Excess around a central molecule with application to binary mixtures

It was shown by us (J. Phys. Chem. B, 2006, 110, 12707) that the excess (deficit) of any species i around a central molecule j in a binary mixture is not provided by c(i)G(ij) (where c(i) is the molar concentration of species i in the mixture and G(ij) are the Kirkwood-Buff integrals) as usually considered and that an additional term, involving a volume V(j) which is inaccessible to molecules of species i because of the presence of the central molecule j, must be included. In this paper, the new expression is applied to various binary mixtures and used to establish a simple criterion for preferential solvation in a binary system. First, it is applied to binary Lennard-Jones fluids. The conventional expression for the excess (deficit) in binary mixtures, c(i)G(ij), provides always deficits around any central molecule in such fluids. In contrast, the new expression provides excess for one species and deficit for the other one. In addition, two kinds of binary mixtures involving weak (argon/krypton) and strong (alcohols/water) intermolecular interactions were considered. Again, the conventional expression for the excess (deficit) in a binary mixture, c(i)G(ij), provides always deficits for any central molecule in the argon/krypton mixture, whereas the new expression provides excess for argon (a somewhat smaller molecule) and deficit for krypton. Three alcohol/water binary mixtures (1-propanol/water, tert-butanol/water and methanol/water) with strong intermolecular interactions were considered and compared with the available experimental information regarding the molecular clustering in solutions. We found (for 1-propanol/water and tert-butanol/water) a large excess of alcohols around a central alcohol molecule and a large excess of water around a central water molecule. For both mixtures the maximum of the calculated excess with respect to the concentration corresponds to the maximum in the cluster size found experimentally, and the range of alcohol concentrations in which the calculated excess becomes very small corresponds to the composition range in which no clusters could be identified experimentally.     

Multiexponential decay autocorrelation function in dynamic light scattering in near-critical ternary liquid mixture

The dynamic structure factor of a ternary liquid mixture is calculated from the theory of thermodynamic fluctuations with the help of linearized hydrodynamic equations. The theoretical model allows evaluating and classifying the transport properties near a critical solution point of a ternary mixture. In the vicinity of the critical solution point, experimental dynamic light scattering measurements reveal two hydrodynamic relaxation modes with well-separated characteristic relaxation times. From the autocorrelation functions, we can determine two effective diffusivities D(1) and D(2). As theoretically predicted by a model developed in this work, one of these two modes can be associated with thermal diffusion and the other with mass diffusion. In the special case of an incompressible liquid mixture limit, D(1) and D(2) are decoupled, becoming thermodiffusion coefficient D(T) and mutual mass diffusion coefficient D(ij). A possible physical meaning of D(1) and D(2) for a ternary mixture is discussed.     

Syntheses, structural analyses and redox kinetics of four-coordinate [CuL2]2+ and five-coordinate [CuL2(solvent)]2+ complexes (L = 6,6'-dimethyl-2,2'-bipyridine or 2,9-dimethyl-1,10-phenanthroline): completely gated reduction reaction of [Cu(dmp)2]2+ in nitromethane

[Cu(2,9-dimethyl-1,10-phenanthroline)(2)](2+) and [Cu(6,6'-dimethyl-2,2'-bipyridine)(2)](2+/+) complexes with no coordinated solvent molecule were synthesized and the crystal structures were analyzed: the coordination geometry around the Cu(i) center was in the D(2d) symmetry while a D(2) structure was observed for the four-coordinate Cu(ii) complexes. Coordination of a water or an acetonitrile molecule was found in the trigonal plane of the five-coordinate Cu(ii) complex in the Tbp(trigonal bipyramidal) structure. Spectrophotometric analyses revealed that the D(2) structure of the Cu(ii) complex was retained in nitromethane, although a five-coordinate Tbp species (green in color), was readily formed upon dissolution of the solid (reddish brown) in acetonitrile. The electron self-exchange reaction between D(2d)-Cu(I) and D(2)-Cu(II), observed by the NMR method, was very rapid with k(ex)=(1.1 +/- 0.2) x 10(5) kg mol(-1) s(-1) at 25 degrees C (DeltaH*= 15.6 +/- 1.3 kJ mol(-1) and DeltaS*=-96 +/- 4 J mol(-1) K(-1)), which was more than 10 times larger than that reported for the self-exchange reaction between D(2d)-Cu(I) and Tbp-Cu(II) in acetonitrile. The cross reduction reactions of D(2)-Cu(ii) by ferrocene and decamethylferrocene in nitromethane exhibited a completely gated behavior, while the oxidation reaction of D(2d)-Cu(i) by [Ni(1,4,7-triazacyclononane)(2)](3+) in nitromethane estimated an identically large self-exchange rate constant to that directly obtained by the NMR method. The electron self-exchange rate constant estimated from the oxidation cross reaction in 50% v/v acetonitrile-nitromethane mixture was 10 times smaller than that observed in pure nitromethane. On the basis of the Principle of the Least Motion (PLM) and the Symmetry Rules, it was concluded that gated behaviors observed for the reduction reactions of the five-coordinate Cu(ii)-polypyridine complexes are related to the high-energy C(2v)--> D(2d) conformational change around Cu(ii), and that the electron self-exchange reactions of the Cu(ii)/(i) couples are always adiabatic through the C(2v) structures for both Cu(ii) and Cu(i) since the conformational changes between D(2d), D(2) and C(2v) structures for Cu(i) as well as the conformational change between Tbp and C(2v) structures for Cu(ii) are symmetry-allowed. The completely gated behavior observed for the reduction reactions of D(2)-Cu(ii) species in nitromethane was attributed to the very slow conformational change from the ground-state D(2) to the entatic D(2d) structure that is symmetry-forbidden for d(9) metal complexes: the very slow back reaction, the forbidden conformational change from entatic D(2d) to the ground-state D(2) structure, ensures that the rate of the reduction reaction is independent of the concentration of the reducing reagent.     

Ethanol, acetic acid, and water adsorption from binary and ternary liquid mixtures on high-silica zeolites

Adsorption isotherms were measured for ethanol, acetic acid, and water adsorbed on high-silica ZSM-5 zeolite powder from binary and ternary liquid mixtures at room temperature. Ethanol and water adsorption on two high-silica ZSM-5 zeolites with different aluminum contents and a high-silica beta zeolite were also compared. The amounts adsorbed were measured using a recently developed technique that accurately measures the changes in adsorbent/liquid mixture density and liquid concentration. This technique allows the adsorption of each compound in a liquid mixture to be measured. Adsorption data for binary mixtures were fit with the dual-site extended Langmuir model, and the parameters were used to predict ternary adsorption isotherms for each compound with reasonable accuracy. In ternary mixtures, acetic acid competed with ethanol and water for adsorption sites and reduced ethanol adsorption more than it reduced water adsorption.     

Prediction of ternary vapor–liquid equilibria for 33 systems by molecular simulation

A set of molecular models for 78 pure substances from prior work is taken as a basis for systematically studying vapor–liquid equilibria (VLE) of ternary systems. All 33 ternary mixtures of these 78 components for which experimental VLE data are available are studied by molecular simulation. The mixture models are based on the modified Lorentz–Berthelot combining rule that contains one binary interaction parameter which was adjusted to a single experimental binary vapor pressure of each binary subsystem in prior work. No adjustment to ternary data is carried out. The predictions from the molecular models of the 33 ternary mixtures are compared to the available experimental data. In almost all cases, the molecular models give excellent predictions of the ternary mixture properties.     

Reassessment of the binary, ternary, and quaternary interactions in mixed electrolytes from thermodynamic quantities: The systems with uncommon ions containing hydrophobic character

Accurate estimates of the binary, ternary, and quaternary interactions in aqueous ionic mixtures with uncommon ions with hydrophobic character are presented. For this purpose, the values of the excess Gibbs free energy of mixing, Delta m G(E), obtained from our earlier isopiestic osmotic coefficients (Kumar, A. J. Phys. Chem. B2003, 107, 2808) for the mixtures of NaCl with four guanidinium (Gn+) salts-CH3COOGn, GnNO3, GnClO4, and Gn2SO4-are analyzed with the help of the method developed by Leifer and Wigent. The methodology of Leifer and Wigent is based on the equations of Scatchard-Rush-Johnson and Friedman's cluster integral expansion theory. The Scatchard-Rush-Johnson theory explicitly considers the quaternary and higher-order ionic interactions in the mixtures as compared to the specific ion interaction theory of Pitzer, which accounts for binary and ternary interactions only. The contributions due to binary, ternary, and quaternary interaction terms to total Delta m G(E) are estimated and discussed critically. Also, the interaction between the same two cations, for example, Gn+ - Gn+, is estimated and found significant, which otherwise cannot be obtained by the use of Pitzer's theory. The information obtained from the analysis of Delta(m)G(E) is also supported by the newly measured excess volumes of mixing, Delta m V(E), at 298.15 K. The individual contributions of the binary, ternary, and quaternary interaction terms to total Delta m V(E) are described. The binary, ternary, and quaternary interaction terms for both Delta m G(E) and Delta m V(E) are analyzed in terms of Friedman's cluster integral expansion theory.     

Molecular dynamics simulations of gas separations using faujasite-type zeolite membranes

Gas separations with faujasite zeolite membranes have been examined using the method of molecular dynamics. Two binary mixtures are investigated, oxygen/nitrogen and nitrogen/carbon dioxide. These mixtures have been found experimentally to exhibit contrasting behavior. In O(2)/N(2) mixtures the ideal selectivity (pure systems) is higher than the mixture selectivity, while in N(2)/CO(2) the mixture selectivity is higher than the ideal selectivity. One of the key goals of this work was to seek a fundamental molecular level understanding of such divergent behavior. Our simulation results (using previously developed intermolecular models for both the gases and zeolites investigated) were found to replicate this experimental behavior. By examining the loading of the membranes and the diffusion rates inside the zeolites, we have been able to explain such contrasting behavior of O(2)/N(2) and N(2)/CO(2) mixtures. In the case of O(2)/N(2) mixtures, the adsorption and loading of both O(2) and N(2) in the membrane are quite competitive, and thus the drop in the selectivity in the mixture is primarily the result of oxygen slowing the diffusion of nitrogen and nitrogen somewhat increasing the diffusion of oxygen when they pass through the zeolite pores. In N(2)/CO(2) systems, CO(2) is rather selectively adsorbed and loaded in the zeolite, leaving very little room for N(2) adsorption. Thus although N(2) continues to have a higher diffusion rate than CO(2) even in the mixture, there are so few N(2) molecules in the zeolite in mixtures that the selectivity of the mixture increases significantly compared to the ideal (pure system) values. We have also compared simulation results with hydrodynamic theories that classify the permeance of membranes to be either due to surface diffusion, viscous flow, or Knudsen diffusion. Our results show surface diffusion to be the dominant mode, except in the case of N(2)/CO(2) binary mixtures where Knudsen diffusion also makes a contribution to N(2) transport.     

Experimental and predicted excess molar volumes of the ternary system.

Summary Experimental excess molar volumes for the ternary system x₁MTBE+x₂1-propanol+(1-x₁-x₂) heptane and the three involved binary mixtures have been determined at 298.15 K and atmospheric pressure. Excess molar volumes were determined from the densities of the pure liquids and mixtures, using a DMA 4500 Anton Paar densimeter. The ternary mixture shows maximum values around the binary mixture MTBE+heptane and minimum values for the mixture MTBE+propanol. The ternary contribution to the excess molar volume is negative, with the exception of a range located around the rich compositions of 1-propanol. Several empirical equations predicting ternary mixture properties from experimental binary mixtures have been applied.     

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.     

用二元交互作用函数预测高压下多组分体系的气液平衡

用和体系的状态有关且满足不变性条件的二元交互作用函数,结合F函数修改的立方状态--方程FRKS方程,预测高压下多组分体系的气液平衡.选择15个三元体系及其组分二元系来检验方法的可行性,这些体系覆盖了从简单的接近理想溶液行为的体系到高度非理想体系.计算结果表明,该方法不仅能相当精确地关联各种类型二元系的气液平衡,而且能在仅用组分二元系参数的条件下较准确地预测所考察的所有三元体系的气液平衡     

Viscosities of the ternary mixture (cyclohexane+tetrahydrofuran+chlorocyclohexane) at 298.15 and 313.15 K

Viscosities of the ternary mixture (cyclohexane+tetrahydrofuran+chlorocyclohexane) and the binary mixtures (cyclohexane+tetrahydrofuran and cyclohexane+chlorocyclohexane) have been measured at normal pressure at the temperatures of 298.15 and 313.15 K. The viscosity data for the binary and ternary mixtures were fitted to a McAllister-type equation [R.A. McAllister, AIChE J. 6 (1960) 427–431]. Viscosity deviations for the binary and ternary mixtures were fitted to Redlich–Kister's and Cibulka's equations [I. Cibulka, Coll. Czech. Chem. Commun. 47 (1982) 1414–1419]. The group contribution method proposed by Wu [D.T. Wu, Fluid Phase Equilib. 30 (1986) 149–156] has been used to predict the viscosity of the binary and ternary systems.     

Experimental excess molar volumes of the ternary mixture and comparisonwith several empirical methods

Experimental excess molar volumes for the ternary system {x₁MTBE+x₂1-propanol+(1–x₁–x₂)nonane} and the three involved binary mixtures have been determined at 298.15 K and atmospheric pressure. Excess molar volumes were determined from the densities of the pure liquids and mixtures, using a DMA 4500 Anton Paar densimeter. The ternary mixture shows maximum values around the binary mixture MTBE+nonane and minimum values for the mixture MTBE+propanol. The ternary contribution to the excess molar volume is negative, with the exception of a range located around the rich compositions of 1-propanol. Several empirical equations predicting ternary mixture properties from experimental binary mixtures have been applied.     

Determination of the individual specific heat capacities of solids from multi-component powder mixtures and polymorphic mixtures

This study describes a method to determine the specific heat capacities of individual solids from multi-component solid mixtures. To achieve this end, powder X-ray diffraction measurements are used to provide information on the number and identity of constituents as well as their compositions while calorimetry measurements give the specific heat capacities of the bulk solid mixtures. The method is applied to investigate three different solid mixture systems, namely (i) ternary organic mixtures containing α-glycine, α-lactose monohydrate, and paracetamol; (ii) ternary inorganic mixtures containing calcium fluoride, titanium nitride, and tungsten carbide; and (iii) polymorphic mixtures of α- and γ-glycine. All systems are investigated at 298.15 K and at atmospheric pressure. The results show that the specific heat capacities of individual solids determined from multi-component solid mixtures are in good agreement with those directly determined from pure solid compounds.     

Thermodynamic consistency of high pressure ternary mixtures containing a compressed gas and solid solutes of different complexity

A thermodynamic consistency test applicable to high pressure binary gas–solid mixtures is extended to ternary mixtures containing a compressed gas and two solid solutes. A high pressure mixture containing carbon dioxide as solvent and two chemically similar solutes (2,3 dimethylnaphthalene and 2,6 dimethylnaphthalene) and a high pressure mixture containing carbon dioxide as solvent and two chemically different solutes (capsaicin and β-carotene), are considered in the study. Several sets of isothermal solubility data for binary and ternary mixtures are considered in the study. The Peng–Robinson equation of state with the mixing rules of Wong and Sandler have been employed for modeling the solubility of the solid in the case of binary mixtures, while the classical van der Waals mixing rules were used for modeling the ternary mixtures containing two solid solutes. Then the proposed thermodynamic consistency test has been applied. The results show that the thermodynamic test for ternary mixtures can be applied with confidence determining consistency or inconsistency of the experimental data used.     

Spinodal decomposition with varying chain lengths and its application to designing polymer blends

The diffusion equations of spinodal decompositions with unique diffusivities for each species are derived for binary systems and ternary systems. These dynamic equations are linearized to show that the minimum size for growth is independent of diffusivity and is identical to the thermodynamic minimum on phase volume. Increases in chain length will destabilize mixtures and increase quench depth. Numerical simulations were conducted for two-dimensional systems. The considerable influences of chain lengths on morphology represent a competition between smaller diffusivities and larger quench depth when chain length is increased. These influences on several important morphologies in binary and ternary systems are described. The understanding of independent variable chain lengths represents one further step towards the systematical design of polymer blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 897–907, 1997     

Volumetric behavior of a bolaamphiphile in different amides-water and ethylene glycol-water mixtures

The effect of binary aqueous mixtures of ethylene glycol (EG), formamide (FA), N-methylformamide (NMF), dimethylformamide (DMF), and their pure phase on the apparent molar volume phi(V) of the bolaamphiphile decamethonium bromide (C10Me6) has been investigated at 298.15 K. The behavior of standard molar volumes V2(0) and transfer volumes Delta(t)phi(V) of C10Me6 from water to solvent/water (S/W) binary mixtures, shows different minima and maxima depending on the composition of the solvent. This behavior is influenced by the nature of the cosolvent and on the type of the solute and more or less corresponds to volumetric changes in the S/W mixture. The investigation of the transfer volumes in different fixed concentrations reveals an inversion of Delta(t)phi(V) values between the compositions, which suggests a differentiation of the effects of different volume contributions on the partial molar volume of ions. The correlation of Delta(t)phi(V) with the dielectric constant of the aqueous amide mixtures shows that the behavior of Delta(t)phi(V) vs x(amide) reflects the changes of epsilon(E) vs x(amide).     

Ternary mixture MTBE+1-pentanol+nonane at 298.15 K and atmospheric pressure

Densities at 298.15 K and atmospheric pressure have been measured, using a DMA 4500 Anton Paar densimeter, for the ternary mixture methyl tert-butyl ether (MTBE)+1-pentanol+nonane and for the involved binary mixture 1-pentanol+nonane. In addition, excess molar volumes were determined from the densities of the pure liquids and mixtures. Suitable fitting equations have been used in order to correlate adequately the excess molar volumes. Experimental data were also used to test several empirical expressions for estimating ternary properties from experimental binary results.     

The Kirkwood-Buff theory of solutions and the local composition of liquid mixtures

The present paper is devoted to the local composition of liquid mixtures calculated in the framework of the Kirkwood-Buff theory of solutions. A new method is suggested to calculate the excess (or deficit) number of various molecules around a selected (central) molecule in binary and multicomponent liquid mixtures in terms of measurable macroscopic thermodynamic quantities, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volumes. This method accounts for an inaccessible volume due to the presence of a central molecule and is applied to binary and ternary mixtures. For the ideal binary mixture it is shown that because of the difference in the volumes of the pure components there is an excess (or deficit) number of different molecules around a central molecule. The excess (or deficit) becomes zero when the components of the ideal binary mixture have the same volume. The new method is also applied to methanol + water and 2-propanol + water mixtures. In the case of the 2-propanol + water mixture, the new method, in contrast to the other ones, indicates that clusters dominated by 2-propanol disappear at high alcohol mole fractions, in agreement with experimental observations. Finally, it is shown that the application of the new procedure to the ternary mixture water/protein/cosolvent at infinite dilution of the protein led to almost the same results as the methods involving a reference state.     

The prediction of isobaric phase equilibria for non-ideal multicomponent mixtures from heat of mixing data

A method for predicting isobaric binary and ternary vapor—liquid equilibrium data using only isothermal binary heat of mixing data and pure component vapor pressure data is presented. Three binary and two ternary hydrocarbon liquid mixtures were studied. The method consists of evaluating the parameters of the NRTL equation from isothermal heat of mixing data for the constituent binary pairs. These parameters are then used in the multicomponent NRTL equation to compute isobaric vapor—liquid equilibrium data for the ternary mixture. No ternary or higher order interaction terms are needed in the ternary calculations because of the nature of the NRTL equation. NRTL parameters derived from heat of mixing data at one temperature can be used to predict vapor—liquid equilibrium data at other temperatures up to the boiling temperature of the liquid mixture.For the systems studied this method predicted the composition of the vapor phase with a standard deviation ranging from 1–8% for the binary systems and from 4–12% for the ternary systems.