Solution structure and Kirkwood-Buff theory: Informativity and sensitivity to specific interactions

A comparative significance of the contribution from density and excess Gibbs energy into Kirkwood-Buff integrals G _ij has been considered exemplified by H₂O-sulfolane, H₂O-THF and model mixtures. It is shown that some salient features of the volume properties which are generally thought to be the sign of strongly hydrophobic behavior of solutes, do not clearly manifest themselves in the concentration dependences of these integrals. Literature data for G _ij have been analyzed and the structural information inherent to G _ij is assessed. Contributions from the first and the following solvation spheres to G _ij have been evaluated from the distribution functions of model mixtures computed by the Born-Green equation and it is shown that with no new chemical bonds, the contribution from the first solvation sphere does not govern the whole of G _ij and, consequently, G _ij as calculated from the thermodynamic properties contain no direct information as far as the details of short-range interactions are concerned.     

Excess Isentropic Compressibilities for 1,3-Dioxolane or 1,4-Dioxane <Emphasis Type="Italic">+</Emphasis> Water <Emphasis Type="Italic">+</Emphasis> Formamide or N,N-Dimethylformamide Ternary Mixtures at 308.15 K

Speeds of sound, u_ijk, of 1,3-dioxolane or 1,4-dioxane (i) + water (j) + formamide or dimethylformamide (k) ternary mixtures and of their binary subsystems, u_ij, of 1,3-dioxolane or 1,4-dioxane (i) + formamide or dimethylformamide (j), and water (i) + formamide or dimethylformamide (j) have been measured over the entire composition range at 308.15 K. The experimental data have been used to evaluate the excess isentropic compressibilities of binary (κ_s^E)_ij and ternary (κ_s^E)_ijk mixtures using their densities calculated from molar excess volume data. The Moelwyn-Huggins concept [M. L. Huggins, Polymer 12, 389 (1971)] of interaction between the surfaces of components of a binary mixture has been employed to evaluate the excess isentropic compressibilities (using the concept of connectivity parameter of third degree of a molecule, ³ξ, which in turn depends on its topology) of binary mixtures, and this method has been extended to predict excess compressibilities of ternary mixtures. Values of (κ_s^E)_ij and (κ_s^E)_ijk have also been calculated by the Flory theory. It was observed that (κ_s^E)_ij and (κ_s^E)_ijk predicted by the Moelwyn-Huggins approach compare well with calculated and experimental values.     

A test of the onsager reciprocal relations and a discussion of the ionic isothermal vector transport coefficientsI Ij for aqueous AgNO3 at 25°C

Values ofI _ij calculated from experimental data are given for AgNO₃ at 25°C. Experimental values of the ratioI ₁₂/I₂₁ are calculated to provide a sensitive direct test of the Onsager reciprocal relations,I ₁₂=I₂₁. This ratio is found to be unity within experimental error (ca. 2%). The general physical interpretation ofI _ij/N as mobilities is discussed. An approximate way of estimatingI _ij for dissociated salts is considered. A comparison is made between AgNO₃ I _ij data and corresponding data for NaCl and KCl. It is concluded that ion-pair formation (1) sharply increases the magnitude of the interaction mobility,I ₁₂/N; and (2) increases the intrinsic mobility of Ag⁺,I ₁₁/N, and decreases the intrinsic mobility of NO ₃ ^– ,I ₂₂/N.     

Effect of Particle Size Distribution on the Rheology of Dispersed Systems

The rheological properties of aqueous polystyrene latex dispersions from three synthetic batches, with nearly the same z-average particle sizes, 400 nm, but varying degrees of polydispersity, 0.085, 0.301, and 0.485, respectively, were systematically investigated using steady-state shear and oscillatory shear measurements. The particles were sized with photon correlation spectroscopy and transmission electron microscopy and were stabilized sterically with PEO–PPO–PEO triblock copolymer (Synperonic F127). Results from steady-state shear measurements show that the viscosities of the systems exhibit shear-thinning behavior at high solid fractions. However, the degree of shear thinning depends on the breadth of particle size distribution, with the narrowest distribution suspension exhibiting the highest degree of shear thinning. The Herschel–Bulkley relationship best describes the flow curves. The relative viscosities as a function of volume fraction data were compared, and it was found that the broadest distribution suspension had the lowest viscosity for a given volume fraction. In addition, the data were fitted to the Krieger–Dougherty equation for hard spheres. A reasonable agreement of theory with experiment is observed, particularly and surprisingly for the very broad distribution. However, when the contribution to the volume due to the adsorbed polymer layer is considered, the agreement between experiment and theory becomes closer for all the suspensions, although the agreement for the broad distribution suspension is now worse. Fitting the Dougherty–Krieger theory to the experimental data based on our experimental maximum packing fractions gives very good agreement for all the systems studied. From oscillatory shear measurements, the moduli were obtained as a function of frequency at various latex volume fractions. The results show general change of the dispersions from viscous (G" > G′) at low volume fractions (0.25–0.30) to moderately elastic (G′ > G") at moderately high volume fractions (0.41–0.45). The change at this concentration level is likely due to some compression and interpenetration of the stabilizing polymer chain at the periphery, indicating the dominance of the interparticle forces. Overall, the very broad distribution was found to have the lowest elastic modulus for a given volume fraction.     

Isentropic Compressibility Changes of Mixing for 1,3-Dioxolane or 1,4-Dioxane + Water + Propanol Ternary Mixtures

Speed of sound data, u_ijk, of 1,3-dioxolane or 1,4-dioxane(i) + water(j) + propan-1-ol or propan-2-ol(k) ternary mixtures and their sub-binary mixtures, u_ij, of 1,3-dioxolane or 1,4-dioxane(i) + water or propan-1-ol or propan-2-ol(j) and water(i) + propan-1-ol or propan-2-ol(j) mixtures have been measured over the entire composition range at 308.15 K. Isentropic compressibility changes of mixing, (κ_s^E)_ij and (κ_s^E) _ijk, for the binary and ternary mixtures have been determined by employing the observed speeds of sound data and densities (calculated from their molar excess volumes data). The (κ_s^E) _ij and (κ_s^E) _ijk values have also been predicated by the graph theoretical approach and the Flory theory. It has been observed that (κ_s^E) _ij and (κ_s^E) _ijk predicted by the graph theoretical approach compare well with their corresponding experimental values.     

Ions in Aqueous Acetic Acid Mixtures: Solvent Reorganization around Protons and Gibbs Energies of Transfer from Water

The photo-absorbing, basic sensor, 4-nitroaniline, has been used to determine theequilibrium constant for solvent reorganization around the proton in mixtures ofvarying composition of water with acetic acid. In all the mixtures used, theself-ionization of the acetic acid was suppressed. In contrast to mixtures of waterwith the related ethanol or acetone, this equilibrium is shifted more toward thewater-solvated species as the mole fraction x ₂ of the cosolvent increases. TheGibbs energy of transfer of protons from water into the mixture G ^o _t (H⁺) can bederived with the aid of this equilibrium constant for the solvent reorganization.Using G ^o _t (H⁺), G ^o _t (i) for i denoting anions and other cations can be evaluated.In comparison the G ^o _t (i) for cations have lower negative values than when eitherethanol or acetone is added to water. Correspondingly, for halide anions, thepositive G ^o _t (i) with added acetic acid are rather less than is found with eitherethanol or acetone added. The influence on the ion-solvent interaction of bothelectron withdrawing hydroxy and carbonyl groups in acetic acid may beresponsible for this. Although G ^o _t (i) for C10^– ₄ and Re0^– ₄ are also positive, both picrateions and OH^– give negative values with acetic acid added to water. With picrateions, the hydrophobic effect of the carbon ring produces stabilization in themixture relative to water. With OH^–, complete conversion to acetate anionsoccurs. As is found with other cosolvents, the contribution of the charge onacetate anion to G ^o _t (CH₃COO^–) is found to increase as x ₂ rises. The aciddissociation constant K _a for acetic acid is found to decrease slowly as x ₂ rises to0.5, followed by a rapid decrease for x ₂ greater than 0.7 where dimerization ofacetic acid occurs.     

Inversion of the Kirkwood–Buff Theory of Solutions: Application to Tetrahydrofuran + Aromatic Hydrocarbon Binary Liquid Mixtures

The Kirkwood–Buff (K-B) integrals play an important role in characterizing the intermolecular interactions in liquid mixtures. The interaction is represented by the K-B parameters, G _AA,G _BB, and G _AB, which reflect correlation between like-like and like-unlike species in the mixture. The K-B integrals of binary mixtures of tetrahydrofuran with benzene, toluene, o-xylene, m-xylene, p-xylene and mesitylene at 298.15 K and atmospheric pressure have been computed from the experimental data of ultrasonic speed and density. We have used the similar inverse procedure (as proposed by Ben-Naim) to compute the K-B parameters of the mixture, in which thermodynamic information on mixtures, such as partial molar volumes, isothermal compressibility and experimental data of partial vapor pressures were used. A new route has been incorporated by using regular solution theory in the computation of excess Gibbs energy for obtaining the partial vapor pressures of binary liquid mixtures. The low values of excess entropy, S ^E≈0, obtained for these mixtures indicate the applicability of regular solution theory to the mixtures. The values of the K-B parameter, G _AB, obtained using this procedure indicate that the correlation/affinity between THF and aromatic hydrocarbon molecules follows the order: benzene > toluene > o-xylene > m-xylene > p-xylene > mesitylene, which is in good agreement with the results obtained from the trends exhibited by the excess functions of these mixtures.     

Predicting Excess Enthalpies of Ether and/or Hydrocarbon Binary Mixtures

Previous applications of the Flory–Patterson theory in the analysis of the excess molar enthalpies at 25°C for some binary mixtures composed of ethers, n-alkanes, br-alknes, and cycloalkanes are reviewed. The possibility of correlating the Flory interaction parameters X _ij in terms of the acentric factors of the components is examined. For selected ether (1) + n-alkane(2) mixtures, a set of linear relations between X ₁₂ and the acentric factors of the n-alkanes are reported.Visiting Professor on sabbatical leave from the     

Intradiffusion coefficients in perchloric acid solutions: Water at 5°C; water and perchlorate ion at 25°C

Intradiffusion coefficients for tritiated water (³HHO) and perchlorate ion (³⁶ClO ₄ ^- ) were measured in perchloric acid solutions. At 5°C the diffusion coefficient measured for the tritiated species increases to a maximum near 1.3 mol-dm^–3. The data at 25°C have been used to calculate distinct diffusion coefficients, D _ij ^d . As a precursor for those calculations, new estimates were made of the Onsager phenomenological coefficients, l _ij . The l _ij and D _ij ^d are similar to the respective coefficients in hydrochloric acid solutions.     

Effect of Solvent Polarity on the Electronic Structure and Emission Frequencies of Exciplexes of Aromatic Hydrocarbons with Methoxybenzenes and Methylnaphthalenes

The dependence of exciplex emission spectra on the solvent polarity was studied for exciplexes with the Gibbs free energy of excited-state electron transfer, G ^* _et , exceeding –0.1 eV (for pyrene, fluoranthene, 1,12-benzoperylene, and 9-cyanoanthracene with methoxybenzenes or dimethylnaphthalene). These exciplexes showed stronger changes in the spectral shift of exciplex emission and the extent of charge transfer with increasing solvent polarity than the exciplexes having more negative G ^* _et values. The parameters (difference in energy of charge transfer (CT) and locally excited (LE) states in a vacuum, (H ⁰ ₂₂– H ⁰ ₁₁), and the matrix element for electronic coupling of CT and LE states H ₁₂and mrelated to the dipole moment of the CT state and the size of the exciplex) determining the extent of charge transfer, the spectral shift, and other properties of exciplexes were evaluated. The parameters H ₁₂and mfor the exciplexes examined fall in the interval 0.1–0.5 and 1.0–1.7 eV, respectively, and the difference (H ⁰ ₂₂– H ⁰ ₁₁) is proportional to G ^* _et .     

Potential-dependent chemisorption of carbon monoxide on platinum electrodes: new insight from quantum-chemical calculations combined with vibrational spectroscopy

Density functional theory (DFT) using the finite cluster approach is utilized to compute binding energies, bond geometries, and vibrational properties of carbon monoxide adsorbed on Pt(111) as a function of the external interfacial field, focusing attention on the metal–CO bond itself. Comparison with electrode potential-dependent frequencies for the metal–CO (ν_M–CO) as well as the much-studied intramolecular C---O (ν_CO) vibration, as measured by in-situ Raman and infrared spectroscopy, facilitate their interpretation in terms of metal-chemisorbate bonding for this archetypal electrochemical system. Decomposing the calculated metal–CO binding energy and vibrational frequencies into individual orbital and steric repulsion components enables the role of such quantum-chemical interactions to the field- (and hence potential-) dependent bonding to be assessed. No simple relationship between the field(F)-dependent binding energies and the ν_M–CO frequencies is evident. While the DFT ν_M–CO–F slopes are negative at positive and small–moderate negative fields, reflecting the prevailing influence of back-donation, a ν_M–CO–F maximum is obtained at larger negative fields for atop CO, and a plateau for hollow-site CO. This Stark-tuning behavior reflects largely offsetting field-dependent contributions from π and σ surface bonding, and can also be rationalized on the basis of changes in the electrostatic component of ν_M–CO from increasing M–CO charge polarization. A rough correlation between the field-dependent ν_M–CO frequencies and the corresponding bond distances, r_M–CO, is observed for hollow and atop CO in that r_M–CO shortens towards less positive fields, but becomes near-constant at moderate–large negative fields. A more quantitative correlation between the field-dependent C---O frequencies and bond lengths is also evident. In harmony with earlier findings (and unlike the ν_M–CO–F behavior), the ν_CO–F dependence is due chiefly to changes in the back-donation bonding component. The overall vibrational frequency-field behavior predicted by DFT is also in semi-quantitative concordance with experimental potential-dependent spectra.     

Calculating poly(ethylene-co-acrylic acid)-solvent phase behavior with the SAFT equation of state

Statistical Associating Fluid Theory (SAFT) is used to model the cloud-point behavior of poly(ethylene-co-acrylic acid), with up to 7 mol % acid content, in propane, butane, propylene, butene, and dimethyl ether at temperatures to 250°C and pressure to 2600 bar. The values for the pure component temperature-independent segment volumes, nonspecific interaction energies, and the numbers of segments per molecule are equal to those used for polyethylene, because these copolymers contain modest amounts of acrylic acid repeat units. Two different approaches are used to determine values of the pure component energy of hydrogen bonding, ?/k, and the binary interaction parameter, k_ij. In one approach, ?/k for acid dimerization is obtained from literature spectroscopic data and a constant value of k_ij is fit to each copolymer-solvent cloud-point curve. Increasing the value of k_ij shifts the predicted cloud-point curves to higher temperatures and pressures. For the five solvents used in this study, k_ij decreased steadily in the range of 0.040 to ?0.025 as the acid content in the copolymer increased. The predicted cloud-point curves are in good agreement with experimental data, and the impact of hydrogen bonding on the phase behavior is well represented, even if k_ij is set equal to zero. For the second approach, ?/k is set to ～ 90% of the value obtained from spectroscopic data as determined from a fit of a single poly(ethylene-co-acrylic acid)-butane cloud-point curve, while k_ij is fit to the corresponding polyethylene-solvent system. This approach requires less mixture data than the previous approach, and the calculated cloud-point curves are also in good agreement with experimental data, except for the EAA-DME systems. © 1995 John Wiley & Sons, Inc.     

Molecular Interactions in Formamide + Isomeric Butanols: An Ultrasonic and Volumetric Study

Densities, , ultrasonic speeds, u and viscosities, of the binary mixtures of formamide (FA) with 1-butanol, 2-methyl-1-propanol, and 2-methyl-2-propanol, including those of pure liquids, were measured over the whole composition range at 35°C. Using the experimental values of , u and , the deviations in isentropic compressibility, _s , excess volume, V ^E, viscosity, , and excess Gibbs energy of activation of viscous flow, G* ^E , were calculated from the linear dependence of these parameters on composition of mixtures. The apparent molar isentropic compressibility, K _,2 and apparent molar volume, V ^,2 of alcohols in FA were also calculated. The variations of these parameters with composition are discussed from the point of view of intermolecular interactions in these mixtures. The V ^E data have also been analyzed using Prigogine–Flory–Patterson theory. An analysis of each of the three contributions, viz., interactional, free volume, and P* effect to V ^E shows that P*, the internal pressure parameter of the theory, plays a dominant role in deciding the sign and magnitude of V ^E.     

Thermodynamics of molecular interactions in ethyl iodide+toluene mixtures

The excess Gibb's free energy of mixing, G^E, for ethyl iodide+toluene at 25°C have been obtained from the measured vapor pressuure data. The H^E and G^E values for ethyl iodide+toluene are positive throughout the ethyl iodide concentration range and G^E>H^E. The results have been analyzed in terms of Flory and ideal associated model theory of nonelectrolyte solutions. It has been observed that the ideal associated model approach which assumes the presence of AN and A₂B molecular species describes well (within±10 J-mol^–1 in the worst case) the general dependence of H^E on X_A (mole fraction of ethyl iodide) over the whole composition range for ethyl iodide+toluene mixtures. The equilibrium constants for A+A AB and 2A+BA₂B reactions along with the enthalpies of formation of AB and A₂B molecular species have been calculated.     

Theoretical studies of the benzene oxide—oxepin valence tautomerism

We have calculated the geometry and energy of the valence tautomers benzene oxide and oxepin using the semiempirical AM1 model and the 6–31G and 6–31G^* basis sets utilizing full geometry optimization. In the oxide the folding angle, the angle between the epoxide ring and the adjacent plane containing four carbon atoms, is about 106°. The carbon skeleton is almost planar, the folding angle, the angle between the two four-carbon atom planes being about 175°. In contrast, oxepin is found to have a marked boat-shaped structure with the corresponding and angles about 137° and 159°, respectively. The AM1, 6–31G, and 6–31G^* calculations give –11.4, –10.8, and –2.9 kcal mol^–1 for the energy change that accompanies the valence tautomerism, oxide-oxepin, compared to an experimental value of about +0.3 kcal mol^–1. Single point calculations of the energies at the 6–31 G^* geometry using Møller-Plesset perturbation theory to second order (MP2/6–31 G^*) and third order (MP3/6–31G^*) give E _T =+3.3 and +0.8 kcal mol^–1. The values for the energy change in the transfer of epoxide oxygen from ethylene oxide to benzene using AM1, 6–31G, and 6–31G^* are in good agreement, viz., +31.1, +34.5, and +33.6 kcal mol^–1, respectively. A large positive energy change is to be expected in view of the loss of benzene aromaticity.     

MD Simulation of an Infinitely Dilute Aqueous Solution of Formamide. Study of Thermodynamic, Structural, Dynamic, and Spectroscopic Properties

A molecular dynamics simulation of an infinitely dilute aqueous solution of formamide was carried out using an MP2-CP ab initio potential to describe the solute–solvent interaction. Various static and dynamic properties were calculated using this potential obtained by fitting the formamide–water interaction energies to a 12-6-1 type function. These energies were calculated with the supermolecular approach by considering the MP2 correlation and the CP superposition. The values presented for the thermodynamic functions (H _S–W = –25.5 kcal-mol^–1 and G _S–W = –15.9 kcal-mol^–1), the structure of the first hydration layer (with 5 to 6 solvent molecules bonded to the solute), the solute's translational (D= 1.50 × 10^–5 cm²-s^–1) and rotational ( = 6.6 ps) mobility in the surrounding medium, and the positions of the H···O hydrogen bond spectral bands corresponding to these motions (_i = 92, 246, 379, and 636 cm^–1), are in agreement with the available results for this and other similar systems. In addition, the results are compared with those obtained by using parameters transferred from other systems. We observed that these values depend strongly on the potential used and concluded that it is advisable to avoid the use of such parameters.     

Reexamination of the C2H4F potential surface. the status of the classical 2-fluoroethyl cation: a local minimum or transition structure?

According to ab initio molecular orbital calculations carried out with full geometry optimization at the MP2/6–31G^** level, the classical 2-fluoroethyl cation, FCH₂CH₂⁺, is a transition structure for H-scrambling in CH₃CHF⁺. Single point MP4/6–31G^** calculations at the optimized geometries predict the cyclic ethylene fluoronium ion to lie 24.2 kcal mol⁻¹ above CH₃CHF⁺ and 5.4 kcal mol⁻¹ below the 2-fluoroethyl cation. ΔG‡ for ring opening of the cyclic fluoronium ion at -60° is estimated to be ca 15 kcal mol⁻¹. This barrier is largely attributable to the powerful negative fluorine hyperconjugation in the transition state as described by Hoffmann and coworkers. When electron correlation effects are ignored a qualitatively different potential surface is obtained on which the 2-fluoroethyl cation is calculated to be a local minimum separated from the stable 1-fluoroethyl cation by an H-bridged transition state.     

Ab initio investigation of tautomeric stability,molecular structure,and internal rotation of methylphosphonic dicyanide,methoxydicyanophosphine, and their isocyano analogs

The equilibrium geometric parameters and structures of the transition states of internal rotation for MeP(O)(CN)₂, McOP(CN)₂, and their isocyano analogs, MeP(O)(NC)₂ and MeOP(NC)₂, have been calculated by theab initio SCF method and with inclusion of electron correlation effects according to the second-order Muuller-Plesset perturbation theory (MP2). At both levels the 6-31G* basis set has been used. The estimation of relative stability of these tautomeric forms depends largely on the calculation level. The total energies of the cyanides calculated by the MP2 method are 25–30 kcal mol^–1 lower than those of the corresponding isocyanides. The oxo-tautomeric forms containing four-coordinate phosphorus are 15–25 kcal mol^–1 more stable than the three-coordinate phosphorus aci-derivatives. The internal rotation potential curves of the aci-forms are characterized by a deep minimum for thetrans-arrangement of the methoxy group and phosphorus lone electron pair. Two additional less clearly pronounced minima are located symmetrically on both sides of the weak maximum, which corresponds to thecis-arrangement. The equilibrium oxo-form structures have a staggered configuration of the methyl group with respect to the phosphorus atom bonds.Translated from izvestiyaAkademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1104–1115, May, 1996.     

Structure of Liquid Pb-Bi Alloys by X-ray Diffraction

Abstract

X-ray diffraction measurement were made at temperatures about 50°C above liquidus in the Pb-Bi system. Three partial structure factors S_ij(Q) were evaluated from the observed X-ray intensities assuming that each S_ij(Q) is independent on the relative abundance of the constituent elements in the alloys. The partial reduced distribution functions G_ij(r) were also calculated. The functions S_ij(Q) and G_ij(r) have maxima which lie between those of the pure elements. The radii of the first coordination sphere show a linear dependence on the concetration as expected from random distribution of the atoms in liquid Pb-Bi alloys. A comparison was made between the partial and total structure factors obtained in this work and those calculated from the hard sphere model. Adequate agreement was obtained on the first peak, but good agreement of the damping behaviour and phase was not necessarily found.     

Application of Kirkwood-Buff theory of liquid mixtures to water-butanol system

The various integrals over the pair correlation functions G_AA' G_WW, and G_AW were calculated for the t-butanol(A)-water(W) system (0 to 8 mole % alcohol) at 25°C by utilizing the thermodynamic quantities, the isothermal compressibility, partial molal volumes, and vapour pressure and by the application of an inverse procedure for Kirkwood-Buff theory of solutions as suggested by Ben-Naim. It is observed that as functions of concentration G_AA', G_AW, and G_WW have extrema in the concentration range studied. The results are interpreted on the basis of structural changes of solvent water. The behavior of G_AA in the concentration range of 0 to 4 % of t-butanol indicates that the strength of hydrophobic interactions decreases with concentration as x_A increases from 0 to 0.04.