Esin and Markov coefficient

Generally, for ideally polarized electrodes, the plots of the electrode potential against either the chemical potential of the component in question or its activity are referred to as the Esin and Markov plots the slope of the plot is called the Esin and Markov coefficient.82 Aogaki etal.19 first established the expression of the critical pitting potential with respect to the composition of the solution (i.e., the Esin and Markov relations corresponding to the critical condition of the instability obtained in the preceding sections) and also verified them experimentally in the case of Ni dissolution in NaCl solution. 

An increase in the bulk iodide concentration causes a gradual shift of the sigmoidal curves in Fig. 6 towards more negative potentials, while leaving the height of the plateau unaltered. In Fig. 7 this potential shift at constant aM on Ag(lll) is plotted against log cs, for sulfide, iodide, bromide and chloride. The slope of the resulting plots is just a measure of the Esin and Markov coefficient (cE dns)a, where fis is... 

Sabia, R. and Ukrainczyk, L., Surface chemistry of SiO2 and TiOj-SiOj glasses as determined by titration of soot particles, 7. Non-Cryst. Solids, 277, 1, 2000. Lyklema, J., The electrical double layer on oxides, Croat. Chem. Acta, 43, 249, 1971. Lyklema, J., The Esin and Markov coefficient for double layers with colloid chemical importance, 7. Electroanal. Chem., 37, 53, 1972. 

Iv) Cross-differentiation also yields Esin-Markov coefficients p. Introduced in sec. I.5.6d. These coefficients contain information on the relative contributions of the cations and anions to the countercharge, l.e. they help to obtain the composition of the double layer. Experimentally, is measured as the horizontal spacing between ff°(pAg) or salt concentrations and defined as... 

The availability of r° (or pAg) curves at several electrolyte concentrations enables the establishment of the Esin-Markov coefficient 3.4.14) and the ensuing determination of the ionic components of charge, integrating 3.4.16] l Figures 3.45 and 3.46 give results of the former and the latter, respectively. 

The theory of the AV-A behavior developed by L.M.B. (2) was based on earlier calculations by Mingins and Pethica (M.P.) (9) from their experimental work on monolayers of SODS at the A—W interface. Recently these authors (10) reported a numerical error in their earlier work their conclusions question the model of the ionized monolayers used by L.M.B. (2) to explain the A V-A curves. The so-called Esin-Markov coefficient for adsorbed ions at the charged mercury/aqueous electrolyte has received considerable attention (11, 12, 13) particularly since it clearly demonstrates the discrete-ion effect. Its counterpart at ionized monolayers may be defined by the differential expression... 

Currently no adequate quantitative theory of the discrete-ion potentials for adsorbed counterions at ionized monolayers exists although work on this problem is in progress. These potentials are more difficult to determine than those for the mercury/electrolyte interface because the non-aqueous phase is a dielectric medium and the distribution of counterions in the monolayer region is more complicated. However the physical nature of discrete-ion potentials for the adsorbed counterions can be described qualitatively. This paper investigates the experimental evidence for the discrete-ion effect at ionized monolayers by testing our model on the results of Mingins and Pethica (9, 10) for SODS. The simultaneous use of the Esin-Markov coefficient (Equation 3) and the surface potential AV as functions of A at the same electrolyte concentration c yields the specific adsorption potentials for both types of adsorbed Na+ ions—bound and mobile. Two parameters which need to be chosen are the density of sites available to the adsorbed mobile Na+ ions and the capacity per unit area of the monolayer region. The present work illustrates the value... 

AV and Esin—Markov Coefficient of Mingins and Pethica. Mobile Primary Planea... 

Another indicator of specific adsorption of charged species is the Esin-Markov effect, which is manifested by a shift in the PZC with a change in electrolyte concentration (33). Table 13.3.2 provides data compiled by Grahame (2). The magnitude of the shift is usually linear with the logarithm of electrolyte activity, and the slope of the linear plot is the Esin-Markov coefficient for the condition of = 0. Similar results are obtained at nonzero, but constant, electrode charge densities hence the Esin-Markov coefficient can be written generally as... 

In order to obtain insight into the nature of the adsorbed species, Esin-Markov coefficients for S04 adsorption from two series of solutions were determined (1) at constant pH and variable K2SO4 concentration (2) at constant K2SO4 concentration and variable pH. The Esin-Markov coefficients were used to identify the nature of the adsorbed species (S04 or HS04 ). The authors arrived at the conclusion that S04 ion is the adsorbed species even if HS04 predominates in the bulk of the solution. Similar results were reported in Ref. [96]. 

Cations adsorption is of interest for interpretation and prediction of pzc dependences on salt concentration, considered in a general form in Ref. 102. Experimental data for solutions of various anionic composition (Fig. 6c) demonstrate no pronounced slope difference for anions of essentially different adsorption behavior. All slopes are very low (even lower than expected in the absence of Esin-Markov effect studied earlier for similar systems.) The decrease of slope can result from two contributions (decrease of cations adsorption with potential and displacement of hydrogen with increase of anion concentration). This result means that the straightforward interpretation of Esin-Markov coefficients for platinum metals (if any) should take into accoimt that these values can be underestimated. 

Equation (19) relates the dependence of the pzc on the concentration of the electrolyte solution in the presence of specific adsorption (F 0 when au = 0) and its variation with the electrode charge. The dependence of the pzc of a mercury electrode on the logarithm of KI concentration was used for the first time for studying the iodide specific adsorption in [17] and later was named the Esin-Markov effect. As follows from the model theories of the electric double layer (see Sect. 3.2), the limiting slope of the aforementioned dependence should tend to the value —RT/kF, where the coefficient X(0 < X < 1) characterizes the discrete nature of the charge of specifically adsorbed anions. 

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