Free energy of water

As a result of the high surface free energy of water, the vapor pressure of a water droplet increases with decreasing radius of curvature, r, as deduced by Kelvin ... 

Sakane, S. Yezdimer, E. M. Liu, W. B. Barriocanal, J. A. Doren, D. J. Wood, R. H., Exploring the ab initio/classical free energy perturbation method the hydration free energy of water, 7. Chem. Phys. 2000,113, 2583-93... 

The list of fluids which exhibit important quantum effects is not large. Getting back to the original question of this chapter, it is clear that for liquids like helium and hydrogen, a full quantum treatment is necessary. Liquids such as neon and water, however, show modest quantum effects which can be modeled with approximate free energy methods. The quantum correction to the free energy of water is roughly 10%... 

Gibbs free energies of water sorption, AG "(/l), can be extracted from isopiestic vapor sorption isotherms this analysis shows that AG (T) < AG", where AG" = -44.7 kj moH is the Gibbs free energy for vapor sorption at a free water surface at ambient condihons. Water absorbed by the membrane is therefore more strongly bound than water at a free bulk water surface this affirms the hydrophilic nature of water sorption in PEMs. 

For water uptake by capillary condensation, the Gibbs free energy of water in pores is given by... 

Gibbs free energy of water sorption by Nation 117. Comparison of energies obtained from sorption isotherms (solid line), corresponding to Figure 6.10(a), and from capillary isotherms (dashed line), corresponding to Figure 6.10(b). 

The parameter g12 is the change of the free energy of water molecules when they are driven back to the bulk water system. The exergonic character of process (2.9) will favor the concurrent process (2.7) of protein adsorption onto the material. 

Fig. 7. Calculated relative free energies of water dissociation from the hexacoordinate iron complex la.

Advantageous gain of free energy of water molecules, often a part of hydrophobic bonding, but no particular structure requirement. 

In particular, the extension of the van der Waals and Platteeuw method addresses the first assumption listed at the beginning of Section 5.1.1—namely that encaged molecules do not distort the cavity. In the development of the statistical thermodynamic hydrate model (Equation 5.23), the free energy of water in the standard hydrate (empty hydrate lattice), gt, is assumed to be known at a given temperature (T) and volume (v). Since the model was developed at constant volume, the assumption requires that the volume of the empty hydrate lattice, 7, be equal to the volume of the equilibrium hydrate, v11, so that the only energy change is due to occupation of the hydrate cavities, as shown in Figure 5.3. 

Fig. XI-7.—Gibbs free energy of water, as function of pressure and temperature...

Table 17-2. Solvation free energies of water molecule and their components computed by the QM/MM-ER method. Units are in kcal/mol...

From a molecular view, the decrease of entropy upon hydrophobic hydration is not mitigated by a large hydration enthalpy and this translates into an increase in the free energy of water. A system will tend to minimize this increase in free energy through association of the hydrophobic moieties. This phenomenon that explains the salting in of a neutral hydrophobic molecule by hydrophobic ions is expected to amplify with the sizes of the hydrophobic moieties [49]. Attractive forces between two hydrophobic ions and repulsive forces between hydrophilic and hydrophobic... 

Figure 7.6 Cluster-variation of the hydration free energy of water. The open circles give the chemical contribution, A 7 lnxo. The open squares give the packing contribution, —kTlnpQ. The open triangles give the sum of outer-sphere electrostatic and dispersion contributions. The net free energy is shown by a solid line. The minimum is within 1 kcal/mol. of the experimental value of —6.1 kcal/mol.

Extrapolation of the AG = /(C ) curves to the water free energy axis enable us to estimate the maximum magnitude of variations in the free energy of water caused by adsorption (AG, i,x). The AG ux value determined in accordance with this method and the data for the free surface energy calculated using Eq. (2) are listed in Table 8. The values of maximum water layers thickness (t/ " ) perturbed by the surface, calculated on the basis of the Cw " value, are also listed in Table 8. These data permit us to conclude that the free surface energy for the adsorbents studied increases in the following order ... 

It can be inferred from the osmotic model of clay swelling (discussed in the previous section) that any influence on the clay-water system that lowers the free energy of water in the aqueous phase will reduce clay swelling. As seen earlier, high salt... 

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