Esin-Markov coefficient

The degree of specific adsorption should vary with electrolyte concentration, just as there should be a change in the point of zero charge due to specific adsorption of charges. This is the Esin-Markov effect, expressed by the Esin-Markov coefficient, / ... 

Esin-Markov coefficient — Various cross-differential relationships can be obtained from the - Gibbs-Lippmann equation because it is a complete differential. For instance,... 

For nonpolarizable electrodes (dy/dE) gives QA the value of which depends on the choice of reference component. Various cross-differential relationships can also be obtained (see -> Esin-Markov coefficient). 

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. 

Figure 3.45. The Esin-Markov coefficient for the double layer on silver iodide. (Redrawn from J. Lyklema. J. Electroanal. Chem. 37 (1972) 53.)...

The effect of ionic strength on the charging curves can be quantihed in a form of the Esin-Markov coefficient ... 

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... 

For the model where the mobile adsorbed Na+ ions are situated on the primary plane, Equation 3 for the Esin-Markov coefficient may be written as... 

Fig. 8. The dependence of the peak potential of the faceting transition on chloride concentration. Assuming the transition occurs at a fixed charge, the slope -0.061 V/dec is proportional to the Esin-Markov coefficient.

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... 

Nonspecific adsorption provides no mechanism for the electrode potential to depend on the concentration of the electrolyte, so the Esin-Markov coefficient should be zero in the absence of specific adsorption. 

A very important indicator of the occurrence of specific adsorption is the so-called Esin-Markov coefficient, which in a generalized form can be given by the following equation ... 

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. 

Shielding of charged surface sites is described quantitatively by the Esin-Markov coefficient, P [18,22]. This coefficient was introduced initially in the case of the mercury/electrolyte interface. It represents the variation in applied potential required to maintain a constant surface charge when electrolyte acitivity increases ... 

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