Plait Point Research Articles

Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior.

The use of amorphous solid dispersions (ASDs) in commercial drug products has increased in recent years due to the large number of poorly soluble drugs in the pharmaceutical pipeline. However, the release behavior of ASDs is complex and remains not well understood. Often, the drug release from ASDs is rapid and complete at lower drug loadings (DLs) but becomes slow and incomplete at higher DLs. The DL where release becomes hindered is termed the limit of congruency (LoC). Currently, there are no approaches to predict the LoC. However, recent findings show that one potential cause leading to the LoC is a change in phase morphology after water-induced phase separation at the ASD/solution interface. In this study, the phase behavior of ASDs in contact with aqueous solutions was described thermodynamically by constructing experimental and computational ternary phase diagrams, and these were used to predict morphology changes and ultimately the LoC. Experimental ternary phase diagrams were obtained by equilibrating ASD/water mixtures over time. Computational ternary phase diagrams were obtained by Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). The morphology of the hydrophobic phase was studied with fluorescence confocal microscopy. It was demonstrated that critical point (plait point) composition approximately corresponded to the ASD DL, where the hydrophobic phase, formed during phase separation, became interconnected and hindered ASD release. This work provides mechanistic insights into the ASD release behavior and highlights the potential of in silico ASD design using phase diagrams.

Experimental and theoretical bulk phase diagram and interfacial tension of ouzo.

Ouzo is a well-known drink in Mediterranean countries, with ingredients water, alcohol and trans-anethole oil. The oil is insoluble in water, but completely soluble in alcohol, so when water is added to the spirit, the available alcohol is depleted and the mixture exhibits spontaneous emulsification. This process is commonly known as the louche or ouzo effect. Although the phase boundaries of this archetypal ternary mixture are well known, the properties of coexisting phases have not previously been studied. Here, we present a detailed experimental investigation into the phase behaviour, including tie-lines connecting coexisting phases, determination of the critical point (also called the plait point in ternary systems) and measurements of the surface tension and density for varying alcohol concentrations. Additionally, we present a theory for the thermodynamics and phase diagram of the system. With suitable selection of the interaction parameters, the theory captures nearly all features of the experimental work. This simple model can be used to determine both bulk and non-uniform (e.g. interfacial) properties, paving the way for a wide range of future applications of the model to ternary mixtures in general. We show how our accurate equilibrium phase diagram can be used to provide improved understanding of non-equilibrium phenomena.

Ternary Mixtures of Hard Spheres and Their Multiple Separated Phases

We study the liquid phase behavior of ternary mixtures of monodisperse hard spheres in solution. The interactions are modeled in terms of the second virial coefficient and can be additive hard sphere (HS) or non-additive hard sphere (NAHS) interactions. We give the set of equations that defines the phase diagram for mixtures of three components. We calculate the theoretical liquid–liquid phase separation boundary for two-phase separation (the binodal) and, if applicable, the three-phase boundary, as well as the plait points and the spinodal. The sizes of the three components are fixed. The first component (A) is the smallest one, the second component (B) is four times the size of the smallest component, and the third (C) component is three times the size of the smallest one. The interaction between the first two components is fixed, and this AB sub-mixture shows phase separation. The interactions of component C with the other two components are varied. Component C can be compatible or incompatible with components A and B. Depending on the compatibility of the components, the phase diagram is altered. The addition of the third component has an influence on the phase boundary, plait points, stability region, fractionation, and volume ratio between the different phases. When all sub-mixtures (AB, AC, and BC) show phase separation, a three-phase system becomes possible when the incompatibility among all components is high enough. The position and size of the three-phase region is dependent on the interactions between the different sub-mixtures. We study the fractionation off all components depending on specific parent concentrations.

Measurements, correlations and thermodynamic modeling of aqueous two-phase systems of polyvinylpyrrolidone (PVP) + sulfate/citrate salts

Aqueous two-phase systems (ATPS) can be described as an alternative to traditional liquid-liquid extraction systems, typically consisting of a polymer and a salt solution. An alternative polymer called polyvinylpyrrolidone (PVP) has emerged as a viable option for ATPS due to its low cost, stability, and potential. This study aimed to investigate the effect of the molecular weight of poly (vinylpyrrolidone) (PVP) (K17, K25, and K30) and the temperature (298.15, 303.15, and 308.15 K) in the system ATPSs composed of PVPs and sodium sulfate/potassium sulfate/tri sodium citrate. The tie-line data were determined by measuring the density (ρ) and refractive index (nD). Moreover, the phase compositions and plait point are investigated for different PVPs molecular weight, temperature, and salt type. In addition, the effect of these parameters on the binodal curve, tie-line length (TLL), and slope of tie line (STL) are analyzed in detail by comparing them with the literature data. The impact of the parameters on the binodal curves was investigated by utilizing the values of the effective excluded volume parameter (EEV) that were calculated from the LLE data. Furthermore, the binodal curves and the tie-line compositions were well-fitted by using some semi-empirical equations. The phase separation ability is enhanced with temperature and PVPs molecular weight. The modified UNIFAC-NRF is used to correlate the liquid-liquid equilibrium data of the studied systems and the optimized binary group interaction parameters were determined.

Thermodynamic insights into phase behavior a new aqueous two-phase system at different temperatures: Experimental equilibria, data correlation and modeling

In the current research, a novel aqueous ternary-two-phase system (ATPS) containing a deep eutectic solvent (DES formed by mixing choline chloride with polyethylene glycol 400) and the non-ionic surfactant Triton X-100 was designed. The phase behavior of this system including phase diagrams (binodal curves) and tie-line compositions was thermodynamically investigated at the temperature range of 298.15 to 316.15 K under atmospheric pressure. This system presented a DES-rich top phase and a surfactant-rich bottom phase. The plait point of binodal diagrams together with the tie-lines length (TLL) and the slope of tie-lines (STL) were determined at each of the operational temperatures. The influence of temperature on the binodal curves and the tie-lines was analyzed from which it was found that an increase in the temperature expands the two-phase region in the binodal curve as well as increases the length of the tie-lines. Moreover, the binodal curves data and the tie-line compositions were successfully correlated using a series of semi-empirical models with satisfactory results. Finally, the molar Gibbs energy, molar enthalpy and molar entropy of the cloud points of binodal curve were calculated and the results showed that the formation of the two-phase system is spontaneous and endothermic as well as the entropy is its driving force.

EXTRACTION OF ETHANOL FROM AQUEOUS SOLUTION USING 1-HEXANOIC ACID AND 1-NONANOIC ACID

Ternary phase equilibrium data for ethanol-water-1-hexanoic acid and 1-nonanoic acid were experimentally obtained with a view to evaluate the possibility of separation of ethanol from aqueous solutions by distributing each between water and ethanol phases. The mutual solubility curves, tie lines and plait points were constructed from the experimental results. Distribution coefficients and separation factors were computed for these systems. Hand’s method was used to correlate tie lines and to calculate coordinates of plait points. Tie line data were satisfactorily correlated by the Othmer-Tobias method on a mass fraction basis.

Towards Predicting Partitioning of Enzymes between Macromolecular Phases: Effects of Polydispersity on the Phase Behavior of Nonadditive Hard Spheres in Solution.

The ability to separate enzymes, or cells or viruses, from a mixture is important and can be realized by the incorporation of the mixture into a macromolecular solution. This incorporation may lead to a spontaneous phase separation, with one phase containing the majority of one of the species of interest. Inspired by this phenomenon, we studied the theoretical phase behavior of a model system composed of an asymmetric binary mixture of hard spheres, of which the smaller component was monodisperse and the larger component was polydisperse. The interactions were modeled in terms of the second virial coefficient and could be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component was subdivided into two subcomponents and had an average size ten or three times the size of the monodisperse component. We gave the set of equations that defined the phase diagram for mixtures with more than two components in a solvent. We calculated the theoretical liquid–liquid phase separation boundary for the two-phase separation (the binodal) and three-phase separation, the plait point, and the spinodal. We varied the distribution of the polydisperse component in skewness and polydispersity, and we varied the nonadditivity between the subcomponents as well as between the main components. We compared the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We found that when the compatibility between the polydisperse subcomponents decreased, the three-phase separation became possible. The shape and position of the phase boundary was dependent on the nonadditivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the subcomponents increases.

Prediction and programming of microemulsion phase behavior simulation

In the process of microemulsion flooding, microemulsion phase state may be affected by the adsorption of core and the distribution of oil and water, and the upper phase, the middle phase or the lower phase microemulsion will appear. Accurate description of microemulsion phase state and quantitative discrimination of equilibrium phase composition are of great theoretical value and research significance for the design of microemulsion flooding system and improving the recovery efficiency of microemulsion. Therefore, in this paper, microemulsion phase model is deeply studied. Aiming at the difficulty of solving the existing Hand model and the unknown parameters of the improved HLD-NAC model, we introduce the binodal curve range parameter D and the asymmetric migration degree parameter B, and establish a new phase behavior description method of the binodal curve, the two-phase plait point lines and the III-phase node line. Then the phase discrimination programming of microemulsion was carried out, and the change laws of phase number, phase type and mass fraction of equilibrium phases of any microemulsion system under different salinity were revealed. The results show that the simulation results of microemulsions accord with the salinity scanning law, and can accurately identify the complex microemulsion phase states.

Suitable Experimentation-Modeling Binomial to Design the Extraction of an Alkanol with Water in Aqueous Ternary Solutions of Ester-Akanol

This work presents an investigation on phase equilibria in partially miscible systems comprised of water, esters, and alkanols. Experimental liquid–liquid equilibria (LLE) were determined for ternaries of water+H2u–1Cu–1CO2CvH2v+1+CwH2w+1(OH) (u = 3,4; v = 2,3; w = 1–4) at 298.15 K and for the four corresponding water+ester binaries, in the temperature interval T = [283–328] K. The results reveal a complex behavior of the ternary LLE. The ester barely dissolves in the aqueous phase, even in the presence of alkanol (xmax,esterII ≈ 0.15). However, the organic phase contains high quantities of water when the compositions approach the plait point (xmax,waterI ≈ 0.75). Data modeling was carried out with a multiparametric model, obtaining an acceptable correlation with a maximum deviation in the compositions of sx = 0.031 for the system water(1)+propyl butanoate(2)+propan-1-ol(3). Estimations with COSMO-RS and UNIFAC differed from experimental values in all cases, especially in the systems containing propan-1-ol, since both models predict a nonreal immiscibility at 298.15 K in the binary water+propan-1-ol. Therefore, the simulation of the extractive process using UNIFAC was not adequate.

Spontaneous Ouzo Emulsions Coexist with Pre-Ouzo Ultraflexible Microemulsions.

Even in the absence of surfactants, polymers, or particles, spontaneous emulsions produced by dilution with water can be stable over days. This "Ouzo effect" used by the industry is obtained by rapid dilution from an identified "pre-Ouzo" domain of composition where weak aggregates are present: nanometer-sized clusters covered by a surface layer enriched in a hydrotrope such as ethanol. In these systems, Ostwald ripening is not an effective destabilizing mechanism. Using in situ autodilution small-angle X-ray scattering (SAXS), we follow the morphological transitions occurring in a ternary mixture of water/n-octanol/ethanol throughout the monophasic and biphasic regions. This allows for the first time an online characterization of the multiscale coexisting microstructures. Small-angle neutron scattering (SANS) profiles on metastable emulsions as well as phase-separated samples complete the SAXS data, taking advantage of contrast variation via isotopic substitution. After crossing the phase boundary into the two-phase region, coexisting phases are both ternary solutions structured at the nanometer scale when the emulsion is stable. The transition from single phase to two phases is asymmetric around the plait point. When the initial concentration of the hydrotrope is below the minimum hydrotrope concentration (MHC), emulsification failure occurs, i.e., emulsions cream within seconds. Beyond MHC, the low interfacial tension between coexisting ternary fluids results in a Laplace pressure below 100 Pa, explaining the puzzling resilience of spontaneous emulsion to the universal mechanism of Ostwald ripening.

Phase Equilibria of Aqueous Two-Phase Systems of PEG with Sulfate Salt: Effects of pH, Temperature, Type of Cation, and Polymer Molecular Weight

The present work reports the liquid–liquid equilibrium (LLE) measurements and the construction of binodal curves for polyethylene glycols (PEG) + zinc sulfate/ammonium sulfate + water at three different temperatures (298.15, 303.15, and 308.15 K) and pH values (3.00, 4.70, and 5.21). PEGs with different molecular weights of 2000 g·mol–1 (PEG 2000), 3000 g·mol–1 (PEG 3000), and 8000 g·mol–1 (PEG 8000) were chosen for this study. The phase composition was obtained by measuring the refractive index (nD) and density (ρ) and was further used to obtain the tie-line length (TLL) and the slope of tie-line (STL). The tie-lines are reported at different polymer lengths, pH values, and temperatures. The values of the effective excluded volume (EEV) were employed to analyze the effect of the parameters on the binodal curves. Moreover, the impact of those parameters on the TLL and STL and plait point are discussed and compared with the results of the literature. Furthermore, the binodal curves data and the tie-lines’ ends were fitted using some semiempirical equations with satisfactory results. Finally, the UNIFAC is used to calculate the LLE data of the above system and the adjusted binary group interaction parameters of the model were reported.

Intelligent modelling and analysis of biodiesel/alcohol/glycerol liquid-liquid equilibria

This paper provides an accurate intelligent model for the phase behavior of biodiesel/alcohol/glycerol ternary system. The proposed model is developed and generalized over 643 experimental data for different ternary systems (28 fatty acid alkyl esters (FAAE)/2 methanol + ethanol/glycerol) at atmospheric pressure within temperature ranges [298.15393.15 K]. The models were verified by comparison with activity models (i.e., UNIQUAC/Dortmund) in terms of accuracy. The proposed model was validated with data of two ternary systems out of the considered datasets. The validity of the developed model was also checked by an Othmer-Tobias plot. The Othmer-Tobias plot predicts the plait point corresponds to the system biodiesel/ethanol/glycerol with RMSE 0.665%.

Liquid-Liquid Equilibrium Data of the Ternary Mixture of (Water + Phosphoric Acid + Heptyl Acetate) at 298.2 K and ≈ 102 kPa

Solubility data and tie-line points were experimentally determined for the ternary system (water + phosphoric acid + Heptyl acetate) at T = 298.2 K and ambient pressure. The cloud point method was used to measure the immiscibility region. Type-1 LLE behavior was observed for the investigated system and the plait point data were calculated using the Treybal’s method. The compositions of both aqueous and esteric layers were determined by using of acid-base titration, HPLC method and mass balance equation. The Othmer–Tobias and Hand equations were applied to prove the reliability of tie-line data. Obtained tie-line points were then correlated using the UNIQUAC model and the rmsd results showed that the measured points were satisfactorily regressed by the thermodynamic model. To evaluate the ability of the studied solvent for purification of phosphoric acid, distribution coefficients and separation factors were calculated over the biphasic area. Separation factors were greater than one in all investigated feeds of phosphoric acid for the studied system. Heptyl acetate showed the highest separation factors between all the investigated n-alkyl acetate esters.

Liquid-liquid equilibria, solubility and critical states in the system propionic acid – 1-propanol – n-propyl propionate – water at 303.15 K

New experimental data on liquid-liquid equilibria (LLE), solubility and critical states in quaternary system propionic acid – 1-propanol – n-propyl propionate – water at 303.15 K and atmospheric pressure are presented. LLE was studied by Gas Chromatography (GC). Solubility and critical (plait) points were investigated by “cloud-point technique” method. Binodal curves and surfaces are presented in concentration tetrahedron. The critical curve is presented in 3d concentration space. A comparative analysis of the results obtained in the work with literature data is carried out. The experimental data are correlated by NRTL model. Standart deviation σ for quaternary mixture does not exceed 0.344%.

Quaternary liquid-liquid equilibrium, solubility and critical states: Acetic acid – n-butanol – n-butyl acetate – water at 318.15 K and atmospheric pressure

Experimental data on solubility, critical states and liquid–liquid equilibrium (LLE) for the quaternary system acetic acid – n-butanol – n-butyl acetate – water and ternary subsystems acetic acid – n-butanol – water, n-butanol – n-butyl acetate – water and acetic acid – n-butyl acetate – water were obtained at 318.15 K and at atmospheric pressure. The solubility and critical states were studied by isothermal titration method (“cloud-point technique”). The LLE was determined using gas chromatographic analysis. Binodal surface in quaternary system and binodal curves in ternary systems were constructed. Compositions of critical points (plait points) and critical curve were determined. The NRTL model was applied to calculate the LLE data for the quaternary and ternary systems. The results of NRTL modeling are in good agreement with the experimental data.

Effect of temperature on the phase-separation ability of KCl in aqueous two-phase systems composed of propanols: Determination of the critical temperature and extension of the results to other salts

The phase-forming ability of KCl in propanols has been investigated, aiming to assess its utility in aqueous two-phase extraction. Equilibrium data of the different equilibrium regions (SLLV, SLV, LLV, and LV) of aqueous two-phase systems (ATPSs) of water + KCl + 1-propanol and water + KCl + 2-propanol have been determined at the boiling temperatures of the mixtures and 101.3 kPa. In addition, the lowest critical solution temperature (LCST) for the water + KCl + 1-propanol system was measured to be 271.2 K, and the equilibrium behavior of the system in the vicinity of the LCST (at 268.1 and 273.1 K) was also determined. Finally, using various methods such as the effective excluded volume (EEV) theory, Setchenov-type equations, and the plait point of the liquid-liquid region, different salt and alcohol systems have been studied and classified according to their ability to produce ATPSs.

Phase equilibria of aqueous mixtures of PEG with formate salt: Effects of pH, type of cation, polymer molecular weight and temperature

Liquid-liquid equilibrium (LLE) data for poly (ethylene glycol) (PEG) of different molecular weights (600, 1500, 3000, 6000) + sodium formate (NaCHO2), potassium formate (KCHO2) + water at different temperatures (298.15 and 308.15 K) and for PEG (1500) + sodium formate + water at different pH values (8.05, 9.06, 10.92), were determined experimentally. The tie lines and plait point are reported at different PEG molecular weight, pH, temperature and type of cation. Furthermore, the effect of those parameters on binodal curve, tie-line length (TLL) and slope of tie line (STL) are discussed in detail by comparing the results to that of literature data. The effective excluded volume (EEV) values obtained from the LLE data were used to study the effect of the parameters on the binodal curves. The phase composition and the tie-lines’ ends were obtained by measuring the density (ρ) and refractive index (nD). Furthermore, the binodal curves and the tie-line compositions were well-fitted by using some semi empirical equations.

Solubility and critical surface in the system propionic acid–ethanol–ethyl propionate–water at 293.15, 303.15 and 313.15 K

New experimental data on solubility and critical states in quaternary system propionic acid–ethanol–ethyl propionate–water at 293.15, 303.15 and 313.15 K and atmospheric pressure are presented. Solubility and critical (plait) points were obtained by “cloud-point technique” method. Experimental results on critical states in quaternary system at polythermal conditions (293.15–313.15 K) are presented as a critical surface in composition tetrahedron. The experimental data are compared with the results of calculations on the base of UNIFAC model.

Liquid-liquid equilibrium data and thermophysical properties for ternary systems composed of water, acetic acid and different solvents

Liquid-liquid equilibrium (LLE) data for water + acetic acid + {1-butanol or isopentanol or methyl-terc-butyl ether (MTBE) or methyl isobutyl ketone (MIBK) or diisobutyl ketone (DIBK) or isoamyl propionate} systems at T = {293.2 and 313.2} K and P ≈ 95 kPa were determined. Immiscibility region (LLE envelope) were determined experimentally through binodal curves (cloud point data). Thermophysical properties, i.e., density, refractive index, speed of sound, isentropic compressibility and molar refractivity were obtained for each cloud point. Tie lines were attained using indirect method utilizing equations obtained through cloud point data fit and partition coefficients, selectivities and percent of extraction were calculated in order to evaluate the effects of solvent type and temperature on acetic acid removal from water. Besides, thermophysical properties for all systems were compared. LLE data were correlated with NRTL model, presenting root mean square deviation equal to 1.2366% for 66 tie lines. NRTL modelling also estimated plait points for all systems.

Thermodynamic Studies of the Aqueous Two-Phase System Containing Polyethylene Glycol Dimethyl Ether 2000 and Sodium Nitrite at (298.15, 308.15, and 318.15) K

Liquid–liquid equilibrium data including binodals and tie-line compositions have been measured for aqueous ternary biphasic system containing polyethylene glycol dimethyl ether 2000 (PEGDME2000) and sodium nitrite at three temperatures (298.15–318.15) K and atmospheric pressure (≈ 85 kPa). The salting-out of the polymer by the salt was studied at different temperatures. Furthermore, the ΔGc, ΔHc, and ΔSc of the cloud points were computed at working temperatures from which it was found that the entropy is the driving force for phase separation. For representing the experimental binodal data two empirical equations with the temperature dependency were used. The Setschenow equation was utilized for correlating the measured tie-lines. Different versions of nonrandom two-liquid models were also selected in generating the obtained tie-lines. The plait point, and the characteristics of tie-lines (slope and the length) have been determined at working temperatures. The partitioning behavior of the iodine molecule ...