Frumkin function

The notion of pzc is absent in early textbooks. A table with pzc values for about 10 metals (but for only 5 are reliable values claimed) was given by Parsons in 1954 in the first volume of this series.4 After a more complete attempt by Frumkin in 196520 to compare work function, extensive work on pzc was reported by Perkins and Andersen9 in this series and by Frumkin etal.8 in another series. Compilations of pzc values were also made by Campanella, Trasatti, Frumkin et al., and Frumkin and Petrii14 up to 1979. A book by Frumkin10 devoted entirely to the potential of zero charge was published posthumously in 1979. 

Results for other metals of the Pt-group are due to Frumkin and co-workers8,10,11,14 (Table 22). However, an electrode with the surface renewed in closed circuit has been used by Lazarova767 to study depend linearly on pH with a slope ofca. 55 mV. This has been explained by the adsorption properties of Rh toward H and O, which shift <7-0 to more negative values. Anions have been observed to specifically adsorb on Rh more strongly than on Pt in the sequence... 

Thus far, Ft has never found a definite position in Ea vs. correlations, more for the uncertainty in the reliability of its pzc than for its work function. On the other hand, Pt is a highly heterogeneous metal and the fact that only polycrystalline surfaces have been used in double-layer studies has not helped remove suspicions. According to Frumkin s data,10,14 the pzc ofpc-Pt is around 0.2 V(SHE) (in acidic solution). If this value is introduced into Fig. 14 (the 0 of pc-Pt is around 5.5 eV),22,65 343,856 865,866 the point of Pt would fall far distant from the line of mercurylike metals and near the line of d-metals. 

It is an experimental fact that the capacitance of an electrode in a given solvent is a function of the nature of the metal. This was pointed out by Frumkin et al,333 and has been discussed several times in the literature.7 349 94 99 999 Trasatti34 901 showed that the reciprocal of the differential capacitance at a = 0 is linearly correlated with the strength of the metal-water interaction. The reader is referred to the original papers for a detailed discussion. 

A correlation between the amount of adsorbed ions and the electrode potential, in particular E. , has been identified apparently for the first time by Frumkin and Obrutschewa [26Fru]. A minimum of ionic adsorption was found at E, this is equivalent to the absence of specific adsorption at Ep c- The measurement of the amount of adsorbed ions was performed by measuring the ionic concentration in the solution as a function of the electrode potential or by measuring the surface concentration of adsorbed ions by e.g. radiotracer techniques (see also 4.2). (Data obtained with this method are labelled lA). 

Sinee replaeement of an adsorbed solvent moleeule by an adsorbate molecule generally results in a ehange of the eomposition of the first layer of the eleetrolyte solution being in contact with the electrode, the different values of the dieleetrie properties of the solvent and adsorbate moleeules as well as their different size result in a change of the value of Cdl- Evaluation of the changes of Cdl as a function of the concentration of the adsorbate in the solution phase results in adsorption isotherms. Various isotherms (Frumkin, Langmuir etc.) have been used in the further evaluation [75Damj. Beeause of interferenees of the kineties of the adsorption proeess in particular by slow transport and slow adsorption tensammetry... 

FIGURE 14.9 Volumes of the departing gas bubbles as a function of wetting angle (the solid line is the calcnlated function). (From Kabanov and Frumkin, 1933). 

Fig. 4.8 compares data on the adsorption of lauric acid (C12) and caprylic acid (Cs) at a hydrophobic surface (mercury) as a function of the total bulk concentration for different pH-values. As is to be expected the molecular species becomes adsorbed at much lower concentrations than the carboxylate anions. The latter cannot penetrate into the adsorption layer without being accompanied by positively charged counterions (Na+). As was shown in Fig. 4.4, the adsorption data of pH = 4 can be plotted in the form of a Frumkin (FFG) equation. Fig. 4.9 compares the adsorption of fatty acids on a hydrophobic model surface (Hg) with that of the adsorption on Y-AI2O3. 

In electrochemical conditions, the electrons are transferred from the metal to the solution rather than to a vacuum. Moreover, the metal/solution interface is charged and the potential difference between the metal and the solution should be taken into account. The situation is simplified when the work function and uncharged interface are considered. The relationship between the work function and potential of zero charge was propos nearly 30 years ago by Bockris and Argade and by Frumkin (see e.g., Ref. 66) and later intensively discussed by Trasatti (e.g., Refs. 5, 21, 67). The relationship is given by the equation... 

These two equations present the extension of the Frumkin model to the adsorption of one-surfactant system with two orientational states at the interface. The model equations now contain four free parameters, including cou co2, and b. The equations are highly nonUnear, and regression used in the analysis of surface tension data involves special combinations of Eqs. 23 and 24, which produces a special model fimction used in the least-square minimization with measured surface tension data. Since the model function also contains surface... 

Figures 6.117 and 6.58 show examples of the amount of surface covered by different organic molecules as a function of the concentration of the organic molecule in the electrolyte. We can identify these curves as isotherms (see Table 6.10). In organic adsorption, the most-used isotherm is the Frumkin one, namely,...

Underpotential deposition usually follows Frumkin-type adsorption isotherms due to strong lateral interactions and the interaction parameter, g, varies stepwise with coverage which is a function of the electrode potential. This is due to important structural and electric changes operative in the upd layers as coverage increases. 

The assumption underlying the derivation of the Frumkin isotherm is tantamount to assuming that the surface charge density is a linear function of coverage at constant potential, as seen in Eq. 18J. This is by no means generally correct, although it may constitute a fairly good approximation in many cases. 

Disregarding for a moment the electrochemical aspect of this isotherm, we note that 0 is proportional to logC, (as opposed to the Langmuir isotherm, where it is proportional to a linear function of the concentration.) A simitar "logarithmic isotherm" was developed by Temkin. His derivation is much more complex, but in the final analysis it is based on the same physical assumptions. It has, therefore, become common to refer to Eq. 141 as the Temkin isotherm, although Temkin has never used it in this form. It is this approximate form of the Frumkin isotherm which is applied to electrode kinetics, as we shall see below. 

We noted earlier that the equilibrium constant is an exponential function of coverage, when adsorption follows the Frumkin isotherm ... 

The maxima of fo.ads at certain A (Fig. 3.41) more or less coincide with the inflection points of the corresponding I E) isotherms (Fig. 3.36), indicating thatf ct turns maximal for an occupation of half of the adsorption sites of a given pattern. Such behavior is expected if the adsorption and desorption rates are steeply increasing functions of -6 and 9, respectively, near the point of half-coverage. This is true even in a primitive Frumkin or Langmuir-type adsorbate, because in that case... 

The PZC is an important point of reference in discussing the properties of a polarizable interface. Its location depends on the nature of all of the components which are at the interface, that is, on the metal, on the solvent used for the electrolyte solution, and on the nature and concentration of the solute components in this solution. Its importance was first pointed out by Frumkin [G3] who was able to carry out the first experiments at polarizable electrodes other than mercury. He showed that there is a fairly simple relationship between the PZC and the work function of the metal for a given solution composition and reference electrode. In this section the relationship is derived and its consequences illustrated with experimental data. Then a model which describes the role of the metal in interfacial properties, namely, the jellium model, is presented. 

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