Relative surface excess metal ions

For an example of a metal electrode in equilibrium with a solution of metal ions, the equation for the relative surface excess of the metal ions is... 

Two types of EDL are distinguished superficial and interfacial. Superficial EDLs are located wholly within the surface layer of a single phase (e.g., an EDL caused by a nonuniform distribution of electrons in the metal, an EDL caused by orientation of the bipolar solvent molecules in the electrolyte solution, an EDL caused by specific adsorption of ions). Tfie potential drops developing in tfiese cases (the potential inside the phase relative to a point just outside) is called the surface potential of the given phase k. Interfacial EDLs have their two parts in dilferent phases the inner layer with the charge density in the metal (because of an excess or deficit of electrons in the surface layer), and the outer layer of counterions with the charge density = -Qs m in the solution (an excess of cations or anions) the potential drop caused by this double layer is called the interfacial potential... 

What is noteworthy about the series is that for the monatomic alkali metal cations their order does not agree with their size or charge density or their lyotropic series (Voet 1937b). This apparent disorder (note the position of Cs+) is not universal, however, since cases where the lyotropic series is followed are also known. An instance is the rate of the penetration of the alkali metal cations through leaf cuticles that decreases in the order Cs+ >Rb+ > K+ > Na+ > Li+, i.e., in the expected order according to their surface charge densities. The cuticular pores were supposed by McFarlane and Berry to be lined with a protein that has exposed positive sites (McFarlane and Berry 1974). The critical micelle concentration (cmc) of sodium dodecylsulphate increases in the reverse order by these cations (Maiti et al. 2009), where Cs+ is at the expected position. The transition of a mixed surfactant (sodium dodecylsulfate + dodecyltrimethylammonium bromide with an excess of the former) from micelles to vesicles (Sect. 4.5) is also promoted in this sequence, explained by counter-ion association depending on relative ease of ion dehydration (Renoncourt et al. 2007). 

The Berea sandstone had been split into clay and quartz fractions, but the Berea whole rock was still more negative relative to the other core listed for this study. Even though the trend was the same for both brines, the divalent cations in the 2.1% TDS brine produced less negatively charged surfaces than did the NaCl brine. This behavior was attributed to adsorption of these ions into the Stem layer or, in the case of earbonates, to preferential dissolution of CO over Ca or Mg in the presenee of excess divalent cations in the aqueous phase. It was also noted that adsorption of metal hydroxide ions or mineral transformation reaetions at the solid surface may play a role. 

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