Excess compressibility free energy

Energies, Excess Enthalpies, Excess Volumes, and Isothermal Compressibilities of Cyclohexane + 2,3-Dimethylbutane , J. Client. Thermodyn., 6, 35-41 (1974). J. B. Ott, K. N. Marsh, and R. H. Stokes, Excess Enthalpies, Excess Gibbs Free Energies, and Excess Volumes for (Cyclohexane + n-Hexane), and Excess Gibbs Free Energies and Excess Volumes for (Cyclohexane + Methylcyclohexane) at 298.15 and 308.15 K , J. Chem. Thermodyn., 12, 1139-1148 (1980). 

Ewing, M. B. Marsh, K. N. Excess Gibbs free energies, excess enthalpies, excess volumes, and isothermal compressibilities of cyclohexane + 2,3-dimethylbutane J. Chem. Thermodyn. 1974, 6, 35-41... 

Once it has been established that the components of a binary monolayer are to some degree miscible, the energetics of their interaction may be calculated directly from the 11/A isotherms of the mixture and its individual components. As proposed by Goodrich (1957), this technique employs the differences in the work of compression of the binary film and the work required to compress each of the films of the pure components to the same surface pressure. The result is the total free energy of mixing as expressed by the sum of the excess and ideal free energies of mixing in (14), where Nt... 

Goodrich s original derivation and treatment for obtaining excess free energies of mixing utilizes the differences between the free energies of compression of the pure film components and their mixtures from II 0 to some specified pressure as expressed by (17). 

Since it has been shown that nonideal mixing occurs in the 2.5-15.0 dyn cm 1 range, the excess free energies of interaction were calculated for compressions of each pure component and their mixtures to each of these surface pressures. In addition, these surface pressures are below the ESPs and/or monolayer stability limits so that dynamic processes arising from reorganization, relaxation, or film loss do not contribute significantly to the work of compression. 

The main excess properties are the free energy gE, enthalpy hB, entropy sE, and volume v (per molecule) data on other excess properties (specific heat, thermal expansion or compressibility) are rather scarce. In most cases gE, hE, sE, and vE have been determined at low pressures (<1 atm) so that for practical calculations p may be equated to zero their theoretical expressions deduced from Eqs. (33) and (34) are then as follows ... 

Jjet us consider as an example the case of a saturated vapor which has been suddenly and adiabatically compressed to a vapor pressure P which is in excess of its equilibrium vapor pressure Po at the final temperature T. In order for liquid to form, it must grow by the growth of small droplets. If, however, we consider a very small droplet of the liquid phase present in the vapor, it will have an excess free energy, compared to bulk liquid, that is due to its extra surface. The magnitude of the excess surface energy is 4irrV, where surface tension and r is the radius of the drop. In order for the drop and vapor to be in equilibrium, the vapor pressure P must exceed the saturation vapor pressure Po by an amount which can be calculated from the Gibbs-Kelvin equation... 

The free energy profile obtained from Monte Carlo simulations of a small Lennard-Jones monomer system and the above approximations utilizing values of the interface tension and compressibility extracted from independent simulations are shown in Fig. 6. Of course, the simple expressions overestimate the value of the excess free energy, but the qualitative shape of the free energy profile is predicted well. Snapshots of the simulations are presented in Fig. 7. These corroborate the correct identification of the dominant system configurations. 

First of all we give the general expressions for the excess free energy, enthalpy and compressibility at zero pressure. It follows directly from (9.3.8) that... 

Nor can the theory of regular solutions based on the simplified lattice model (cf. Ch. Ill) give any indication on the excess properties related to the equation of state such as the excess volume, the excess compressibility and hence the excess entropy and the excess specific heat all of which are closely related to the equation of state. In fact, no equation of state at all is introduced in this model. The lattice model can only be used to calculate the excess free energy and the excess enthalpy which should be equal in the zerbth approximation. However the experimental data invalidate this conclusion. 

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