Electrosorption Capacitance

Some species, however, can undergo a well-defined Faradaic charge- 

This reaction has been suggested as a vehicle for capacitative energy storage (4) and demonstrated in a solid polymer electrolyte configuration (5-7). At least some of the transition metal oxide systems, discussed in greater detail later, also fall intothis category, e.g., thermal RuOj and IrOj. 

Because the proton adsorbs at a specific site on the surface, with a well-defined enthalpy of adsorption, the dependence of differential capacitance on electrode potential may be quite strong. On platinum, for example, several different site energies may be resolved in the underpotential deposition region. 

Each adsorption process may be described in terms of an adsorption isotherm, which quantifies the relationship between the degree of coverage, B, and the electrode potential. The simplest example is the Langmuir isotherm (9), which assumes no interaction between the adsorbed species (i.e., a constant free energy of adsorption, A G°). The coverage is just the balance between an enthalpic term (driving the adsorption process) and the entropic term, giving the isotherm  

More sophisticated treatments of electrosorption equilibria lead to other formulations of the isotherms (10)( 11). Terms that may be included are those due to surface heterogeneity and lateral interactions between the adsorbed species. In the Temkin isotherm, these terms appear as a parameter, r, which reduces the free energy of adsorption  

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Yang, K.L., Yiacoumi, S., and Tsouris, C. Electrosorption capacitance of nanostructured carbon aerogel obtained by cyclic voltammetry. J. Electroanal. Chem. 540, 2003 159-167. 

Recent interest in this topic [102] has been tremendous, spurred not only by the opportunity (and indeed desperate need ) to further enhance the performance of batteries but, especially so, to develop novel supercapacitors [68], Among the 41 papers published only in 2007 (through October)—a remarkable number, indeed—and identified as directly relevant to this section of the chapter, 24 were devoted primarily to carbon capacitance issues [71,95,103-124], 7 to redox behavior [125-131], 6 to electrosorption [132-137], and the others to more general electrochemical properties and behavior. 

The results presented in this section confirm that an adequate pore size is more important than a high surface area for an optimization of the capacitance values. For the production of compact systems, an important objective is to limit as much as possible the useless porosity in order to enhance the volumetric capacity. Moderately activated carbons, with pores at the boarder of the ultramicropore region, e.g., 0.7-0.9 nm, are the most profitable for ions electrosorption. 

From the researches achieved recently, three main breakthroughs might be observed. The first one concerns the traditional concept of EDL in a nanoporous carbon. It has been demonstrated from independent experiments performed by few groups that the highest capacitance related with electrosorption is observed when the nanopores of carbons perfectly fit the dimensions of ions. Some experiments have even shown some swelling of the carbon host which could be attributed to an intercalation/insertion-type penetration of ions. Moreover, the ions could penetrate desolvated in the pores. From the foreword, it is obvious that some computational work is now necessary for a better interpretation of these experimental observations. Especially, the energy calculations should... 

Electrosorption is a replacement reaction. We have already discussed the role of the solvent in the interphase, in the context of its effect on the double-layer capacitance. It is most important for our present discussion to know that the electrode is always solvated and that the solvent molecules are held to the surface both by electrostatic and by chemical bonds. Adsorption of a molecule on such a surface requires the removal of the appropriate number of solvent molecules, to make place for the new occupant, so to speak. This is electrosorption. In this chapter we shall restrict our discussion to the electrosorption of neutral organic molecules from aqueous solutions, without charge transfer. Using the notation RH for an unspecified organic molecule, we can then represent electrosorption in general by the reaction... 

An additional method for the determination of adsorption on solid electrodes by capacitance measurements, based on the theory of electrosorption developed by Frumkin, is discussed in Section 22.2. 

Pseudo-capacitance Related with Reversible Hydrogen Electrosorption in Nanoporous Carbons . 

As it has been introduced in the previous section, hydrogen electrosorption in carbon materials under negative polarization has a direct impact on the energy density of a supercapacitor operating in an aqueous electrolyte. Due to the overpotential of dihydrogen evolution, the electrochemical stability window can be extended to lower potential values. Moreover, the electro-desorption of hydrogen by anodic oxidation gives rise to a pseudo-faradic contribution in addition to the EDL capacitance of the material. 

Figure 3. Equivalent circuit for an electrosorption process R, is the bulk solution resistance, is the charge transfer (kinetic) resistance, is the double-layer capacitance, and is the adsaption pseudocapacitance.

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