Hildebrand Theory Research Articles

GaP-GaN Pseudobinary System. Crystal Growth of GaN from the Solution in the Liquid GaP

Phase diagram of pseudobinary GaP-GaN system has been calculated using Phillips-Van Vechten theory of solid solutions and Hildebrand theory of nonelectrolytic liquids. Large miscibility gap in the solid phase, was predicted. Solubility of P in GaN is negligible which opens the possibility of GaN crystal growth from the molten GaP. The theoretical results were confirmed by crystal growth of GaN from molten GaP under high N2 pressure. High pressure of nitrogen, 17 - 20 kbar, assures the stability of GaN growing at temperatures exceeding GaP melting. Single crystals of GaN have been grown. As predicted, the presence of phosphorus in GaN was not detected by EDX technique.

Mixing rule for liquid viscosities of refrigerant mixtures

An investigation of mixing rules for liquid viscosities of refrigerant mixtures is reported. Measured liquid viscosities of seven azeotropes and their corresponding pure components are compared with available mixing rules and Hildebrand's correlation. The results indicate that the viscosities of pure refrigerants are a strong function of volume, supporting Hildebrand's theory. The mixing rules popular in the refrigeration industry are not universally valid for all the mixtures considered. The volume change due to mixing is responsible for almost all of the deviations of the liquid viscosities of mixtures from ideal values. A simple relationship between excess viscosity and excess volume is developed, which results in deviations of less than 2% when used with Grunberg and Nissan's correlation. Based on this study, it is recommended that density measurements are accompanied by viscosity measurements for refrigerant mixtures.

A Model for the Diffusion of Moisture in Adhesive Joints. Part I: Equations Governing Diffusion

Abstract A methodology is proposed to relate the diffusion coefficient of small penetrant molecules in polymers to temperature, strain, and penetrant concentration. The approach used is based on well-known free volume theories. It is assumed that the transport kinetics is governed by the constant redistribution of the free volume, caused by the segmental motions of the polymeric chains. An expression for the diffusion coefficient is inferred from the temperature, strain, and penetrant concentration dependence of the free volume. The stress dependence of solubility is predicted from the Hildebrand theory. It is shown that the resulting constitutive equations exhibit many features desirable for joint durability studies. Finally, a non-Fickian driving force arising from differential swelling is included in the governing equations.

Carbon Isotope Separation by Absorptive Distillation

Abstract The feasibility of separating carbon isotopes by absorptive distillation has been studied for CO absorption by cryogenic solvents. Phase equilibrium, isotopic separation, and mass transfer data were taken between 77.4 and 114.3 K for the following solvents: propane, propylene, 1:1 propane-propylene, 1-butene, isobutane and nitrogen. Carbon monoxide solubility followed Henry's Law, with a maximum experimental solubility of 6.5 mole per cent. Isotopic separation between CO in the gas and liquid phases using hydrocarbon solvents was several times that for pure CO vapor-liquid equilibrium. The maximum observed isotopic separation factor was 1.029 at 77.4 K with the propane-propylene solvent mixture. Mass transfer measurements yielded calculated HTU's of 2 to 5 cm for a possible separation system. An attempt has been made to correlate isotopic separation data using Hildebrand's theory of solutions. The differential absorption of isotopic CO species is expressed as a difference in solubility of the iso...

A predictive method for calculating the solubility of solids in supercritical gases application to apolar mixtures

A thermodynamic method is proposed for calculating the solublities of apolar solids compounds in apolar supercritical gases. The method, analogous to the Hildebrand theory of solids' solubilities in liquid solvents, is mainly based on the application of Scatchard-Hildebrand equation to supercritical fluid mixtures. The derived method is applied to the determination of the ethylene/naphthalene equfiibria at 5 temperatures between 12 and 50°C and over pressure ranges of 50–270 ata. Calculated data are compared with the experimental data by Diepen and Scheffer. Methods for determining the solubility parameters of supercritical gases are discussed. The possibility of extending the proposed theory to polar mixtures of condensed phases in supercritical gases is also indicated.

Use of Hildebrand and Lamoreaux's theory to predict solubility and related properties of gas-liquid systems

There is a need in many fields such as chemical engineering, process chemistry and pharmacology for reliable data on the solubility, entropy of solution and partial molar volume of gases in liquids. Experimental data are not available for many systems of practical and academic importance and consequently a reliable theory to predict values for these properties would be of great use. Recent refinements of solubility parameter theory have been successful in predicting such values for several systems and in this paper results obtained from this theory are compared with experimental measurements on a large range of gas-liquid systems. The agreement found is satisfactory in the most part, but for helium, neon, xenon, hydrogen and deuterium, the predicted results deviate consistently from the experimental values. This is to be expected on the basis of some of the earlier results of solubility parameter theory and an empirical modification is proposed that yields significant improvements in the predicted values. This has also been used to predict values for carbon dioxide, tetrafluoromethane and sulphur hexafluoride to which the theory is not directly applicable. Values predicted by solubility parameter theory are compared with those obtained by Battino and co-workers from scaled particle theory. In general, the two theories are equally successful in predicting solubilities, but refined solubility parameter theory yields better values of entropy of solution. It is concluded that the theory provides a useful means of predicting solubility and entropy of solution but that prediction of partial molar volume results is limited because of the paucity of data for the thermal pressure coefficients of the solvents. Attention is drawn to apparent inaccuracies in certain experimental measurements. The interrelationship between the various forms of the entropy of solution used by different workers is clarified. A value of the energy of vaporisation of carbon dioxide, δE2v=2.64±0.15 kcal/mol is calculated.

A thermodynamic method of predicting the transport of steroids in polymer matrices

AbstractApplication of Hildebrand's theory of the solubility of microsolutes in ordinary solvents, and of the Flory‐Huggins theory to the solubility of steroids in polymers, has permitted the derivation of a predictive correlation between polymer permeability and steroid crystalline melting temperature, other correlating parameters being the entropy of fusion of the steroid and the (computed) solubility parameters of steroid and polymer. The correlation permits prediction of the permeability of any steroid in any polymer with reasonable accuracy.

Liquid-vapor equilibrium in systems formed by hydrogen chloride with ethane, propane, acetylene, and ethyl chloride

1. The liquid-vapor equilibrium was studied in the systems hydrogen chloride-acetylene, hydrogen chloride-ethane, hydrogen chloride-propane, and hydrogen chloride-ethyl chloride, and the dependence of the coefficient of separation on the temperature was investigated in the interval from −112 to −90°, and the dependence on the concentration of the trace impurity from 5·10−3 to 5·10−1 vol. %. These systems obey Henry's law within the indicated concentration region. 2. The large values of the coefficient of separation for the systems studied are evidence of the possibility of profound purification of HCl from trace impurities of organic substances by the method of low-temperature fractional distillation. 3. The coefficient of thermodynamic activity of the indicated trace impurities was calculated by various statistical methods. It was shown that the calculation based on the use of the cell variations of the theory of the liquid state is in better agreement with the experiment than the calculation based on the Hildebrand theory.

Vapour-liquid equilibria for cryogenic mixtures

The Scatchard—Hildebrand theory of liquid solutions gives a quantitative description of vapour—liquid equilibria for simple mixtures when the geometric-mean assumption for the cohesive energy density is relaxed through the introduction of a characteristic binary constant. Solubility parameters and molar volumes are given for thirteen common cryogenic fluids and characteristic binary constants are reported for twenty-eight binary mixtures. Extension to multicomponent mixtures is straightforward; no ternary (or higher) constants are required. The correlation presented here is useful for design of separation processes at low temperatures and moderate pressures.

Studies in regular solution theory. Part 1.—Solubolity studies of tetraphenyltin in simple non-polar solvents

The solubility of tetraphenyltin in a number of non-polar solvents is presented. The data are analyzed in terms of Hildebrand's theory of regular solutions. The large molar volume of this solute requires the inclusion of a Flory-Huggins term in the saturation solubility equation. The possible limitation of the interaction-energy geometric-mean rule are examined and a comparison is made with data for the solubility of stannic iodide, iodine and sulphur in a similar set of solvents.

COMPLEXES OF STANNIC IODIDE WITH AROMATIC HYDROCARBONS

Spectrophotometric measurements on solutions of stannic iodide were found to provide evidence for complex formation with aromatic hydrocarbons. Calculations, based on spectra for mixed solutions of benzene and stannic iodide in carbon tetrachloride, yield values of 0.26 for the equilibrium constant (mole fraction), 28 400 1/mole cm for the molar extinction coefficient of the benzene – stannic iodide complex. Kinetic evidence indicates that the order of decreasing complex stabilities is from xylene to toluene to benzene. The formation of stannic iodide – aromatic hydrocarbon complexes provides an explanation for the discrepancy between measured solubilities of stannic iodide in benzene, toluene, and xylene, and the solubilities predicted by the Hildebrand theory of regular solutions.

Thermodynamic properties of the benzene and cyclopentane system

Total vapour pressure data have been obtained for the system benzene + cyclopentane at 25, 35 and 45°C. These data, along with volumetric data for the pure liquids and calculations of gas-phase properties for the mixtures, were reduced to excess free energies of mixing using the method of Barker. The excess free energies of this system are nearly symmetrical in mole fraction; at 35°C the excess free energy of the equimolar mixture is 65·0 cal/g mole. However, this system does not form regular solutions; the product of the temperature and the excess entropy of mixing at constant pressure is 64·3 cal/g mole for the equimolar mixture at 35°C. Calculations of the excess functions at constant volume were made using the equations of Scatchard and the excess volume data of Klapproth. These calculations show that, contrary to the refined Hildebrand theory of solutions of nonpolar molecules, the excess entropy is far from negligible even if corrections are made for the observed volumetric expansion which accompanies the solution process.

MICROCALORIMETRIC DETERMINATION OF THE CRITICAL CONCENTRATION AND THE MOLECULAR DIMENSIONS OF POLYVINYL ACETATE IN SOLUTION

Heats of mixing of polyvinyl acetate fractions with s-tetrachloroethane and methanol have been determined for the low concentration region. At the lowest concentrations the graphs of ΔH vs. volume fraction are linear as predicted by the van Laar, Scatchard, and Hildebrand theory. As the concentration increases, an inflection point appears, the enthalpy increment being smaller for a short concentration interval and then resuming its former value up to the limit of the range studied. The position of the critical interval depends on the solvent employed and on the molecular weight of the fraction. An equation, based on Flory's theory, has been developed for predicting the critical concentration from intrinsic viscosity. Assuming that, at the critical concentration, the molecules are just coming into contact, it is possible to calculate the diameter of the sphere equivalent to a molecule. Comparison of the dimensions obtained from the critical concentration and the root-mean-square end-to-end distance of the molecule calculated by the Flory equation leads to agreement within 10%.

Methylene dichloride and 1 :2‐dichloroethane. I. Solubility of water. II. Vapour pressure

AbstractThe solubility of water in methylene chloride and I: 2‐dichloro‐ethane over the temperature range ‐ 20° to 40° and 80° respectively has been determined. The vapour pressures of the solvents, alone and in admixture, have been measured, and the composition of the varour phases of the mixed solvents determined at 10° intervals. over the range 20‐50°. Evidence of the formation of azeotropes with water is given; boiling point: composition and vapour pressure: boiling point relationships are derived. Mixtures of the two solvents are found closely to obey Raoult's law. The results are discussed in the light of Hildebrand's theory of liquids.

Activities of Associating Solutes

THERE are comparatively few cases of binary mixtures in which the activity or fugacity of one component has been interpreted in terms of molecular properties. Well-known instances of such treatments are the Debye–Huckel theory of electrolytes and Hildebrand's theory of regular solutions. We have examined the case of a binary mixture where interaction between the two components is negligible, but where one of the components (the solute) has a tendency to form multiplets of any degree of complexity by means of association, Since interaction is assumed to be negligible, the non-ideality of the solute is attributable entirely to association, and each multiplet species (including the monomer) may be supposed to constitute an ideal sub-system. We propose to call mixtures of this type 'perfect associating mixtures'.

Hildebrand's Theory of Alliteration.

Hildebrand's Theory of Alliteration.