Free energy of charging

Warshel A, Sussman F, King G (1986) Free energy of charges in solvated proteins Microscopic calculations using a reversible charging process. Biochemistry 25 8368—8372. 

A more fundamental way to describe the preferential interaction coefficient follows by a variational formulation of the PB equation. The variational technique applied to the PB equation allows the electrostatic free energy of charges in solution to be expressed as [75]... 

The functionals of this type allow calculating the equilibrium value of the polarization and free energy of the system, spatial correlation function of the polarization, contribution of the solvent reorganization to the activation free energy of charge transfer processes in polar media, etc. 

Bryantsev, V.S., Diallo, M.S., Goddard, W.A. Calculation of solvation free energies of charged solutes using mixed cluster/continuum models. J. Phys. Chem. B 2008,112(32), 9709-19. 

A simple continuum approximation was also included to account for long-range contributions to the solvation free energy of charged solutes. The total solvation free energy (AGsol) in terms of the contributions defined in Eq. (5) can be written in the general form ... 

The first term, Pt ch. can be called the free energy of charging the set of ions, held in fixed positions PT(0) is the potential of the average force for discharged ions. We limit our discussion to Wch. 

The free energy of charging a set of ions can be similarly decomposed. This decomposition is unambiguous if the ions are fairly distant from one another. In fact, we can write for one ion... 

As a by-product , the free energy of charging a single ion can be calculated by a very similar treatment. In the last section we shall describe an attempt to calculate explicitly, thus also evaluating the contribution of dielectric saturation— for a very simple solvent model, of course. 

We apply the model used in Section IV-B to the case of a single ion. The free energy of charging, wf is expanded in powers of the ionic charge, q, to give a series of Thiele semiinvariants, and then every semi-invariant is expanded in powers of (—/SF) to generate the a priori averages over the orientations of the dipoles this procedure finally yields for a perturbation series in ny = and in r =... 

EXAMPLE 22.7 The free energy of charging a parallel-plate capacitor. What is the free energy for charging up two parallel plates Start with two uncharged plates and transfer charge from one to the other. At the end of this process, the... 

AG is the free energy of discharging the ion in a vacuum, AG> = 0 is the electrostatic free energy of transferring the neutral particle to the solvent, and AG] is the free energy of charging up the ion in the solvent. 

Free energy of charging a sphere. A sphere with radius n in a medium with dielectric constant D is uniformly filled with a charge of volume density p. Derive the electrical free energy of this sphere in tw o different ways ... 

Having found the electrostatic potential, we can now obtain the interaction potential per unit area from the electrostatic free energy of charging both surfaces relative to charging the surfaces at infinite separation ... 

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