Electrostatic self energy

Consequently, if we transfer the charged sphere from a vacuum to the solvent, its electrostatic self-energy is lowered by an amount ATT ... 

For polar solvents like water, DMSO, or 100% sulfuric acid, D l is quite small compared to unity (Table 13.1) so the electrostatic self-energy of a gaseous ion is almost entirely eliminated on transferring the ion to a polar solvent. For an ionic compound to be freely soluble in a given solvent, the solvation energies of its anions and cations must outweigh the lattice energy sufficiently, otherwise an ionic solid results instead. Ionic solids are therefore not usually very soluble in solvents of low D. 

The unit of length, e2/me1 = 2.82 x 10-13 cm, is called the classical electron radius, because a classical distribution of charge totalling the electronic charge must have a radius of this order for its electrostatic self-energy to be equal to the electronic mass energy. This estimate of the size of an electron is crude, but still the only one available. 

The polymer length at which the electrostatic self-energy is of order k- T, that is, Wei — follows as... 

Since the flexoelectric effect is associated with curvature distortions of the director field it seems natural to expect that the splay and bend elastic constants themselves may have contributions from flexoelectricity. The shape polarity of the molecules invoked by Meyer will have a direct mechanical influence independently of flexoelectricity and can be expected to lower the relevant elastic constants.The flexoelectric polarization will generate an electrostatic self-energy and hence make an independent contribution to the elastic constants. In the absence of any external field, the electric displacement D = 0 and the flexoelectric polarization generates an internal field E = —P/eo, where eq is the vacuum dielectric constant. Considering only a director deformation confined to a plane, and described by a polar angle 9 z), and in the absence of ionic screening, the energy density due to a splay-bend deformation reads as ... 

Multiplying the last equation by the number of beads rig per chain, one obtains the combined electrostatic self-energy of all beads. The electrostatic repulsion between beads can be estimated as... 

In a first step, we determine the potential of a charge distribution in the form of a double helix wrapped around a cylinder. The cylinder serves as a confining surface only, with cylinder-polyelectrolyte interactions being taken into account via the electrostatic self-energy of the complex. 

The electrostatic self-energy (66) per length (per pitch) of the helices becomes... 

Electrostatic self energy is associated with the work in producing an external electric field due to dipole surface charges. 

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