Helmholtz, binary systems

Figure 4.3.1. The excess Gibbs and Helmholtz energies of mixing for the methanol and benzene binary system at 373 K calculated u ith the Wong-Sandler fWS) mixing rule and the PRSV equation of state at 1 and 1000 bar.

The temperature dependence of the separation factor (see Eq. (5.18)) and of the azeotropic composition of binary systems depends on the type of azeotrope (pressure maximum, pressure minimum), the temperature dependence of the vapor pressures, and the composition and temperature dependence of the activity coefficients. These dependencies can be described with the help of the heats of vaporization and partial molar excess enthalpies following the Clausius-Clapeyron respectively the Gibbs-Helmholtz equation [38] (derivation see Appendix C, B9) ... 

MFLG DESCRIPTION OF BINARY SYSTEMS A two component system is in the MFLG approximation treated as a pseudo-ternary mixture of constituents 1, 2 and holes (index 0). The appropriate thermodynamic function for the description of fluid phase equilibria is the Helmholtz free energy of mixing vacant and occupied sites, and reads in the simplest version of the model ). 

Ideas that go back to van der Waals [217, 218] and Lord Rayleigh [219] on inhomogeneous systems were applied by Cahn and Hilliard [216] to the interface problem. In inhomogeneous fluids, the Helmholtz free energy is a functional of the component density distributions. Although exact formal expressions for this functional have been derived [220,221] from statistical mechanics, they are impractical without approximation [222]. In the gradient approximation, this functional has been expressed as the sum of two contributions one is a function of the local composition and the other is a function of the local composition derivatives [216, 223, 224]. The free energy for a binary system is postulated to have the form ... 

In the lattice representation of a polymer solution, each polymer segment or solvent molecule occupies one lattice site, while the system is regarded as a binary mixture of polymer and solvent. The Helmholtz energy of system can be expressed as... 

The Peng-Roblnson EOS was recently found to yield the best values of binary critical volumes for class 1 systems and to perform reliably for other critical properties as well (13). The expression of A in terms of T, V, and x along with the relationships between second and third derivatives of Gibbs and Helmholtz free energies are given by Peng and Robinson (11). 

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