Critical points of adsorbed phases using a 2D lattice gas equation of state

The types of critical phase diagrams for adsorbed binary mixtures that can be predicted by an equation of state (EOS) based on a two-dimensional lattice gas theory are investigated. The search for critical point conditions was done using the Hicks and Young algorithm, switching to the Heidemann and Khalil algorithm in the close of vicinity of a critical point. We observed that the model can predict critical points that represent the conditions in which a vapor-like and a liquid-like adsorbed phases collapse. The critical diagrams were classified using an analogy with the van Konynenburg and Scott scheme for classifying the critical behavior of binary bulk mixtures. The original classification scheme is based on the critical lines on the pressure–temperature plane; we used a straightforward extension based on the critical lines on the spreading pressure–temperature plane. Five of the six types of phase behavior classified by von Konynenburg and Scott were observed using this thermodynamic model. The transitions between the types of phase diagram were also observed in temperature–mole fraction projections. These results extend previous observations that suggested the possibility of very interesting phase behaviors for adsorbed mixtures. However, experimental data would be necessary to confirm the predicted types of critical diagrams.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

Simulation of adsorption of liquid mixtures of N2 and O2 in a model faujasite cavity at 77.5 K

Grand canonical Monte Carlo simulations of adsorption of N₂ and O₂ and their mixtures in a model zeolitic cavity 14 Å in diameter were performed at 77.5 K for pressures ranging from zero up to saturation, where the adsorbed phase is in equilibrium with coexisting vapor and liquid phases. The same intermolecular potential functions were employed for gas-gas interactions in the vapor, liquid, and adsorbed phases. The gas-solid interaction potential includes dispersion-repulsion energy, induced electrostatic energy, and an ion-quadrupole term to model the interaction of the electric field in zeolites like NaX with polar molecules like N₂. The simulation of the coexisting vapor and liquid phases reproduces the saturation properties of pure liquid oxygen and nitrogen at 77.5 K. Activity coefficients in the adsorbed phase derived from simulations as a function of cavity filling and composition show negative deviations from Raoult's law, even though the non-idealities in the bulk liquid phase have the opposite sign. The simulation of the surface excess isotherm for adsorption from liquid mixtures exhibits preferential adsorption of N₂ and has the commonly-observed quadratic shape skewed toward the more strongly adsorbed component. Micropore condensation is observed for oxygen but not for nitrogen. The condensation of oxygen is similar to a first order phase transition but because of the small number of molecules that can fit into a micropore, coexistence of the two phases is replaced by oscillations between gas- and liquid-like densities.     

Thermodynamics of adsorption of binary aqueous organic liquid mixtures on a RPLC adsorbent

The surface excess adsorption isotherms of organic solvents commonly used in RPLC with water as co-eluent or organic modifiers (methanol, ethanol, 2-propanol, acetonitrile and tetrahydrofuran) were measured on a porous silica surface derivatized with chlorotrimethylsilane (C1-silica with 3.92 micromol C1 groups per m2 of SiO2), using the dynamic minor disturbance method. The 5 microm diameter particles were packed in a 150 mm x 4.6 mm column. The isotherm data were derived from signals resulting from small perturbations of the equilibrium between the aqueous-organic solutions and the adsorbent surface. The partial molar surface area of the adsorbed components were assumed to be the same as those of the pure components. The difference sigma-sigmai* between the surface tensions of the adsorbed mixtures and that of the pure liquids was measured as a function of the organic modifier molar fraction. A simple and unique convention for the position of the Gibbs dividing surface was proposed to delimit the Gibbs's adsorbed phase and the bulk liquid phase. The activity coefficients of the organic modifiers and of water and their thermodynamic equilibrium constants between the two phases were measured. The strong non-ideal behavior of the adsorbed phase is mostly accounted for by the surface heterogeneity. Some regions of the surface (bonded -Si(CH3)3 moieties) preferentially adsorb the organic compound while the regions close to unreacted silanols preferentially adsorb water.     

On the retrograde condensation of one or two liquids

This contribution discusses the phenomena of retrograde condensation of one or two liquids. It w1 be shown that both phenomena can be well understood. Also the relation of retrograde condensation of one liquid phase with the condensation behavior of natural gas will be discussed. Similarly that of two liquid phases with multiple phase behavior occurring in low temperature reservoir fluids will be pointed out.     

Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

We propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.     

Perfect wetting along a three-phase line: theory and molecular dynamics simulations

Wetting behavior along a three-phase equilibrium has been obtained by density gradient theory (DGT) and molecular dynamics simulations for a type-II equal size Lennard-Jones mixture. In order to perform a consistent comparison between both methodologies, the molecular parameters of this type of mixture were defined from the global phase diagram of equal size Lennard-Jones mixtures. We have found excellent agreement between predictions from the DGT (coupled to a Lennard-Jones equation for the bulk phases) and simulations results for both the phase and interface behavior, in the whole temperature, pressure, and concentration ranges. For all conditions explored in this work, this type-II mixture shows a three-phase equilibrium composed by a bulk immiscible liquid phase (L1) and a bulk gas phase (G) separated by a second immiscible liquid phase (L2). A similar phase distribution is obtained from the interfacial concentration profile in the whole range of conditions used in this work. This type of structure is a clear evidence that L2 completely wets the GL1 interface. The wetting behavior is also confirmed by the values and evolution of the interfacial tensions. In summary, this kind of type-II mixture does not show wetting transitions and exhibits a permanent perfect wetting in all the thermodynamic conditions explored here.     

Comparative thermodynamic analysis of the binary system Bi−Sb

Results of the comparative thermodynamic analysis of the binary system Bi?Sb obtained by DTA measurements and predicting are presented in this paper. Activities, activity coefficients, partial and integral molar quantities for Bi and Sb at temperatures 973, 1073 and 1173 K in the investigated binary system Bi?Sb determined by DTA measurements and thermodynamic predicting are given. An excellent agreement between the experimental and predicted results is reached. Also, a phase diagram of the investigated system Bi?Sb obtained by DTA shows good agreement with literature and it can be concluded that DTA could be satisfactorily used for quantitative thermodynamic analysis of any binary system containing equilibrium between solid and liquid solutions. It was also determined that conclusion about linear dependence ofgKs constant for binary eutectic systems and systems with phase transformation is valid for binary system containing equilibrium between solid and liquid solutions too.     

Solid-liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid-liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid-liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid-liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter (k_ij) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.     

Phase separation in aqueous mixtures of hydrophobically modified cellulose derivatives with their nonmodified analogues

Mixtures of hydrophobically graft-modified cellulose derivatives and their nonmodified analogues have been studied in aqueous solution. A qualitatively similar behavior was found in the phase behavior of nonionic as well as of cationic polymer systems. Over a large range of total polymer concentrations and mixture ratios the solutions phase separated into two phases of similar polymer concentration, with one of the phases enriched in the hydrophobically modified polymer. From the manufacturing process the cellulose derivatives investigated are likely to contain polymer chains with a rather continuous distribution in degrees of substitution and, possibly, substitution patterns. This causes a complex phase behavior that cannot be adequately described by a ternary representation. The multicomponent nature became apparent from composition analyses of the phases in equilibrium. It may thus be more appropriate to view the phase separation as a fractionation. A phase of small relative volume with a highly enhanced hydrophobe content (compared to the original hydrophobically modified polymer sample) was created. This was particularly obvious in more dilute solutions. Sometimes the phase separation was difficult to observe because the phases in equilibrium had similar polymer concentrations and, therefore, similar refractive indices. The observations presented here call for the attention of producers and users of these types of polymers. Received: 6 July 2000 Accepted: 6 September 2000     

Characterization of cyclodextrin-modified infrared chemical sensors: Part I. Modeling the mechanisms of interaction

To explore the properties of cyclodextrins (CDs) as an optical sensing phase, the behavior of immobilized CD in interaction with analytes was studied in this work. CDs having different cavity sizes were immobilized onto the surface of infrared (IR) internal reflection-sensing element (IRE) to kinetically monitor the behavior of CD in interaction with analytes. Several aromatic compounds having various molecular sizes and functional groups were used to characterize the interaction mechanism. A two-layer modification method was proposed in this work, which utilized a thin hydrophobic film (polyvinyl benzyl chloride) to stick on the IRE and to covalently bond to the CDs through an ethylene diamine linker. The synthesized CD phases exhibited high stability in aqueous solution. To analyze the behavior during the formation of complexes between the guest molecules and the CD phases, we modeled the interaction behavior and treated the kinetic data with the theoretical equations developed in this work. The results indicate that the behavior of the interaction between guest molecules and CDs was explained by considering the formation of two types of complexes: adsorbed complexes and inclusion complexes. The formation of the inclusion complexes was relatively fast, the time required to reach equilibrium could be shorter than a few minutes. The adsorbed complexes were also observed, but their rate of formation was relatively slow; equilibrium could be reached at times greater than 60 min. Based on the signals observed under equilibrium conditions, the concentration of inclusion complexes was approximately three times than that of the adsorbed complexes.     

Swelling of N-isopropyl acrylamide hydrogels in aqueous solutions of sodium chloride

Hydrogels are three-dimensional networks of hydrophilic polymer chains. Hydrogels can absorb/desorb water and hydrophilic solutes. This behavior is called swelling/shrinking, as it is accompanied by a volume change. The amounts of absorbed substances depend on the structure of the hydrogel and the composition of the coexisting liquid phase. This paper deals with experimental investigations of the swelling behavior of nonionic, chemically crosslinked, synthetic hydrogels of N-isopropyl acrylamide. The swelling equilibrium of some hydrogels in aqueous solutions of sodium chloride was investigated at 298 K. The experimental results are presented, discussed and correlated/predicted with a thermodynamic model which combines an expression for the Gibbs energy of a liquid phase with an expression for the Helmholtz energy of an elastic network.     

Isosteric heat of adsorption in liquid–solid equilibria: Theoretical determination and measurement by liquid chromatography/mass spectrometry

The isosteric heat of adsorption of a pure compound dissolved in a solution in equilibrium with a solid adsorbent was determined, based on the Gibbs surface excess model. The exact isosteric heat of adsorption differs from the usual value derived from the variation of the Henry’s constant with the reciprocal temperature because this procedure assumes ideal behavior of the bulk liquid solution, which, in most cases, is only approximately so. An experimental protocol, based on the determination of the excess adsorption isotherms by combining frontal analysis (for strongly adsorbed components) and spectrometric tracer pulse chromatography (for weakly adsorbed compounds) is proposed. It allows the determination of the exact isosteric heat of adsorption provided that the activity coefficient of the compound in the bulk solution can be explicitly expressed as a function of the bulk liquid composition.     

Modelling of high-pressure phase equilibria using the Sako–Wu–Prausnitz equation of state: II. Vapour–liquid equilibria and liquid–liquid equilibria in polyolefin systems

Phase equilibria in binary and ternary polyolefin systems are calculated using the cubic equation of state proposed by Sako–Wu–Prausnitz (SWP). Calculations were done for high-pressure phase equilibria in ethylene/polyethylene (LDPE) systems and for liquid–liquid equilibria (LLE) in systems containing either high-density polyethylene or poly(ethylene-co-propylene). The calculations for the copolymer/solvent systems are compared with those using the SAFT EOS. The two equations of state can describe UCST, LCST as well as U-LCST behaviour with similar accuracy. Whereas, the binary interaction parameter is temperature-independent for SAFT, it is found to be a function of temperature for the SWP model. Moreover, the influence of an inert gas on the LCST of the polyethylene/hexane system is investigated using the SWP EOS. The polydispersity of the different polyethylenes is considered in the phase equilibrium calculations using pseudocomponents chosen by the moments of the experimental molecular weight distributions.     

Understanding the interfacial properties of nanostructured liquid crystalline materials for surface-specific delivery applications

Nonlamellar liquid crystalline dispersions such as cubosomes and hexosomes have great potential as novel surface-targeted active delivery systems. In this study, the influence of internal nanostructure, chemical composition, and the presence of Pluronic F127 as a stabilizer, on the surface and interfacial properties of different liquid crystalline particles and surfaces, was investigated. The interfacial properties of the bulk liquid crystalline systems with coexisting excess water were dependent on the internal liquid crystalline nanostructure. In particular, the surfaces of the inverse cubic systems were more hydrophilic than that of the inverse hexagonal phase. The interaction between F127 and the bulk liquid crystalline systems depended on the internal liquid crystalline structure and chemical composition. For example, F127 adsorbed to the surface of the bulk phytantriol cubic phase, while for monoolein cubic phase, F127 was integrated into the liquid crystalline structure. Last, the interfacial adsorption behavior of the dispersed liquid crystalline particles also depended on both the internal nanostructure and the chemical composition, despite the dispersions all being stabilized using F127. The findings highlight the need to understand the specific surface characteristics and the nature of the interaction with colloidal stabilizer for understanding and optimizing the behavior of nonlamellar liquid crystalline systems in surface delivery applications.     

Behavior of large nucleic acids in reversed-phase high-performance liquid chromatography.

Large nucleic acids can be separated by reversed-phase high-performance liquid chromatography. Analysis shows that the retention time depends not only on the chain length but also on the base composition and the secondary structure of the molecule. A model is proposed to interpret their behavior. This model, called "multiple-point interaction theory" is based on the observation that macromolecules are flexible and very large compared to the hydrophobic phase (octadecylsilane) of the column. It explains the behavior of large nucleic acids in terms of an equilibrium of the macromolecule between the two phases through a multiple-point attachment to the chromatographic matrix, the parameters of the equilibrium being both the hydrophobicity of the base and the number of attachment points. This model fits the experimental data and can be applied to all types of flexible macromolecules, especially proteins and nucleic acids, when they are chromatographed on reversed-phase columns. The model is used to explain the separation of nucleic acids of importance in molecular biology.     

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.