Free Energy Approaches

FIGURE 8.4 The variation of the molar Gibbs free energy of an ideal gas with pressure. The Gibbs free energy has its standard value when the pressure of the gas is 1 bar. The value of the Gibbs free energy approaches minus infinity as the pressure falls to zero. 

There are two basic approaches to the solution of a species distribution problem (1) The equilibrium constant approach, and (2) the Gibbs free energy approach. Most... 

Poliak. E. Quantum theory of activated rate processes a maximum free energy approach,... 

Williams, N.A. and Amidon, GL. An excess free energy approach to the estimation of solubility in mixed solvent systemsl, Pharm. Sci.73, 9-12, 1984. 

Fig. 26 Dissociation of a polymer with N=20 monomers as a function of the distance D from the interface to a low-dielectric half-space (idealized by =0, see text). Shown are degree of dissociation a and free energy per monomer, f/kBT for fixed pH-pKa=5 for different salt concentrations. As the polymer moves towards the interface the degree of dissociation and the free energy approach zero, the polyelectrolyte is repelled from the interface...

We conclude that there is decomposition upon heating V20 (t) in an inert atmosphere or in vacuo. The use of an oxygen atmosphere suppresses decomposition but in the transpiration-weight loss experiment it has not been verified that the weight loss is indeed 4 10 calculate a decomposition temperature, as that temperature at which the free energy approaches zero for the... 

The comparison of the hysteresis behavior in simulation and experiment, shows that the hysteresis is mainly due to the existence of metastable states rather than due to kinetic effects. The asymmetry in the freezing and melting branches of the adsorption curve is explained based on the Landau free energy surfaces. The Landau free energy approach is a powerful tool in determining the freezing temperature, nature of the phase transition, structure of the confined phases, existence of metastable states and origin of the hysteresis behavior. 

Both the brute force approach and the free energy approach have been used. In the following subsections the main results are reviewed and several examples taken from work in my group are discussed. 

The previously described measurements have been performed on lipids in aqueous solutions, but lipid bilayers also swell in some other solvents (12) and the results of such measurements compare quite well with the aqueous case. In addition, hydration (solvation) forces act between DNA polyelectrolytes (13) and polysaccharides (14). These facts make the interpretation of the forces even more complicated and it is no wonder that different approaches to explain the nature of this solvation force exist. So far no truly ab initio theory has been proposed. The existing theories include models based on the electrostatic approach, the free energy approach, and an approach based on the entropic or protrusion model. 

Free Energy Approach. Nearly immediately after the publication of the first data on the hydration force (10), Marcelja and Radic (MR) proposed a very elegant theory to explain the nature of the observed strong force (20). According to MR theory the force is due to the modification of water structure near the membrane-water interface. The water molecules near the interface differ from the water molecules in the bulk they are more ordered. To describe this order, one can introduce an order parameter T (%) and perform a Landau-type expansion of the free energy density g(x) that is,... 

Theory Viscoelastic fluids elastic free energy approach Van Oene, 1972... 

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