Electrostatic work

The calculation involved here is conceptually a complex one, and for the necessarily detailed discussion needed to do it justice, the reader is referred to Verwey and Overbeek [5] and Kruyt [6] or to Hamed and Owen [10]. Qualitatively, what must be done is to calculate the reversible electrostatic work for the process ... 

The electrochemical potential is defined as the total work of bringing a species i from vacuum into a phase a and is thus experimentally defined. It.may be divided into a chemical work p , the chemical potential, and the electrostatic work ZiC0 ... 

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Consider the processes (1), (2), and (3) of Fig. 1. In each case, initially no electrostatic field exists. When we bring ions into the solvent, we have to do the electrostatic work required to set, up their fields in the dielectric. These ionic fields are weak compared with the fields which would be set up in a vacuum—which are, in fact, set up in processes (2 0<.), and (3 ) where the same ions are brought into a... 

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... 

In this process we obtain two ions of opposite sign, as in (117). But the electrostatic work is not so large as in (117) because there is initially the energy in the field surrounding the NTI3l CH2COO- particle, and only the additional amount of energy has to be supplied. 

In this equation, the second term describes purely electrostatic work, connected with an infinitely slow transfer of charge zF from infinity in a vacuum into the bulk of the second phase, i.e. to a point with electric potential 0. Here only electric charge is transferred, not a material species with which it might be connected. The ratio of this work to the transferred charge is equal to the inner electrical potential 0 of the given phase. 

It is interesting to note that according to Ref.136) regardless of the model used, the CNDO/2 treatment predicts a larger ir-polarization for cyclopropenone than for tropone. This means that the electrostatic work to achieve a cyclopropenium oxide structure is considerably less than for cycloheptatrienylium oxide. From this reason, cyclopropenone seems to be a closer approximation to an aromatic system than tropone which can be described better as a polyolefin. 

Substituting this into Eq. (4.15) gives for the electrostatic work required to adsorb one particle ... 

An early continuum treatment of solvation, associated with Born,17 comes out of the analysis of the electrostatic work involved in building up a charge Q on a conducting sphere of radius R in a medium with dielectric constant e. From Poisson s equation, it follows that the potential outside of the sphere is Q/eR. Thus the work of charging is the result of each additional element dq interacting with the charge q already present 87... 

Theoretically this term reflects the electrostatic work in transporting ions through the interfacial potential gradient (e.g., Stumm et al., 1970 Stumm and Morgan, 1981 Morel, 1983). Since... 

Rate constant for homogeneous self exchange, corrected for electrostatic work terms using Debye-Huckel-Bronsted model. Data taken from sources quoted in ref. 15 unless otherwise stated. 

Esr line broadening. When one of the couples if uncharged, the electrostatic work term is approximately zero. Structural differences between the two species are also likely to be small (X small). The effect of solvent is contained in Using Eqns. (5.23) and (5.25)-(5.27), a plot of log A .xch vs (Dop -ZJ " ) should be linear with negative slope. 

There is a decreased electrostatic work term due to a large distance of closest approach with Ru(en)3. This is small at larger and the important factor is a reduced outer-... 

Here v is the number of ions per unit time and area transferring from the solution layer next to the electrode, to the electrode. It will at once be noticed that as long as the interfacial potential difference d< > is negative, the electrostatic work term Pde0 increases the velocity of the ion transfer reaction in an exponential way (Fig. 7.10). 

Finally, we must consider the contribution of the electrostatic work required to transfer one electron into free space. After overcoming the short range chemical forces, the electron must be moved a certain distance against the electric field in the surface. Under the assumption that the lines of force of the electric field are located between the ion defects in the boundary layer and the surface charges represented by the chemisorbed gas atom, we obtain the expression afi for this electrostatic work term. is the boundary field strength represented in Equation (11), and a is the distance between the surface of the oxide and the centers of charge of the chemisorbed atoms in the a-phase. 

It is important to notice that the rate of a given outer sphere electrode redox reaction should be independent of the nature of the metal electrode if allowance is made for electrostatic work terms or double layer effects which will, of course, be dependent on the nature of the electrode material. Inner sphere reactions, on the other hand, are expected to be catalytic with kinetics strongly dependent on the electrode surface due to specific adsorption interactions. 

The analogy between the two physical problems, though with different symmetries, can be also found in the electrostatic work terms associated both to the kinetics of homogeneous ionic reactions and electrode reactions. (For the former, see Vol. 2, Chap. 4 and for the latter, see Sect. 3.5, below.)... 

These effects are due to the electrostatic work necessary to bring the electroactive ion to a charged interface, where the electrode reaction takes place, and it is essentially equivalent to the electrostatic contribution to the free energy of activation in homogeneous ionic reactions in solution (Vol. 2, Chap. 4). 

Probably the most important outcome of the Marcus theory is the relationship between homogeneous homonuclear (fcs) and heterogeneous electron transfer rate coefficients (feei) after corrections for electrostatic work terms... 

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