature dependence on the composition using the Multipurpose Genetic Algorithm (MGA). It was determined that the system is characterized by the formation of continuous solid solutions with tetragonal Tl5Te3-type structure (δ-phase). The boundaries of the uncertainty band for the liquidus and solidus surfaces of the δ-phase and the TlTbTe2 compound are determined. The thermodynamic functions of mixing of the solid solutions depending on the composition and temperature are determined based on the model of regular solutions of non-molecular compounds. It was established that the δ-phase possess thermodynamic stability in the entire concentration interval

Temperature–Composition Dependence of Thermodynamic Mixing Functions of Co–Cr–Cu–Fe–Ni Melts

Temperature–Composition Dependence of Thermodynamic Mixing Functions of Co–Cr–Cu–Fe–Ni Melts

Solution thermodynamics and preferential solvation of sulfamethazine in ethylene glycol + water mixtures

The solubility of sulfamethazine (SMT) in ethylene glycol (EG) + water (W) cosolvent mixtures was determined at nine temperatures (278.15, 283.15, 288.15, 293.15, 298.15, 303.15, 308.15, 313.15 and 318.15 K) by means of the stirring method. From the solubility data, the thermodynamic functions of solution, transfer and mixing were calculated using the Gibbs and van´t Hoff equations. On the other hand, the preferential solvation parameters of SMT were determined by means of the method of the inverse integrals of Kirkwood-Buff (IKBI). In general terms, the solubility of SMT is favored by the increase in temperature and the decrease in the polarity of the cosolvent system, thus the maximum solubility is reached in pure EG at 318.15 K and the minimum in pure water at 278.15 K. Gibbs energy is positive in all cases, with a higher contribution from the energy component (enthalpy of solution). Regarding enthalpy-entropic compensation, the process is driven in all cases by the enthalpy of solution. Finally, SMT is preferentially solvated by water in mixtures with higher polarity and by EG in less polar mixtures.

Thermodynamic analysis and preferential solvation of gatifloxacin in DMF + methanol cosolvent mixtures

This paper presents the thermodynamic analysis of solubility of gatifloxacin in the N,N-Dimethylformamide (DMF) + methanol (MeOH) cosolvent system at 10 temperatures. From the solubility data, the thermodynamic functions of solution, mixing, and transfers are calculated and analyzed using the Perlovich graphical method. On the other hand, an enthalpy-entropy compensation analysis is performed and the preferential solvation parameters are calculated using the inverse Kirkwood-Buff integral (IKBI) method. The result of the performed calculations indicates that the gatifloxacin solution process is endothermic with entropic favor, where the addition of DMF has a positive cosolvent effect in all cases. Regarding preferential solvation, the results are not entirely conclusive, since in all cases the values of the preferential solvation parameter are less than 0.01, so that, negligible preferential solvation takes place.

Thermodynamics of Solutions and Azeotropy in Zinc–Calcium Melts

The partial and integral thermodynamic functions of mixing and vaporization are calculated for Zn–Са alloys from the vapor pressures determined by the boiling point method. Alloy formation over the whole range of concentrations proceeds with heat release, with attendant considerable ordering in the system relative to an ideal solution up to ~70 at % Са in the alloy and with a minor increase in disorder when calcium concentration exceeds this value. The curves of integral functions of vaporization feature extremes at ~85 at % Ca: a minimum entropy of 85.48 J/(mol K) and a maximum enthalpy of 156.44 kJ/mol. The vapor pressures of alloy components were used to supplement the Zn–Са phase diagram with the liquid and vapor coexistence fields at the atmospheric pressure (101.33 kPa) and in a vacuum (1.33 and 0.7 kPa). The existence of a liquid containing 93.2 ± 6.7 at % Ca that boils unseparably at 1494°С was discovered. As the pressure (boiling temperature) decreases, the azeotrope composition shifts (in accordance with the Vrevsky law) toward the zinc edge of the phase diagram, where zinc has a lower enthalpy of vaporization compared to that of calcium (118.6 kJ/mol against 153.7 kJ/mol). The positions of boundaries of the vapor–liquid equilibrium fields indicate the impracticability of distillation separation of the Zn–Са system to the constituent metals.

Solubility modelling and solvent effect on solid-liquid equilibrium of 2,2-bis(hydroxymethyl)butyric acid at different temperatures

In this work, the solid-liquid equilibrium of 2,2-bis(hydroxymethyl)butyric acid (DMBA) was investigated experimentally in various solvents: namely, ethylacetate, butylacetate, methyl isobutyl ketone, cyclopentyl methyl ether, toluene, gamma-butyrolactone and 1,4-dioxane over the temperature range (298.15 to 353.15) K. The experimental solubility data were correlated with the Apelblat equation, Buchowski–Książczak λh equation and NRTL model. Results showed that the mole fraction solubility of DMBA increased, as temperature increased. The Apelblat equation and NRTL model indicated a good correlation with the experimental solubility data and can be used to describe the solid-liquid equilibrium. Further, the apparent thermodynamic dissolution functions and thermodynamic functions of mixing were evaluated from the solubility data.