Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

A Comparative Investigation of Mixing Rules for Property Prediction in Multicomponent Electrolyte Solutions

A mathematical technique is developed to investigate physicochemical property prediction of solution mixtures from the corresponding properties of the pure dissolved systems, as is often expressed in empirical ‘mixing rules’ such as those of Young and of Zdanovskii. A systematic method to distinguish between the inherent characteristics of such rules is needed because experimental studies have proved indecisive. Sound mixing rules must be found to support current efforts in thermodynamic modelling where conventional approaches like the Pitzer equations lack robustness. Density differences relative to pure water, osmotic coefficients and heat capacities are investigated with mixtures including {NaCl + MgCl₂}(aq) and {NaCl + Na₂SO₄}(aq) as specific examples representing common-anion and common-cation asymmetric strong electrolyte solutions respectively. Water activity curves for hydrochloric acid and the alkali metal chloride solutions are also considered. The results confirm that, at the present state of the art, differences between mixing rules are for the most part insignificant at 25 °C, being about the same or less than would be expected from experimental uncertainty. As the predicted differences are even smaller at higher temperature, it can be posited that all reasonably well-established mixing rules in the literature will give approximately equivalent and satisfactory predictions of solution properties under superambient conditions. This is particularly important since the effects of temperature on the magnitude of ternary interactions are not well known from experiment.     

On the thermodynamics of the McMillan–Mayer state function

The osmotic second virial coefficient is a key parameter in light scattering, protein crystallisation, self-interaction chromatography, and osmometry. The interpretation of the osmotic second virial coefficient depends on the solution theory. On the macroscopic level an expansion of the osmotic pressure is employed. A common statistical interpretation of the osmotic second virial coefficient of the expansion employs the McMillan–Mayer framework and the potential of mean force to characterise the solute–solute interaction. Supplementary to the statistical interpretation, it may be advantageous to develop the McMillan–Mayer framework in a classical thermodynamic context for which we develop the relationship between the state function of the McMillan–Mayer framework and the Helmholtz state function.     

Thermodynamic studies of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol at 25°C

The osmotic coefficients of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol wer measured at 25°C up to 8 mol-kg^–1 in methanol and 5.5 mol-kg^–1 in ethanol. The activity coefficients of the solute were calculated from Bjerrum's relation. From the osmotic and activity coeficients the excess Gibbs energies of solution as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were calculated. In addition, the difference in the Gibbs energy of solvation for the solvent in solution relative to the pure solvent was calculated, as well as the partial molar volumes and excess partial molar volumes of solutes at infinite dilution, and the coefficients of pairwise contributions to the excess volume were determined. The thermodynamic parameters obtained are discussed on the basis of solute-solvent and solute-solute interactions.     

Hydrophobic interactions and osmotic second virial coefficients for methanol in water

A recent theory of the hydrophobic effect together with a simple model for an alcohol molecule is used to calculate the osmotic (McMillan-Mayer) second virial coefficientB ₂ for methanol dissolved in water. We use this calculation to study the validity of common arguments that try to draw microscopic structural information from experimental virial coefficient data. In disagreement with many workers, we find that the hydrophobic interaction between hard spheres in water is attractive and that its strength diminishes as temperature is raised. Models that have come to the opposite conclusions have neglected complications inherent to real solutes such as the role of the hydroxy groups in affecting the correlations between the apolar portions of neighboring alcohols. The calculations reported here indicate that this neglect is a poor approximation for methanol. Our calculations also show that osmotic virial coefficients are sensitive to subtle details in the potentials of mean force. Therefore, slowly varying (e.g., dispersion) interactions may also contribute significantly to the values of these coefficients without significantly changing the solvent structure near the solute molecules.     

Osmotic Coefficients of Aqueous Solutions of Some Poly(oxyethylene) Glycols at the Freezing Point of Solution

Summary. The freezing temperatures of dilute aqueous solutions of some poly(oxyethylene) glycols (PEG, HO–(CH₂CH₂O) _n –H, n varying from 4 to 117) were measured over a solute to solvent mass ratio from 0.0100 to 0.3900. The second and third osmotic virial coefficient (A ₂₂ and A ₂₂₂) of poly(oxyethylene) glycols in aqueous solution were determined. The molecular weight dependence of the second virial coefficient can be described by a simple relation A ₂₂=2×10^–5 M _n ^1.86, and the third virial coefficient is A ₂₂₂=0.038A ₂₂ ². The activity coefficients of the solute were calculated using the Gibbs-Duhem equation as applied by Bjerrum. From the osmotic and activity coefficients the excess Gibbs energies of solution, as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were estimated. The second and the third osmotic virial coefficients are correlated with the Mc-Millan-Mayer virial coefficients.     

Osmotic Coefficients of Aqueous Solutions of Some Poly(oxyethylene) Glycols at the Freezing Point of Solution

The freezing temperatures of dilute aqueous solutions of some poly(oxyethylene) glycols (PEG, HO–(CH₂CH₂O) _n –H, n varying from 4 to 117) were measured over a solute to solvent mass ratio from 0.0100 to 0.3900. The second and third osmotic virial coefficient (A ₂₂ and A ₂₂₂) of poly(oxyethylene) glycols in aqueous solution were determined. The molecular weight dependence of the second virial coefficient can be described by a simple relation A ₂₂=2×10^–5 M _n ^1.86, and the third virial coefficient is A ₂₂₂=0.038A ₂₂ ². The activity coefficients of the solute were calculated using the Gibbs-Duhem equation as applied by Bjerrum. From the osmotic and activity coefficients the excess Gibbs energies of solution, as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were estimated. The second and the third osmotic virial coefficients are correlated with the Mc-Millan-Mayer virial coefficients.     

Isopiestic Study of Water + Mannitol(sat) + Sodium Chloride + Ammonium Chloride + Barium Chloride at <Emphasis Type="Italic">T</Emphasis> = 298.15 K and Comparison with the Ideal-Like Solution Model

Isopiestic measurements have been carried out at the temperature 298.15 K for the quinary system (water + mannitol(sat) + sodium chloride + ammonium chloride + barium chloride) saturated with mannitol and its ternary sub-systems (water + mannitol(sat) + sodium chloride), (water + mannitol(sat) + ammonium chloride) and (water + mannitol(sat) + barium chloride). Taking aqueous sodium chloride as reference solutions, osmotic coefficients of the other aqueous solutions were determined. The experimental results show that the isopiestic activities of the quinary system in relation to its ternary sub-systems are in excellent agreement with the ideal-like solution model.     

Thermodynamic studies of drug-alpha-cyclodextrin interactions in water at 298.15 K: promazine hydrochloride/chlorpromazine hydrochloride + alpha-cyclodextrin + H(2)O systems

Data on osmotic coefficients have been obtained for a binary aqueous solution of two drugs, namely, promazine hydrochloride (PZ) and chlorpromazine hydrochloride (CPZ) using a vapor pressure osmometer at 298.15 K. The observed critical micelle concentration (cmc) agrees excellently with the available literature data. The measurements are extended to aqueous ternary solutions containing fixed a concentration of alpha-cyclodextrin (alpha-CD) of 0.1 mol kg(-1) and varied concentrations (approximately 0.005-0.2 mol kg(-1)) of drugs at 298.15 K. It has been found that the cmc values increase by the addition of alpha-CD. The mean molal activity coefficients of the ions and the activity coefficient of alpha-CD in binary as well as ternary solutions were obtained, which have been further used to calculate the excess Gibbs free energies and transfer Gibbs free energies. The lowering of the activity coefficients of ions and of alpha-CD is attributed to the existence of host-guest (inclusion)-type complex equilibria. It is suggested that CPZ forms 2:1 and 1:1 complexed species with alpha-CD, while PZ forms only 1:1 complexed species. The salting constant (ks) values are determined at 298.15 K for promazine-alpha-CD and chlorpromazine-alpha-CD complexes, respectively, by following the method based on the application of the McMillan-Mayer theory of virial coefficients to transfer free energy data. It is noted that the presence of chlorine in the drug molecule imparts better complexing capacity, the effect of which gets attenuated as a result of hydrophobic interaction. The results are discussed from the point of view of associative equilibria before the cmc and complexed equilibria for binary and ternary solutions, respectively.     

Protein—Protein Interactions in Aqueous Ammonium Sulfate Solutions. Lysozyme and Bovine Serum Albumin (BSA)

Osmotic pressures have been measured to determine lysozyme—lysozyme,BSA—BSA, and lysosyme—BSA interactions for protein concentrations to 100 g-L^–1in an aqueous solution of ammonium sulfate at ambient temperature, as a functionof ionic strength and pH. Osmotic second virial coefficients for lysozyme, forBSA, and for a mixture of BSA and lysozyme were calculated from theosmotic-pressure data for protein concentrations to 40 g-L^–1. The osmotic second virialcoefficient of lysozyme is slightly negative and becomes more negative withrising ionic strength and pH. The osmotic second virial coefficient for BSA isslightly positive, increasing with ionic strength and pH. The osmotic second virialcross coefficient of the mixture lies between the coefficients for lysozyme andBSA, indicating that the attractive forces for a lysozyme—BSA pair areintermediate between those for the lysozyme—lysozyme and BSA—BSA pairs. For proteinconcentrations less than 100 g-L^–1, experimental osmotic-pressure data comparefavorably with results from an adhesive hard-sphere model, which has previouslybeen shown to fit osmotic compressibilities of lysozyme solutions.     

Thermodynamic studies of aqueous and CCl4 solutions of 15-crown-5 at 298.15 K: an application of McMillan-Mayer and Kirkwood-Buff theories of solutions

The density and osmotic coefficient data for solutions of 15-crown-5 (15C5) in water and in CCl4 solvent systems at 298.15 K have been reported using techniques of densitometry and vapor pressure osmometry in the concentration range of 0.01-2 mol kg-1. The data are used to obtain apparent molar and partial molar volumes, activity coefficients of the components as a function of 15C5 concentration. Using the literature heat of dilution data for aqueous system, it has become possible to calculate entropy of mixing (DeltaS(mix)), excess entropy of solution (DeltaS(E)), and partial molar entropies of the components at different concentrations. The results of all these are compared to those obtained for aqueous 18-crown-6 solutions reported earlier. It has been observed that the partial molar volume of 15C5 goes through a minimum and that of water goes through a maximum at approximately 1.2 mol kg(-1) in aqueous solutions whereas the opposite is true in CCl4 medium but at approximately 0.5 mol kg(-1). The osmotic and activity coefficients of 15C5 and excess free energy change for solution exhibit distinct differences in the two solvent systems studied. These results have been explained in terms of hydrophobic hydration and interactions in aqueous solution while weak solvophobic association of 15C5 molecules in CCl4 solutions is proposed. The data are further subjected to analysis by applying McMillan-Mayer and Kirkwood-Buff theories of solutions. The analysis shows that osmotic second virial coefficient value for 15C5 is marginally less than that of 18C6 indicating that reduction in ring flexibility does not affect the energetics of the interactions much in aqueous solution while the same gets influenced much in nonpolar solvent CCl4.     

Mutual selective exclusion of unlike polymers in dilute solution and its measurement by light scattering

The interaction of unlike polymer molecules (components 2 and 4) in a ternary solution can be regarded as selective exclusion or desorption of one polymer by another. A relation is derived between the coefficient of selective sorption and the interaction parameters A₂₄ and A₂₄₄ which are analogs of the second and third virial coefficients. The ratio between the apparent light-scattering molecular weight and the true value for a polymer solute in a ternary system with one component of a binary solvent polymeric is more involved than in a ternary system in which both solvent components are of low molecular weight. Under certain conditions, the introduction of polymer component 2 into a dilute solution of polymer component 4 may lead to a decrease in the total intensity of scattered light.     

Hygrometric Determination of Water Activities and Osmotic and Activity Coefficients of NH4Cl–KCl–H2O at 25°C

Relative humidities have been measured for mixed aqueous electrolyte system of ammonium and potassium chlorides by the hygrometric method at total molalities from 0.3 to 6 mol-kg^–1for ionic-strength fractions yof NH₄Cl of 1/3, 1/2, and 2/3 at 25°C. The data allow the calculation of new water activities and osmotic coefficients. The proposed ECA (extended composed additivity) rule of calculation of water activity in mixed aqueous electrolyte solutions from the water activities of a single component is extended to this system. The experimental results and the predictions of the ECA rule are compared with the Robinson–Stokes, Reilly–Wood–Robinson, the Pitzer, and the Lietzke–Stoughton II models. Predictions made using these models are, in general, consistent with our results. From these measurements, the Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture for different ionic-strength fractions.     

Precision measurements of osmotic pressure in concentrated polymer solutions—II

Precision measurements of osmotic pressure have been carried out with several polymers (polystyrene, polymethylmethacrylate and polyvinyl acetate) in organic solvents. The concentration dependence of the osmotic pressure over a wide range of concentrations (up to 0·2 g/cm³) was established and the osmotic virial coefficients were evaluated. From the temperature dependence of the osmotic pressure, the partial molar heats and entropies of mixing were also determined. In the system polystyrene-cyclohexane, measurements were carried out near the θ-temperature; variation of the virial coefficients with temperature and molecular weight was studied. It was found that the conventionally defined θ-temperature is molecular weight dependent. At the θ-temperature, the third virial coefficient is positive and tends to a nonzero limit when the molecular weight tends to infinity.     

The osmotic second virial coefficient and the Gibbs–McMillan–Mayer framework

The osmotic second virial coefficient is a key parameter in light scattering, protein crystallisation, self-interaction chromatography, and osmometry. The interpretation of the osmotic second virial coefficient depends on the set of independent variables. This commonly includes the independent variables associated with the Kirkwood–Buff, the McMillan–Mayer, and the Lewis–Randall solution theories. In this paper we analyse the osmotic second virial coefficient using a Gibbs–McMillan–Mayer framework which is similar to the McMillan–Mayer framework with the exception that pressure rather than volume is an independent variable. A Taylor expansion is applied to the osmotic pressure of a solution where one of the solutes is a small molecule, a salt for instance, that equilibrates between the two phases. Other solutes are retained. Solvents are small molecules that equilibrate between the two phases. The independent variables of the solvents are temperature, pressure, and chemical potentials. The derivatives in the Gibbs–McMillan–Mayer framework are transformed into derivatives in the Gibbs framework. This offers the possibility for an interpretation and correlation of the osmotic second virial coefficient using activity coefficient models.     

Interactions between small molecules of biological interest. Excess enthalpies of ternary solutions of oligomers of glycine and isomeric pentoses in water at 25°C

Enthalpies of dilution of ternary aqueous solutions containing an oligomer of glycine (glycyl-glycine and glycyl-glycyl-glycine) and one of the pentoses: L-arabinose, D-lyxose, D-ribose, D-xylose, were experimentally determined. The cross coefficients of the virial expansion of the excess enthalpies were evaluated and compared with those relative to the solutions containing the same pentoses and other structure breaking solutes (glycine, urea, thiourea, biuret). The trend of these coefficients seems to depend very little on the particular pentose, with the exception of a pronounced minimum for D-ribose. Also, the cross coefficients for each of the four pentoses studied do not seem to depend on the nature of the oligomers of glycine. The results were interpreted in terms of a prevailing release of water from the hydration cosphere of the sugars. These last substances show, once more, a behavior in water more complex than that commonly thought.     

Representation of activity coefficients of fundamental biochemicals in water by the UNIFAC model

The assignment of UNIFAC parameters has been newly examined to represent the activity coefficients of fundamental biochemicals in aqueous solutions containing sugars, imino acids, urea, amino acid salts, inorganic salts, and sugar salts.

In this work, several new groups have been introduced to represent the activity coefficients for many biochemicals with better accuracy. For sugars, a portion containing asymmetric carbon atoms in an aldohexose molecule was defined as a new group for many stereoisomers. In the case of electrolytes like amino acid salts, the Pitzer-Debye-Hückel term was added to the UNIFAC equation to take the long-range electrostatic interaction into account.

All new interaction parameters for the fundamental biochemicals have been determined from osmotic coefficient as well as activity coefficient data reported in the literature. The new parameters provided good calculated results for these biochemicals.

In addition, the activity coefficient data for the ternary systems water/amino acid/urea and water/amino acid/sucrose were used to determine the interaction parameters between the constituent groups of an amino acid and those of the second solute, urea or sucrose. The correlated results for the system containing urea were in satisfactory agreement with the literature data.     

Water Activities, Osmotic and Activity Coefficients and Some Correlation of Aqueous Mixtures of Alkaline-Earth and Ammonium Nitrates, NH4NO3-Y(NO3)2-H2O with Y ≡ Ba2+, Mg2+ and Ca2+ at T = 25 °C

The thermodynamic properties of the mixed aqueous electrolyte of ammonium and alkaline earth metal nitrates have been studied using the hygrometric method at 25?°C. The water activities of these {yNH₄NO₃+(1?y)Y(NO₃)₂}(aq) systems with Y ≡ Ba²⁺, Mg²⁺ and Ca²⁺ were measured at total molalities ranging from 0.10 mol?kg^?1 to saturation for different NH₄NO₃ ionic-strength fractions of y=0.20, 0.50 and 0.80. These data allow the calculation of osmotic coefficients. From these measurements, the ionic mixing parameters are determined and used to calculate the solute activity coefficients in the mixtures at different ionic-strength fractions. The results of these ternary solution measurements are compared with those for binary solutions of the alkaline earth nitrates of magnesium, calcium and barium with ammonium nitrates. The behavior of the aqueous electrolyte solutions containing mixtures of barium or calcium or magnesium with ammonium nitrates are correlated and show that ionic interactions are more important for the system containing Mg²⁺ than for Ca²⁺ or Ba²⁺. The trends are mainly due to the effects of the ionic size, polarizability and the hydration of the ions in these solutions.     

Volumetric Study of Aqueous Solutions of Polyethylene Glycol as a Function of the Polymer Molar Mass in the Temperature Range 283.15 to 313.15 K and 0.1 MPa

Density measurements were made for binary aqueous solutions of polyethylene glycol at seven temperatures: 283.15, 288.15, 293.15, 298.15, 303.15, 308.15, and 313.15 K. Polyethylene glycol samples with nominal average molar masses of 3000 g⋅mol⁻¹ (PEG 3000), 6000 g⋅mol⁻¹ (PEG 6000), 10000 g⋅mol⁻¹ (PEG 10000) and 20000 g⋅mol⁻¹ (PEG 20000) were used. These results were used to determine the specific volumes of solutions with solute-to-solvent mass ratios (mass of the solute/mass of the solvent) in the range 0.0546 to 1.4932 for PEG 3000, from 0.0553 to 1.4986 for PEG 6000, from 0.0552 to 1.2241 for PEG 10000, and from 0.0530 to 1.2264 for PEG 20000. The differences between the specific volume of a solution and the specific volume of the pure solvent, at a given temperature, were represented by a virial-type equation in terms of solute concentration. The first-order coefficient of the expansion is the partial specific volume of the solute at infinite dilution. The higher-order coefficients are related to the contribution of pairs, triplets, and higher-order solute aggregates, according to the Constant-Pressure Solution Theory. The functional dependence of the virial coefficients upon temperature is discussed in terms of solute-solute and solute-solvent interactions. The effect of the PEG molar mass on the partial specific volume of solute at infinite dilution, as well as the contributions of pairs of solute molecules to the solution volume, are also investigated. The apparent specific volume, apparent specific expansibility, apparent specific expansibility at infinite dilution and virial coefficients of the apparent specific expansibility are also presented.     

Lateral intermolecular forces between biomembrane lipids in two dimensions: 1,2-dipalmitin at the heptane/water interface compared with phospholipids

The lateral interaction forces between phospholipids in two-dimensional arrays are fundamental to understanding membrane biophysics. In previous studies the related thermodynamic functions have been measured for spread phospholipid monolayers at the oil/water interface over a range of temperatures and densities, and the two-dimensional virial coefficients obtained. These coefficients have been computed from a model that emphasizes the head group zwitterion interactions. In this study we examine the contribution of the diglyceride portion of phospholipid molecules to the lateral intermolecular forces. Measurements of the heptane/water interfacial tension as a function of the concentration of 1,2-dipalmitoyl glycerol (DP) in the heptane were made over a range of low surface pressures at 25 degrees C. Infrared measurements on the DP solutions show that the solutions are ideal. The results are interpreted to give two-dimensional virial coefficients for the adsorbed monolayer. The second virial coefficient B2(T) for DP is +0.31 nm2/molecule, in marked contrast to the much larger positive values found for the corresponding phospholipids at the same interface and temperature, and clearly indicating an attractive component to the lateral potentials of mean force between pairs of DP molecules. The contribution of the diglyceride moiety to the pair potentials of the phospholipids thus appears to be minor but not negligible. The differences in the second virial coefficients for DP and the phospholipids are interpreted primarily in terms of the orientation of the ester carbonyl dipoles, also drawing on spectroscopic and diffraction evidence from related structures.