Molecular excess free energy

Conformal (second-order) solution theory has been applied to a mixture of almost equal-sized hard spheres of diameters 1 and 1 + p, p< l, by Buchowski and Bellemans. Denoting by n and x the number density and mole fraction of hard spheres of diameter 1 at temperature T and pressure p they find the exact low density result to terms of order p for the molecular excess free energy g of the mixture... 

Hermans, J. Pathiaseril, A. Anderson, A., Excess free-energy of liquids from molecular-dynamics simulations — application to water models, J. Am. Chem. Soc. 1988,110, 5982-5986. 

In general, use of the ideal gas functional in terms of the molecular density requires computation. Despite the computational intensive nature of the resulting theory, this is probably the most widely used functional for polymers and is described greater detail below. As mentioned earlier, the approximations for the excess free energy functional are similar to those used for simple liquids. The exact expression for the ideal gas functional in this case is... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

Molecular Interpretation of the Excess Free Energy of Organic Compounds in Aqueous Solutions... 

Enthalpic and Entropic Contributions to the Excess Free Energy Molecular Picture of the Dissolution Process Model for Description of the Aqueous Activity Coefficient Box 5.1 Estimating Molar Volumes from Structure Illustrative Example 5.2 Evaluating the Factors that Govern the Aqueous Activity Coefficient of a Given Compound... 

Before we deal with these molecular aspects in detail, it is instructive to inspect the enthalpic () and entropic (-T Sj,j,) contributions to the excess free energies of various organic compounds in aqueous solution (Table 5.3). Values representative of saturated aqueous solutions of the compounds have been derived from measurements of the enthalpies of dissolution of the liquids (i.e., = AwJ //, Fig. 5.1) or solids (// ... 

It should be noted that when replacing the London dispersive interactions term by other properties such as, for example, the air-hexadecane partition constant, by expressing the surface area in a more sophisticated way, and/or by including additional terms, the predictive capability could still be somewhat improved. From our earlier discussions, we should recall that we do not yet exactly understand all the molecular factors that govern the solvation of organic compounds in water, particularly with respect to the entropic contributions. It is important to realize that for many of the various molecular descriptors that are presently used in the literature to model yiw or related properties (see Section 5.5), it is not known exactly how they contribute to the excess free energy of the compound in aqueous solution. Therefore, when also considering that some of the descriptors used are correlated to each other (a fact that... 

Using an automated film balance the behavior of mixed monomolecular films exhibiting deviations from ideality was studied. Particular attention was paid to condensation effects obtained when cholesterol is mixed with a more expanded component. The deviations at various film pressures are discussed in terms of the partial molecular areas of the film components. Slope changes in these plots are caused by phase transitions of the expanded monolayer component and do not indicate the formation of surface complexes. In addition, the excess free energies, entropies, and enthalpies of mixing were evaluated, but these parameters could be interpreted only for systems involving pure expanded components, for which it is clear that the observed condensation effects must involve molecular interactions. 

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