A method of computation of the pressure effect on melt viscosity

Simha's equation of state provides the relation between reduced pressure, temperature, and volume (P?, T?, and ?, respectively) and the occupied site fraction, y = y (P?, T?). The latter theoretical parameter combines the P and T effects on the occupied and unoccupied (“free volume”) part of the model liquid. It can be computed for each liquid once the thermodynamic reducing parameters are known. Empirical correlation between published zero shear viscosity data, η = η (P, T), and y indicates that for n-paraffins and molten polymers η is a single parameter function: η = η (y). The mathematical form of this dependence was explicitly given for n-paraffins. However, for polymers the correlation depends on molecular weight, molecular weight distribution, branching, composition, etc. In Practical terms, η = η (y) should be determined for each polymer by measuring the temperature dependence of η in as wide a range of T as possible. Then pressure effect on η can be determined from η = η(y) plot, knowing the y = y(P?, T?) relation.     

New models for the binary interaction parameters of nitrogen–alkanes mixtures based on the cubic equations of state

In this study, the goal was to derive a new purely predictive model to obtain binary interaction parameters based on intermolecular theories. The Lorentz–Berthelot and Halgren HHG molecular combining rules were coupled with the vdw1 mixing rule to derive the new equations for binary interaction parameters. These equations were used with the PR and ER EoSs to calculate the vapor–liquid equilibria of 14 binary mixtures of nitrogen with either methane, ethane, propane, iso-butane, n-butane, iso-pentane, n-pentane, n-hexane, n-heptane, n-octane, n-nonae, n-decane, n-dodecane, or n-tetradecane over wide ranges of temperature and pressure. To increase the accuracy for all of the investigated systems, we have additionally suggested a new correlative mode for the proposed equations. For some of the systems, the proposed predictive equations enhance the accuracy of vapor–liquid equilibria predictions up to three times in comparison to the case where binary interaction parameters are set to zero.     

A correlation for predicting diffusion coefficients in alkanes

A correlation was developed for predicting limiting mutual diffusion coefficients of gaseous and liquid solutes in normal alkane solvents with carbon numbers ranging from 7 to 28 at temperatures to 570 K. The functional form of the correlation is based on the rough hard sphere theory. The parameters needed in the correlation are the molecular weights and hard sphere diameters of the solute and solvent molecules and molar volume of the solvent. The data used in the development of the correlation included 143 measurements with solute/solvent molecular mass ratios ranging from 0.005 to 2.26 and size ratios ranging from 0.3 to 1.3. The average absolute error in predictions was only 6.3%. When the correlation was used to predict literature values for binary n-alkane systems, the average absolute error was 16.7%.     

Vapor–liquid equilibria for benzene/polybutadiene and cyclohexane/polybutadiene systems at 333, 355, and 373 K using gas chromatography

A perturbation chromatography apparatus has been designed and constructed for determining the vapor–liquid equilibrium between a two-component (solvent/helium) vapor phase and a two-component (polymer/solvent) liquid phase. The apparatus performed very well, giving reproducible and reliable results that agree with independent, previously reported studies. All tests of the equipment indicated that it was successful in meeting the conditions of low column pressure drop, small perturbations, and slow flow rate that are required for perturbation chromatography. Binary polymer/solvent data were obtained for polybutadiene (PBD)/benzene or polybutadiene/cyclohexane systems at solvent partial pressures to 40 kPa and for n-hexane at infinite dilution, all at the three temperatures of 333.15, 355.00, and 373.15 K. The experimental data for each system can be represented within experimental error by the Flory–Huggins polymer solution theory using a single binary interaction parameter that is independent of temperature and concentration.     

Vapor liquid equilibrium data for alcohol n-Amylamine binary systems at 333.15 K. Reduction of the experimental data by a novel model-free method

Vapor liquid equilibrium measurements for the binary systems of n-amylamine with methanol, ethanol and 1-propanol at 333.15 K are reported. The measurements were made in a static equilibrium cell of the Van Ness type and the experimental data were reduced using a model-free method. This model-free method is an adaptation of the method of Mixon et al. in which a material balance is introduced to correct for the mols of the gas phase. Second virial coefficients of n-amylamine and cross second virial coefficients for the binary systems were measured in this work and parameters for the Tsonoupolos correlation are reported.     

A Separation Factor Method for the Analysis of Ideal Binary Mixtures in Gas-Solid Adsorption

Abstract

A correlation formula based on the separation factor is proposed for the mixture concentration in the adsorbed phase of an ideal binary solution in gas-solid adsorption. This formula is shown to apply to two binary systems (viz., 1,3-butadiene and n-butane on cross-linked polystyrene at 25°C, and acetylene and ethane on activated carbon at 25°C) with similar molecular and thermodynamic properties in the two components for each system. Comparison between the calculated and experimental values of the separation factor showed that the assumption of an ideal mixture is justified for each of these two binary systems. Mixture isotherms for the two ideal binary systems are calculated by the proposed correlation formula from the corresponding single-component isotherms. Good agreement between the calculated and experimental mixture isotherm data confirms that a binary system of two components with similar molecular properties (viz., molecular weight, normal boiling point, vapor pressure, number of carbon atoms in molecules, etc.) tends to form an ideal mixture (i.e., one with a constant separation factor).     

The use of PVC powder as a subtractive agent in gas chromatography

An investigation is described in which subtraction “loops” filled with PVC powder have been used to study the affinity between the powder and model compounds. Optimum temperature conditions are 70 °C. The study reveals that the PVC has a strong affinity for aromatic compounds and compounds containing functional groups although this is qualified by the configuration of the molecule. It is shown that in view of these properties PVC can be used in subtraction “loops” as an aid to the identification of aromatics in mixtures of aromatics, n-, iso- and cycloparaffins and also that its effectiveness in differentiating between aromatics and n-paraffins is comparable with molecular sieve 5A. Its behaviour is different, however, in that it removes aromatics whereas the molecular sieve 5A removes the n-paraffins. It is as effective as molecular sieve 5A in removing hydrocarbons containing functional groups. The PVC is cheap, requires no preparation prior to use and when “exhausted” it can be readily replaced.     

Effective separation of aromatic hydrocarbons by pyridine‐based deep eutectic solvents

Many promising qualities of deep‐eutectic solvents made them suitable solvents in separation process. In this work, the pyridine‐based deep eutectic solvents were designed and synthesized with N‐ethylpyridinium bromide and two HBDs (N‐formyl morpholine and levulinic acid). Two ternary systems, benzene + cyclohexane + DES and toluene + n‐heptane + DES, were studied by the liquid‐liquid extraction. The effect of different HBDs, extraction time, volume ratio of DES to system solution, and the initial concentration of aromatic were studied. The DES with N‐formyl morpholine showed better separation performance than that with levulinic acid. The liquid‐liquid extraction equilibrium could be obtained in 10 minutes. The volume ratio of DES to system solution was set as 1:1. Both DESs showed their best separation performance at low temperatures (20°C) and low aromatic concentration system. For the benzene + cyclohexane system, the distribution coefficient of benzene was 1.733 and the selectivity was 23.8 at 20°C. For the toluene + n‐heptane system, the distribution coefficient of toluene was 0.853 and the selectivity was 40.7. Tie‐lines for two ternary systems were obtained, and the Othmer‐Tobias correlation was used to check the reliability of the obtained liquid‐liquid extraction experimental data. The experimental LLE data were correlated using the NRTL model and the calculated data correlated significantly with the experimental data.     

Influence of Membrane Solvent on Strontium Transport from Reprocessing Concentrate Solutions through Flat-Sheet-Supported Liquid Membranes

Abstract

The influence of membrane solvents on strontium transport from nuclear fuel reprocessing concentrate solutions to demineralized water through a flat-sheet-supported liquid membrane has been studied using dicyclohexano-18-crown-6 as the extractant and Celgard 2500 as the solid support. Even though the highest values of the distribution coefficients of strontium were obtained with nitrated compounds as membrane solvents, strontium permeabilities were determined only when a membrane solvent was used for which stable SLMs were obtained. Among the latter, the use of 4-nonylphenol as a phase modifier is not satisfactory for long-term strontium transport experiments due to its reactivity with the nitric acid of the aqueous feed solution. We achieved a good correlation between strontium permeability and two parameters of the membrane diffusion coefficient (molecular weight and viscosity of the membrane solvent) for aromatic solvents modified with isotridecanol or 1-decanol. The best results were obtained with n-hexylbenzene (0.7 mol·L^?1 isotridecanol) which should lead to a high strontium decontamination by hollow-fiber-supported liquid membranes. The transport of nitric acid and nonradioactive cations through the membrane was not greatly influenced by the membrane solvent used.     

Morphology development and characterization of the phase-separated structure resulting from the thermal-induced phase separation phenomenon in polymer solutions under a temperature gradient

This paper studied the morphological development during the fabrication of anisotropic polymeric materials using the thermal-induced phase separation phenomenon (spinodal decomposition) in a model binary polymer solution under a linear spatial temperature gradient using mathematical modeling and computer simulation. The model incorporated the non-linear Cahn-Hilliard theory for spinodal decomposition and the Flory-Huggins theory for polymer solution thermodynamics. Moreover, the slow mode theory and Rouse law were used to account for polymer diffusion. The two-dimensional numerical results showed that an anisotropic morphology was developed when a temperature gradient was imposed along the polymer solution sample. The droplet size and droplet density decrease as temperature increases during the intermediate stage of spinodal decomposition. The spatial temperature gradient, however, had insignificant effect on the droplet shape.     

Measurement of vapor sorption equilibria of polymer solutions and comparative correlation by g E -models and lattice equations of state

Solvent sorption equilibrium data of binary solvent-polymer systems were measured with a vacuum electro-microbalance equilibrium cell. Tested solvents were benzene,n-pentane, cyclohexane,n-hexane, water and methanol. Polymers tested were poly(dimethylsiloxane), poly(iso-butylene), polypropylene oxide) and poly(vinyl alcohol). Data obtained in the present study, together with existing literature data, were correlated by twog ^E- models, such as UNIQUAC and the Flory-Huggins model, and four equations of state which stem from the lattice fluid theory, such as models proposed by Flory, Sanchez and Lacombe, Panayiotou and Vera, and the NLF model proposed recently by the present authors. For each solvent-polymer system, the provided models give a quantitative correlation. The advantages and drawbacks of the g^E-model and equation of state approaches are also discussed.     

Phase Transitions of Branched Fatty-Acid Calcium Salt/Water Systems

Calcium (Ca) salts of fatty acids are powder materials, which exhibit lubricant, hydrophobic, and bactericidal properties. These physical and biological properties depend on the chemical structure of the alkyl chain of the fatty acids. In this study, the phase behavior of iso-stearic acid Ca salt/water binary systems was studied, and the effect of the branched structure in the alkyl chain was analyzed. Herein, calcium chloride is added to the iso-stearic acid aqueous solution. The state of the binary systems changed with the molar ratio (R) of [Ca²⁺]/[iso-stearic acid]. Precipitation occurred when R was more than 0.05, whereas the mixture changed from a micelle phase (W_m) to an oil phase (O) through a liquid crystalline phase (LC) when R was less than 0.01. The polarized microscopy images and small-angle X-ray scattering profiles showed that the LC is in a lamellar liquid crystalline state. In addition, we evaluated the crystal structure of the precipitated material. These results showed that the iso-stearic acid Ca salt was in the amorphous state. In contrast, the n-stearic acid Ca salt formed only the W_m and gel phases. These findings suggest that the branched structure of fatty acids induces loose intermolecular packing of liquid crystalline structures.     

A Comparison of the Phase Behaviour of Polystyrene in Cycloalkanes and n-Alkanes

Cloud point curves for several narrow fractions of polystyrene dissolved in cycloheptane, in cyclooctane and in cyclodecane have been established, and the critical solution temperatures extrapolated to give the respective temperatures. All three cycloalkanes are good solvents for the polymer. A comparison is made between the phase behaviour of polystyrene dissolved in cyclic alkanes and in n-alkanes using free volume polymer solution theory.     

An integrated criterion of efficiency for Pt catalysts in the dehydrogenation of higher <Emphasis Type="Italic">n</Emphasis>-paraffins

The deactivation of catalysts by coke-forming structures in the dehydrogenation of higher n-paraffins is discussed. The patterns of coke formation on a catalyst subject to process conditions are presented. A mathematical model of the process is described to show its adequacy. A calculation algorithm for the optimum mode of operation of a dehydrogenation catalyst is constructed, and the calculation results are given. Dehydrogenation catalysts of different brands are compared with respect to several parameters (coke formation on catalysts, the yield of the reaction by-product, and the dynamics of temperature rise in the reactor). The model can be used to estimate the efficiencies of catalysts in a cycle and to compare them.     

Swelling of crosslinked polyacrylates in isotropic and anisotropic solvents

The purpose of this study was to examine the swelling and deswelling of photochemically crosslinked poly(n‐butylacrylate) networks in isotropic and anisotropic solvents. The phase diagrams were established in terms of composition and temperature for five isotropic solvents, acetone, cyclohexane, methanol, tetrahydrofuran, and toluene, and two low‐molecular‐weight nematic liquid crystals, 4‐cyano‐4′‐n‐pentyl‐biphenyl and an eutectic mixture of cyanoparaphenylenes. Networks were formed by ultraviolet curing in the presence of 0.5 wt % difunctional monomer (hexane diol‐di‐acrylate) and 0.5 wt % photoinitiator (Darocur 1173). Immersion in excess solvent allowed us to measure the solvent uptake by weight and to determine the size increase by optical microscopy in terms of temperature. We calculated weight and diameter ratios considering the swollen‐to‐dry network states of the samples. Phase diagrams were analyzed with the phantom network model according to the Flory–Rehner theory of rubber elasticity, and for the anisotropic solvents, modeling was supplemented with the Maier–Saupe theory of nematic order for free energy. The polymer–solvent interaction parameter was deduced as a function of temperature, but the values were in discrepancy with Fedors's model of solubility parameters, which overestimated the interaction. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1–9, 2004     

Role of the steric effects for the progress of alkanes intercalation in CsC24

The ability of various alkanes to be intercalated into the second-stage cesium graphitide, CsC₂₄, was investigated using the two-bulb technique. The structural changes occurring during intercalation were studied by real-time neutron diffraction. At moderate pressure, the intercalation of large molecules such as n-butane, n-pentane and n-hexane simultaneously leads to a mixture of a second-stage ternary phase and a first-stage binary phase “CsC₈”. Under increased pressure a pure first-stage ternary phase is finally formed. The intercalation of cyclopentane occurs in two steps: a pure second-stage ternary phase is first observed, whereas CsC₈ only appears at about half filling. For the smallest alkane, CH₄, complete ternarization leads to a second-stage ternary phase together with a small amount of an enriched second-stage binary derivative. Owing to the formation of binary domains rich in alkali metal during the ternarization, the cesium density is smaller in the second-stage ternary phase than in the starting binary compound. The in-plane cesium concentration of the ternary phase strongly depends on the projected surface area of the alkane molecule. During invasion of the interlamellar space, large molecules induce a decrease of the average distance between cesium ions. Electrostatic repulsive energy between cations is minimized through expulsion of cesium in binary domains. A pleated-layer model with canted fronts is presented, in order to account both for the various phases existing within each grain, and for the structural transformations caused by the intercalation reaction.     

High-pressure phase behavior in polyethylene/n-butane binary and polyethylene/n-butane/CO2 ternary systems

Solubility of polyethylene molecular weight standards (M_w = 2150, 16,400, 108,000, and 420,000 and M_w/M_n = 1.14, 1.16, 1.32, and 2.66, respectively) has been studied in near- and supercritical n-butane and n-butane/CO₂ mixtures at pressures up to 70 MPa. For each polyethylene/solvent system at selected compositions, demixing pressures have been determined using a high-pressure variable-volume view-cell at temperatures up to 200°C. Solutions in pure n-butane are found to display LCST (lower critical solution temperature)-type behavior. The behavior of the solutions in n-butane/CO₂ mixtures are observed to change from the LCST to the UCST (upper critical solution temperature) with increasing CO₂ content in the binary solvent. Sanchez–Lacombe theory has been used to model these systems. The predictions correctly describe the nature of the phase diagrams for both binary and ternary systems and the calculations are in reasonable agreement with experimental data. © 1994 John Wiley & Sons, Inc.     

Comparison of the performance of the LCVM model (an EoS/GE model) and the PHCT EoS (the Perturbed Hard Chain Theory Equation of State) in the prediction of the Vapor–Liquid Equilibria of binary systems containing light gases

The purpose of this work is to compare two models, which are able to perform Vapor–Liquid Equilibrium (VLE) predictions. The first one, the LCVM model, is an EoS/G^E one and it has been successfully applied in the prediction of the VLE behavior of polar and non-polar systems, as well as, systems of dissimilar component size, such as those containing gases with large n-alkanes. The second one is PHCT, an equation of state based on the perturbed hard chain theory. It has also been successfully applied in binary systems of supercritical fluids and non-polar molecules and in systems containing light gases and large n-paraffins. The comparisons results presented in this paper, proved that the two models are comparable, concerning the ability to predict the VLE, as well as, the volumetric behavior of systems with low to medium component size difference (supercritical fluids with non-polar components up to about 10 carbon atoms). However, as the size difference increases, LCVM performs better, especially in the near critical region of such systems.     

Contact Angle of Ethanol and n‐Propanol Aqueous Solutions on Metal Surfaces

The contact angles of the aqueous solution of ethanol and that of n‐propanol on copper, aluminum, and stainless steel surfaces are reported. The contact angles were measured under atmospheric conditions, and then under vapor‐liquid equilibrium conditions at 1 atm and different temperatures. The results showed the variations of the contact angles with the concentrations of aqueous solutions on different metal material surfaces with different roughness. Some unstable behavior of the wetting ability around the azeotropic point of a binary solution is reported. Influences of concentration, kind of materials, and the surface roughness on the wetting ability are discussed. The model for predicting the contact angle of alcohol aqueous solutions on metal surfaces under atmospheric and vapor‐liquid two‐phase equilibrium conditions at 1 atm is derived from the Young equation.