Solid-liquid Equilibrium Research Articles

Solubility, Correlation, Dissolution Properties, and Molecular Simulations of an Explosive Intermediate in Twelve Pure Solvents

The solubility and thermodynamic properties of N-nitropyrazole (N-NP) in different pure solvents are crucial for crystallization, purification, and further theoretical research. The solid–liquid equilibrium solubility of N-NP in the range of 293.15–323.15 K was determined in 12 pure solvents of water, mesitylene, n-hexane, cyclohexane, ethanol, chlorobenzene, benzonitrile, propylene glycol, anisole, dimethyl sulfoxide, N,N-dimethylformamide, and o-dichlorobenzene by the laser dynamic method at an atmospheric pressure of 0.1 MPa. In the temperature range of 293.15–323.15 K, the solubility of N-NP in water, mesitylene, n-hexane, cyclohexane, ethanol, chlorobenzene, benzonitrile, propylene glycol, anisole, dimethyl sulfoxide, N,N-dimethylformamide, and o-dichlorobenzene displayed the mole fraction solubility of 0.001271–0.003540, 0.033858–0.139782, 0.001966–0.009268, 0.002621–0.013898, 0.013601–0.058669, 0.097849–0.310726, 0.170722–0.387823, 0.017647–0.065427, 0.069507–0.379656, 0.225911–0.457260, 0.210072–0.415353, and 0.017651–0.172345, respectively. The measured solubility data of N-NP had a good correlation with the modified Apelblat equation, the NRTL equation, the Wilson equation, as well as the λh equation. Through the comparison of the minor average of the root-mean-square deviation (103RMSD) and the coefficient of determination (R2), the Wilson equation yielded a more satisfactory correlation result. Thermodynamic parameters of mixing enthalpy (ΔmixH), mixing entropy (ΔmixS), and mixing Gibbs energy (ΔmixG) were calculated and analyzed based on the experimental data. The positive ΔmixH and ΔmixS implied that the dissolution process of N-NP in the selected solvents was endothermic and entropy-driven. The relative contributions of enthalpy and entropy demonstrated that enthalpy was the main contributor to the Gibbs free energy in the dissolution process. In addition, the solute–solvent interaction was calculated to elaborate the solubility of N-NP in selected solvents deeply. In addition, the solid–liquid surface tension and the surface entropy factor of N-NP were discussed on the basis of the experimental solubility data.

Study of wetting promotion mechanism of Pb/Cu interface assisted by ultrasonic vibration from molecular dynamics simulation and experiments

In the paper, the molecular dynamics method was used to study the wetting promotion mechanism of liquid Pb/solid Cu system under ultrasonic vibration, which provided theoretical guidance for the application of ultrasonic wetting. The result showed that both ultrasound and temperature increase could improve the wettability of the system by promoting the dissolution and diffusion of the solid-liquid interface. However, ultrasound had a more obvious promotion effect. At 900K, the contact angle without ultrasound was 22.3°, while the contact angle with ultrasound was reduced to 0°, and the system was completely wetted. In addition, it was found that ultrasonic frequency had a significant effect on wettability. The 250 GHz ultrasonic vibration had an obvious effect on the wetting, but there were a large number of Cu atoms dissolved at the edge of the droplet, which hindered the spreading of the droplet, while the 25 GHz ultrasonic frequency only promoted the spreading of the droplet. In addition, experiment at different temperatures confirmed that ultrasonic vibration improved the wettability of the system. The wetting promotion mechanism of ultrasonic was that ultrasonic vibration caused the system to generate tension and pressure at the solid-liquid interface, which promoted the spreading of droplet and the diffusion of interface atoms, and reduced the solid-liquid interface energy and equilibrium contact angle.

Experimental Study and Modeling of Solid-liquid Equilibrium for Binary and Ternary Pharmaceutical and Food Systems

Background: The experimental measurement of the solubility of a solute in a given solvent is a difficult task; hence, there is a need for reliable thermodynamic models for its prediction. However, these models require either molecular or group interaction parameters, which are not always available. Objective: The objective of the present study is to measure experimentally the solubility of different solutes in solvents selected from pharmaceutical or food fields on the basis that not all the required model interaction parameters are available to use the obtained experimental data for their determination. Methods: The experimental study of solid-liquid equilibrium for chosen binary and ternary systems at different temperatures was carried out using differential scanning calorimetry to determine the essential thermophysical properties like melting temperature and enthalpy. The modeling of these phase equilibrium data was performed using thermodynamic models like Random Two Liquids (NRTL) and Universal Functional Activity Coefficient (UNIFAC). The required NRTL interaction parameters were determined by minimizing a well-defined objective function using the simplex method. Results: The solubilities of the solutes in the different considered solvents at different temperatures obtained experimentally provided the required NRTL molecular interaction parameters. Solute solubilities were obtained using NRTL, UNIFAC, and ideal models. The comparisons showed an excellent agreement between the experimental values and the NRTL results, contrary to UNIFAC and ideal case models. Conclusion: This study shows the importance of thermodynamic modeling to predict solubility data that may be difficult, time-consuming, and costly to obtain experimentally.

Equilibrium solubility of 6-propyl-2-thiouracil in nine pure solvents: Determination, correlation, Hansen solubility parameter and thermodynamic properties

Investigation upon the solid–liquid equilibrium on solubility data of 6-propyl-2-thiouracil (PLT) in pure organic solvents is essential for separation and purifying in industry process. In this work, PLT solubility in nine neat solvents was experimentally determined at 278.15 K–323.15 K under P = 0.1 MPa. These selected solvents were tetrahydrofuran(THF), acetone, acetonitrile,1-butanol,1-pentanol, 2-butanol, methyl acetate, ethyl acetate,1-propyl acetate, respectively. Experiment results showed that solubility was consistent with temperature and decreased according to the order: THF > acetone>1-butanol≈1-pentanol> 2-butanol > methyl acetate > ethyl acetate>1-propyl acetate > acetonitrile. Solvent effect and Hansen solubility parameter (HSP) were incited to explain dissolution rule on solute. Four thermodynamic models (modified Apelblat model, Van't model, λh model and NRTL model) were adopted to correlate PLT solubility and provide good correlations on basis of RD, ARD and RMSD. In addition, thermodynamic properties (ΔH°, ΔS° and ΔG°) of PLT dissolution process in pure solvents were discussed and proved to be endothermic, entropically driven and non-spontaneous process.

Phase Equilibria and Thermodynamic Properties of Phases in the H2O–Gd(NO3)3 System

Solid–liquid equilibria in the system H2O–Gd(NO3)3 were measured from –20 to 70°C using the isothermal saturation method. The Pitzer–Simonson–Clegg thermodynamic model was implemented to obtain the temperature dependence of Gd(NO3)3⋅6H2O solubility constant, to calculate salt solubility and to construct a phase diagram of the system from eutectic point to hydrate melting. Thermochemical properties of gadolinium nitrate aqueous solutions, such as dilution enthalpies and heat capacities, were assessed also. The model has shown to be reliable for phase equilibria calculation from –35 to 90°C and from 0 up to ~15 mol % of salt as well as the thermodynamic properties of Gd(NO3)3 aqueous solutions at room temperature and around it.

Solubility of Amino Acids in the Eutectic Solvent Constituted by Sodium Acetate Trihydrate and Urea and in Its Mixture with Water

Industrial fish and aquaculture processing leads to the generation of a huge quantity of by-products, whose accumulation and mismanagement involve serious environmental consequences as well as high economic losses. Taking advantage of these residues as a source of added-value compounds must be a priority in a circular economy. This work is a preliminary study to analyze the possibility of using the eutectic mixture of urea and sodium acetate trihydrate as a solvent for collagen extraction. To that end, the solid-liquid equilibrium of the system was determined in order to define the exact composition and temperature of the eutectic. The solubility in this solvent of the main amino acids that constitute fish collagen was studied at several temperatures and atmospheric pressure. At 308.15 K, solubilities of the major constituents of the target protein, namely L-proline, trans-4-hydroxy-L-proline, and glycine, were 0.19, 0.16, and 0.12 (mass fraction), respectively. These values increased with temperature. Dilution with water (50 wt%) allowed operation at lower temperature and led to an increase in the solubilities. The van 't Hoff model was satisfactorily used to correlate the experimental data and to calculate apparent properties of dissolution. All the dissolution processes studied herein are endothermic, non-spontaneous, and enthalpy-driven. Both the eutectic and its mixture with water are promising solvents for the design of an environmentally benign process for collagen extraction.

Alkane-based eutectic phase change materials doped with carbon nanomaterials.

Cold thermal energy storage is an issue of increasing importance on a global scale particularly in the format of passive thermal protection. This study presents three eutectic Phase Change Materials (ePCMs) composed of n-alkanes, which provide passive temperature control (their operation is automatically induced by exceeding the limit temperature without the need for a control system) around 4 °C (277.2 ± 2 K) and are chemically neutral. The solid-liquid equilibrium (SLE) in the following binary systems was investigated: {n-tetradecane + n-heptadecane}, {n-tetradecane + n-nonadecane}, {n-tetradecane + n-heneicosane}, allowing the determination of two ePCMs with enthalpies close to 220 J g-1 and one significantly lower (155.5 J g-1). Moreover, two solid-liquid-liquid equilibrium (SLLE) phase diagrams were determined for systems: {n-tetradecane + 1,6-hexanediol} and {n-tetradecane + 1,12-dodecanediol}. In addition, the work provides a systematic analysis of the problem of designing ePCMs with specific properties and the aspects that need to be considered. The possibility of predicting the parameters of eutectic mixtures using the UNIFAC (Do) equation and the equation of ideal solubility was verified. A method for predicting the enthalpy of melting of eutectic was also proposed and confronted with the results of DSC analysis. Thermodynamic studies have been supplemented with measurements and correlation of experimental data of ePCMs density and dynamic viscosity as a function of temperature. The final issue is the improvement of the thermal conductivity of paraffins by the addition of nanomaterials such as Single Wall Carbon Nanotubes (SWCNTs), Expandable Graphite (GIC) or Expanded Graphite (EG). The possibility of forming a long-lasting composite material composed of ePCMs and 1 wt% of SWCNTs with a thermal conductivity significantly higher compared to pure ePCMs has been proven via stability testing under operating conditions.

Modified version of the COSMO-SAC model for the prediction of vapour-liquid equilibria of mixtures containing halogen compounds

• COSMO-SAC (+OH-Cl), (+OH-Br) and (+OH-ClBr), extensions of the COSMO-SAC model were developed to take into account hydrogen bonds formed with chlorine or bromine atoms, in particular in mixtures containing deep eutectic solvents and water, alcohols or carboxylic acids. • The new parameters of the extended models were optimized with a data base of 1402 vapour-liquid data points. • Performances were tested with vapour-liquid, liquid-liquid and solid-liquid databases with 2237, 787 and 503 data points, respectively. • Improvements of the prediction of the vapour-liquid equilibria for mixture containing halogens atoms were obtained. • Comparisons between the results from the three extended models showed that the distinction between chlorine and bromine atoms in terms of hydrogen bonds was not necessary within the COSMO-SAC models. In this work, the prediction of the phase behaviour of mixtures containing chlorine or bromine atoms involved in hydrogen bonding is investigated. Based on the COSMO-SAC (2010) model, extended models named COSMO-SAC (+OH-Cl), COSMO-SAC (+OH-Br) and COSMO-SAC (+OH-ClBr) are presented. The extension of the base model focuses on the hydrogen bond contribution. For this contribution, the addition of two parameters in an empirical equation introduces a dependence in temperature. The parameters were optimized using a databased composed of vapour-liquid equilibria data of mixtures comprised of both ionic liquids or deep eutectic solvents and regular compounds. The mixtures always involve halides or halocarbons as well as molecules of water, alcohol or carboxylic acids. The extended models are shown to improve the predictions of such systems for vapour-liquid equilibria as well as being able to keep providing satisfying results for both liquid-liquid and solid-liquid equilibria.

Interactions in plasticizer mixtures used for sugar replacement

In our quest for novel ingredients to be used in sugar replacement strategies, we have investigated the thermodynamics of polycarboxylic acids, such as citric acid. We have demonstrated the applicability of the Flory-Huggins (FH) theory to describe the thermodynamics of polycarboxylic acids solutions. Moreover, for citric acid we can describe the complete phase diagram with the theory. It shows that polycarboxylic acids have similar plasticizing and hygroscopic properties as sugars and polyols.Regarding mixtures of polycarboxylic acids and carbohydrates, the FH theory is able to describe a) the water activity of the mixtures, b) the solubility of ternary mixtures of acids and sugars, c) the lowering of the deliquescence point for binary mixtures of crystals, and d) the melting point depression in eutectic mixtures. Unexpectingly, our investigations show there is a strong non-zero FH interaction parameter between carboxylic acids and carbohydrates. In our prior sugar replacement strategy we have assumed zero interactions between plasticizers. Here, we will readdress this assumption. Carefull investigations of solid-liquid equilibrium of eutectic mixtures involving polycarboxylic acids and/or carbohydrates, shows nearly zero interaction in eutectic mixtures consisting only of two carbohydrates or two polycarboxylic acids. We now hold the hypothesis that there is strong non-zero interaction if the mixture contains plasticizers strongly differing in the amount of hydrogen bonding groups. This strong interaction explains why these mixtures, like polycarboxylic acids and carbohydrates, are excellent candidates as deep eutectic solvents. Furthermore, we conclude that polycarboxylic acids are useful additions to the toolbox of sugar replacers, albeit that there are some limitations to their amounts used.

Liquid structure of a water-based, hydrophobic and natural deep eutectic solvent: The case of thymol-water. A Molecular Dynamics study

The structural organization of the first example of a water-based, type V, hydrophobic, natural deep eutectic solvent (DES) is investigated in this work, exploiting the synergy of X-ray scattering and computational techniques. The stoichiometric mixture of thymol:water (4.8:1) has been recently reported to behave as a DES, with a melting point at −6 °C, well below the one foreseen for the ideal liquid mixture. Our study provides an atomistic insight into the structural correlations in this system, highlighting the major role played by hydrogen bonding (HB) correlations in affecting morphology as well as the solid–liquid equilibrium. Thymol engages HB-mediated interactions with both thymol and water molecules: evidences of conventional HB interactions involving the hydroxyl group are found, together with indications of π⋯HO hydrogen bonding correlations with both thymol and water. Overall, in the mixture, thymol is involved in a larger number of HB interactions than in its neat liquid state. Such a strong interference of water into thymol structural organization strongly hinders the development of HB-mediated thymol hexamers that is the structural leitmotif in crystalline thymol. On the other hand, only 30 % of the present water molecule can engage into correlations with at least another water molecule, thus preventing the formation of an extended HB network among water molecules that would result incompatible with the otherwise hydrophobic environment. Evidences of mesoscopic organization are observed experimentally and confirmed by simulations: these are related to the clustering of thymol hydroxyl groups with water molecules, leading to the formation on polar nano-pools embedded into the apolar matrix. This new solvent extends the range of water based, type V, hydrophobic DES, and represents an additional contribution to the development of sustainable technologies, with appealing properties.

Continuous and simultaneous conversion of phosphogypsum waste to sodium sulfate and potassium sulfate using quaternary phase diagram.

In this present work, the transformation of the Moroccan phosphogypsum (PG) waste, considered a potential source of sulfate, into potassium sulfate compound could help reduce environmental impact and create a new value chain for the phosphate industry. Generally, solid-liquid equilibria are frequently applied in chemical industries. They are a valuable aid in visualizing the precipitation, separation, and purification of a solid phase and the pathways by which crystallization can occur. This process aims to produce potassium sulfate (K2SO4), a high-value fertilizer, from sulfate solutions obtained after dissolving PG in a NaOH medium. The quaternary phase diagram Na+, K+//Cl-, SO42--H2O at 25°C was especially used to determine the operating conditions and the design of a crystallization process during the PG conversion into K2SO4. The Jänecke representation of this system enables the determination of the optimal trajectory in the phase diagram for the double decomposition reaction. X-ray fluorescent (XRF) and X-ray diffraction (XRD) techniques were conducted to identify the crystalline phases formed during our process. In summary, the results of this study could contribute to the development of a sustainable valorization PG. Furthermore, K2SO4 represents a good alternative to potassium chloride for chloride-sensitive crops.

Estimating VLE behavior from SLE data in aqueous mixtures of choline chloride-sorbitol deep eutectic solvents: Experimental investigation and thermodynamic modeling using the e-NRTL model

Knowledge of solid–liquid equilibria (SLE) and vapor–liquid equilibria (VLE) for mixtures containing deep eutectic solvents (DESs) is of paramount importance. We have conducted experiments to obtain additional data for SLE systems and then used the e-NRTL model to predict the VLE behavior in mixtures of DESs comprised of choline chloride (ChCl), sorbitol (S), and water (W). The systems under investigation include three 2-component systems (S/W, ChCl/W, ChCl/S), and one 3-component system (DES/W) where the DES is obtained by mixing ChCl and S at a molar ratio of 1. Using the e-NRTL activity coefficient model, the adjusted binary interaction parameters of the proposed model are determined solely from the experimental SLE data obtained from this work and also those in the literature. There is an excellent agreement between the SLE solubility data and the e-NRTL results. The tuned model is then used to predict the bubble pressure in three aqueous systems (S/W, ChCl/W, and DES/W) with an overall AARD value of 2.21%. The excellent agreement between the experimental and predicted VLE data demonstrates the viability of the proposed thermodynamic modelling framework to represent the equilibrium systems containing DESs. The outcome from our study can be used to relate the SLE and VLE data without the need to perform experiments for both cases for the given system of interest. Compared to the VLE experiments, the SLE tests are much simpler and safer because there is little compressibility and the effect of pressure on solubility is minimal which makes it possible to conduct SLE tests at room conditions (at least for liquids with negligible non-ideality). Therefore, conducting the high-pressure VLE calculations without the need to perform VLE experiments and through SLE experimental data alone will be of practical significance.

Solid-liquid equilibrium solubility, thermodynamic properties, and solvent effect of flavoxate hydrochloride in twelve pure solvents ranged from 278.15 K to 323.15 K

The mole fraction solubility data of flavoxate hydrochloride in twelve experimentally selected solvents were measured at atmospheric pressure by the laser monitoring method. The experimental temperature range was 278.15 to 328.15 K. The solubility of flavoxate hydrochloride showed a nonlinear increase with temperature increase. At a fixed experimental temperature, the order of solubility is: ethylene glycol > methanol > 2-methoxyethanol ≈ dimethyl sulfoxide > N-Methyl-2-pyrrolidone > water > 2-propoxyethanol > 2-ethoxyethanol > ethanol > n-butanol > n-propanol > acetonitrile. Also, solubility data were correlated by two semi-empirical models and three activity coefficient models. From the average relative deviation and root mean square deviation data of the five models, it can be seen that the Modified Apelblat model has the best correlation. Furthermore, in this work, the effect of solvent on the solubility of flavoxate hydrochloride was analyzed using the KAT-LSER model. Furthermore, the thermodynamic parameters (ΔdisG0, ΔdisH0, ΔdisS0) of the dissolution process of flavoxate hydrochloride were calculated by the Van’t Hoff model. The data indicate that the dissolution process of flavonoid hydrochloride in twelve experimentally selected solvents is endothermic and entropy-driven.

Experimental measurement and thermodynamic modeling of solubility of Riluzole drug (neuroprotective agent) in supercritical carbon dioxide

Experimental measurement of solubility data is framework for nanoparticle synthesis using supercritical fluid (SCF) technology. Accordingly, the solubility of Riluzole (RLZ) as a neuroprotective agent, in supercritical carbon dioxide (SC-CO2), was measured at various temperatures and pressures, for the first time, for modeling and correlating of new experimental data through different methods to evaluate their abilities. Solubility data measured from the static process range from 4.95 × 10−5 to 1.49 × 10−4 (mole fraction). To correlate the solubility data, three thermodynamic models of (1) eight density-based correlations, (2) two equations of state (EoSs), and (3) COSMO-Vacancy (Vac) activity coefficient were used. Empirical models of Jouyban and Bian presented the best correlation Combining SRK and PR EoSs separately with Wilson activity coefficient by means of Wong Sandler (WS) mixing rule with three curve-fitting parameters, illustrated an excellent fit with the experimental data by AARD%, 5.0 and 7.0%, respectively. Afterward, solid-liquid equilibrium for RLZ+SC-CO2 system was considered by COSMO-Vac model via conductor like screening model theory. Using quantum computational solvation calculation, the average logarithmic deviation was smaller than unity (0.42) which indicate the suitability of the model without considering the adjustable parameter. Finally, thermodynamic enthalpies of RLZ was calculated for the first time.

Reference materials for phase equilibrium studies. 2. Solid–liquid equilibria (IUPAC Technical Report)

Abstract This article is the second of three projected IUPAC Technical Reports on reference materials for phase equilibrium studies. The goal of this project was to select reference systems with critically evaluated property values for the verification of instruments and techniques used in phase equilibrium studies of mixtures. This report proposes seven systems for solid–liquid equilibrium studies, covering the four most common categories of binary mixtures: aqueous systems with organic solutes, aqueous systems with inorganic solutes, non-aqueous systems, and systems with low solubility. For each system, the available literature sources, accepted data, smoothing equations, and estimated uncertainties are given.

Measuring Nintedanib esylate solubility in binary mixed solvents: Molecular dynamic simulation, solid-liquid phase equilibrium and thermodynamic analysis

By laser monitoring method, the solid–liquid phase equilibrium solubility of Nintedanib esylate in the four binary mixtures (including methanol (MeOH) + ethyl acetate (EtOAC), N,N-Dimethylformamide(DMF) + ethyl acetate (EtOAC), N,N-Dimethylacetamide (DMAC) + ethyl acetate (EtOAC), and methanol (MeOH) + methyl tert-butyl ether(MTBE)) was achieved at different temperatures and atmospheric pressure. The result demonstrated that the solubility in the four binary mixed solvents was positively correlated with temperature and the mass fractions of DMAC, DMF and MeOH at a certain temperature. Correlation fitting was performed for the solubility data through Apleblat model, Ma model, λh model, CNIBS/R-K model and NRTL model, and the result showed that the CNIBS/R-K model had much lower relative average deviations than the others for the four solvents being researched. By using RDF and MD simulation, the intermolecular interactions of Nintedanib esylate and the chosen solvents proved that the ranks of the interactions between solute and solvent, as well as solvent and solvent, were bound up with the order of the saturation solubility of Nintedanib esylate in the chosen solvents. The calculation of Hansen solubility parameters of the solute molecules showed that the Hansen solubility parameters could explain the solubility of the solute in the four binary solvents and the solubility of the solute in the four binary solvents was affected by various factors such as dispersion force, hydrogen bond force and polarity force between molecules. The NRTL model and Van't Hoff equation were used to calculate the thermodynamic properties of the solute mixing process and the apparent thermodynamics of the solute dissolution process in the mixed solvent. The results show that: The mixing process of Nintedanib esylate in the selected four mixed solvents is spontaneous and entropy increasing process, and the dissolution process is enthalpy driven, endothermic and non-spontaneous process.

Thermodynamic modeling of MDEA(aq)-NH3(aq)-K2CO3(aq)-CO2(aq) using the Extended UNIQUAC model

The development of advanced processes for carbon dioxide capture requires reliable thermodynamic models to ensure accurate process design. This work presents an optimized parameter set of the Extended UNIQUAC model for advanced mixed solvent solutions containing CO2-MDEA-NH3-K2CO3 in water. The model was parameterized using vapor–liquid equilibrium, pure component saturation pressure, excess enthalpy, heat of absorption, molar heat capacity, apparent molar heat capacity, and solid–liquid equilibrium. These thermal and equilibrium properties cover temperatures between 253.6K to 600K and pressures up to 75.6bar. The current model represents an extension of previous versions that were suitable for modeling aqueous NH3 and K2CO3 solutions. This parametrization accounts for molecular interactions between MDEA and these two components, which allows for the design of advanced capture processes. This paper demonstrates that the new model parameters are valid within the range of operational conditions typically found in CO2 capture processes.

Assessment of solid–liquid equilibrium behavior and thermodynamic analysis of natural plant extracts artemisinin (Form I) in twelve mono-solvents

Solid-liquid equilibrium solubility of artemisinin (ART) Form I in twelve mono-solvents namely N, N-dimethylformamide (DMF), oxolane (THF), n-propanol (NPA), 4-methylpentan-2-one (MIBK), ethyl formate (EF), butyl acetate (BAC), 2-ethoxyethanol (EGEE), 1,4-Dioxane, 2-methoxyethanol (EGME), 2-propoxyethanol (EGPE), propyl acetate (NPAC) and 2-butoxyethanol (EGBE) from 283.15 K to 323.15 K were determined by a laser dynamic method under 0.1 MPa. The minimum solubility of ART (Form I) was found in NPA at 283.15 K (0.004541), the maximum mole fraction solubility of ART (Form I) was observed as 0.2523 in DMF at 323.15 K. At the temperature of 298.15 K, the experimental mole fraction solubility order of ART Form I in the tested solvents was DMF (0.1559) > 1,4-Dioxane (0.09117) > THF (0.08301) > MIBK (0.05054) > EF (0.04902) > NPAC (0.03860) > BAC (0.03658) > EGME (0.02031) > EGEE (0.01859) > EGPE (0.01817) > EGBE (0.01689) > NPA (0.007185). The solubility behavior was computationally correlated by Margules model, Wilson model, NRTL model, NRTL-SAC model, Buchowski-Ksiazczak λh model and UNIQUAC model, the total RMSD was no>0.025 in the selected models. With the help of Hansen solubility parameters (HSPs) analysis, molecular similarities of ART (Form I) in twelve mono-solvents were investigated. Besides, Hirschfeld surface analysis (HSs) was considered to evaluate the intermolecular interaction of artemisinin. Moreover, thermodynamic properties including ΔmixH, ΔmixG, ΔmixS, lnγ1, lnγ1∞ of ART (Form I) in the selected solvents were estimated. All the negative ΔmixG and positive ΔmixS values indicated that the mixing process were spontaneous and entropy-increasing.

Thermodynamic models for determination of solid–liquid equilibrium of para-tert-butylbenzoic acid in binary and ternary solvent system

Accurate solubility data is essential to make critical decisions from the earliest stage of drug discovery, through the entire process development, formulation, and up to process design. The present research work aims to evaluate the solid–liquid equilibrium data of para-tert-butylbenzoic acid (PTBBA) in binary systems such as acetonitrile + water, isopropyl alcohol + water, and isopropyl alcohol + acetonitrile at 288.15 to 328.15 K and a ternary solvent mixture of isopropyl alcohol + acetonitrile + water system in the temperature range of 298.15 to 323.15 K with varying mass fraction of the binary mixture (isopropyl alcohol + acetonitrile) for a constant mass fraction of water (0.1 and 0.3) using gravimetric and titrimetric methods. It is observed that the solubility of PTBBA increases with an increase in temperature for all the selected solvent systems. Moreover, the solubility of PTBBA in the binary and ternary system is affected by an increase in the mass fraction of water at a given temperature, which acts as an antisolvent. The measured data is correlated with various thermodynamic models such as Van’t Hoff equation, Modified Apelblat equation, Buchowski equation, and Wilson models. It is observed that there is a good agreement between measured and calculated values with an average relative deviation of 0.95 for isopropyl alcohol + acetonitrile system in the case of the modified Apelblat equation.

Phase Equilibria of the Ternary System of Lithium Sulfate + Polyethylene Glycol (PEG3000) + Water at Different pH: Experiment Determination, Correlation, and Thermodynamic Modeling

The phase equilibrium data for the ternary systems [lithium sulfate (Li2SO4) + polyethylene glycol (PEG3000) + water] were measured at 298.15 K and at various pH values (2.94, 4.90, and 6.80). The solid–liquid equilibrium data including the solubility, density, and refractive index were determined using the isothermal dissolution equilibrium method. The liquid–liquid equilibrium (LLE) data for the aqueous two-phase system were obtained experimentally by measuring the biphasic physical properties, including the density and refractive index at 298.15 K. Subsequently, the binodal curves were correlated by using the Pirdashti and Merchuk equations, the effective excluded volumes were calculated from the binodal curve data, and the tie-line compositions were adjusted to the Othmer–Tobias and Bancroft equations, respectively. Results show that the solubility of Li2SO4 in the aqueous polymeric solution mitigates as the content of PEG increases, eventually. It was found that the more acidic solution induces the salting-out effect, and the LLE formed easily at the lower pH of studied systems. Finally, the extended UNIQUAC, the modified UNIQUAC-FV, and the modified UNIFAC-NRF models were selected to correlate the LLE data of the studied systems, and the modified UNIQUAC-FV model gives a better correlation for tie-lines data.