Helmholz

Fig. 20.2 Helmholz double layer (H.D.L.) consisting of a plate of excess negative charges on the surface of the metal and a counterbalancing plate of excess positive charges (cations) in solution, the double layer as a whole being electrically neutral. The double layer can be regarded as equivalent to a capacitor in which the plates are separated by a distance ...

A simple model of the e.d.l. was first suggested by Helmholz in which the charges at the interface were regarded as the two plates constituting a parallel plate capacitor, e.g. a plate of metal with excess electrons (the inner Helmholz plane I.H.P.) and a plate of excess positively charged ions (the outer Helmholz plane O.H.P.) in the solution adjacent to the metal the... 

The simple Helmholz model, in which the charge on the model is regarded as the plate of a capacitor that attracts a counter layer of ions of opposite charge and results in two parallel plates of the same charge density, is inconsistent with the shapes of the electrocapillary curves obtained in practice. It can be shownthat if the Helmholz model applied, the electrocapillary curve would conform to the relationship... 

A further inconsistency in the Helmholz model is revealed by the differential capacitance C which is given by... 

The Stern model (1924) may be regarded as a synthesis of the Helmholz model of a layer of ions in contact with the electrode (Fig. 20.2) and the Gouy-Chapman diffuse model (Fig. 20.10), and it follows that the net charge density on the solution side of the interphase is now given by... 

The interface region from the electrode to the Helmholz plane (the locus of the centres of the ions in contact with the electrode) across which the potential varies linearly. 

The region from the Helmholz plane into the solution, across which the potential varies exponentially attaining a value of zero at some distance in this region the ions are subjected to both ordering electrical forces and disordering thermal forces. 

Two alternative structures for the simple Helmholz double layer (Fig. 20.11) have been provided ... 

On the other hand, as already discussed in Chapter 2, Eq. (2.21), AO is directly related to the coverage, 0Na> of the backspillover Na8 species and to its dipole moment Pna via the Helmholz equation (2.21). Thus one can directly derive the equations ... 

The variation in Q of a metal M with the coverage 0j of an adsorbate, i, is given by the Helmholz equation ... 

We now examine what happens to the modified electrochemical Langmuir isotherm (Eq. 6.36) when AO is created only by the presence of the adsorbate j, i.e. in absence of any coadsorbing ionic species. Substituting equation (6.49) into equation (6.36) and expressing AO via the Helmholz equation (5.16) one obtains ... 

Also the rate plateau at low O values is strongly reminiscent of the observed behaviour with Pt/YSZ. Thus the behaviour is qualitatively very similar. The inserted 0Na abscissa in Fig. 9.2 is constructed on the basis of Eq. (4.25) or of the following equivalent form of the Helmholz equation ... 

The electrochemically induced change in work function AO (eq. (1 1.6)) is related to the coverage 0j of the promoting species (e.g. O5 ) on the catalyst surface via the Helmholz equation ... 

In contrast to the useful conceptual framework provided by the approximate approach just described, the results of more detailed molecular orbital calculations have on the whole been rather disappointing. Thus, although some semi-empirical SCF treatments were attempted, most of the earlier MO calculations for metallocene systems (18, 161, 162, 163, 164,165) suffered from such deficiencies as the neglect of the a-framework, or the use of various one-electron Hamiltonians, for example the various Wolfsberg-Helmholz techniques. Of late, Drago and his coworkers have carried out further Extended Htickel type computations for a wide range of both metallocene and bis-arene species (153, 154), and similar... 

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