Enthalpic potential

In the first category of solutions ( regular solutions ), it is the enthalpic contribution (the heat of mixing) which dominates the non-ideality, i.e. In such solutions, the characteristic intermolecular potentials between unlike species differ significantly from the average of the interactions between Uke species, i.e. 

An important part of the optimization process is the stabilization of the monomer-template assemblies by thermodynamic considerations (Fig. 6-11). The enthalpic and entropic contributions to the association will determine how the association will respond to changes in the polymerization temperature [18]. The change in free volume of interaction will determine how the association will respond to changes in polymerization pressure [82]. Finally, the solvent s interaction with the monomer-template assemblies relative to the free species indicates how well it will stabilize the monomer-template assemblies in solution [16]. Here each system must be optimized individually. Another option is simply to increase the concentration of the monomer or the template. In the former case, a problem is that the crosslinking as well as the potentially nonselective binding will increase simultaneously. In the... 

It is known that the penultimate unit influences the conformation of both model radicals and propagating radicals.32 3 Since addition requires a particular geometric arrangement of the reactants, there are enthalpic barriers to overcome for addition to take place and also potentially significant effects on the entropy of activation. Comparisons of the rate constants and activation parameters for homopropagation with those for addition of simple model radicals to the same monomers also provide evidence for significant penultimate unit effects (Section 4.5.4). 

It is sometimes informative to separate AG into hypothetical enthalpic and entropic terms, and then the Arrhenius factors may be related to the transition state activation parameters by Eqs 10.4 and 10.5. Thus, the Arrhenius activation energy can be approximately related to the potential energy of a transition state, and the preexponential A value includes probability factors. 

Reaction rates are macroscopic averages of the number of microscopical molecules that pass from the reactant to the product valley in the potential hypersurface. An estimation of this rate can be obtained from the energy of the highest point in the reaction path, the transition state. This approach will however fail when the reaction proceeds without an enthalpic barrier or when there are many low frequency modes. The study of these cases will require the analysis of the trajectory of the molecule on the potential hypersurface. This idea constitutes the basis of molecular dynamics (MD) [96]. Molecular dynamics were traditionally too computationally demanding for transition metal complexes, but things seem now to be changing with the use of the Car-Parrinello (CP) method [97]. This approach has in fact been already succesfully applied to the study of the catalyzed polymerization of olefins [98]. 

To conclude, a related thermodynamic treatment has been extended to the calculation of the enthalpic variation for redox couples, AH°C = H°ed - if°x. Such a treatment is useful to understand how enthalpic or entropic factors may influence the magnitude and sign of the free energy, or the electrode potential, of a redox change.20 In fact, one must consider that ... 

Simple thermodynamic considerations state that the reduction process is favoured (i.e. more positive cu(ii)/cu(p potential values are obtained) if the electron transfer is exothermic (AH° negative) and if the molecular disorder increases (AS° positive). It is therefore evident that the positive potential value for the reduction of azurin (as well as that of the most blue copper proteins) is favoured by the enthalpic factor. This means that the metal-to-ligand interactions inside the first coordination sphere (which favour the stability of the reduced form over the oxidized form) prevail over the metal complex-to-solvent interactions inside the second... 

Figure 5,17 Enthalpic interactions in the various binary joins of aluminiferous garnets. calorimetric data results of interionic potential calculations. The corresponding subregular Margules interaction parameters are listed in table 5.26 (from Ottonello et al., in prep.).

Figure 4 Two arbitrary potential energy surfaces in a two-dimensional coordinate space. All units are arbitrary. Panel A shows two minima connected by a path in phase space requiring correlated change in both degrees of freedom (labeled Path a). As is indicated, paths involving sequential change of the degrees of freedom encounter a large enthalpic barrier (labeled Path b). Panel B shows two minima separated by a barrier. No path with a small enthalpic barrier is available, and correlated, stepwise evolution of the system is not sufficient for barrier crossing.

The + 2/0 reduction potentials have enthalpic contributions from the terms in the equation ... 

A2 from equation (5.16) or the cross second virial coefficient from equation (5.17). In turn, this knowledge of the second virial coefficients and their temperature dependence allows calculation of the values of the chemical potentials of all components of the biopolymer solution or colloidal system, as well as enthalpic and entropic contributions to those chemical potentials. On the basis of this information, a full description and prediction of the thermodynamic behaviour can be realised (see chapter 3 and the first paragraph of this chapter for the details). 

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