Coulomb repulsion free energy

The linear dependence of the pitting potential on ionic radius is likely a reflection of the similarly linear relationship between the latter and the free energy of formation of aluminum halides.108 It is reasonable to assume that the energy of adsorption of a halide on the oxide is also related to the latter. Hence, one could postulate that the potential at which active dissolution takes place is the potential at which the energy of adsorption overcomes the energy of coulombic repulsion so that the anions get adsorbed. 

The first simplification in the TDAN model is to consider only a few electronic orbitals on the scattered atom. For many applications, it is sufficient to consider one only, that from which, or into which, an electron is transferred. Let the ket 10 > denote the spatial part of the orbital. When far from the surface, suppose its energy is So> let Uq be the Coulomb repulsion integral associated with the energy change when it is occupied by two electrons of opposite spin. In terms of creation and annihilation operators and Co for 0>, with ff( = aorfi)a spin index, that part ofJt which refers to the free atom is... 

The total energy is expressed in terms of kinetic energy, potential energy including nuclear attraction, Coulomb repulsion and LDA exchange, and correlation energy. Minimization of the free energy F = E — TS, with respect... 

For the same charges, the free energy and Coulombic forces are positive, and the charges are repulsive. For opposite charges, the free energy and Coulombic forces are negative, and the charges are attractive. Equation (3.26) shows that the Coulombic... 

AFf — AFf, calculated from is approximately 0.9 kcal. at pH 2.0 and 1.3 kcal. at pH 10.0. It appears reasonable to interpret the additional 0.4 kcal. free energy requirement at high pH as arising from a greater coulombic repulsion in the activated state for isotactic placement than in the activated state for syndiotactic placement. The ionic strength of the polymerization medium is very high (of the order of 2) at high pH it would therefore appear that an even more marked effect of pH... 

Within these broad constraints there is considerable latitude in choosing a model which might realistically describe the in situ adsorptive process, James and Healy (28) have developed an important model in which the free energy of adsorption (AG ads) results from the difference in electrostatic contributions between coulombic attraction (AG coul) and repulsion due to change in solvation energy (AG solv). The complete process is governed by... 

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