Phase Diagrams Of Binary Mixtures Research Articles

Closed-loop fluid–fluid immiscibility in binary lipid–sterol membranes

We present two binary lipid-sterol membrane systems that exhibit fluid-fluid coexistence. Partial phase diagrams of binary mixtures of dimyristoylphosphatidylcholine with 25-hydroxyxholesterol and 27-hydroxycholesterol, determined from small-angle X-ray scattering and fluorescence microscopy studies, show closed-loop fluid-fluid immiscibility gaps, with the appearance of a single fluid phase both at higher and lower temperatures. Computer simulations suggest that this unusual phase behavior results from the ability of these oxysterol molecules to take different orientations in the membrane depending on the temperature.

An Insight into the Solid-State Miscibility of Triacylglycerol Crystals.

The crystallization properties of triacylglycerols (TAGs) strongly determine the functional properties of natural lipids. The polymorphic and mixing phase behavior of TAG molecules have long been, and still are, a hot topic of research with special relevance for the cosmetic, pharmaceutical, and food industry. To avoid the difficulties arising from the study of whole real fats, studies at the molecular level on mixtures of a limited number of TAGs has become an indispensable tool to identify the underlying causes of the physical properties in lipid systems. In particular, phase diagrams of binary mixtures of TAGs exhibiting a different degree of heterogeneity (monoacid or mixed fatty acids; molecular symmetry; the presence of cis or trans double bonds) have resulted in a significant breakthrough in our knowledge about structure–interaction–function relationships. The present work aims to provide an overview of the main reports regarding binary and ternary TAG systems, from the early studies to the most recent developments.

Geometric investigation of the three-coefficient Redlich-Kister expansion global phase diagram for binary mixtures

The Redlich-Kister (RK) three-coefficient expansion for gE is investigated geometrically and its global phase diagram is presented. The azeotropy and stability conditions yield surfaces (envelopes) in the three-dimensional azeotropy space and stability space respectively, whose axes represent variables determined from Henry's constants, pure substance vapor pressures and the highest-order RK coefficient. Zeotropy, single, double, triple, and tangent azeotropy (or saddle-point azeotropy), as well as stability, are identified in regions of the azeotropy and stability spaces. The connection between the two spaces is established. Envelopes for gE = 0 and dgE/dx=0 are also constructed in the azeotropy or stability spaces, to indicate the gE shape. Some results regarding the shape of gE are transferable to hE and vE when these are described independently by three-coefficient Redlich-Kister expansions. The analysis is applied to eleven actual mixtures, whose state is represented in the azeotropy and stability space. Fitting temperature-dependent RK coefficients allows to estimate the continuous path the mixture follows in both spaces at varying temperature, revealing possible intermediate states and the mixture tendency at the extreme temperatures.

Infinite-pressure phase diagram of binary mixtures of (non)additive hard disks.

One versatile route to the creation of two-dimensional crystal structures on the nanometer to micrometer scale is the self-assembly of colloidal particles at an interface. Here, we explore the crystal phases that can be expected from the self-assembly of mixtures of spherical particles of two different sizes, which we map to (additive or non-additive) hard-disk mixtures. We map out the infinite-pressure phase diagram for these mixtures using Floppy Box Monte Carlo simulations to systematically sample candidate crystal structures with up to 12 disks in the unit cell. As a function of the size ratio and the number ratio of the two species of particles, we find a rich variety of periodic crystal structures. Additionally, we identify random tiling regions to predict random tiling quasicrystal stability ranges. Increasing non-additivity both gives rise to additional crystal phases and broadens the stability regime for crystal structures involving a large number of large-small contacts, including random tilings. Our results provide useful guidelines for controlling the self-assembly of colloidal particles at interfaces.

The Solid–Liquid Phase Diagram of Binary Mixtures Dissolved in an Inert Oil: Application to Ternary Blends that Can Form Organogels

AbstractA simple generalization of the Hildebrand equation is presented for the prediction of the solid–liquid phase diagram of a binary mixture of structuring agents dissolved in an inert liquid. The model is a thermodynamic interpolation between three well‐known limits: (1) the freezing depression curve of liquid A under influence of the addition of the solvent, (2) the freezing depression curve of liquid B under influence of the addition of the solvent, and (3) the binary solid–liquid phase diagram of substances A and B. The theory is shown to be valid as long as the freezing temperature of the liquid is well below the freezing temperatures of the structurants. The theory is compared to literature data for three different mixtures: (1) stearyl alcohol and stearic acid dissolved in sunflower oil, (2) hentriacontane+melissic acid in safflower oil, and (3) lauric acid + behenic acid in canola oil. The agreement between the thermodynamic calculation and experimental data is good. The solid–liquid phase behavior of glyceryl tristearate + stearic acid in edible oil is also studied. The location of the eutectic point of the latter system is predicted to shift toward an axis with zero tristearate concentration as the structurant concentration decreases from 50% to 5% (w/w).

Construction of global phase diagrams for binary mixtures with equal and unequal size of molecules by using the modified van der Waals model

The global phase diagram or master diagram is constructed for binary mixtures consist of the equal and unequal size of molecules by using the modified van der Waals model. The Griffiths shield region is also presented on the master diagram. The influence of various size differences ratio of molecules on the master diagram is investigated and discussed. It is observed that the GPD are symmetrical around ζ=0 for the equal-size of molecules and the deterioration in the symmetric behavior of GPD increases as differences of size of molecules increase. From the master diagram, all possible main types of phase behavior for every given interaction energy parameters and various size differences ratio of molecules can be seen directly without long and difficult calculations.

Construction of phase envelopes for binary and multicomponent mixtures with Euler-Newton predictor-corrector methods

New algorithms for the calculation of constant composition phase envelopes of binary and multicomponent mixtures and constant temperature (P-x,y), constant pressure (T-x,y) phase diagrams of binary mixtures are presented. The proposed numerical methods are Euler-Newton predictor-corrector methods that sequentially trace the entire family of solutions (phase diagrams), corresponding to given specifications. Different sets of independent variables are used for the sequential calculation of constant composition phase envelopes of mixtures and the resulting methods are compared. The variable set that shows the best behavior in terms of efficiency, robustness and conditioning is utilized subsequently in constructing new methods that trace phase diagrams of binary mixtures at constant temperature or pressure. In this case, the methods are based on different combinations of thermodynamic equations and are evaluated with respect to the condition number of the corresponding Jacobian matrix and the ability to trace different types of phase diagrams.

Can cholinium chloride form eutectic solvents with organic chloride-based salts?

The high melting point of a large number of organic salts with potential ionic liquid-like properties, hinders their applicability as solvents. Considering the success of cholinium chloride on lowering the melting temperature of several substances and its success on forming deep eutectic solvents, this work studies its mixing with organic chlorides to lower their melting points producing eutectic ionic liquids.The solid-liquid phase diagrams for binary mixtures composed of cholinium chloride and ten organic halides were experimentally measured. Surprisingly, cholinium chloride presented, for all these systems, significant positive deviations from ideal liquid behaviour that restricted its ability to lower the melting points of these mixtures. Only for mixtures with ammonium chloride, tetramethylammonium chloride, bis(2-hydroxyethyl)dimethylammonium chloride or cholinium bromide was cholinium chloride able to significantly lower the melting point of the mixture, but without reaching values close to room temperature (298 K). For a better understanding of the results obtained, the solid-liquid phase diagrams of four alkylammonium chloride-based mixtures were experimentally assessed and used to show that these compounds are better than cholinium chloride at inducing negative deviations from ideality, leading to greater melting point depressions.

Phase Boundary of Frank–Kasper σ Phase in Phase Diagrams of Binary Mixtures of Block Copolymers and Homopolymers

The Frank–Kasper σ phase and the dodecagonal quasicrystal (DDQC) have been found in binary mixtures of block copolymers and homopolymers. In this study, the effect of the molecular weight length an...

Особливості розрахунку для процесів екстракції матеріального балансу трьохфазних сумішей

Мета: Вдосконалення алгоритму розрахунку рівноваги рідина-рідина-пара для бінарних та трьохкомпонентних сумішей (для процесів екстракції). Методи: Аналіз фазових діаграм, моделювання відсікання частини рівноважної фази, алгебраїчні перетворення системи рівнянь задачі одноразового випаровування трьохфазної суміші заданого складу. Результати: Для двох типів фазових діаграм двокомпонентних сумішей з обмеженою розчинністю компонентів в рідкій фазі отримані обмеження на можливі значення молярних часток парової та двох рідких фаз за умов рівноваги рідина-рідина-пара для суміші заданого загального складу. Для трьохкомпонентних сумішей отримані аналітичні вирази для розрахунку складів трьох фаз за заданими двома наборами коефіцієнтів розподілу. Отримані формули для розрахунку молярних часток парової та двох рідких фаз за заданим загальним складом суміші. Наведені формули застосовані для розрахунку трьохфазної рівноваги суміші бутилен-н-бутан-вода на підставі законів Рауля та Генрі. Обговорення: Для трьохкомпонентних сумішей для орієнтовних розрахунків можна застосувати отримані формули як для визначення складів співіснуючих рівноважних фаз, так і для визначення молярних часток фаз. Для бінарних сумішей доцільно доповнити вхідну інформацію задачі одноразового випаровування суміші заданого складу припустимим значенням молярної частки парової фази.

Molecular simulation of binary phase diagrams from the osmotic equilibrium method: vapour pressure and activity in water–ethanol mixtures

ABSTRACTHerein, an approach for simulating phase diagrams of binary mixtures is presented, where a bulk liquid and its corresponding vapour phase are simulated by means of molecular dynamics using explicit polarisation. Time-averaged density profiles for the pure compounds and mixtures at different mole fractions provide information about the spatial distribution in the bulk liquid and the amount of evaporated species in the adjacent vapour phase. The activities in the liquid phase are calculated from the mean vapour phase densities at a given composition, providing a good qualitative agreement compared to experimental data and the precision of the method follows a previously developed Poisson model of evaporation. With the Redlich–Kister approach for the activities in a binary mixture, the directly obtained activities are fitted providing corrected activity coefficients of the two species. This method is applied to ethanol water mixtures at different mole fractions. The obtained structural data are in good agreement with experimental data and time-averaged density profiles provide a detailed insight into the composition of the liquid–vapour interface. An azeotropic point is obtained for an excess concentration of ethanol at 87% as percentage by mass compared to the experimental value of 95%.

Miscibility and carrier transport properties in binary blend system of non-peripherally octa-hexyl-substituted phthalocyanine analogues

The thermal phase transition and charge carrier mobility in binary mixtures of the liquid crystalline phthalocyanine 1,4,8,11,15,18,22,25-octahexylphthalocyanine (C6PcH2) and its analogue 1,4,8,11,15,18,22,25-octahexyltetrabenzotriazaporphyrin (C6TBTAPH2) were studied, and the relationship between the miscibility and carrier transport properties is discussed. The phase diagram for binary mixtures consisting of C6PcH2 and C6TBTAPH2 was determined by differential scanning calorimetry and X-ray diffraction analysis. The hole mobilities in the columnar mesophase and crystal phase were evaluated by the time-of-flight technique. The complete miscibility in the columnar mesophase and the limited miscibility in the crystal phase were clarified. The dependence of the hole mobility on the blend ratio of C6PcH2 to C6TBTAPH2 is discussed by taking the molecular packing structure into consideration.

Solid liquid phase diagrams of binary fatty acid mixtures—Palmitic/stearic with oleic/linoleic/linolenic acid mixture

The solid liquid phase diagrams of binary mixtures of the five main saturated and unsaturated fatty acids present in most edible plant oils have been determined in this paper. These binary mixtures comprise of a saturated fatty acid, either palmitic (C16:0) or stearic (C18:0) and an unsaturated one, oleic (C18:1), linoleic (C18:2) or linolenic (C18:3) acid. Differential scanning calorimetry (DSC) was used to obtain an overview of the solid liquid transition behaviour including the metastable ranges of these mixtures. In order to describe all the phase transformations in these systems, the boundary functions have been determined and compared. Phase diagrams determined, illustrate characteristic behaviour in accordance to literature. This work specifically focuses on to describe the solid liquid transitions of the mixtures and not on every single transition or reaction. This paper contributes to the elucidation of the phase behaviour of these important mixtures which are applied in diverse industries.

(Solid + liquid) equilibrium phase diagrams in binary mixtures containing terpenes: New experimental data and analysis of several modelling strategies with modified UNIFAC (Dortmund) and PC-SAFT equation of state

In this study, interactions between terpenes and alcohols or hydrocarbons have been considered and investigated. With this aim, the (solid + liquid) equilibrium (SLE) phase diagrams for binary systems of {(−)-menthol, or thymol + 1-decanol, or benzyl alcohol, or 2-cyclohexanethanol, or n-decane} were determined at ambient pressure. A dynamic method was used over a broad range of terpene mole fraction and temperature. The simple eutectic mixtures with a complete miscibility in the liquid phase were detected for all systems. The basic thermal properties of the pure terpenes and some solvents, i.e. melting temperatures as well as the enthalpy of fusion, have been measured with differential scanning calorimetry. Thermodynamic modelling of the phase diagrams in terms of the well-known group contribution method modified UNIFAC (Dortmund) as well as molecular-based PC-SAFT equation of state, was carried out in order to assess overall performance of these approaches when used to describe SLE in such complex cross-associating mixtures like these under study. In particular, different predictive strategies for assessing the binary interaction parameters of PC-SAFT model were proposed and tested.

Sedimentation stacking diagrams of binary mixtures of thick and thin hard rods.

We use Onsager theory and the local density approximation to study sedimentation-diffusion equilibrium density profiles of binary mixtures of thick and thin hard rods. We construct stacking diagrams for three diameter ratios, and find that even a simple spindle-shaped phase diagram with only isotropic-nematic demixing can lead to counter-intuitive stacking sequences such as an isotropic phase sandwiched between two nematic phases. For the most complex phase diagram considered here, we find sixteen distinct stacking sequences, including several with five sedimented layers. By adding sedimentation paths to composition-pressure and density-density phase diagrams and calculating density and composition profiles, we show that conclusions about bulk phase diagrams of binary mixtures on the basis of sedimentation-diffusion equilibria should be drawn warily.

Phase diagram of two-dimensional binary Yukawa mixtures

ABSTRACTWe have used Ramakrishnan–Yussouff (RY) density functional theory (DFT) to explore the topology of the phase diagram of two-component charge stabilised colloidal suspensions confined to a two-dimensional plane. The particles of the system interact via purely repulsive soft core Yukawa potential. Pair correlation functions (PCFs) used as input informations in DFT were calculated by solving both the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories. To test the relative performance of the HNC and PY theories in the context of phase transitions, we have also studied the corresponding one-component systems. We found that RY DFT with HNC PCFs does not stabilise solid in both the one- and two-component cases, whereas the PY theory does. By considering the freezing into the substitutionally disordered triangular solid, we found that the temperature-composition phase diagrams of the binary mixture are narrow spindles whose thickness depends on the symmetry of the mixture components and the value of the screening constant of the Yukawa potential. Although the phase diagram obtained by RY DFT with structural inputs calculated by the PY theory is found to be shifted to higher temperature region in the temperature-composition plane, however, it captures qualitatively all the essential features of the phase diagram. Our results are in principle verifiable through computer simulations and experiments.

Force-Field Based Quasi-Chemical Method for Rapid Evaluation of Binary Phase Diagrams.

We present the Pair Configurations to Molecular Activity Coefficients (PAC-MAC) method. The method is based on the pair sampling technique of Blanco (Fan, C. F.; Olafson, B. D.; Blanco, M.; Hsu, S. L. Application of Molecular Simulation to Derive Phase Diagrams of Binary Mixtures. Macromolecules 1992, 25, 3667-3676) with an extension that takes the packing of the molecules into account by a free energy model. The intermolecular energy is calculated using classical force fields. PAC-MAC is able to predict activity coefficients and corresponding vapor-liquid equilibrium diagrams at least 4 orders of magnitude faster than molecular simulations. The accuracy of the PAC-MAC method is tested by comparing the results with experimental data and with the results of the COSMO-SAC model (Lin, S.-T.; Sandler, S. I. A Priori Phase Equilibrium Prediction from a Segment Contribution Solvation Model. Ind. Eng. Chem. Res. 2002, 41, 899-913). PAC-MAC (using the OPLS-aa force field) is shown to be comparable in accuracy to COSMO-SAC, at the considerable advantage that PAC-MAC in principle does not require quantum calculation, provided proper force fields to be available.

Tuning the mesomorphic properties of carbosilane-terminated and conventional 2-alkoxy-5-(4-alkoxyphenyl)-1,3,4-thiadiazole liquid crystals as binary mixtures with bimodal length distributions

The phase diagrams of binary mixtures of smectic C (SmC) mesogens – the carbosilane-terminated mesogen 2-(6-chlorohexyloxy)-5-(4-(12,12,14,14,16,16-hexamethyl-12,14,16-trisilaheptadecyloxy)phenyl)-1,3,4-thiadiazole (QL13-6) and one of nine conventional 2-alkoxy-5-(4-alkoxyphenyl)-1,3,4-thiadiazole mesogens (QL14-m/n) – with a molecular length ratio QL13-6/QL14-m/n ranging from 1.24 to 1.46 show the induction of a smectic A (SmA) phase in the mole fraction range 0.1 ≤ xQL13-6 ≤ 0.6. The results show that the temperature range of the induced SmA phase is remarkably sensitive to the molecular length ratio, and that this approach to tuning the mesomorphic properties of SmA–SmC liquid crystal mixtures may provide a powerful new tool in the formulation of mixtures for SSFLC and electroclinic applications.

On the phase and interface behavior along the three-phase line of ternary Lennard-Jones mixtures: a collaborative approach based on square gradient theory and molecular dynamics simulations.

This work focuses on the application of a two-way approach, where Molecular Dynamics (MD) simulations and the Square Gradient Theory (SGT) have been used for describing the phase and interface behavior of binary and ternary Lennard-Jones (LJ) mixtures, along a condition of three-phase equilibrium. The unequivocal correspondence between MD and SGT has been achieved by using the global phase diagram of binary mixtures composed by equally sized Lennard-Jones molecules, from which representative molecular parameters for Type-I, Type-II, and Type-III systems have been determined. The so selected binaries have been used then to scale the behavior of a ternary mixture characterized by complex phase equilibrium patterns. For the case of the theoretical SGT approach applied to the Lennard-Jones equation of state was used for predicting phase equilibrium and interfacial properties. In addition the corresponding MD simulations of these macroscopic properties have been conducted for the LJ potential by using equivalent molecular parameters and conditions than in the theoretical approach. Excellent agreement has been observed between the predictions obtained from theory and simulations. Particularly, our results concerning the characterization of the three phase line of a binary Type-III mixture indicate that the bulk liquid (α) and the bulk gas (G) regions are sharply separated by a bulk liquid region (β) for all the explored temperature, pressure, and concentration conditions. The structural analysis of these bulk phases reveals that a secondary liquid phase (β) perfectly wets the liquid-gas interface (α-G), as previously found for Type-II mixture [A. Mejía and L. F. Vega, J. Chem. Phys. 124, 244505 (2006)]. The exploration along the three-phase line for the ternary mixture shows good agreement between SGT and MD. Particularly, we observed the specific influence of a third component in the phase and interface behavior. From all the previous results, we conclude that the SGT applied to an EoS with appropriate mixing rules produces reliable predictions of the properties of ternary mixtures.

On the solid–liquid phase diagrams of binary mixtures of even saturated fatty alcohols: Systems exhibiting peritectic reaction

Abstract The solid–liquid phase diagrams of the following binary mixtures of even saturated fatty alcohols are reported in the literature for the first time: 1-octanol (C8OH) + 1-decanol (C10OH), 1-decanol + 1-dodecanol (C12OH), 1-dodecanol + 1-hexadecanol (C16OH) and 1-tetradecanol (C14OH) + 1-octadecanol (C18OH). The phase diagrams were obtained by differential scanning calorimetry (DSC) using a linear heating rate of 1 K min−1 and further investigated by using a stepscan DSC method. X-ray diffraction (XRD) and polarized light microscopy were also used to complement the characterization of the phase diagrams which have shown a complex global behavior, presenting not only peritectic and eutectic reactions, but also the metatectic reaction and partial immiscibility on solid state.