Ideal Solution Theory Research Articles

Petrology, elasticity, and composition of the mantle transition zone

We compare the predictions of compositional models of the mantle transition zone to observed seismic properties by constructing phase diagrams in the MgO‐FeO‐CaO‐Al2O3‐SiO2system and estimating the elasticity of the relevant minerals. Mie‐Grüneisen and Birch‐Murnaghan finite strain theory are combined with ideal solution theory to extrapolate experimental measurements of thermal and elastic properties to high pressures and temperatures. The resulting thermodynamic potentials are combined with the estimated phase diagrams to predict the density, seismic parameter, and mantle adiabats for a given compositional model. We find that the properties of pyrolite agree well with the observed density and bulk sound velocity of the upper mantle and transition zone. Piclogite significantly underestimates the magnitude of the 400‐km velocity discontinuity and overestimates the velocity gradient in the transition zone. Substantially enriching piclogite in Al provides an acceptable fit to the observations. Invoking a chemical boundary layer between the uppermost mantle and transition zone leads to poor agreement with observed seismic properties for the compositions considered. Within the transition zone, the dissolution of garnet to Ca‐perovskite near 18 GPa may explain the proposed 520‐km seismic discontinuity. Below 700 km depth, all compositions disagree with observed bulk sound velocities, implying that the lower mantle is chemically distinct from the upper mantle.

Retrograde dissociation of protein–surfactant complexes induced by mixed micelle formation

The binding of sodium n-dodecyl sulfate (SDS) to bovine insulin in the presence of constant concentrations of the less hydrophobic surfactants, sodium n-decyl sulfate (SDeS), sodium n-octyl sulfate (SOS) and n-octyl-β-D-gly- copyranoside (OBG) has been measured by equilibrium dialysis by using radiolabelled [14C]SDS. The binding isotherms for all the binary surfactant systems (SDS–SDeS, SDS–SOS and SDS–OBG) exhibit maxima and the binding levels at the maxima decrease with increase in the constant concentration of the less hydrophobic surfactant. The maxima are explained in terms of the greater stability (lower critical micelle concentration) of mixed micelles formed by the binary mixture of the surfactants relative to the stability of the protein–surfactant complexes. By the use of ideal-solution theory for mixed micelle formation between the anionic surfactant mixtures and regular solution theory for anionic–non-ionic surfactant mixtures it is shown that the protein–surfactant complexes dissociate as the mixed micelles become enriched in the more hydrophobic surfactant. It is suggested that the phenomenon might be termed ‘retrograde dissociation’.

Theory of Clathrates

A review is presented of the theory of clathrate compounds, starting with the first quantitative theory suggested by van der Waals and Platteeuw and ending with the current ideas. A brief description is given of the theory of ideal and non-ideal solid clathrate solutions and of the theory allowing us to describe clathrates with an unstable, empty host lattice. The review is composed of results obtained by the different methods based on various approximations.

Eutectic interactions in binary systems containing cholesterol, cholesteryl esters and triacylglycerols

Binary phase behavior of saturated cholesterol esters with trilaurin or cholesterol, and cholesterol with trilaurin, is studied. The existence of specific molecular interactions is detected by comparing the liquidus curve of the eutectic with ideal theory of freezing point depression and correcting the theoretical curve with the Bragg-Williams model when necessary. X-ray data indicate that all eutectic solids are nearly totally fractionated. The phase diagrams are sometimes well-explained by ideal solution theory indicating that polar interactions (e.g., the hydrogen bonding of cholesterol) are much less important than van der Waals interactions between neighboring molecules. However, the hydrogen bonding networks of cholesterol can lead to nonideal solution behavior with other lipids, a phenomenon consistent with previous observations on simpler molecular binaries. An observed nonideal solution behavior of triacylglycerol with cholesterol esters, on the other hand, is unexpected since significant polar interactions are expected to be ‘buried’ in the predominant nonpolar volume of the molecules involved.

Eutectic interactions between saturated and unsaturated chain cholesteryl esters: comparison of calculated and observed phase diagrams

Binary phase behavior of saturated chain with unsaturated chain cholesteryl esters is evaluated by analysis of the phase diagrams in terms of ideal solution theory. Cholesteryl palmitate, which crystallizes in the bilayer structure, forms a eutectic with either cholesteryl oleate or cholesteryl linoleate and, as indicated by low angle X-ray data, the components are nearly totally fractionated in the solid state. The fit of the two experimental liquidas curves by a calculation of freezing point depression for an ideal solution indicates that the molecular interactions are nonspecific in the binary liquid state. Cholesteryl caprylate and cholesteryl oleate, both of which crystallize as the monolayer II form, also form a eutectic. X-ray data again indicate nearly total fractionation. The liquidus curve is reasonably well matched by calculation of ideal freezing point depression. However, dissimilar molecular volumes can cause the melt-cholesteric transition line to deviate from an ideal concentration dependence. Possible fractionation mechanisms for cholesteryl esters in arterial lesions are thereby indicated. For example, when the molecules have greatly different volumes, clustering can occur in the liquid crystalline state. Even when the molecular volumes are similar, the saturated component can solidify in regions where it is relatively abundant, because of the incompatibility of two crystal structures with greatly different layer structures.

Thermodynamic properties of ( xCaF 2 + yAl 2O 3 + (1− x− y)CaO)(l) II. Model description

Experimentally obtained thermodynamic properties of ( xCaF 2 + yAl 2O 3 + (1− x− y)CaO)(l) have been employed to develop a model-description of the system. The model suggested is based on the theory of associated solutions. The liquid solution is supposed to be composed of monomer species CaF 2, Al 2O 3, and CaO, and associated complexes CaO·Al 2O 3 and 2CaO·Al 2O 3. The compositions of the complexes have been chosen so as to be in good agreement with composition functions of a set of physicochemical properties of the melts such as viscosity, electric conductivity, surface tension, and density. In contrast to the regular associated-solution theory the activity coefficients of the monomer species and complexes have been expressed through bulk mole fractions of compounds CaO, Al 2O 3, and CaF 2 in the melt but not as composition functions of monomer molecules and complexes in the solution. The model parameters are supposed to be temperature-dependent, thus accounting for deviations of the entropy of mixing from ideality, caused both by the interactions of particles and their size difference. These assumptions allow us to express equilibrium constants of the association reactions through mole fractions of monomer species complexes, as is accepted in the theory of ideal associated solutions, but not through their activities. As compared with the model of regular associated solutions, the latter result significantly simplifies the calculation procedure. It has been shown that the model suggested describes the thermodynamic properties of ( xCaF 2 + yAl 2O 3 + (1− x− y)CaO)(l) within experimental errors. Computations of a number of phase equilibria have been carried out to prove the reliability of extrapolation of the thermodynamic properties into univestigated regions of ( xCaF 2 + yAl 2O 3 + (1− x− y)CaO)(l). Good agreement between computed and experimentally established phase-equilibria lines was obtained.

Interaction of N-alkylanthracyclines with lipid bilayers: correlations between partition coefficients, lipid phase distributions and thermotropic behavior

The thermotropic behavior of multilamellar vesicles of dipalmitoylphosphatidylcholine (DPPC), or of DPPC in admixture with cardiolipin or cholesterol, in the presence of various N-alkyl derivatives of both adriamycin-14-valerate has been investigated by high sensitivity differential scanning calorimetry. The analogues, particularly the 14-valerate derivatives, which were most lipophilic as judged by their lipid/buffer, and to a lesser extent by their octanol/buffer, partition coefficients, were the most effective in depressing the t m of the investigated lipids; correlations, however, were not absolute. Other factors, such as the distribution of the drugs between the solid and liquid-crystalline phases of the bilayer, were also important to the observed membrane perturbations. With all anthracyclines, however, no major changes in the transition enthalpy were observed. In the case of vesicles prepared from pure DPPC, curve fitting analysis based on ideal solution theory (J.M. Sturtevant (1984) Proc. Natl. Acad. Sci. USA 81, 1398–1400) applied at relatively low drug concentrations where single peak transitions were produced, adequately described the differential scanning calorimetric results. At high drug concentrations, however, the presence of multipeak transitions were indicative of non-ideality.

The effects of calcium channel blocking drugs on the thermotropic behavior of dimyristoylphosphatidylcholine

The effects of four calcium channel blocking drugs, diltiazem, verapamil, nimodipine and nisodlipine, on the main phase transition of dimyristoylphosphatidylcholine have been studied by high resolution differential scanning calorimetry. In all cases, the phase transition temperature is lowered, through much more effectively by nimodipine and nisoldipine than by the other two drugs. Nimodipine and nisoldipine markedly reduce the enthalpy of transition while diltiazem and verapamil have no significant effect on the enthalpy within the drug concentration range studied. Analysis of the data in terms of ideal solution theory is presented. X-ray and neutron scattering studies indicate that nimodipine and verapamil differ significantly with respect to their location within a lipid bilayer, and this difference suggests a partial rationalization of the experimental results presented here.

Study of the equilibrium adsorption of a binary mixture of H2-D2 on zeolite NaX at elevated pressures

1. A method of treatment of experimental data (accounting for nonideality of the gas phase) using the thermal adsorption equation is proposed. The parameters of this equation are found. The proposed approximate dependence satisfactorily describes the experiment. 2. The dependencies of the separation coefficient, α, for a mixture of H2-D2 on the parameters of the adsorptive equilibrium are obtained. It is found that α in a chosen range of parameters does not depend on the total pressure of the gas mixture and with increased temperature ceases to depend on the composition of the gas phase. 3. It is shown that the theory of ideal solution, i.e., the method of estimating the partial pressures of binary mixtures of H2-D2 on zeolite NaX from individual isotherms is not applicable. The given solutions are nonideal and have a positive deviation from Raoult's law.

Co-solubility of saturated cholesteryl esters: A comparison of calculated and experimental binary phase diagrams

Based on ideal solution theory, phase diagrams are calculated for binary compositions of cholesteryl esters and compared to experimental data from pairwise combinations in a saturated acyl chain series from caprylate to arachidate, which encompasses three crystal packing motifs in the solid state. Within a crystal structure class, nearly ideal co-solubility is found for binary solids, where the acyl chain lengths of the pure components differ by one methylene group. Beyond this chain length difference, nonideal solutions occur until fractionation occurs at e.g., six methylene unit increments between the components. The observed liquidus lines of the eutectic are near the theoretical curves when the combinations of two compounds packing in the same crystal structure fractionate. Fractionation also is found when liquids composed of two esters which favor different crystal structures are solidified from the melt, no matter what the chain length difference is; the liquidus curves for re-heated solids, however, are not necessarily predicted by the Schröder equation. In general, co-miscibility can be found in mesophases formed from compounds with two different crystal structures.

The melting temperature of irradiated oxide fuel

The melting temperature of oxide fuel is generally considered to decrease with increasing of burnup because of the buildup of fission products. Melting temperatures were measured for UO 2 and (U, Pu)O 2 fuels. The (U, Pu)O 2 specimens were irradiated to a burnup of 110 GWd/t in FBR. The solidus temperatures of (U, Pu)O 2 were almost independent of burnup up to 50 GWd/t. The melting temperatures were correlated with Pu content, oxygen-to-metal ratio of the fuel and burnup by ideal solution theory.

Sensitivity Analysis on the Comparison between the Gapon and Vanselow Exchange Coefficients

AbstractThe traditional nonthermodynamic Gapon exchange selectivity coefficient (KG) for Na‐Ca exchange has previously been shown in the literature to be in close agreement with the Vanselow coefficient (Kv) for Na equivalent fractions (NNa) in the exchange of <0.20. Furthermore, it has previously been shown for a heterogeneous group of soils that the traditional empirical ESP‐SAR relation (ESP = NNa × 100; ESP = exchangeable sodium percentage and SAR = sodium adsorption ratio) is indistinguishable from the ESP‐SAR relation predicted by the Vanselow equation for NNa <0.40. This study is a sensitivity analysis of the comparison between the Kv and KG for Na+ replacing Ca2+ in the exchange phase. It is carried out by mathematically deriving and graphically demonstrating the interrelationships between Kv and KG. These interrelationships are established on the basis that the Na‐Ca exchange system obeys ideal solid solution theory and thus Kv is reduced to a thermodynamic exchange constant. The results point out that generally, the greater the Kv, the greater the NNa range for which an apparent linear relationship between NNa and SAR is observed. This relationship, however, does not ensure that for the same NNa range the condition KG ≃ Kv is also met. The results show that as NNa approaches 0, KG = 0.50 Kv, and as NNa approaches 1, KG approaches infinity. The results also demonstrate that the condition KG ≃ Kv is dependent on the magnitude of Kv or KG for a limited NNa range, and it is independent of the magnitude of the cation exchange capacity (CEC). The condition KG ≃ Kv appears to have the potential to be met experimentally for Kv values in the range of <0.015 and up to a NNa value of approximately 0.60. At the larger Kv values (≫0.015), the condition KG ≃ Kv is less likely to be met because the absolute difference between Kv and KG is significant even at NNa values <0.20. The Kv, however, is always equal to the KG at NNa = 0.60. This cross‐over point is independent of the magnitude of Kv and CEC.

Prediction of dew points of semicontinuous natural gas and petroleum mixtures. 2. Nonideal solution calculations

A simple method was previously developed based on ideal solution theory for the calculation of dew points of semicontinuous natural gas condensates. The method employed a gamma distribution function with the effective carbon number as the continuous distribution variable. The simple method is extended in this paper to account for nonidealities of the vapor and liquid phases. The new modified approach employs extensions of the viral equation and regular solution theory to continuous mixtures. No adjustable parameters are required, and the predictions are comparable to those of an equation of state method.

Effects of halothane on dipalmitoylphosphatidylcholine liposomes: a Raman spectroscopic study.

Raman spectroscopy has been used to monitor the concentration of halothane (1-bromo-1-chloro-2,2,2-trifluoroethane) in 20% aqueous dispersions of dipalmitoylphosphatidylcholine (DPPC) as well as to follow changes in the acyl chain order within the hydrocarbon interior of the liposomes. Temperature profiles for the gel to liquid-crystalline phase transitions for the liposomes were constructed from changes in peak height intensity ratios in the C-H stretching mode and C-C stretching mode regions. Halothane present at the clinical level produces a change of -0.5 degrees C in the phase transition temperature. A limiting transition temperature of about 21 degrees C and saturation of the gel phase occur when the molar ratio of halothane to DPPC reaches about 1.25. At molar ratios above 2.1, the liquid-crystalline phase is also saturated with halothane. Calculations of the distribution of halothane between the various phases in the system are presented and used to interpret literature data as well as the present experiments. Ideal solution theory accounts rather well for the depression in the transition temperature over most of the mole ratio range, an outcome which implies that halothane is excluded from the hydrocarbon interior but not the head-group region in the gel phase. The role of halothane in the head-group region is discussed.

Prediction of dew points of semicontinuous natural gas and petroleum mixtures. 1. Characterization by use of an effective carbon number and ideal solution predictions

The effective carbon number (ECN) is used as the distribution variable in a gamma distribution function to characterize natural gas and petroleum mixtures containing many components. The ECN offers the advantage over more conventional continuous distribution variables in that it can distinguish between isomers. The resulting function is combined with an ideal-solution theory to develop a simple method to predict dew points of natural gas condensates. The simple method is compared with the modified equation of state approach of other authors and, although it is less accurate in its predictions, is shown to work surprisingly well.

Thermodynamics of mixed micelle formation

A new method of calculating the composition of mixed micelles in equilibrium with monomer of known composition is proposed. This technique applies the Gibbs-Duhem equation to be mixed micelle, which is treated as a pseudophase. The method needs only CMC data as a function of monomer composition, but is limited to binary surfactant systems. The proposed methodology is applied to cationic/cationic, cationic/nonionic, and anionic/nonionic surfactant pairs. The calculated monomer-micelle equilibrium is found to be very similar to that from ideal solution theory for the cationic/cationic system and to the much-used regular solution theory for the nonideal systems.

The vapour pressure behaviour and the association of N-methylethylamine, diethylamine and their N-deuterioanalogues in mixtures with n-hexane

The vapour pressure isotherms of mixtures of N-methylethylamine and N-methyl( N- 2H)ethylamine with n-hexane have been measured between 273 and 323 K. The vapour pressure isotherms of mixtures of diethylamine and ( N- 2H)diethylamine with nhexane between 293 and 353 K have also been measured. In addition, the vapour pressures of the pure amines have been determined down to 228 or 243 K. As evidenced by the small values for the Wilson coefficients, the activity coefficients, the Gibbs free energies and the data derived from the theory of ideal associated solutions, the association of diethlamine is very weak; that of N-methylethylamine is not much larger. The observations on the vapour pressure isotope effect of the two amines and their N-deuterioanalogues are compatible with this interpretation. The normal effect is smaller for diethylamine, with ratios P D/ P H of 0.972–0.997 between 243 and 323 K, than for N-methylethylamine with values of 0.965–0.991, and the partial pressure quotients calculated for mixtures of the two compounds with n-hexane show the transition from the normal to the inverse effect on low dilution. The data for the N-deuterioanalogues and their mixtures with n-hexane suggest a somewhat greater energy of the deuterium bonds.

Effect of substituents on benzoic acid transport across human skin in vitro

The cutaneous transport of substituted bezoic acids is very sensitive to the ring position of the substituent. The flux correlates well with the lipid solubility of the compound, and ideal solution theory can be used to account for the main effects observed.

Solubility of uranium hexafluoride in some low-temperature solvents

The solubility of UF/sub 6/ has been measured in several liquefied gases. Phosgene, nitrous oxide, and sulfur dioxide are found to be good solvents for UF/sub 6/ at temperatures below 0/sup 0/C. The results are compared with ideal and regular solution theory. Regular solution theory provides a reasonably good description of the UF/sub 6//COCI/sub 2/ system but is less good for the UF/sub 6//SO/sub 2/ system.

The effects of water-soluble solutes on the phase transitions of phospholipids.

A previous treatment [Sturtevant, J.M. (1982) Proc. Natl. Acad. Sci. USA 79, 3963-3967], based on ideal solution theory, of the influence of small molecules on the main phase transitions of phospholipid bilayers is extended to include the effect of water solubility of the added solute. This effect is manifested primarily in a sharpening of the phase transition, resulting from a buffering by the aqueous phase of the concentration of the solute in the lipid phases.