Total complexation free energy

The enhanced stability of chelating ligands comes from a combination of entropic (AS°) and enthalpic (AH°) factors that lower the total complexation free energy (AG°), as follows (where T is the temperature in Kelvin) ... 

Chemical Equilibrium The chemical equilibrium approach is more complex computationally than applying the assumption of an infinitely fast reaction. The equilibrium composition of a multicomponent system is estimated by minimizing the Gibbs free energy of the system. For a gas-phase system with K chemical species, the total Gibbs free energy may be written as... 

However, G) is not a true thermodynamic quantity, because it does not express the equilibrium instead it depends on the history of the solid surface formation, as we see above. So far, we have considered only the isotropic solids. If, however, the solid is anisotropic, such crystals can respond differently in different directions when increasing the surface area. This property increases the number of required equations twofold, and the matter is rather complex because it is unclear which shape the anisotropic crystal would prefer for a given volume, if its total surface free energy is minimized this subject is beyond the scope of this book. 

Gels with ionizable pendent groups in the network are far more complex to analyze. Essentially, a Gibbs free energy contribution due to the ionic nature of the gel must be additionally considered in the total Gibbs free energy expression from eqn [1]. The modified version is shown in eqn [6]. 

Table 3-1. Calculated potential and free energy differences for path B (in kcal/mol) between the determined structure and the reactant (ES complex), where Ait is the total HF potential energy difference, A Eqm refers to the QM energy difference between two QM subsystems. A 1 qm/MM is the free energy change in the QM/MM interaction, and A F = AEqm + A I qm/MM- Numbers without parentheses correspond to the present work and numbers in parentheses correspond to our previous determinations (path D) [33]...

The presence of ionic moieties in hydrogels makes the theoretical treatment of swelling much more complex. In addition to the AGm xing and AGgiastic in Eq. (1), there is an additional contribution to the total change in Gibbs free energy due to the ionic nature of the polymer network, AG on c. 

The free energy calculations were calculated with electrostatic and van der Waals contributions evaluated separately for both the complex and the isolated ligand. The total free energy change of -10.3 kcal/mol agreed with experimental measurements of -11.5 kcal/mol6 for netropsin... 

Considering the contribution of the solvent and surface terms to the total free energy change, it is apparent that the enhanced selectivity in the presence of e.g. ethylenediamine corresponds in sign to variations in the solution term and is (in part) due to smaller AG values of hydration of the complex cations. This is exemplified for the Ca-Cu and Ag-Cu cases in the presence and absence of ethylenediamine by the equations ... 

The first ingredient in any theory for the rheology of a complex fluid is the expression for the stress in terms of the microscopic structure variables. We derive an expression for the stress-tensor here from the principle of virtual work. In the case of flexible polymers the total stress arises to a good approximation from the entropy of the chain paths. At equilibrium the polymer paths are random walks - of maximal entropy. A deformation induces preferred orientation of the steps of the walks, which are therefore no longer random - the entropy has decreased and the free energy density/increased. So... 

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