One-phase Region Research Articles

Modeling the Polystyrene–Asphaltenes–Toluene Mixture Using the Perturbed-Chain Form of Statistical Associating Fluid Theory Equation of State

Typically, the addition of a non-adsorbing polymer to a system containing colloidal particles causes a phase separation in a mechanism known as depletion flocculation. Recent experiments have shown that the addition of polystyrene to a mixture of asphaltenes and toluene causes phase separation into two liquids.1 In this paper, this effect is modeled using the perturbed-chain form of statistical associating fluid theory (PC-SAFT) equation of state, demonstrating agreement with the experimental data. The effects of the temperature, pressure, and polystyrene mean molecular weight on the mixture phase behavior are investigated. The phase behavior of the system was not sensitive to pressures up to 1500 atm; however, increasing the temperature or reducing the mean molecular weight of polystyrene caused the one-phase region to expand. The paper demonstrates that a solution model with rigorous physics is able to capture the phase behavior that is typically described as a depletion flocculation mechanism in the co...

Phase-field modeling of mixing/demixing of regular binary mixtures with a composition-dependent viscosity

We simulate the mixing (demixing) process of a quiescent binary liquid mixture with a composition-dependent viscosity which is instantaneously brought from the two-phase (one-phase) to the one-phase (two-phase) region of its phase diagram. Our theoretical approach follows a standard diffuse-interface model of partially miscible regular binary mixtures wherein convection and diffusion are coupled via a nonequilibrium capillary force, expressing the tendency of the phase-separating system to minimize its free energy. Based on 2D simulation results, we discuss the influence of viscosity ratio on basic statistics of the mixing (segregation) process triggered by a rapid heating (quench), assuming that the ratio of capillary to viscous forces (a.k.a. the fluidity coefficient) is large. We show that, for a phase-separating system, at a fixed value of the fluidity coefficient (with the continuous phase viscosity taken as a reference), the separation depth and the characteristic length of single-phase microdomains decrease monotonically for increasing values of the viscosity of the dispersed phase. This variation, however, is quite small, in agreement with experimental results. On the other hand, as one might expect, at a fixed viscosity of the dispersed phase both of the above statistics increase monotonically as the viscosity of the continuous phase decreases. Finally, we show that for a mixing system the attainment of a single-phase equilibrium state by coalescence and diffusion is retarded by an increase in the viscosity ratio at a fixed fluidity for the dispersed phase. In fact, for large enough values of the viscosity ratio, a thin film of the continuous phase becomes apparent when two drops of the minority phase approach each other, which further retards coalescence.

A pseudo-quantitative ternary surfactant ion mixing plane phase diagram for a cationic hydroxyethyl cellulose with dodecyl sulfate counterion complex salt

The surfactant ion mixing plane phase diagram was constructed for cationic hydroxyethyl cellulose dodecyl sulfate (cat-HECDS), sodium dodecyl sulfate (NaDS) and water. The number of phases and structures present in the prepared ternary composition were assessed visually and guided the placement of phase boundaries. Two multi-phase regions surround a large, central one-phase isotropic region. In the dilute portion of the diagram, an isotropic-isotropic two-phase region exists along the water-complex salt axis. A concentrated multi-phase region adjacent to the water-NaDS axis includes a three-phase region defined as isotropic-hexagonal-monoclinic surrounded by three two-phase regions of isotropic-monoclinic, isotropic-hexagonal, and hexagonal-monoclinic.This phase diagram is similar to one previously published in this journal [Svensson et al., Colloids Surf. A, 228 (2003) 91–106]. Here the degree of cationic substitution on the polymer was reduced by half. This resulted in a shift in the locations of the phase boundaries, but not the phases and structures, present in this plane. Evaluating the phase boundaries as a function of anion:cation molar ratio highlighted the impact of the hydrophobic binding of excess surfactant monomers to the polycation-surfactant anion network on the phase transitions in the surfactant ion mixing plane phase diagrams for cat-HECDS.

Stationary and transient Soret separation in a binary mixture with a consolute critical point.

The stationary and transient Soret separation in a binary mixture with a consolute critical point is studied theoretically. The mixture is placed between two parallel plates kept at different temperatures. A polymer blend is used as a model system. Analytical solutions are constructed to describe the stationary separation in a binary mixture with variable Soret coefficient. The latter strongly depends on temperature and concentration and enhances near a consolute critical point due to reduced diffusion. As a result, a large concentration gradient is observed locally, while much smaller concentration variations are found in the rest of the layer. It is shown that complete separation can be obtained by applying a small temperature difference first, waiting for the establishment of stationary state, and then increasing this difference again. In this case, the critical temperature lies between hot and cold wall temperatures, while the mixture still remains in the one-phase region. When the initial (mean) temperature or concentration are shifted away from the near-critical values, the separation decreases. The analysis of transient behavior shows that the Soret separation occurs much faster than diffusion to the homogeneous state when the initial concentration is close to the critical one. It happens due to the decrease (increase) of the local relaxation time during the Soret (Diffusion) steps. The transient times of these steps become comparable for small temperature differences or off-critical initial concentrations. An unusual (non-exponential) separation dynamics is observed when the separation starts in the off-critical domain, and then enhances greatly when the system enters into the near-critical region. It is also found that the transient time decreases with increasing the applied temperature difference.

Phase behavior of a binary fluid mixture of quadrupolar molecules.

We propose a model molecule to investigate microscopic properties of a binary mixture with a closed-loop coexistence region. The molecule is comprised of a Lennard-Jones particle and a uniaxial quadrupole. Gibbs ensemble Monte Carlo simulations demonstrate that the high-density binary fluid of the molecules with the quadrupoles of the same magnitude but of the opposite signs can show closed-loop immiscibility. We find that an increase in the magnitude of the quadrupoles causes a shrinkage of the coexistence region. Molecular dynamics simulations also reveal that aggregates with two types of molecules arranged alternatively are formed in the stable one-phase region both above and below the coexistence region. String structures are dominant below the lower critical solution temperature, while branched aggregates are observed above the upper critical solution temperature. We conclude that the anisotropic interaction between the quadrupoles of the opposite signs plays a crucial role in controlling these properties of the phase behavior.

Budding transition of asymmetric two-component lipid domains.

We propose a model that accounts for the budding transition of asymmetric two-component lipid domains, where the two monolayers (leaflets) have different average compositions controlled by independent chemical potentials. Assuming a coupling between the local curvature and local lipid composition in each of the leaflets, we discuss the morphology and thermodynamic behavior of asymmetric lipid domains. The membrane free-energy contains three contributions: the bending energy, the line tension, and a Landau free-energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams containing fully budded, dimpled, and flat states as a function of the two leaflet compositions. The global phase behavior is analyzed, and depending on system parameters, the phase diagrams include one-phase, two-phase, and three-phase regions. In particular, we predict various phase coexistence regions between different morphologies of domains, which may be observed in multicomponent membranes or vesicles.

Water: A Tale of Two Liquids.

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

Critical phenomena in {bromobenzene + 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide} binary solution

The liquid-liquid coexistence curve for binary solution {bromobenzene + 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C6mim][NTf2])} has been measured in both critical and non-critical regions. The isobaric heat capacities per unit volume were measured in one-phase and two-phase regions. Moreover, the turbidity measurements were also performed in the near-critical one-phase region. From the liquid-liquid equilibrium, heat capacity and turbidity data collected in the critical region, the critical exponents α, β, γ and ν were obtained and shown to be consistent with those predicted for the 3D-Ising universality class. The universal critical amplitude ratios RB and X have been calculated and shown to reasonably coincide with the theoretical predicted values. The asymmetric behavior of the diameter of the coexistence curve was well described by the complete scaling theory, provided that the heat capacity related term was considered. Moreover, the coulombic criticality of the studied system was indicated by the small values of RPM reduced critical density and critical temperature.

Influence of Solution Composition on the Formation of Surface Nanodroplets by Solvent Exchange.

Solvent exchange is a simple process of forming surface nanodroplets on an immersed substrate. In this process, the droplets nucleate and grow in response to transient oversaturation when a good solvent of the droplet liquid is displaced by a poor solvent. Here we will show how the final droplet size is influenced by solution composition in the solvent exchange. To do this, we produced water droplets on a hydrophilic substrate and cyclohexane droplets on a hydrophobic substrate by using a tertiary system of cyclohexane, ethanol, and water. The composition of the good solvent was varied systematically in the one-phase region on the phase diagram. We found that the key feature closely related to the droplet size is the area (A) in the phase diagram defined by the phase boundary and the concentration ratio between the good solvent and the droplet liquid. This area reflects the excessive amount of droplet liquid in the tertiary mixture, which can be complicated by bulk droplet formation during solvent exchange. We will also show that the droplet volume per unit surface area also increases with A. The findings from this work will provide guideline for the selection of solution conditions to achieve a desirable droplet size and number density on the surface.

Gaussian-Charge Polarizable and Nonpolarizable Models for CO2.

A polarizable intermolecular potential model using three classical Drude oscillators on the atomic sites has been developed for CO2. The model is rigid with bond lengths and molecular geometries set to their experimental values. Electrostatic interactions are represented by three Gaussian charges connected to the molecular frame by harmonic springs. Nonelectrostatic interactions are represented by the Buckingham exponential-6 potential, with potential parameters optimized to vapor-liquid equilibria (VLE) data. A nonpolarizable CO2 model that shares the other ingredients of the polarizable model was also developed and optimized to VLE data. Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to evaluate the two models with respect to a variety of thermodynamic and transport properties, including the enthalpy of vaporization, second virial coefficient, density in the one-phase fluid region, isobaric and isochoric heat capacities, radial distribution functions, self-diffusion coefficient, and shear viscosity. Excellent agreement between model predictions and experimental data was found for all properties studied. The polarizable and nonpolarizable models provide a similar representation of CO2 properties, which indicates that the properties of pure CO2 fluid are not strongly affected by polarization. The polarizable model, which has an order of magnitude higher computational cost than the nonpolarizable model, will likely be useful for the study of a mixture of CO2 and polar components for which polarization is important.

Whipped oil stabilised by surfactant crystals.

We describe a protocol for preparing very stable air-in-oil foams starting with a one-phase oil solution of a fatty acid (myristic acid) in high oleic sunflower oil at high temperature. Upon cooling below the solubility limit, a two-phase mixture consisting of fatty acid crystals (length around 50 μm) dispersed in an oil solution at its solubility is formed which, after whipping, coat air bubbles in the foam. Foams which do not drain, coalesce or coarsen may be produced either by increasing the fatty acid concentration at fixed temperature or aerating the mixtures at different temperatures at constant concentration. We prove that molecular fatty acid is not surface-active as no foam is possible in the one-phase region. Once the two-phase region is reached, fatty acid crystals are shown to be surface-active enabling foam formation, and excess crystals serve to gel the continuous oil phase enhancing foam stability. A combination of rheology, X-ray diffraction and pulsed nuclear magnetic resonance is used to characterise the crystals and oil gels formed before aeration. The crystal-stabilised foams are temperature-sensitive, being rendered completely unstable on heating around the melting temperature of the crystals. The findings are extended to a range of vegetable oil foams stabilised by a combination of adsorbed crystals and gelling of the oil phase, which destabilise at different temperatures depending on the composition and type of fatty acid chains in the triglyceride molecules.

A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures

We consider the linear degenerate elliptic system of two first order equations ${\mathbf{u}}=-a(\phi)(\nabla{p} - \mathbf{g})$ and $\nabla\cdot(b(\phi)\mathbf{u})+\phi{p}=\phi^{1/2}{f}$, where $a$ and $b$ satisfy $a(0)=b(0)=0$ and are otherwise positive, and the porosity $\phi\ge0$ may be zero on a set of positive measure. This model equation has a similar degeneracy to that arising in the equations describing the mechanical system modeling the dynamics of partially melted materials, e.g., in the earth's mantle and in polar ice sheets and glaciers. In the context of mixture theory, $\phi$ represents the phase variable separating the solid one-phase ($\phi=0$) and fluid-solid two-phase ($\phi>0$) regions. The equations should remain well-posed as $\phi$ vanishes so that the free boundary between the one- and two-phase regions need not be found explicitly. Two main problems arise. First, as $\phi$ vanishes, one equation is lost. Second, it is shown by stability or energy bounds for the solution that the pre...

The influence of alkyl polyglucosides (and highly ethoxylated alcohol boosters) on the phase behavior of a water/toluene/technical alkyl polyethoxylate microemulsion system

The influence of additives (alkyl polyglucoside, Glucopon 600 CS UP and alcohol ethoxylate C18E100) on the behavior of the water/toluene/Lutensol ON 50 (technical oxoalcohol, i-C10E5) microemulsion system as a function of temperature and composition has been investigated. The phase behavior of the microemulsions was determined by vertical sections through the Gibbs phase prism (fish-like phase diagrams). Alkyl polyglucoside shifts the one phase region to lower temperatures compared with water/toluene/Lutensol ON 50 mixtures. This is contrary to the expectation, considering the extreme hydrophilic nature of the sugar headgroup. The addition of hydrophilic alcohol ethoxylate (C18E100) to the water/toluene/Lutensol ON 50 system increases the solubilization capacity of the surfactant, even if the co-surfactant is used in small quantities, and shifts the one-phase region to higher temperature by a few degrees Celsius.

Thermodynamics of self-assembling of mixture of a cationic gemini surfactant and sodium dodecylsulfate in aqueous solution: Calorimetry, conductivity and surface pressure measurements

The thermodynamics and phase behavior of mixtures of cationic gemini surfactant decanediyl-α,ω-bis(dodecyldimethylammonium bromide) (12-10-12) and sodium dodecylsulfate (SDS) were studied in the dilute SDS-rich region. The enthalpy of interaction between both surfactant monomers before the critical micelle concentration for the mixture (cmcmix) was determined by isothermal titration calorimetry (ITC). After the cmcmix, ITC results exhibited a first process associated with a large endothermic enthalpy change followed by a second one with a very small exothermic enthalpy change. In the same regions, the conductivity curves show an increase in slope after the break, followed by a plateau region, respectively for the two processes. The combined results from the various methodologies used lead us to propose that the first process reflects the formation of non-spherical micelles and the second one the vesicle formation. The area per catanionic complex was obtained through surface pressure measurements, leading to an apparent packing parameter ⩾1. The observed behavior may be rationalized on the basis of the hypothesis that both surfactants distribute asymmetrically in the vesicle bilayers and unevenly in the non-spherical micelle. In order to get structural information Cryo-TEM experiments were performed, which provided images that support this interpretation. From all the information gathered a phase diagram was mapped, including three one-phase regions of spherical micelles, non-spherical micelles and vesicles.

Surfactant-free alternative fuel: Phase behavior and diffusion properties

Phase behavior of the three components, 1-propanol, water and oil is studied at 10, 25, and 40°C. Biodiesel, limonene and diesel are used as oil phases. NMR self-diffusion measurements are performed to investigate the microstructure of the one-phase regions. Tie lines in the two-phase regions are determined both by proton NMR analysis and compared with theoretical calculations. NMR self-diffusion results for the different components in these systems do not show any sign of confinement or obstructions, demonstrating these mixtures to be structureless solutions. A good agreement between the experimental and calculated phase behavior is obtained. The determined tie lines in the two-phase regions show higher affinity of 1-propanol to water than to oil.

Measurements of heat capacities and turbidities for binary mixtures {water + 2,6-dimethylpyridine} and {water, or heavy water + 2,6-dimethylpiperidine} in the critical regions

The isobaric heat capacities per unit volume in both one-phase and two-phase regions and the turbidities in the one-phase region for the significantly asymmetric binary mixtures of {water + 2,6-dimethylpyridine} and {water, or heavy water + 2,6-dimethylpiperidine} were carefully measured, from which the corresponding critical exponents were obtained and found to be consistent with the 3D-Ising values. The values of the system-dependent critical amplitudes for the heat capacity, the correlation length and the osmotic compressibility were deduced, which together with the values of the critical amplitudes related to the coexistence curves reported previously were used to test some universal critical amplitude ratios. Moreover, the importance of the heat capacity related term in the formalism of the complete scaling theory was confirmed. It was also found that the complete scaling formalism possibly becomes somewhat inapplicable for the significantly asymmetric systems.

Critical Anomalies of Two SN1 Hydrolysis Reactions in Critical Binary Solutions.

Rates of SN1 hydrolysis reactions for 2-chloro-2-methylbutane in the critical solution of isobutyric acid + water and for 2-bromo-2-methylpropane in the critical solution of triethylamine + water in the one-phase region and at various temperatures have been determined respectively by conductance measurements. It was found that the reaction rates at different temperatures for those two SN1 reactions were well described by the Arrhenius equation in the noncritical region, whereas near the critical points the critical slowing down was clearly detected. These results are inconsistent with a previous report in the literature (J. Phys. Chem. A 2003, 107, 8435 - 8443). Reanalyzing the literature data, we found that if an Arrhenius equation appropriate to either the one-phase region or the two-phase region being examined was used as the background, a critical slowing down rather than a speeding up was detected for the reaction in both the one-phase region and the two-phase region. The experimental data from different sources were fitted with a simplified crossover formalism characterizing the critical effect on the reactions to determine the critical slowing down exponents, which were found to be about 0.04, showing that only a dynamic critical slowing down could be detected for these reaction systems. This phenomenon was attributed to the fact that the SN1 hydrolysis reaction is neither a first-order nor a pseudo-first-order reaction in the reverse direction and the kinetic measurements were carried out in a region quite far from the equilibrium of the reactions.

Phase Segregation at the Liquid-Air Interface Prior to Liquid-Liquid Equilibrium.

Binary systems with partial miscibility segregate into two liquid phases when their overall composition lies within the interval defined by the saturation points; out of this interval, there is one single phase, either solvent-rich or solute-rich. In most systems, in the one-phase regions, surface tension decreases with increasing solute concentration due to solute adsorption at the liquid-air interface. Therefore, the solute concentration at the surface is higher than in the bulk, leading to the hypothesis that phase segregation starts at the liquid-air interface with the formation of two surface phases, before the liquid-liquid equilibrium. This phenomenon is called surface segregation and is a step toward understanding liquid segregation at a molecular level and detailing the constitution of fluid interfaces. Surface segregation of aqueous binary systems of alkyl acetates with partial miscibility was theoretically demonstrated by means of a thermodynamic stability test based on energy minimization. Experimentally, the coexistence of two surface regions was verified through Brewster's angle microscopy. The observations were further interpreted with the aid of molecular dynamics simulations, which show the diffusion of the acetates from the bulk toward the liquid-air interface, where acetates aggregate into acetate-rich domains.

Anisometric Polyelectrolyte/Mixed Surfactant Nanoassemblies Formed by the Association of Poly(diallyldimethylammonium chloride) with Sodium Dodecyl Sulfate and Dodecyl Maltoside.

The soluble complexes of oppositely charged macromolecules and amphiphiles, formed in the one-phase concentration range, are usually described on the basis of the beads on a string model assuming spherelike bound surfactant micelles. However, around and above the charge neutralization ionic surfactant to polyion ratio, a variety of ordered structures of the precipitates and large polyion/surfactant aggregates have been reported for the different systems which are difficult to connect to globular-like surfactant self-assembly units. In this article we have demonstrated through SAXS measurements that the structure of precipitates and those of the soluble polyion/mixed surfactant complexes of poly(diallyldimethylammonium chloride) (PDADMAC), sodium dodecyl sulfate (SDS), and dodecyl-maltoside (DDM) are strongly correlated. Specifically, SDS binds to the PDADMAC molecules in the form of small cylindrical surfactant micelles even at very low SDS-to-PDADMAC ratios. In this way, these anisometric surfactant self-assemblies formed in excess polyelectrolyte mimic the basic building units of the hexagonal structure of the PDADMAC/SDS precipitate and/or suspensions formed at charge equivalence or at higher SDS-to-PDADMAC ratios. The presence of DDM reduces the cmc and cac for the system but does not alter significantly the structure of the complexes in either the one-phase or two-phase region. The only exception is for samples at SDS-to-PDADMAC ratios close to charge neutralization and a high concentration of DDM where the precipitate forms a multiphasic or distorted hexagonal structure.

Physics of the Jagla model as the liquid-liquid coexistence line slope varies.

The slope of the coexistence line of the liquid-liquid phase transition can be positive, negative, or zero. All three possibilities have been found in Monte-Carlo simulations of a modified spherically symmetric two-scale Jagla model. Since the liquid-liquid critical point frequently lies in a region of the phase diagram that is difficult to access experimentally, it is of great interest to study critical phenomena in the supercritical region. We therefore study the properties of the Widom line, defined in the one-phase region above the critical point as an extension of the coexistence line near which the loci of various response functions extrema asymptotically converge with each other. This phenomenon is predicted by the scaling theory according to which all response functions can be expressed asymptotically in the vicinity of a critical point as functions of the diverging correlation length. We find that the method of identifying the Widom line as the loci of heat capacity maxima becomes unfruitful when the slope of the coexistence line approaches zero in the T-P plane. In this case, the specific heat displays no maximum in the one-phase region because, for a horizontal phase coexistence line, according to the Clapeyron equation, the enthalpy difference between the coexisting phases is zero, and thus the critical fluctuations do not contribute to enthalpy fluctuations. The extension of the coexistence line beyond the critical point into the one-phase region must in this case be performed using density fluctuations. Although the line of compressibility maxima bifurcates into a symmetrical pair of lines, it remains well-defined. We also study how the glass transition changes as the slope of the coexistence line in the T-P plane approaches zero. We find that for the case of positive slopes, diffusivity shows a fragile-to-strong transition upon crossing the Widom line, while for horizontal slope, diffusivity shows the behavior typical for fragile liquids.