Free energy electrostatic part

The term G T, a,, A/, ) is the Gibbs free energy of the full electrochemical system x < x < X2 in Fig. 5.4). It includes the electrode surface, which is influenced by possible reconstructions, adsorption, and charging, and the part of the electrolyte that deviates from the uniform ion distribution of the bulk electrolyte. The importance of these requirements becomes evident if we consider the theoretical modeling. If the interface model is chosen too small, then the excess charges on the electrode are not fuUy considered and/or, within the interface only part of the total potential drop is included, resulting in an electrostatic potential value at X = X2 that differs from the requited bulk electrolyte value < s-However, if we constrain such a model to reproduce the electrostatic potential... 

In the two bulk phases the potential of mean force is constant, but it may vary near the interface. The difference in the bulk values of the chemical part is the free energy of transfer of the ion, which in our model is —2mu (we assume u < 0). Let us consider the situation in which the ion-transfer reaction is in equilibrium, and the concentration of the transferring ion is the same in both phases the system is then at the standard equilibrium potential 0oo- In Ihis case the potential of mean force is the same in the bulk of both phases the chemical and the electrostatic parts must balance ... 

Fig. 4.13. Free energy profile for glycophorin A as a function of helix-helix distance in A. The figure on the right shows the individual contributions of helix-helix van der Waals and electrostatic forces, and helix-solvent forces. Reprinted in part with permision from H6nin et al. 2005 [54], Copyright 2005 American Chemical Society.

On the basis of classical electrostatic theory, a large part of the free energy of a pair of ions depends on the dielectric constant of the medium. In a solvent of high dielectric constant, a charged object creates oriented solvent dipoles by polarization or orients existing... 

The first version of the LIE method employed the linear response approximation to estimate the electrostatic part of the solvation/binding free energies. The linear response result for this component of the solvation... 

In contrast to Equations 7 and 8, based on the binding of counter ion to micelle, an equation including a form for the electrostatic part of free energy of micelle formation, Fgi, evaluated from double... 

The calculation of the energy for the interaction between the solvent and solute is more complicated. Formally, the free energy for the process, AC/ini, is composed of two chemical parts and an essentially entropic term. The chemical terms are associated with van der Waals interactions AGvdw> electrostatic effects, AG, between solute and solvent. The entropic term measures the free volume i.e., the volume a molecule explores before encountering another, which is assumed to be proportional to the molar volume of the solvent. Thus, the free energy change associated with solute-solvent interactions at temperature T is given by... 

The surfactant sodium dodecyl sulphonate (Ci2H2sS03Na) and its sulphate adsorb electrostatically on hematite at low solute concentrations (Han et al., 1973). Hydro-phobic effects operate at high concentrations due to the incompatibility of the hydrocarbon part of the molecule with water. This involves condensation of the alkyl chains at the surface (hemi-micelle interactions), which lowers the free energy of the system and reverses the surface charge. 

The electrostatic part of the ionic solvation energy, AGei (kj rriol ), corresponds to the difference between the electrostatic free energy of an ion in vacuo and that of the ion in a solution of relative permittivity eP It is roughly given by the Born equation ... 

It is important to note that inclusion of solvent effects in the calculation of the mechanism is very important in order to reproduce correctly the reaction profile. Thus, if the electrostatic part of the free energy of solvation (AAsolv) is calculated in the form... 

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