Experimental Solid-liquid Equilibrium Data 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.

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 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).

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.

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.

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.

Solid–liquid equilibrium and mixture properties for the binary systems of Alamine 336 with decane, dodecane, and 1-dodecanol

The separation of the extractant from the diluent solution is a crucial step in the development of clean technologies. Solid–liquid equilibrium (SLE) is used to develop an energy-saving recycling process for extracting solvent. The SLE of the binary systems {Alamine 336+decane}, {Alamine 336+dodecane}, and {Alamine 336+1-dodecanol}, which were used as selective solvents, diluents, and modifiers in the extraction of molybdenum (Mo), was determined at atmospheric pressure by the visual method. The experimental SLE data have been correlated by the Non-Random Two-Liquid (NRTL) model. In addition, we determined the excess molar volume (VE) and deviations in molar refractivity (ΔR) for the same binary mixtures at 298.15K and correlated them with the Redlich–Kister equation.

Solid–liquid equilibrium, excess molar volume, and deviations in the molar refractivity for the binary and ternary mixtures of Alamine 304-1 with 1-octanol, 2-octanol, and 1-decanol

The solid–liquid equilibrium (SLE) of binary systems containing Alamine 304-1 (tri-dodecylamine), which used as a selective solvent in the extraction of molybdenum (Mo), was measured at atmospheric pressure by the visual method. The experimental SLE data for mixtures of Alamine 304-1+1-octanol, Alamine 304-1+2-octanol, and Alamine 304-1+1-decanol were then correlated to the non-random two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) equations. We correlated the excess molar volume (VE) and deviations in molar refractivity (ΔR) of the aforementioned binary mixtures at 298.15K using the Redlich–Kister equation. The VE and ΔR of the ternary mixtures Alamine 304-1+1-octanol+2-octanol, Alamine 304-1+1-octanol+1-decanol, Alamine 304-1+2-octanol+1-decanol, and 1-octanol+2-octanol+1-decanol were predicted by the Radojkovič equation using the correlated binary Redlich–Kister parameters.

Solid–liquid equilibrium data for the binary system methacrylic acid + methanol in the high methacrylic acid concentration range

Experimental solid–liquid equilibrium (SLE) data for the binary system methacrylic acid–methanol in the high concentration range of methacrylic acid were obtained and correlated using several methods. The heat of solution of methacrylic acid was obtained from the results. Several methods of determination of SLE categorized into two kinds of activity coefficient treatments were also studied. The former methods were the modified UNIFAC (Dortmund) model and the calculation from solubility parameters under regular solution assumption using predicted activity coefficients. The later were the NRTL equation and the λ h equation estimating the heat of solution and activity coefficients directly by fitting the experimental SLE data. Based on the results, the recommended method of determination for this system was discussed.

Liquid−Liquid Equilibrium, Solid−Liquid Equilibrium, Densities, and Refractivity of a Water, Chloroform, and Acetylacetone Mixture

Molybdenum is chemically combined with other elements and usually extracted from acid leaching a residual solution of molybdenite. Understanding the behavior of the solvents is important for the optimization of the separation procedures. Therefore, binary and ternary liquid−liquid equilibria (LLE) were measured for a mixture of chloroform, acetylacetone, and water at (293.15 to 333.15) K and atmospheric pressure (101.3 ± 0.7 kPa). The solid−liquid equilibrium (SLE) between chloroform and acetylacetone was also determined by visual techniques. This system has a single eutectic point. The experimental LLE and SLE data were well-correlated by the nonrandom two-liquid (NRTL) and universal quasichemical activity coefficient (UNIQUAC) models. In addition, the excess molar volume (VE) and refractivity (nD) for the binary chloroform + acetylacetone mixture were measured at 298.15 K over the entire composition range. The experimental data were satisfactorily fit using the Redlich−Kister polynomial.

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

AbstractWe modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Solid−Liquid Equilibria in Three Binary Mixtures Containing Diphenyl Carbonate

This study aims to measure the solid−liquid equilibria (SLE) of systems containing diphenyl carbonate (DPC) for production of high-purity DPC as required for a nonphosgene-based polycarbonate production process. SLE data for three binary systems: methanol + DPC, dimethyl carbonate (DMC) + DPC, and phenol + DPC, were determined at atmospheric pressure by visually observing the melting points of a wide range of compositions. An experimental apparatus to allow both accurate control of temperature and visual observation of melting was designed for this study, and the experimental apparatus and procedure were verified by measuring the SLE of the system 2-methyl-1H-imidazole + 1-dodecanol. The binary mixtures DMC + DPC were simple eutectic systems, and the eutectic point was determined. From the experimental SLE for the two binary mixtures methanol + DPC and phenol + DPC, a solid addition compound containing a 1:1 ratio of methanol or phenol and DPC can be expected. The experimental SLE data of the three binary...

Solid−Liquid Equilibria for Binary Organic Systems Containing 1-Methoxy-2-propanol and 2-Butoxy Ethanol

Solid−liquid equilibria (SLE) for the four binary systems of 1-methoxy-2-propanol and 2-butoxy ethanol with benzene and cyclohexane have been measured by a visual method. For correlating the experimental SLE data, the enthalpy of fusion for 1-methoxy-2-propanol has been measured additionally using a Tian-Calvet batch calorimeter. For the description of the SLE data, the Wilson equation has been used with good results. The SLE data were also compared with predicted data using modified UNIFAC (Dortmund).

Using Aniline as an Adductive Agent for Separation of an m-Chlorophenol + p-Chlorophenol Mixture

The experimental solid-liquid equilibrium data of ternary mixtures consisting of m-chlorophenol, p-chlorophenol, and aniline, and those of the constituent binary pairs were determined using the solid-disappearance method. The isomer mixture consisting of m-chlorophenol + p-chlorophenol exhibits one eutectic point at 276.0 K with 0.52 mole percentage of m-chlorophenol. The binary mixture of aniline + m-chlorophenol exhibits two eutectic points, 278.7 K and 257.2 K, at aniline compositions of 0.22 and 0.85, respectively , and one congruent point at aniline mole fraction of 0.5. And another pair of aniline + p-chlorophenol also exhibits two eutectic points, 286.2 K and 259.2 K, at aniline compositions of 0.28 and 0.87, respectively , and one congruent point at aniline mole fraction of 0.5. Ternary mixtures with designated mole ratios of m-chlorophenol to p-chlorophenol exhibit two eutectic points and one congruent point also at aniline mole fraction of 0.5. All the experimental SLE data were fitted by the empirical equation of Ott and Goates with an optimization technique. The results showed the equation of Ott and Goates represents the experimental data fairly well with the average absolute deviation of temperature less than 1.0 K. All the parameters were given and can be used for interpolation purpose. Based on the experimental data and the ternary phase diagram showing all the eutectic and congruent points, three conceptual feasible processes using aniline as an adductive agent for separating m-chlorophenol from p-chlorophenol are proposed.

Experimental Measurement and Model Based Inferencing of Solubility of Polyethylene in Xylene

ANGULYDepartment of Chemical Engineering, Indian Institute ofTechnology, Kharagpur-721302, IndiaKeywords: Solid–Liquid Equilibrium, Laser Sensing, Polyethylene, Model PredictorSolubility of polyethylene in mixed xylene was determined experimentally under atmospheric pres-sure by an indigenously developed laser based technique. In this work, a PC-SAFT equation of state wasused to model solid–liquid equilibrium (SLE). With the experimental SLE data available in the litera-ture for low molecular weight n-alkanes and aromatic compounds under atmospheric pressure, the suit-ability of the developed SLE model based on the PC-SAFT equation of state was tested. Subsequently asensitivity study was performed to understand the effects of different parameters that affect the solubil-ity of polyethylene. The validated model was then used to correlate the experimentally determined solu-bility data for the polyethylene system.