Enthalpy-Entropy Relationships

First of all, we should emphasize that the compensatory enthalpy-entropy relationship cannot be derived directly from the fundamental thermodynamic equations but... 

Extensive theoretical analyses of the compensatory enthalpy-entropy relationship were first carried out by Leffler and later by Leffler and Grunwald, Exner, and Li. The empirical linear relationship between the thermodynamic or activation parameters AH and AS) directly leads to Eq. 11, where the proportional coefficient p, or the slope of the straight line in Figure 9, has a dimension of temperature. Merging Eq. 11 into the differential form of the Gibbs-Helmholtz Eq. 12 gives Eq. 13 ... 

Although the thermodynamic data obtained with different types of host-guest combinations had not been either related to each other or discussed globally, the compensatory enthalpy-entropy relationship was found to be held first in the cation... 

We have hitherto dealt with the complexation thermodynamics in the homogeneous solutions. However, the above interpretation based on the linear enthalpy-entropy relationship may be extended to the complexation behavior in the solvent extraction of aqueous metal salts with ionophores in organic solvent. 

In view of the compensatory enthalpy-entropy relationship observed for a wide variety of ionophore types, we may conclude that the cation-binding behavior, where the weak ion-dipole and dipole-dipole interaction is the major driving force for complexation, can be quantitatively analyzed and characterized by the slope and intercept of the AH-TAS plot without any exception. In this context, it is stimulating to extend the scope of this theory to the inclusion complexation of organic guests with molecular hosts. 

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