Work associated with electrostatic fields

In Sec. 8 we took the point of view that, when a molecule has been dissociated into ions, energy equivalent to the work done may be regarded as stored in the form of potential energy, which will be liberated when the ions recombine. The same point of view can be adopted with regard to the quantities Yvae and Y. The electrostatic part of this energy may be regarded as associated with the ionic field. 

The Electrostatic Energy. In Chapter 2 we drew attention to the fact that, when a proton transfer (117) has been carried out in a solvent, the electrostatic fields of two ions have been created and work must have been done to supply the amount of energy associated with these ionic fields. Let us now compare (117) with the process (123), both in aqueous solution at the same temperature. In both cases an (HaO)+ ion will be formed but in (123), when the proton is removed from the (IIS04)-ion, we have to separate the particles against the mutual attraction of the proton and the doubly charged ion (S04)". Consequently, more work must be done against the electrostatic forces of attraction than in the removal of a proton from a neutral particle. 

In a particular case of (118) it may happen that the amounts of energy associated with the two ionic fields are nearly equal such a proton transfer may be called nearly isoelectric. If in (118) the energy associated with the field of A- is less than that associated with B , electrostatic work... 

Fig. 10. Photoeleotron spectrum of oxygen using the helium resonance line (21-21 e.v.) obtained with a magnetic electron energy analyser (May and Turner, unpublished work). Ionization energy increasing from left to right. The spectrum reveals four levels of ionization and the vibrational structure associated with each state of the ion can be clearly distinguished. This spectrum may be compared with that obtained using an electrostatic retarding field analyser (Al-Joboury et al., 1965).

As in Sect. 2, the early works in this field will only be briefly summarized. Highly charged polyazoniamacro(oligo)cycles and guanidinium crowns bind phosphates and nucleotides via electrostatic interactions [1,65], and polyammonium cations, like spermine, are generally known to associate with the phosphate backbone of RNA and DNA strands [66]. 

The other model for the ionic friction concerns the dielectric response of solvent to the solute perturbation. When an ion is fixed in polar solvent, the solvent is polarized according to the electrostatic field from the ion. If the ion is displaced, the solvent polarization is not in equilibrium with a new position of the ion, and the relaxation of the polarization should take place in the solvent. The energy dissipation associated with this relaxation process may be identified as an extra friction. The extra friction, called the dielectric friction, decreases with increasing ionic radius, thereby, with decreasing electrostatic field from the ion. The dielectric friction model developed by Born [66], Fuoss [67], Boyd [68] and Zwanzig [69, 70] has taken a complete theoretical form due to the work by Hubbard and Onsager [71, 72] who proposed a set of continuum electrohydrodynamic equations in which the electrostatic as well as hydrodynamic strains are incorporated. 

As in previous chapters we work in the continuum limit employing quantities averaged over macroscopically infinitesimal volume elements and disregarding microscopic local variations associated with the molecular structure (see Brown 1956). These considerations will be limited to processes sufficiently slow to restrict the treatment to time independent or quasistatic fields. The validity of Maxwell s equations of electrostatics is presupposed. The basic electric state variables are the electric field strength vector E, the electric flux density (or electric displacement) vector D, and the electric polarization vector P, related by... 

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

The Kelvin method is based on the vibrating capacitor principle an inert electrode (a small piece of sheet metal or a grid is placed in front of the surface at a distance of d 10-100 (tm. As discussed above, the Fermi level aligns at equilibrium. Hence, different work functions of the two electrodes give rise to an electric field between them and accordingly to a potential difference (contact potential difference). The electrostatic potential difference eUis associated with a charge q on the electrodes ... 

Work Function (WF) plays a key role in the physics and chemistry of materials. Phenomena such as the semiconductor field effect, photo- and thermionic electron emission (Allen and Gobelli, 1962), catalysis (Vayenas et al 1996), and the like are dominated by the WF. This fundamental property of electronic materials is defined as the minimum work required to extract an electron from the Fermi level Ep of a conducting phase, through the surface and place it in vacuum just outside the reach of the electrostatic forces of that phase (Trasatti and Parsons, 1986). The reference level for this transfer is thus called the vacuum reference level. Because even a clean surface is a physical discontinuity, a surface dipole t] with its associated electric field always appears at the surface of the condensed phase. Thus, the work of extracting the electron can be conceptually divided between the work required to... 

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