Rational potential

Incidentally, a quantity called the rational potential is defined as E for the mercury-water interface (no added electrolyte) so, in general, = E + 0.480 V if a normal calomel reference electrode is used. 

The basic equations of ZINDO/1 are the same as those m IXDO, except I orL i y. In stead of usiri g th e electron egativity in INDO, ZlNDO/l uses th e ion i,ration potential for computing Llj,... 

Figure 4.4 depicts the dependence of 02 on E — Zspzc (the rational potential ) for various electrolyte concentrations. 

Fig. 4.4 The dependence of the potential difference in the diffuse layer on the difference E — Epzc (the rational potential) for various concentrations of the surface inactive electrolyte KF. (According to R. Parsons)... 

Comparison between the polarized electrode-electrolyte interface and the reversible (Al203) oxide-electrolyte interface. Surface tension (interfacial) tension, charge density and differential capacity, respectively, are plotted as a function of the rational potential vy (at pzc vy is set = 0) in the case of Hg and as a function of ApH (pH-pH ) in the case of Al203 (pH = pHpzc when a = 0). 

Rational potential — is the - electrode potential in a reduced scale, as referred to potential of zero charge of the same electrode material in solution of given composition. This quantity is used in studies of the electric double layer as the so-called Grahame rational scale [i]. A detailed discussion of the rational p. was given by Antropov [ii]. 

Rational potential -+potential RDE - rotating disk electrode... 

Other factors, of course, come into play in an actual plating bath. For example, plating from an acid bath takes place at around 0.3 V, NHE, whereas in a cyanide bath, copper is deposited at a much more negative potential. The former occurs at a positive rational potential, while the latter occurs at a negative rational potential. This affects the choice of additives and their adsorption characteristics. Also, the values of ( ) and d( ) /d( ) may be different in the two cases. The foregoing example is not intended to be a quantitative interpretation of the benefits of cyanide baths, but rather an illustration of how considerations of a rather fundamental nature can assist in solving applied problems. 

NaF). The bromide ion is no longer adsorbed when the potential is about - 0.25 V versus E in the same solution. Adsorption of an anion at a negative rational potential is a clear indication that "chemical" or some other "nonelectrostatic" interactions are involved. The negative potential needed to drive an anion out of the interphase is a quantitative measure of the strength of the chemical bond holding it there. 

Note that we have replaced here the rational potential E by the poten tial E, measured versus some reference electrode. The difference between them is a constant, which we can lump into the equilibrium constant. 

The inner potential drop across the ITIES, Aq2 0, is related to the rational potential [57], Aq 0r = E-Ep f., and the two diffuse layer potentials, each in the aqueous phase and in the organic phase, and 0°through... 

Depending on the mechanism of the reactions leading to the appearance of the species i, its coverage apart from the chemical properties of the smdace will be determined in various ways by the rational potential. This would support the choice of the potential of zero charge for rates of reactions involving adsorbed species. 

The novel design and functional possibilities offered by MIDs and the rationalization potential of the respective production methods have inevitably led to a quantum leap in electronics production. The most important functions that can be integrated into an MID are depicted in Figure 39. So far, cost savings of up to 40% have been achieved by integration, depending, of course, on the specific product, lot sizes, and other boundary conditions. 

Oj"n)> where /o g is the bound charge density of the metal and solvent in contact and is the charge density of electrolyte ions. Subtracting from this equation the same equation at <7 = 0, for the so-called rationalized potential, 4>(z) = fa (z) - foiz), we get... 

Fig. 15.10 (a) CV curves in Ar-purged 0.1 M KOH on Ag (hkl) sifffaces. All CVs were obtained at room temperatine with a sweep rate of 50 mV s . (b) FractiOTial charge per atom, obtained by integrating the anodic sweep direction of CV (fiorn a) after accounting for the different surface atom density of different Ag(hkl) orientations, (c) Fractional charge per atom expressed rm the rational potential scale (RPS) [47]... 

In the past, there has been some dispute as to the zero potential at which rates on different metals should be compared. Most early discussions centered around the use of the p.z.c. of the metal (Antropov, Ref. 31 Grahame, Ref. 32 the latter calling the scale the rational potential scale ). Bockris and Potter decided that the rates of the electrocatalytic hydrogen evolution reaction should be compared at the zero-charge potentials of different metals, because of the log rate—O correlations reported in Ref. 7. This comparison is not only difficult to make, on account of the general problem of accurately determining the p.z.c. values in most cases, but, as shown above, is also not necessary. Indeed, it is clear that wide variations in... 

Figure 3. Electrocapillary data for Pb in molten KCI at 1093 K. Experimental data shown as points, solid curve corresponds to double-integrated capacitance curve, and 0 is the rational potential for the Pb electrode. (Reproduced from Ref. 1 by kind permisssion John Wiley and Sons, Inc.)...

An additional difficulty which arises in the interpretation of adsorption measurements on solid electrodes is the uncertainty with regard to the real surface area of the electrode. Various methods have been suggested for the determination of the roughness factor, (i.e., the ratio between real and apparent surface area) none of which is quite satisfactory. Frumkin et al. obtained the roughness factor by comparison of the capacity in the double-layer charging region (i.e., where no Faradaic process takes place) with that obtained on mercury at the same rational potential. Brodd and... 

The term rational potential was first introduced by Grahame and refers to the potential relative to the potential of zero charge (p.z.c.) in the same system. 

The concentration of ions near the electrode surface depends on charge density and hence on potential. For example, in 0.1 M solution of a 1 -1 electrolyte at a rational potential of + 0.5 V, the concentration of anions at the outer Helmholtz plane, calculated from the Gouy-Chapman theory, is 4.7 M. At this concentration. 

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