Experimental Solid-liquid Equilibrium Research Articles

Estimating the nonideality of eutectic systems containing thermally unstable substances.

Eutectic systems design requires an in-depth understanding of their solid-liquid equilibria (SLE). Modeling SLE in eutectic systems has as prerequisites, the melting properties and activity coefficients of components in the liquid phase. Thus, due to the unavailable melting properties of thermally unstable substances, it is impossible to estimate their activity coefficients from experimental SLE data and model the SLE phase diagram of their eutectic systems. Here, we evaluate the activity coefficients of thermally unstable constituents in the liquid phase, which were calculated independent of their melting properties by correlating the SLE data of their cocrystals. Differential scanning calorimetry and powder x-ray diffraction were employed to obtain the SLE phase diagram of three eutectic systems, i.e., tetramethylammonium chloride/catechol, tetraethylammonium chloride/catechol, and betaine/catechol systems, and identify the formation of nine cocrystals. The non-random, two-liquid equation was used to calculate the activity coefficients of the components in the liquid phase. The substantial negative deviation from ideality in the three studied systems indicated strong hydrogen bonding interactions in the liquid solution. Furthermore, modeling ion-ion interactions in eutectic systems containing ionic constituents is of utmost importance for understanding their nonideality.

A cryogenic visual apparatus for solid-liquid equilibrium and the measurement of CH4 + C2H6

In this work, an apparatus was designed to measure the phase equilibrium for cryogenic pure fluids and mixtures. The apparatus features view windows and an internal stirrer, and the solid-liquid equilibrium (SLE) is determined through a combination of visual observation and thermal analysis. The apparatus is capable of operating over a range of temperatures (40–300 K) and pressures (0–5 MPa), and has been validated through the measurement of triple points of various fluids. The standard combined uncertainties of temperature, pressure and mole fraction for the SLE measurements are no greater than ±0.70 K, ±0.012 kPa, and 0.010, respectively. The performance of the apparatus is further demonstrated through the presentation of experimental SLE data for methane-ethane binary mixtures.

Bridging Machine Learning and Redlich–Kister Theory for Solid–Liquid Equilibria Prediction of Binary Eutectic Solvent Systems

Eutectic solvents (ESs) have gained significant interest in various chemical processes due to a broad spectrum of attractive properties, whereas their rational design is currently still in its infancy. To bridge this gap, Redlich–Kister (RK) theory and machine learning are linked for the solid–liquid equilibria (SLE) prediction of ES systems, which is thermodynamically the cornerstone for ES design. RK theory with two or three parameters is first evaluated by fitting experimental SLE of an extensive ES database, demonstrating that the two-parameter-based one is sufficiently reliable for eutectic behavior correlation. Three machine learning methods, namely, Random Forest, multiple linear regression, and ElasticNet, are developed for relating the parameters of RK theory to the RDKit descriptors of ES components. The SLE predictions from RK theory parametrized by the developed machine learning models are carefully evaluated and further externally examined on several recently reported ES systems.

Experimental solid–liquid equilibria and solid formation kinetics for carbon dioxide in methane for LNG processing

AbstractIn cryogenic liquefaction processes, CO2 poses a solid‐formation risk even in trace concentrations. We present solid–fluid equilibrium (SFE) data for CO2 in liquid methane at CO2 concentrations from (52 to 500) ppm, extending the available data and indicating that models tuned to existing data over predict the solubility of CO2 at LNG storage temperatures (~112 K) by nearly a factor of 3. The new data are used to improve the SFE model in the ThermoFAST software package. The formation kinetics of CO2 solids in liquid methane are elucidated at conditions relevant to cryogenic gas processing. Repeated, ramped‐temperature formation measurements provide a statistical basis for quantifying solidification risk. Nucleation rates extracted from the ramped‐temperature data, consistent with those measured at fixed temperature, were used to extract parameters describing CO2 solid formation in methane. These results significantly improve the ability to predict CO2 solid formation risk in cryogenic natural gas processing.

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.

Scaling trend of coal chemical saline wastewater in falling film evaporator: experimental solid–liquid equilibrium and numerical simulation

Abstract It was important to establish the scaling mechanism to slow down scaling, which is one of the important problems faced by saline wastewater treatment with falling film evaporators. In this paper, the phase equilibrium data of ternary system NaCl-CaCl2-H2O at 303.15–373.15 K were measured, and the prediction of the flow characteristics and scaling tendency of salt-containing wastewater in the evaporation tube was investigated by numerical simulation based on the phase equilibrium results. The results showed that the mesostable phase diagram of the ternary system was of simple type, and w(NaCl) and w(CaCl2) showed regular variation with temperature when w(NaCl) in the system was 15–28%. Moreover, the components of the four saline wastewaters (10% NaCl + 9, 10, 11, 12% CaCl2) with less salt content had a faster heating and a faster rate of evaporation of the liquid film in the evaporation tube. Based on the solubility in the experiments and simulations, it was concluded that NaCl crystals were precipitated at tube lengths of 718 mm, 942 mm, 966 mm, and 1,000 mm for four salt concentrations in the evaporation process by comparison, and the reliability of the predicted loci was also demonstrated by a falling film evaporation experimental setup.

Solid–Liquid Equilibria for Five Binary Mixtures of Tetradecanoic Acid or Dodecanoic Acid with Three Heavy Paraffins Using DSC Measurements

Solid–liquid equilibrium (SLE) results for binary mixtures of either tetradecanoic acid (C14H28O2) or dodecanoic acid (C12H24O2) with three heavy paraffins of octadecane (C18H38), eicosane (C20H42), and docosane (C22H46) are presented in this study. The experimental measurements were conducted using differential scanning calorimetry (DSC). The experimental SLE data for five binary systems are reported and all systems show simple eutectic behavior. The fractional transformation values were determined using the heat generated during various time intervals from DSC analyses. Eutectic compositions were evaluated by plotting the eutectic fraction against composition. These experimental SLE data were correlated using the Wilson activity coefficient model, and the best-fitted binary parameters for all systems are illustrated. These novel SLE data supply useful information for the separation process or the design of phase-change materials (PCMs).

Solid–Liquid Equilibria of Binary Systems Containing Amines: Experimental Data and Prediction with DISQUAC and UNIFAC Models

Group contribution models can be used to predict the thermodynamic properties. The basic data used to determine the interaction parameters are VLE, HE and infinite dilution activity coefficient data. However in the absence of the required data, SLE measurements of eutectic systems are of great interest for fitting interaction parameters of group contribution methods. The knowledge of solid–liquid equilibria (SLE) of binary mixtures is essential for the design and development of separation process involving crystallization. In the present study, experimental SLE of binary mixtures containing N,N-dimethylaniline, diethylamine, cyclohexylamine, n-alkanes, and cyclohexane were measured by a static method of direct thermal analysis, using an apparatus derived from that of Smit. The experimental data obtained with this technique are compared with those predicted by Group contribution models: Mod. UNIFAC (Do) and DISQUAC models. The liquid-phase activity coefficients were also calculated. The experimental results illustrated that these systems showed a eutectic behavior, and a good agreement is obtained between experimental and predicted SLE. The use of the new c-CHNH2 group instead of the CHNH2 group in the modified UNIFAC Dortmund model showed excellent results.

Solid-liquid equilibrium, structural features and separation process of ammonium potassium dihydrogen phosphate solid solution

• Solid-liquid equilibrium of the NH 4 + , K + //H 2 PO 4 − -H 2 O system at 283.15 K and 313.15 K was investigated. • By characterization determined infinite substitutional solid solutions. • Two solid solutions are analyzed by FTIR, TG-DSC, EDS (mapping). • A multistage purification process was developed and proved feasibility for AQ-SS. Solid-liquid equilibrium for NH 4 H 2 PO 4 + KH 2 PO 4 + H 2 O ternary system was investigated at 283.15 K and 313.15 K, which revealed complete mixed crystals in the solid phase. By analysis of XRD and the formation rule of the substituted solid solution, it is further confirmed infinite substitutional solid solution. Then, from the analysis of FT-IR, TG-DSC and mapping of [K 0.78 (NH 4 ) 0.22 ]H 2 PO 4 and [K 0.11 (NH 4 ) 0.89 ]H 2 PO 4 solid solution, we can conclude that two solid solutions are similar, but the absorption position have slight shift to low wave number direction as the increasing of K + content; the homogeneous distribution of K + and NH 4 + elements. Finally, applying the experimental solid-liquid equilibrium data, multistage fractional crystallization experiment to obtain the purity of the KH 2 PO 4 is close to 97% after five times operation and purity of the NH 4 H 2 PO 4 reaches about 98% after four times operation, which proves multistage fractional purification is verified as an effective purification method for AQ-SS.

Evaluation of COSMO-RS for solid–liquid equilibria prediction of binary eutectic solvent systems

For the design of eutectic solvents (ESs, usually also known as deep eutectic solvents), the prediction of the solid–liquid equilibria (SLE) between candidate components is of primary relevance. In the present work, the SLE prediction of binary eutectic solvent systems by the COSMO-RS model is systematically evaluated, thereby examining the applicability of this method for ES design. Experimental SLE of such systems are first collected exhaustively from the literature, following which COSMO-RS SLE calculations are accordingly carried out. By comparing the experimental and predicted eutectic points (eutectic temperature and eutectic composition) of the involved systems, the effects of salt component conformer and COSMO-RS parameterization as well as the applicability for different types of components (specifically the second component paired with the first salt one) are identified. The distinct performances of COSMO-RS SLE prediction for systems involving different types of components are further interpreted from the non-ideality and fusion enthalpy point of view.

The role of ionic vs. non-ionic excipients in APIs-based eutectic systems

Aiming to contribute to drug pre-formulation, new eutectic mixtures were developed. Thymol, coumarin, or quaternary ammonium chlorides as excipients, were combined with the active pharmaceutical ingredients (APIs) acetylsalicylic acid, acetaminophen, ibuprofen, ketoprofen, or lidocaine. Their solid-liquid equilibrium (SLE) binary phase diagrams were measured to study eventual phase separation between the compounds, preventing manufacturing problems, and to study the molecular interactions between the APIs and ionic or non-ionic excipients. The Conductor-like Screening Model for Real Solvents (COSMO-RS) capability to predict the SLE of mixtures containing non-ionic excipients was further evaluated. COSMO-RS gives a good quantitative description of the experimental SLE being a tool with great potential in the screening of eutectic systems containing APIs and non-ionic excipients. While thymol presents strong interactions with the APIs, and consequently negative deviations to thermodynamic ideality, systems containing coumarin follow a quasi-ideal behavior. Regarding the ionic excipients, both choline chloride and the tetraalkylammonium chlorides are unable to establish relevant interactions with the APIs, and no significant negative deviations to ideality are observed. The liquefaction of the APIs here studied is favored by using non-ionic excipients, such as thymol, due to the strong interactions it can establish with the APIs.

Measurement and modelling of solid-liquid equilibria, density and viscosity of fatty acid methyl or ethyl esters

The solid-liquid equilibria (SLE), densities and viscosities of few selective methyl or ethyl esters, required for the reformulation of biodiesel fuel, have been studied at different temperatures and at atmospheric pressure 0.1 MPa. The SLE, density (ρ) and kinematic viscosity (ν) of ethyl decanoate (1) + methyl laurate (2) or methyl myristate (2) binary systems were measured at different temperatures from 298.15 K to 318.15 K and were further used to derive other thermodynamic properties like excess molar volume (VmE) and deviations in dynamic viscosity (Δη). The experimental SLE data showed single eutectic point and correlated well with common nonrandom two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) equations. The kinematic viscosity (ν) data were best correlated with McAllister equation and deviations in dynamic viscosity (Δη) were described by Singh approach whereas excess molar volume (VmE) data were predicted well with Prigogine–Flory–Patterson (PFP) theory for the composition x1 ≤ 0.5634. The derived thermodynamic properties were also correlated with Redlich-Kister polynomial.

Measurement and correlation for solubilities of succinic acid, glutaric acid and adipic acid in five organic solvents

In this study, the solid-liquid equilibrium (SLE) data of succinic acid (SA) and glutaric acid (GA) and adipic acid (AA) in N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMAC), dimethyl sulfoxide (DMSO), 1-Methyl-2-pyrrolidinone (NMP) and sulfolane were determined by using the method of dynamic laser at atmospheric pressure. The experimental SLE data indicates that within the temperature range studied (286.25–358.75 K), the solubilities of SA, GA and AA in above five solvents is proportional to the temperature. Meanwhile, three thermodynamic models (Apelblat model, λh model, the modified nonrandom two liquid (NRTL) activity coefficient model) were used to correlate the experimental data, the results show that the correlated data is generally consistent with the experimental data. The result of Akaike Information Criterion (AIC) analysis filter out the best model for every system. In addition, the thermodynamic functions (dissolution enthalpy, entropy, Gibbs energy) were obtained from the SLE data by calculating the van't Hoff equation.

Phase equilibria of (water + [EMIM] bromide) and (water + [EMIM] tosylate)

This work presents a detailed phase equilibria study on the aqueous solutions of two hydrophilic ILs that are solid at room temperature: 1-ethyl-3-methylimidazolium bromide ([EMIM][Br]) and 1-ethyl-3-methylimidazolium tosylate ([EMIM][TOS]). The melting temperatures of the pure ILs were measured to discriminate between existing literature data that show some disparity. Solid-liquid equilibrium (SLE) data for (water + [EMIM][Br]), so far lacking in the literature, were determined by a dynamic method over the major portion of the entire composition range. Using a chilled mirror dew point technique, extensive and accurate vapor-liquid equilibrium (water activity) measurements were further conducted for the aqueous solutions of both ILs. The temperature and concentration dependences of the activity data were correlated simultaneously by an extended NRTL model, whereby establishing a common description of pertinent equilibria and related thermodynamic behavior of these systems. Good performance of this model was verified against other experimental data from the literature and this work. In particular, correct predictions of experimental SLE data proved the model to extrapolate well beyond the temperature range of data underlying the correlation. Excess thermodynamic properties calculated from the model revealed that these systems exhibit large negative deviations from Raoult's law, a strongly exothermic mixing and, except for (water + [EMIM][TOS]) in the water-rich region, positive excess entropies. Comparing the two ILs, the observed deviations from ideality are always more pronounced for [EMIM][Br], which indicates that [Br]– is a more hydrophilic anion than [TOS]–. The observed pattern of thermodynamic behavior was rationalized on the molecular level by means of simple MD simulations. They showed that while there are more H-bonds formed between water and [TOS]–, these bonds are weaker than those between water and [Br]–.

Solid–liquid equilibria for selected binary systems containing diphenyl carbonate

The solid–liquid equilibrium (SLE) data for five binary systems containing diphenyl carbonate (DPC), i.e., ethanol, 1-propanol, 2-propanol, diethyl carbonate, or dipropyl carbonate + DPC, were determined experimentally. We designed a new experimental apparatus based on a synthetic method for the SLE measurements. We verified the applicability of the designed apparatus by determining the binary SLE data for the system dimethyl carbonate + DPC. The experimental SLE data were represented by a non-random two-liquid model. Predictions of SLE data for the binary systems were also tested on the basis of the National Institution of Standards and Technology-modified universal functional activity coefficient group contribution model.

Experimental measurement and prediction by the UNIFAC and the DISQUAC models of the solid–liquid equilibrium diagrams of piperidine + benzene and piperidine + n-octane systems

This work is a continuation of our researches on the study of thermodynamic properties of organic compound mixtures and made up of two sections: an experimental section and a theoretical section. The experimental solid–liquid equilibrium diagrams of binary systems: piperidine + benzene and piperidine + n-octane, measured at atmospheric pressure, have been obtained by means of an apparatus derived from that of Smit. The advantage of this apparatus compared to that of Rossini and that of Jacob is the higher measurement accuracy and the low amount of product used. In the theoretical section, in addition to the calculation of the liquidus curves in the ideal case, the DISQUAC model and the Dortmund-UNIFAC method were applied to the two mixtures to predict the liquidus curves and make a comparison.

Ternary phase diagram and the formation mechanism of two distinct solid solutions of amino acid systems: l -Valine/ l -norvaline and l -valine/ l -alanine

Abstract The ternary phase diagram of l -valine ( l -Val)/ l -norvaline ( l -Nva)/water system was determined at 293.15 K, in which the tie lines clearly indicate the formation of complete solid solution and X-ray powder diffraction (XRPD) analysis of the solid phases further confirms complete miscibility of l -Val and l -Nva molecules in the solid state. Further, homogeneous solid solution can be obtained via mechano-chemical method of non-solution system and via anti-solvent method. Similar composition analysis of solid and liquid phase suggests that l -Val and l -alanine ( l -Ala) is partially miscible with only a narrow scope of component substitution. The similarity degree of the three amino acids in cell dimensions and supramolecular organization determines the miscibility of l -Val and l -Nva or l -Val and l -Ala, and the investigation in molecular incorporation of l -Val/ l -Nva system was developed. Applying the experimental solid-liquid equilibrium data, fractional crystallization is verified as an effective purification method.

Thermodynamic Study of Molecular Interactions in Eutectic Mixtures Containing Camphene.

Terpenes are an abundant and diverse class of chemicals having numerous applications in different areas of chemistry. Therefore, a detailed knowledge of physical and thermodynamic properties of terpenes and their mixtures with other compounds is highly desired. This paper reports both a thermodynamic study on solid-liquid equilibrium (SLE) phase diagrams in binary systems formed by (±)-camphene (a representative terpene) and one of the following solvents: n-decane, n-dodecane, 1-decanol, 1-dodecanol, phenylmethanol, 2-phenylethanol, 2-cyclohexylethanol. The observed trends in the measured SLE data are discussed in terms of structure (alkyl chain length, aromacity) of the solvent and molecular interactions. Modeling of the considered SLE phase diagrams with three well-established thermodynamic models, namely, modified UNIFAC (Dortmund), perturbed-chain statistical associating fluid theory (PC-SAFT) and conductor-like screening model for real solvents (COSMO-RS), is presented. A comparative analysis of their performance is given in terms of average absolute deviations between predicted and experimental SLE temperature.

SOLUBILITY OF A NEW ANTIRETROVIRAL DRUG (CRS 74) IN AQUEOUS ETHANOL MIXTURES

This study concerns a new antiretroviral drug named CRS 74, which has a limited bioavailability because of its low aqueous solubility and dissolution rate. To improve these properties, CRS 74 can be recrystallized by using Liquid Anti-Solvent (LAS) crystallization. Ethanol is chosen as the solvent under study for the molecule and water as the anti-solvent. Since solubility data is limited, it is necessary to collect experimental data for the molecule in relation to ethanol and water-ethanol mixtures at different temperatures in order to select suitable mixture compositions and temperature for LAS process design. In this work, the CRS 74 solubility measured in the temperature range 288.15-303.15 K in pure ethanol and in 95% water 5% w/w ethanol mixtures, and the CRS 74 solubility measured at 303.15 K in water-ethanol mixtures containing from 30 to 70% w/w ethanol are presented. Measurements were performed using the shake-flask method for generating the saturated solutions followed by compositional analysis by HPLC of the solution. The experimental data showed that the solubility of CRS 74 in binary hydroalcoholic mixtures increases upon increasing the temperature and mass fraction of ethanol. In order to better understand the behavior of the system and to estimate supersaturation conditions for a larger range of CRS 74 crystallization conditions, two models have been chosen to describe the experimental data: UNIQUAC and Jouyban-Acree models. The modeling of experimental solid-liquid equilibrium data proved that both models could correlate satisfactorily the solubility of the studied drug. This study provided valuable data for the recrystallization of CRS 74 by using the Liquid Anti-Solvent (LAS) crystallization process.

Phase equilibria study of binary systems comprising an (ionic liquid + hydrocarbon)

In this study, the interaction of two ionic liquids with hydrocarbons has been investigated. With this aim, (solid+liquid) equilibria (SLE) and (liquid+liquid) equilibria (LLE) for binary systems of {1-methyl-1-propyl-pyrrolidinium triflate [PMPyr][CF3SO3]+heptane, or benzene, or thiophene, or benzothiophene} and {N-butyl-4-cyanopyridinium tricyanomethanide [BCN4Py][TCM]+heptane, or toluene, or 2-methylthiophene, or benzothiophene} were measured at ambient pressure. A dynamic method was used over a broad range of mole fractions and temperatures from (T=270 to 370)K. An upper critical solution temperature (UCST) was detected for all mutually immiscible systems. The immiscibility gap for [BCN4Py][TCM] in benzene and thiophene is larger than those for [PMPyr][CF3SO3]. Conversely, in heptane it is slightly larger for [PMPyr][CF3SO3]. The basic thermal properties of the pure ILs, i.e. melting and glass-transition temperatures as well as the enthalpy of fusion have been measured using a differential scanning microcalorimetry technique (DSC). The well-known NRTL model has been used to correlate the experimental SLE data points.