Pseudocapacitance Adsorption

The capacitance is a readily measured interfacial property and it gives qualitative information on the adsorption of species at the electrode surface. Since the surface charge density, q, is a function of the potential and of coverage, the measured capacitance may be expressed as the sum of a true (high frequency) capacitance and an adsorption pseudocapacitance, i.e. q f(E,6) and hence... 

Tlie capacitive nature of the adsorption pseudocapacitance can be further illustrated by considering its ac response. Let us assume that a low amplitude sinusoidal voltage signal is applied to a system at equilibrium ... 

The adsorption pseudocapacitance can be readily calculated from the appropriate isotherm, with the use of its definition, given in Eq. 391. This is shown next for the Langmuir and Frumkin isotherms. 

We proceed here to derive the expressions for the adsorption pseudocapacitance under Frumkin conditions, which we shall denote C. ... 

There is an apparent discrepancy between the treatment of electrode kinetics under Temkin conditions, at intermediate values of the coverage, and the results shown in Fig. 141(b) for the adsorption pseudocapacitance in the same region. For the purpose of calculating the kinetic parameters, we have assumed that 0 is a linear function of potential. This is a valid assumption, as we can see in Fig. 21. Yet such a linear dependence of 6 on should give rise to a constant value... 

Fig. lOK Open-circuit decay of overpotential. (1) constant capacitance (2) potential dependent adsorption pseudocapacitance, (3) corresponding variation of with T]. From Gileadi,... 

The plots we have shown, which are all based on simulated data, serve the purpose of illustrating the principles involved. Tlie results of real experiments are rarely so simple and easy to interpret. This is caused by two types of factors on the one hand, the reaction may not be as simple as is assumed in the model. The formation of adsorbed intermediates, for example, can lead to an adsorption pseudocapacitance. The corresponding equivalent circuit usually has two widely different time constants that show up as two semicircles, which could be partially overlapping. Surface heterogeneities are tantamount to different values... 

Thus, the adsorption isotherm also yields the dependence of charge on potential. This allows us to define a new type of differential capacitance, which we call the adsorption pseudocapacitance C ... 

The dependence of the impedance associated with on frequency can be visualized with the aid of the equivalent circuit shown in Fig. 121(b). Here the adsorption pseudocapacitance is part of a more complete circuit, showing the other circuit elements we have already... 

T te adsorption pseudocapacitance under Frumkin conditions is thus ... 

Since, by definition, 0 < 0 < 1, Eq. 591 has physically meaningful solutions only for / < - 4. A plot of the Frumkin isotherm for negative values of the parameter / is shown in Fig. 171. For / = - 12, the solution of Eq. 591 yields 0 = 0.11 and 0.89. Between these values, the coverage appears to increase with decreasing potential, which would imply a negative value of the adsorption pseudocapacitance. This does not represent physical reality, of course. If we trace the potential in the positive direction, 0 will Jump from 0.11 to 0.999. When the... 

Tafel slopes for the anodic and the cathodic process double-layer capacitance ( lF/cm ) capacitance of the Helmholtz double layer capacitance of the diffuse double layer double-layer capacitance at 0 = 0 double-layer capacitance at 0 = 1 adsorption pseudocapacitance (llF/cm ) adsorption pseudocapacitance derived from the Langmuir isotherm... 

Another complication with the use of this treatment must be noted it lies in the nature of the pseudocapacitance quantity used. The adsorption pseudocapacitance is defined as the product of the charge density for monolayer coverage, ij, and the derivative of coverage with potential, Eq. (45) ... 

In the more interesting case here where 6 is significant and potential dependent, Qi must be replaced, to an approximation, by Qi + where is the adsorption pseudocapacitance of the chemisorbed intermediate derived from differentiating the (Langmuir) isotherm... 

The 0H results are recovered in the form of profiles of H adsorption pseudocapacitance, Q [Eqs. (66) and (67)], as a function of overpotential, t), which can be integrated to give changes of coverage by H with increasing overpotential (shown below in Figs. 19 and 20). 

The difference in behavior of pyrolytic graphite, examined in Ref. 2, and the glassy carbon investigated in this more recent work, is probably done to the different electrocatalytic surfaces that these materials present. Thus, impedance measurements we have made indicate little adsorption pseudocapacitance for adsorbed Br species at glassy carbon whereas, at pyrolytic graphite, an adsorption capacitance is measurable. The results depend on edge or basal-plane exposure. 

Adsorption pseudocapacitance can come from two-dimensional surface reactions that involve faradaic desorption and adsorption of an electroactive species from the electrolyte at a metal surface [69], One good example is the adsorption/desorption of hydrogen (H) at Pt in the acid solution, following the reaction [41,69]... 

The adsorption pseudocapacitance is dominated by the term ddjdE and hence a plot of Cq versus-S gives information about the coverage directly. Figure 1.15 shows a set of Cs-E plots for a pentanol solution at a mercury electrode. The peaks are due to adsorption/desorption processes, so, for example, from the 0.1 M solution, the alcohol adsorbs in the potential range between —0.1 V and —1.1 V. 

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