Gibbs free energy, interactions

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

There are two ways in which the volume occupied by a sample can influence the Gibbs free energy of the system. One of these involves the average distance of separation between the molecules and therefore influences G through the energetics of molecular interactions. The second volume effect on G arises from the contribution of free-volume considerations. In Chap. 2 we described the molecular texture of the liquid state in terms of a model which allowed for vacancies or holes. The number and size of the holes influence G through entropy considerations. Each of these volume effects varies differently with changing temperature and each behaves differently on opposite sides of Tg. We shall call free volume that volume which makes the second type of contribution to G. 

In some cases, an alternative explanation is possible. It may be assumed that any very complex organic counterion can also interact with the CP matrix with the formation of weak non-ionic bonds, e.g., dipole-dipole bonds or other types of weak interactions. If the energy of these weak additional interactions is on the level of the energy of the thermal motion, a set of microstates appears for counterions and the surrounding CP matrix, which leads to an increase in the entropy of the system. The changes in Gibbs free energy of this interaction may be evaluated in a semiquantitative way [15]. 

Table 9 shows that the value of AGn of the cooperative interaction between bonding centers is within the error in the determination of integral AG values. This fact can either indicate the slight mutual influence of the centers or be caused by the compensation between the enthalpy and entropy components of Gibbs free energy. 

It is known that thermodynamic and structural studies are mutually complimentary and both are necessary for a complete elucidation of the molecular details of any binding process for the delineation of the molecular interaction involved at the interaction site. The Gibbs free energy change (AG) may be determined from the binding constant from the relation ... 

Here, AS° = AS i + AS n, but since identical vibrational levels have been assumed for the two electronic levels, AS jb = 0. In addition, AS j is related to the electronic degeneracies of the two levels by ASei = K In ( l/ h)- Finally, if the transformation takes place at constant pressure, AH° = NAE where AE is defined as above. Consideration of the Gibbs free energy for an assembly of N molecules thus produces the same relation for the HS fraction Uh as the potential energy for the isolated molecule, if only the interaction between the molecules is neglected. 

Here G is the Gibbs free energy of the system without external electrostatic potential, and qis refers to the energy contribution coming from the interaction of an apphed constant electrostatic potential s (which will be specified later) with the charge qt of the species. The first term on the right-hand side of (5.1) is the usual chemical potential /r,(T, Ci), which, for an ideal solution, is given by... 

As noted in Chapter 2, the Gibbs free energy is composed of both an enthalpic and an entropic term. For reversible binding interactions, we can use the equality AG = AH - TAS, together with Equation (3.8) and a little algebra to obtain... 

The papers of Wagner and Schottky contained the first statistical treatment of defect-containing crystals. The point defects were assumed to form an ideal solution in the sense that they are supposed not to interact with each other. The equilibrium number of intrinsic point defects was found by minimizing the Gibbs free energy with respect to the numbers of defects at constant pressure, temperature, and chemical composition. The equilibrium between the crystal of a binary compound and its components was recognized to be a statistical one instead of being uniquely fixed. 

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