Free energy mixed-potential theory

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

Electromotive force measurements of the cell Pt, H2 HBr(m), X% alcohol, Y% water AgBr-Ag were made at 25°, 35°, and 45°C in the following solvent systems (1) water, (2) water-ethanol (30%, 60%, 90%, 99% ethanol), (3) anhydrous ethanol, (4) water-tert-butanol (30%, 60%, 91% and 99% tert-butanol), and (5) anhydrous tert-butanol. Calculations of standard cell potential were made using the Debye-Huckel theory as extended by Gronwall, LaMer, and Sandved. Gibbs free energy, enthalpy, entropy changes, and mean ionic activity coefficients were calculated for each solvent mixture and temperature. Relationships of the stand-ard potentials and thermodynamic functons with respect to solvent compositions in the two mixed-solvent systems and the pure solvents were discussed. 

It is simply a measure of how the free energy changes with composition and is the driving force for the two phases to come to equilibrium (i.e., for their compositions to adjust until Equation 11-46 is satisfied). The chemical potentials in the Flory-Huggins theory can be simply obtained by differentiating the free energy of mixing, which for... 

The previous work of Cukier and coworkers [7, 12] differs from the formulation described in this chapter in a number of fundamental ways. In contrast to the multistate continuum theory described in this chapter, Cukier and coworkers did not calculate mixed electronic/proton vibrational free energy surfaces as functions of two solvent coordinates. Instead, they calculated solvated proton potentials obtained by the assumption that the inertial polarization of the solvent responds instantaneously to the proton position. (This is the limit opposite to the standard adiabatic limit of the fast proton vibrational motion responding instantaneously to... 

The general theory of swelling assumes that the free energy of mixing and the elastic free energy in a swollen network are additive. The chemical potential difference between gel and solvent is given by the equation ... 

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