Solid-fluid and solid-solid phase equilibrium in a model of n-alkane mixtures

Solid-fluid and solid-solid phase equilibrium for binary mixtures of hard sphere chains modeling n-hexane, n-heptane, and n-octane has been calculated using Monte Carlo computer simulations. Thermodynamic integration was used to calculate the Gibbs free energy and chemical potentials in the solid and fluid phases from pure component reference values. A multiple stage free energy perturbation method was used to calculate the composition derivative of the Gibbs free energy. Equation of state and free energy data for the fluid phase indicate ideal solution behavior. Nonideality is much more significant in the solid phase with only partial solubility of shorter chains in the longer chains and essentially no solubility at the other end of the composition range. The miscibility decreases with increasing chain length difference between the components. For the model of n-hexane/n-octane mixtures solid--solid phase separation has been observed directly in some of the simulations, with the components segregating between the layers of the solid structure. The behavior is similar to that seen in some binary n-alkane mixtures with longer chain lengths but comparable chain length ratios between the components. Such phase separation, although indicated thermodynamically, is not seen directly in the simulations of the n-heptane/n-octane mixture due to the difference in the pure component crystal structures.     

Theory of the thermodynamic properties of binary mixtures of organic molecules with size mismatch

The Flory expression for the Gibbs free energy of mixing of a binary mixture is improved by introducing a hard-sphere form for the entropy of mixing. The resulting expression is used to describe the characteristic features of organic mixtures of globular molecules with size mismatch. In particular, we show that the above model, with an interchange energy depending on temperature, accounts for the thermodynamic properties and concentration fluctuations of a number of octamethylcyclotetrasiloxane-based mixtures.     

Induced smectic phases in phase diagrams of binary nematic liquid crystal mixtures

To elucidate induced smectic A and smectic B phases in binary nematic liquid crystal mixtures, a generalized thermodynamic model has been developed in the framework of a combined Flory-Huggins free energy for isotropic mixing, Maier-Saupe free energy for orientational ordering, McMillan free energy for smectic ordering, Chandrasekhar-Clark free energy for hexagonal ordering, and phase field free energy for crystal solidification. Although nematic constituents have no smectic phase, the complexation between these constituent liquid crystal molecules in their mixture resulted in a more stable ordered phase such as smectic A or B phases. Various phase transitions of crystal-smectic, smectic-nematic, and nematic-isotropic phases have been determined by minimizing the above combined free energies with respect to each order parameter of these mesophases. By changing the strengths of anisotropic interaction and hexagonal interaction parameters, the present model captures the induced smectic A or smectic B phases of the binary nematic mixtures. Of particular importance is the fact that the calculated phase diagrams show remarkable agreement with the experimental phase diagrams of binary nematic liquid crystal mixtures involving induced smectic A or induced smectic B phase.     

Bulk and interfacial wetting behavior of binary mixtures induced by associating between unlike-pair molecules

The statistical associating fluid theory of Wertheim is applied to describe binary mixtures with associating between unlike-pair molecules. The phase behavior of this binary mixture would fall into five different types (I, II, III, V, and VI) of the classification scheme of van Konynenburg and Scott by varying the associating strength and the energy parameters. Both interfacial wetting behavior and wetting transitions are carefully examined in all the vapor-liquid-liquid (gamma-beta-alpha) three-phase-coexisting regions of the binary mixtures. The global wetting behavior and wetting transitions are delineated by scanning the parameter space. In certain regions, the middle beta phase exhibits interfacial phase transitions sequentially, nonwetting --> partial-wetting --> nonwetting, at the interface separating lower alpha and upper gamma phases along with increasing temperature.     

A new grand canonical ensemble method to calculate first-order phase transitions

A theory about first-order phase transition of pure fluids is proposed. The theory is developed by combining grand canonical ensemble with density functional for homogeneous fluids. It is based on the fact that the grand partition function of one macroscopic volume is the product of the grand partition functions of its subvolumes. Density fluctuations of molecules determine the relation between the grand partition function and the free energy density. By combining pairs of subvolumes successively, the free energy density is transformed and rapidly becomes stationary. The stationary curve versus molecule density is convex and its linear segments represent phase transitions. The transform leads to the new grand canonical method to calculate phase equilibrium, which is more robust than classic ones. The transform suggests that classical van der Waals loop is physical and essential to phase transition.     

Bubble point measurements of binary mixtures formed by ethyl benzene with selected compounds at 95.35 kPa

Bubble point temperatures (at 95.35 kPa) over the entire composition range were measured for the binary mixtures formed by ethyl benzene with: acetyl acetone, o-, and p-cresols, 1-hexanol, and tetraethoxysilane, employing a Swietoslawski type ebulliometer. Wilson equation was used to represent the measured liquid phase composition versus bubble point temperature data, and the computed values of the vapor phase mole fractions, activity coefficients, and excess Gibbs free energy were tabulated and briefly discussed.     

Synergy in lipofection by cationic lipid mixtures: superior activity at the gel-liquid crystalline phase transition

Some mixtures of two cationic lipids including phospholipid compounds (O-ethylphosphatidylcholines) as well as common, commercially available cationic lipids, such as dimethylammonium bromides and trimethylammonium propanes, deliver therapeutic DNA considerably more efficiently than do the separate molecules. In an effort to rationalize this widespread "mixture synergism", we examined the phase behavior of the cationic lipid mixtures and constructed their binary phase diagrams. Among a group of more than 50 formulations, the compositions with maximum delivery activity resided unambiguously in the solid-liquid crystalline two-phase region at physiological temperature. Thus, the transfection efficacy of formulations exhibiting solid-liquid crystalline phase coexistence is more than 5 times higher than that of formulations in the gel (solid) phase and over twice that of liquid crystalline formulations; phase coexistence occurring at physiological temperature thus appears to contribute significantly to mixture synergism. This relationship between delivery activity and physical property can be rationalized on the basis of the known consequences of lipid-phase transitions, namely, the accumulation of defects and increased disorder at solid-liquid crystalline phase boundaries. Packing defects at the borders of coexisting solid and liquid crystalline domains, as well as large local density fluctuations, could be responsible for the enhanced fusogenicity of mixtures. This study leads to the important conclusion that manipulating the composition of the lipid carriers so that their phase transition takes place at physiological temperature can enhance their delivery efficacy.     

Estimation of infinite dilution activity coefficients in aqueous mixtures via molecular simulation

Molecular dynamics simulations are employed to calculate infinite dilution activity coefficients of water and methanol-like species in binary mixtures using a variant of the Kirkwood coupling parameter method. Differences in residual Gibbs free energies are obtained as integrals over ensemble averages of the derivatives of total potential energy with respect to simple functions of the intramolecular potential energy parameters. The calculated limiting activity coefficients are compared with the experimental values at the same temperature obtained by direct measurement of the water/methanol binary and via extrapolation from vapor–liquid equilibria data.     

Composition of Surface Layer at the Water–Air Interface and Micelles of Triton X-100 + Rhamnolipid Mixtures

Measurements of the surface tensions, densities and viscosities of aqueous solutions of Triton X-100 (TX-100) and rhamnolipid (RL) mixtures, at constant concentration of RL or TX-100, were carried out. The measured values of the surface tension were compared to those determined using different theoretical models and on the basis of the surface tension of aqueous solutions of individual surfactants. From the surface tension isotherms, the Gibbs surface excess concentration of TX-100 and RL, the composition of surface layer and the standard Gibbs free energy of adsorption at the water–air interface were determined. Moreover, on the basis of surface tension, density and viscosity isotherms, the CMC of surfactants mixtures were evaluated. From the density isotherms, apparent and partial molar volumes of TX-100 and RL were also determined. These volumes were compared to those calculated from the sizes of TX-100 and RL molecules. There was observed a synergetic effect in the reduction of water surface tension and micelle formation, which was confirmed by the intermolecular interactions parameter. In the case of micelle formation, this effect was discussed based on the standard Gibbs free energy of micellization as well as of TX-100 and RL mixing in the micelles. The synergism of TX-100 and RL mixtures in the reduction of water surface tension and micelle formation was explained on the basis of electrostatic interactions between the hydrophilic part of TX-100 and RL molecules; this was supported by pH measurements.     

Thermodynamic aspects of phase equilibrium in binary water–organic solvent mixtures

It is shown that the boundary curves of liquid equilibria in binary systems characterize the temperature–concentration boundary of the existence of homogeneous mixtures whose formation is not accompanied by changes in the Gibbs energy of the system and are a combination of two branches that do not convert into each other but intersect at the temperature of homogenization of a mixture of critical composition. The phase diagrams of a number of water–organic solvent systems are analyzed to determine the thermodynamic particularities of the latter.

     

Molecular simulation of the phase behaviour of ternary fluid mixtures: the effect of a third component on vapour–liquid and liquid–liquid coexistence

The Gibbs ensemble algorithm is implemented to determine the vapour–liquid and liquid–liquid phase coexistence of dilute ternary fluid mixtures interacting via a Lennard–Jones potential. Calculations are reported for mixtures with a third component characterised by different intermolecular potential energy parameters. Comparison with binary mixture data indicates that the choice of energy parameter for the third component affects the composition range of vapour–liquid substantially. The addition of a third component lowers the energy of liquid phase while slightly increasing the energy of the vapour phase.     

Prediction of thermodynamic properties of polymer solutions by a group-contribution method

The Flory–Huggins lattice-theory expression for solvent activity in a polymer-solution is commonly used to calculate the thermodynamic interaction parameter χ with the aid of experimental data from vapor pressure osmometry. This expression assumes that χ is independent of composition. However, experimental data for a variety of polymer-solvent mixtures indicate that χ exhibits an appreciable concentration dependence. A group contribution method, UNIFAC (UNIQUAC Functional-Group Activity Coefficients) incorporating the free-volume correction of Oishi and Prausnitz is used to predict the dependence of χ on solvent concentration. Agreement with previously reported experimental data is within 15%. Calculated values of χ obtained from the Flory–Huggins expression for solvent activity and from the corresponding Gibbs free energy of mixing (which does not assume that χ is independent of composition) are compared. Calculations based on the Gibbs free energy of mixing predict a somewhat larger value of χ relative to those based on solvent activity. The specific Gibbs free energy of mixing for polystyrene-solvent mixtures is calculated using the UNIFAC model, and is found to represent qualitatively the phase equilibrium behavior. Quantitative discrepancies are observed, however, for the polystyrene-acetone system in light of the actual experimental solubility reported by Suh and Clark (20). Most of the thermodynamic predictions for polymer-solvent systems investigated herein are correlated qualitatively with the relative mismatch between solubility parameters of both components.     

Excess Gibbs Energy of Mixing for Organic Carbonates from Fitting of Their Binary Phase Diagrams with Nonideal Solution Models

The excess Gibbs energies of mixing in the liquid state were evaluated for all the ten binary combinations of these five organic carbonates: ethylene carbonate (EC), propylene carbonate, dimethyl carbonate (DMC), ethyl methyl carbonate, and diethyl carbonate by fitting their measured binary phase diagrams with thermodynamic nonideal solution models based on the regular solution model. Using the results of these model fits, activity coefficients of the components in the solvent mixtures were calculated for the binary series containing EC and DMC as the common component, and the composition-averaged excess Gibbs energies of mixing were calculated by integrating the energy in the whole composition range for all the binaries. The results showed the excess Gibbs energy of mixing, and therefore the intermolecular forces, to be responsible for the changes in the phase diagrams, in the activity coefficients, and in the composition-averaged excess energy for the different binary solution combinations.     

Study of Molecular Interactions in Binary Mixtures of Aniline with Carboxylic Acids at 293.15 K, 303.15 K and 313.15 K

Ultrasonic velocity, density, refractive index and viscosity of binary mixtures of aniline with acetic acid (AA) and propionic acid (PA) have been measured at 293.15, 303.15 and 313.15 K over the entire composition range. Further, the specific heat ratio, heat capacity, effective Debye temperature and pseudo-Gruensisen parameter and non-linearity parameter have been evaluated using ultrasonic absorption data. The deviation in isentropic compressibility, excess molar volume, excess intermolecular free length, deviation in molar refraction, deviation in viscosity, relaxation time, enthalpy, entropy and Gibbs energy of activation have been calculated from the experimental data and fitted with the Redlich-Kister polynomial equation. A comparative study has also been made between experimental and theoretically calculated values of densities using the HBT and Rackett density models. Mixing rules for the prediction of refractive index, e.g. Lorentz-Lorenz (L-L), Eykmen (Eyk), Weiner (W), Heller (H), Gladstone-Dale (G-D), Arago-Biot (A-B) and Newton (N) have been applied to these binary mixtures.     

The Prediction of Surface Tension and Thermodynamic Analysis of the Surface in Mixtures of Cryogenic Liquids

The surface tensions of 42 binary cryogenic mixtures at low temperature are correlated using the Shereshefsky model and excellent results are obtained. The average percent deviation is about ～ 1.08%. The Gibbs energy change in the surface region is calculated and is used to obtain the excess number of molecular layers in the surface region. Furthermore, the model is used to derive an equation for the standard Gibbs energy of adsorption. The experimental standard Gibbs energy of adsorption is obtained from surface tension data and compared with calculated data. The agreement between experimental and calculated data is found to be very good. The magnitude of the Gibbs energy change in the surface region and the standard Gibbs energy of adsorption are discussed in terms of nature and type of intermolecular interactions in binary mixtures.     

A molecular theory for the thermodynamic behavior of polar mixtures. II. Development of an equation of state based on the local composition mixing rules

In this study, the essential features of a molecular theory developed earlier for the local composition model in solution thermodynamics is used as the basis for more applied calculations of vapor-liquid equilibria for mixtures of molecules vastly different in size, polarity, and strength of interaction. An accurate equation of state is introduced into the method by incorporating the Helmholtz free energy through the Gibbs-Helmholtz relation. In the local composition mixing rules, the interaction energy effects are represented by a multifluid model, while molecular size effects are represented by a one-fluid model, which in spirit corresponds to a mean density approximation for the molecular pair distribution functions. Calculations of the vapor-liquid equilibria of a wide variety of binary mixtures including nonpolar hydrocarbons, hydrogen-bonding alcohols, water, ammonia , and carbon dioxide show good agreement with experimental data.     

Equilibrium density fluctuations and the rate of a Langmuir-Hinshelwood type reaction on microcrystal particles

We investigate the effect of restricting the area of planes of microcrystals and equilibrium density fluctuations in components of binary mixtures on partial isotherms of the adsorption of binary mixtures of molecules and the rate of a surface reaction of the Langmuir-Hinshelwood type. Adsorption of components of mixture is considered in a large canonical assembly, and the rate of an elementary step is calculated in kinetic regime. The value of a section of the surface on a plane contains a number of adsorption centers in the range of 10 to 10⁵. The effect of the structure of a heterogeneous surface on the rate of the considered reaction is studied. The effect of the density fluctuations of adsorbed molecules on partial adsorption isotherms and fluctuations in the rate of reaction on heterogeneous surfaces is discussed. It is shown that the greatest effect of density fluctuations on the rate of a step is observed at low fillings of each plane of a particle and at the almost complete filling of a plane.     

PHYSICAL-CHEMICAL BEHAVIOR OF CONFECTIONERY FATS

Confectionery coatings employ hard butter fat systems made from both lauric and non-lauric source oils. These oils are routinely modified by a combination of treatments including hydrogenation, fractionation and interesterification to achieve desired physical properties. Such processing methods create heterogeneous triglyceride mixtures consisting of a variety of compositional and positional isomers. Published phase diagrams of “simple” binary triglyceride mixtures of closely related molecules are complex, and suggest that innumberable unique liquid and solid phases may co-exist at any given temperature ( and pressure ) in vastly more complex triglyceride mixtures such as confectionery hard butters. Thus we may view confectionery fat systems as multiphasic mixtures (liquid, solid and compositional) with a propensity to undergo liquid content fluctuations and crystal size/morphology changes in response to slight changes in temperature. A true equilibrium among all phases may indeed never be attained, and a potential for movement of certain components in response to temperature change is probably constant. Surface growth of long needle-like fat crystals, “fat bloom”, most likely results from this non-equilibrium condition and serves to reduce the system's free energy. The ever present, ever changing liquid phase(s) is viewed as the vehicle for free energy minimization via triglyceride migration and ongoing crystal growth.