And excess free energies

Solubilities and Aqueous Activity Coefficients of Organic Liquids Solubilities and Aqueous Activity Coefficients of Organic Solids Solubilities and Aqueous Activity Coefficients of Organic Gases Illustrative Example 5.1 Deriving Liquid Aqueous Solubilities, Aqueous Activity Coefficients, and Excess Free Energies in Aqueous Solution from Experimental Solubility Data... 

P 5.1 Calculating Aqueous Activity Coefficients and Excess Free Energies in Aqueous Solution from Experimental Solubility Data... 

K. Quitzsch, Studien zur Thermodynamik Binarer Fliissigkeitsgemische mit Homologen Formamiden , Z. Phys. Chem. Leipzig, 233, 321-332 (1966) D. D. Deshpande and S. L. Oswal, Vapour-Liquid Equilibrium and Excess Free Energies for Benzene + Dioxan and Carbon Tetrachloride + Dioxan Systems , J. Chem. Soc. Faraday Trans. 1, 68, 1059-1064... 

The solid carbonate can also present several potential difficulties in solubility studies. These can be broken down into two major areas heterogeneity in composition, and excess free energy associated with lattice strain or defects and surface free energy. The problem of solid heterogeneity presents itself in most sedimentary carbonates, and is especially important in biogenic carbonates such as magnesian calcites. The problem of lattice strain and high defect density is most... 

The difference in thermodynamic functions between a non-ideal solution and a comparative perfect solution is called in general the thermodynamic excess function. In addition to the excess free enthalpy gE, other excess functions may also be defined such as excess entropy sE, excess enthalpy hE, excess volume vE, and excess free energy fE per mole of a non-ideal binary solution. These excess functions can be derived as partial derivatives of the excess free enthalpy gE in the following. 

Orbey, H., and Sandler, S. 1., 1995c. On the combination of equation of state and excess free energy model. Fluid Phase Eq., 111 53—70. 

Excess properties are just anotlier way of representing the activity coefficient and are used because they tend to simplify notation. We now derive the relationships between the activity coefficient and excess free energy, enthalpy, entropy, and volume. 

The compact core of a micelle is characterized by a uniform polymer density, fiXBs), chemical potential per monomer unit, plb Xbs), and excess free energy per unit area of the core-water interface, kBTy xBs)- Here, Xbs T) is the Hory-Huggins parameter of monomer (B)-solvent (5) interaction, and Xbs T) > Xbs 0) = 1/2 under poor solvent conditions for the monomer units of block B. Although the solubility of polymers in organic solvents usually decreases with a decrease in temperature, dxiT)fdT < 0, the situation is more complex in aqueous solutions. In particular, it appears that the solubility of thermosensitive block B in water typically decreases with an increase in temperature [11], and hence dXBsiJ)/dT>0. In this case, the collapse of blocks B and the aggregation of the block copolymers into micelles occur at r > LCST, where LCST is the lower critical solution temperature. 

For mixed electrolyte solutions in water, the experimental excess free energy functions have been given in parameterized form by Pitzer, and excess free energies and enthalpies have been tabulated by Anderson and Wood. "" ... 

In general, the evaluation of the separation criterion is subject to much the same criticisms as is the entropy index. In this case, however, the problem is even more difficult due to the fact that absolute changes in entropies and internal energies are needed. More work is needed to establish these quantities for particulate suspensions, with the inevitable particle-particle interactions and excess free energies of mixing. Textbooks on thermodynamics are remarkably silent on the subject of thermodynamics of particulate systems and suspensions. 

C. G.M. Dijkhuis, in Molten Salts> Vol.2, Section 1 "Electro-chemistry of Molten Salts Gibbs Free Energies and Excess Free Energies From Equilibrium Type Cells", N.S.R.D.S. -... 

---