Solid-liquid Equilibrium Research Articles

Thermodynamic modeling of the solid-liquid equilibrium of two phenolic compounds in several solvents at temperatures ranging from 283.15 K to 323.15 K

The solubility of two natural phenolic compounds (vanillic acid (VA) and vanillin (V)) in four individual solvents (ethanol, butan-2-ol, ethylene glycol, and ethyl acetate) was measured using the gravimetric method from 283.15 to 323.15 K at atmospheric pressure. The optimization of the complexes between VA–solvents and V–solvents using the B3LYP theoretic technique and the 6-31+G (d, p) basis set indicated that the absolute value of interaction energy was higher, suggesting that the interaction between solute and the solvent was stronger. In addition, two excellent activity coefficient models (NRTL and Wilson) were used to correlate and evaluate the equilibrium solubility results. The highest relative average deviation and root-mean-square deviation values for VA are 4.36% and 3.09 × 10-3, respectively, and 3.35% and 5.52 × 10-3 for V. Furthermore, the excess enthalpy of the solution was determined on the basis of thermodynamic relations and the Wilson model. The findings indicate that the dissolution process was endothermic.
 KEY WORDS: Solid-liquid equilibrium, Vanillin, Vanillic acid, NRTL and Wilson models, Thermodynamic parameters
 Bull. Chem. Soc. Ethiop. 2024, 38(3), 799-810. 
 DOI: https://dx.doi.org/10.4314/bcse.v38i3.19 

Impact of supplementary cementitious materials on the solid–liquid equilibrium curve of calcium in cement hydrates

Impact of supplementary cementitious materials on the solid–liquid equilibrium curve of calcium in cement hydrates

Equilibrium solubility, solvent effect, and equation correlations of cyclosporine in twenty mono solvents and four binary mixtures

In this study, the solid–liquid equilibrium solubility of cyclosporine in 20 pure solvents and four binary mixtures at 298.15 K were determined using shake-flask technique. Solid-state characterization exhibited that no solvate formation or polymorphic transformation occurred during the dissolution of cyclosporine in any of the solvent systems investigated. The experimental solubilities of cyclosporine in 20 pure mono solvents were ranked as follows: DEGME (2.21 × 10−1) > ethanol (1.22 × 10−1) > NMP (1.15 × 10−1) = 1-butanol (1.15 × 10−1) > dichloromethane (1.07 × 10−1) > acetonitrile (1.02 × 10−1) > PEG 200 (9.78 × 10−2) > PEG 300 (9.12 × 10−2) > chloroform (8.98 × 10−2) > PEG 400 (8.11 × 10−2) > DMF (7.65 × 10−2) > 2-propanol (7.09 × 10−2) > 1-propanol (6.57 × 10−2) > methanol (6.14 × 10−2) > propylene glycol (6.08 × 10−2) > tetrahydrofuran (4.69 × 10−2) > DMSO (2.64 × 10−2) > acetone (1.28 × 10−2) > glycerol (1.35 × 10−5) > water (4.29 × 10−7). In the four binary solvents (DEGME + water, PEG 200 + water, PEG 300 + water, and PEG 400 + water), the mole fraction solubility of cyclosporine increased with increasing mass fractions of the four different organic solvents. Based on the Kamlet-Taft linear solvation energy relationship (KAT-LSER) model, the solubility of cyclosporine was mainly affected by the self-cohesiveness of the solvent, which is related to the interaction between the solvent and the solvent. Additionally, the solubility parameter was used to explain and understand the solubility of cyclosporine in four different binary solvents. To correlate the solubility data of cyclosporine, two models (the Yalkowsky Log-Linear and simplified CNIBS/R–K models) were applied. The calculated data based on two mathematical models and experimental mole fraction solubility data for cyclosporine could provide information for the separation, extraction, purification, crystallization, and selection of suitable a solvent system.

Solid–Liquid Equilibrium of GLA-NaCl System and Its Application for Separating GLA and NaCl

Solid–Liquid Equilibrium of GLA-NaCl System and Its Application for Separating GLA and NaCl

Crystallization risk of aromatic compounds in LNG production. Part II: The solubility of p-xylene in methane-rich mixtures down to cryogenic temperatures

New measurements of solubility of solid p-xylene in solvents methane and (90%mol/mol)methane + (10%mol/mol)ethane have been carried out using a cryogenic apparatus and adopting a static-analytic method for temperatures from 273 K down to 128 K at nominal pressures of 3 and 6 MPa. Measured solid-liquid and solid-vapor equilibria have been compared to literature values of solubility of solid p-xylene in methane-rich phases and to modeling results obtained by coupling a cubic equation of state and a model for the solid phase. Results confirm the conclusions reported in our previous study of this system that evidenced of a non-monotonic variation of the solubility of p-xylene with temperature when crossing the critical region of the solvent and that binary interaction parameters regressed on vapor-liquid equilibrium can be used for predicting the solubility at cryogenic conditions.

PREDICTING THE FLARE TEMPERATURE OF BINARY FUEL

A method for calculating the flash point from the results of simulating liquid–solid equilibrium at constant pressure using the Gibbs equation is discussed. A model is used to predict the flash point of the mixture based on the modified Le Chatelier equation, the Antoine equation and a model for estimating the activity coefficient. The flammability hazard of liquids is primarily characterized by their flash point. The flash point is defined as the temperature at which a liquid evaporates and forms a flammable mixture with air. To measure the flash point, closed and open type devices are used. In closed-type devices, the state of equilibrium between the liquid and vapor components of the mixture is studied. Open type devices take into account the interaction of a mixture of flammable liquids with the atmosphere. The flash point of a mixture is a critical property, but experimental data for many mixtures are lacking and obtaining such data is expensive and time-consuming. Therefore, the development of mathematical models for analyzing the state of the environment under conditions of increasing risk of emergency situations is an important scientific and practical task. This paper examines the possibility of predicting the flash point in closed-type devices, i.e. the influence of atmospheric conditions is not taken into account in this approximation. Several models for predicting the flash point for mixtures of various types have been proposed previously. Keywords: binary mixtures, flash point, boiling point, activity coefficients, solvation coefficient, association coefficient.

Solubility of K2SO4, Li2SO4, and (NH4)2SO4 in mixtures of water and methanol at different temperatures: Experimental and application of the modified Pitzer model

The study of electrolyte solutions is crucial for various industrial sectors. A thorough understanding of the solid–liquid equilibrium associated with mathematical models is necessary for the separation and purification of these materials, as well as for developing solution theories and process simulators. This study focuses on the solubility of K2SO4, Li2SO4, and (NH4)2SO4 in binary liquid solutions of water and methanol, at temperatures ranging from 283.2 K to 323.2 K. The results show that as the concentration of methanol increases, solubility decreases drastically while increasing temperature leads to an increase in solubility (except for Li2SO4). The modified Pitzer model was successfully applied to describe the solid–liquid equilibrium, and it also explained the salting-out precipitation by the addition of an antisolvent.

Experimental study of mechanistic factors influencing solvent-driven fractional crystallization of calcium sulfate

To advance dimethyl ether-driven fractional crystallization (DME-FC), a more sustainable method of water treatment and mineral recovery, a range of chemical equilibria were measured. These include varying concentrations of miscible organic solvents (MOS) used to experimentally measure the solvent-induced solid-liquid equilibrium (SLE) of calcium sulfate (CaSO4) in water. Seven MOS, including dimethyl ether (DME), acetonitrile (MeCN), 1,4-dioxane, tetrahydrofuran (THF), acetone, ethanol, and diethylamine, were screened to establish trends associated with molecular volume, functional groups, and physical properties. The effect of MOS on CaSO4 removal differed at concentrations <0.15 mol fraction MOS; MOS with greater molecular volume (THF, 1,4-dioxane, and diethylamine) induced greater CaSO4 precipitation on a per mole basis. The solvent-induced SLE for all MOS converged between 0.15 and 0.2 mol fraction MOS, reaching a CaSO4 concentration consistent with a water to MOS hydration ratio of 5:1 to 6:1, which may correspond to the solvent generating a solution-based pseudo-clathrate structure with continuity within the solution. Solution pseudo-clathrate structures provide a mechanistic basis for DME-FC.

Imiquimod Solubility in Different Solvents: An Interpretative Approach.

Imiquimod (IMQ) has been successfully formulated to date mainly as semi-solid lipophilic formulations for topical application. In this study, we investigated the solubility of IMQ in solvents suitable for developing innovative formulations in the form of powder obtained, for instance, by spray drying; thus, water, ethanol, methanol, acetone, acetonitrile, and dimethyl sulfoxide were tested at different temperatures. Temperature variations, stirring intensity, and the contact time between IMQ and the solvent greatly affected the evaluation of IMQ equilibrium solubility. The attainment of the solid-liquid equilibrium requires 13 days starting from solid IMQ and 2 days from a cooled-down supersaturated IMQ solution. A correlation between IMQ solubility and the solubility parameters of solvents was not found. IMQ solutions in water, ethanol, methanol, acetonitrile, and dimethyl sulfoxide were neither ideal nor regular. The Scatchard-Hildebrand equation does not apply to IMQ solutions because of association phenomena due to intermolecular hydrogen bonds and/or π-stacking, as supported by the hyperchromic effect that was very pronounced in highly polar solvents, such as water, with the increase in temperature. Finally, IMQ solubility values measured in acetone cannot be considered reliable due to the reaction with the solvent, leading to the formation of new molecules.

Estimating the phase diagrams of deep eutectic solvents within an extensive chemical space

Assessing the formation of a deep eutectic solvent (DES) necessitates a solid-liquid equilibrium phase diagram. Yet, many studies focusing on DES applications do not include this diagram because of challenges in measurement, leading to misidentified eutectic points. The present study provides a practical approach for estimating the phase diagram of any binary mixture from the structural information, utilizing machine learning and quantum chemical techniques. The selected machine learning model provides reasonably high accuracy in predicting melting point (R2 = 0.84; RMSE = 40.53 K) and fusion enthalpy (R2 = 0.84; RMSE = 4.96 kJ mol−1) of pure compounds upon evaluation by test data. By pinpointing the eutectic point coordinates within an extensive chemical space, we highlighted the impact of the mole fractions and melting properties on the eutectic temperatures. Molecular dynamics simulations of selected mixtures at the eutectic points emphasized the pivotal role of hydrogen bonds in dictating mixture behavior.

Solid-liquid phase equilibrium and thermodynamic properties analysis of 1,3,5-tribromobenzene in sixteen kinds of organic mono-solvents

Solid-liquid equilibrium solubility of 1,3,5-Tribromobenzene (m-TBB) in 16 pure solvents, including ethyl formate, methyl acetate, ethyl acetate, propyl acetate, butyl acetate, amyl acetate, acetone, 2-butanone, cyclohexanone, 1,2-dichloroethane, chloroform, cyclohexane, toluene, tetrahydrofuran (THF), N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMA) were determined by gravimetric method at different temperatures. The solubility of m-TBB increases gradually with the increase of temperature. The order of solubility of m-TBB in alkanes solvents is: chloroform > 1,2-dichloroethane > cyclohexane. The order of solubility of m-TBB in esters solvents is: amyl acetate > butyl acetate > propyl acetate > ethyl acetate > methyl acetate > ethyl formate. The order of solubility of m-TBB in ketones solvents is: cyclohexanone > 2-butanone > acetone. The order of solubility of m-TBB in other solvents is: THF > toluene > DMA > DMF. The KAT-LSER model was selected to explore the solvent effect of m-TBB in the tested solvents. Four thermodynamic models, i.e., the modified Apelblat model, the λh model, the NRTL model and the Wilson model, were selected for correlate the solubility data of m-TBB in 16 mono-solvents. The RAD and the RMSD values of NRTL model were all less than 1.67 × 10-2 and 3.82 × 10-4, respectively. All the four theoretical models can correlate the solubility data of m-TBB well in the selected solvents. The dissolution process of m-TBB were calculated based on the Wilson model. The dissolution process of m-TBB is endothermic, entropy increase and spontaneous. The entropy contributes more to Gibbs free energy.

Solid-liquid Equilibria (SLE) of the System Containing the Sulfates of Lithium and Potassium at 303.2 and 318.2 K

Solid-liquid Equilibria (SLE) of the System Containing the Sulfates of Lithium and Potassium at 303.2 and 318.2 K

Solid-liquid equilibrium solubility, modeling, Hansen solubility parameter and thermodynamic analysis of 2-Mercaptobenzimidazole in eleven mono-solvents and three binary solvents at different temperatures

The solubility of drugs is an important physicochemical data for its development and design. In this work, the solubility of 2-mercaptobenzimidazole (2-MBI) in eleven mono-solvent solvents (2-propoxyethanol, isopropyl acetate, butyl acetate, 2-methoxyethanol, 2-butanol, ethyl formate, 2-ethoxyethanol, isobutanol, 4-methyl-2-pentanone, 2-butoxyethanol and ethylene glycol) and three binary solvents (2-methoxyethanol + ethyl formate, 2-methoxyethanol + isopropyl acetate, 2-ethoxyethanol+ ethyl formate) was measured by a gravimetric analysis method at the temperatures from 283.15 to 323.15 K. The solubility of 2-MBI in the studied solvents increased with the increasing temperature. The measured solubility data of 2-MBI was described mathematically and back-calculated by CNIBS/R-K model, Margules model, UNIQUAC model, Jouyban-Acree-van't Hoff model and NRTL model. Hansen solubility parameters was calculated to assess the qualitative trend of 2-MBI in all selected mono and binary mixed solvents, analysis results indicating that the solubilization behavior of 2-MBI was intricate and can not only be assessed by one factor. In this study, the apparent thermodynamic parameters including ∆solHo, ∆solSo, ∆solGo, ξH and ξTS were investigated, positive values of ∆solHo indicating that the corresponding dissolution process of 2-MBI in all selected solvents was endothermic. In conclusion, these experimental and thermodynamic analysis can enrich the database and give support for design and optimize the crystallization process of 2-MBI.

Solid-Liquid Equilibrium Study of Binary System Saturated Fatty Acid in Short Chain Alcohols

Unsaturated fatty acids are potential to be used for preventing degenerative diseases and developing brain function in babies. Separation of unsaturated fatty acids from saturated fatty acids efficiently achieved by urea complexation fractionation method. It is considered to be the simplest, most efficient, and lowest cost method. This study aimed to optimize urea complexation for increasing PUFA concentrations by determining solid-liquid equilibrium data of saturated fatty acids in short chain alcohols. In this study, there were two types of short chain alcohol, methanol and ethanol, in various concentrations (99,7%; 95%; 88%; 76% w/w) towards the solubility of saturated fatty acids, palmitic and stearic acid (PA and SA). PA and SA dissolved in various concentration of methanol and ethanol to get homogeneous solutions. When solid SFA disappeared by heating the solution, or first formed by cooling the solution, the temperature was determined as the solid-liquid equilibrium temperature. The results showed that the best composition of solvent within high solubility level is ethanol 95% and methanol 99,7% over palmitic acid because it can dissolve at room temperature and below 0.01 mole fraction.

Revealing Solid–Liquid Equilibrium Behavior of 4-Fluorobenzoic Acid in 12 Pure Solvents from 283.15 to 323.15 K by Experiments and Molecular Simulations

Revealing Solid–Liquid Equilibrium Behavior of 4-Fluorobenzoic Acid in 12 Pure Solvents from 283.15 to 323.15 K by Experiments and Molecular Simulations

A comprehensive thermodynamic modeling of the solubility of sugar alcohols in ionic liquids

Environmental regulations have recently drawn attention from fossil sources to green materials, among which sugar alcohols (SA) have particular importance due to their vast use in the nutrition, pharmaceutical, and chemical industries. Their properties and equilibrium conditions, including the extraction and solubility behavior utilizing novel solvents such as ionic liquids (ILs), are essential for developing further processes and their optimization. On account of this, the present study aims to develop a comprehensive thermodynamic approach based on simple and accurate tools such as activity coefficient models (ACMs) and equations of state (EoSs), which have not been hitherto addressed. To this end, eleven calculation schemes based on these two approaches were applied to the largest databank investigated thus far (13 SAs, 21 ILs, and 653 data points), and the performance of the models was analyzed. NRTL, free-volume Flory-Huggins (FVFH), and Redlich-Kister (RK) ACMs with different schemes, as well as athermal and ideal solution models, were evaluated and compared against well-known cubic EoSs such as Peng-Robinson (PR) and Valderrama-Patel-Teja (VPT). Benefitting from three adjustable parameters and a simple form, the three-parameter RK model yielded the best results with a 0.82 % (2.77 K) deviation in the entire databank. Moreover, employing temperature-dependent interaction parameters with FVFH ACM (3.55 K, 1.05 %), PR EoS (3.60 K, 1.07 %), and VPT EoS (3.66 K, 1.08 %) improved the accuracy of the calculations remarkably. The results of this contribution prove that thermodynamic models based on NRTL, FVFH, and RK ACMs are the best options for calculating solid–liquid conditions equilibrium of SA-IL systems with a simple and precise calculation procedure, and can therefore be employed for the simulation and optimization tools. This study investigates the most extensive SA-IL databank, a large number of models from different routes, and the nature of SA-IL pairs employing the obtained parameters.

Study on the solid-liquid equilibrium and thermodynamic model of the L-phenylalanine + L-tryptophan + water system.

Amino acids hold significant importance in the diagnosis and treatment of various chronic diseases. Accurate solid-liquid equilibrium data are the key to drug synthesis and chemical production. However, the studies on the solid-liquid equilibrium of amino acids remain limited. In this work, the solid-liquid equilibrium of the L-tryptophan + L-phenylalanine + water ternary system under atmospheric pressure at temperatures of 278.15 K-318.15 K was explored via isothermal solution saturation. The isothermal equilibrium phase diagram of the ternary system was constructed. The obtained solid-liquid equilibrium data were correlated with a semi-empirical-model, yielding thermodynamic parameters pa, pb, pc, and k. Furthermore, the model can be used to effectively predict the solid-liquid equilibrium data of ternary systems at other temperatures, and the dY and dP are 0.005 and 4.34%, respectively. The solid-liquid equilibrium data and ternary equilibrium phase diagrams of the system were utilized for the separation and purification of an L-tryptophan and L-phenylalanine mixture. By employing thermodynamic models to calculate the relevant phase diagram data for mixtures with different proportions, effective separation and purification of the mixture could be achieved using the principles of variable temperature phase diagrams. These works are valuable for optimizing chemical processes and have practical implications in the field.

Thermodynamic models for solution behavior and solid-liquid equilibrium in acetate binary systems from low to very high concentration at 25oC

In this study we developed new thermodynamic models for solution behavior and solid-liquid equilibrium in eight acetate binary systems from low to very high concentration at 25oC: six systems of the type 1-1 (X(CH3COO)-H2O with X= (Li, Na, K, Rb, Cs, and Tl)) and two systems of the type 2-1 (Y(CH3COO)2-H2O with Y= (Mg, and Ba)). Models were developed on the basis of Pitzer ion interactions approach. To parameterize models for binary systems we used all available experimental osmotic coefficients data (φ) for the whole concentration range of solutions. To develop models, we used different versions of the standard molality-based Pitzer approach. It was established that for all acetate systems under study application of extended approach with 4 parameters (β0 , β1 , β2 and Cφ ) and variation of 1 and 2 terms in fundamental Pitzer equations leads to the lowest values of standard model-experiment deviation. The predictions of new developed here models are in excellent agreement with experimental φ data, and with recommendations on the mean activity coefficients (±) from low to very high concentration: up to 23.8 m in K(CH3COO)-H2O, up to 39.2 m in Rb(CH3COO)-H2O, and up to 52.2 m in Cs(CH3COO)-H2O. On the basis of evaluated binary parameters important thermodynamic characteristics (Deliquescence Relative Humidity DRH, thermodynamic solubility products Ko sp; standard molar Gibbs free energy of formation, fGo m) for 7 acetate solids were determined at 25oC. The calculated DRH and fGo m values were compared with those reported in the literature. The models described in this study are of high importance, especially in development and improvement of technology for production and purification of acetate solutions and solid phases.

Solubility of fructose and sucrose in mixtures of methanol and water: Experiment and application of equations of state and activity coefficient model

Beyond biochemical functions, carbohydrates have great industrial and economic importance. To improve industrial processes and to develop new applications for these substances, the knowledge of their solubility behavior in different solutions is often necessary. Therefore, the purpose of this work was to collect experimental data on the solubility of fructose and sucrose in hydroalcoholic solutions of methanol and water, using a chromatographic method. The solubility was evaluated for the entire mole fractions of the binary mixture covering the temperatures from 298.15 K to 323.15 K. The results indicated that the chromatographic method is suitable for determining sugar concentration, but it implies an increased uncertainty over the results. The solubility of both sugars was low in methanol-rich binary mixtures, rising with the increasing proportion of water. Greater dependence of the solubility as a function of the composition of the binary mixture was observed for sucrose, indicating stronger molecular interaction and therefore greater deviation from ideality. The NRTL activity coefficient model and the PC-SAFT and CPA equations of state were successfully employed to correlate the solid-liquid equilibrium. The binary interaction parameters were optimized as a function of temperature. The NRTL model has shown greater deviations than those presented by the equations of state. Meanwhile, the equations of state have presented a similar performance.

Measurement and model prediction of solid-liquid equilibrium in the ternary system KCl-MgCl2-H2O at 293.15, 298.15, 303.15, and 308.15 K

Measurement and model prediction of solid-liquid equilibrium in the ternary system KCl-MgCl2-H2O at 293.15, 298.15, 303.15, and 308.15 K