Double layer, capacitance region

For (ideally) polarizable metals with a sufficiently broad double-layer region, such as Hg, Ag, Au, Bi, Sn, Pb, Cd, H, and others, Ea=to can be obtained from measurements of the double-layer capacitance in dilute... 

As was discussed in section 2.1.1, electrocapillarity measurements at mercury electrodes, which have well-defined and measurable areas, allow the double-layer capacitance, CDL, to be obtained as Fm-2. Bowden assumed that the overpotential change at the very beginning of the anodic run in H2-saturated solution was a measure of the double-layer capacity. The slope of the E vs. Q plot in this region was taken as giving 1/CDL, and this gave 2 x 10 5 F. He then assumed that, under these same conditions, the double-layer capacity, in Fm-2, of the mercury electrode is the same. This gave the real surface area of the electrode as 3.3cm 2, as opposed to its geometric area of I cm2. 

Piela and Wrona [8] have employed impedance spectroscopy to study capacitance of the pc-Au electrode in 0.5 M H2SO4 in the double-layer potential region (—0.25 to 1.05 V versus SSCE) and... 

Fig. 8.8. The decay of oveipotential with time in an open-circuit situation with a constant double-layer capacitance over the decay region. The initial oveipotential is anodic and the electrode becomes less positive as the time increases.

Here C is the specific differential double layer capacitance. The two terms on the left side of Eq. (4) describe the capacitive and faradaic current densities at a position r at the electrode electrolyte interface. The sum of these two terms is equal to the current density due to all fluxes of charged species that flow into the double layer from the electrolyte side, z ei,z (r, z = WE), where z is the direction perpendicular to the electrode, and z = WE is at the working electrode, more precisely, at the transition from the charged double layer region to the electroneutral electrolyte. 4i,z is composed of diffusion and migration fluxes, which, in the Nernst-Planck approximation, are given by... 

From their calculations of the surface excess entropy and volume of the electric double layer at a mercury-aqueous electrolyte interface, Hill and Payne (HP) [147] postulated an increase in the number of water molecules in the Stern inner region as the surface charge a of about 30 piC/m2, which is consistent with the results of TC on a silver surface obtained some 30 years later. HP used an indirect method to determine the excess entropy and volume by measuring the dependence on temperature and pressure of the double layer capacitance at the mercury-solution interface. 

Figure 6.3 (a) Schematic representation of equivalent circuit for an ion conductor put between a pair of blocking electrode, and (b) the corresponding Nyquist plot. Ideally the sample-electrode interface is composed only of the double-layer capacitance. However, the practical Nyquist plot that corresponds to this frequency region is not vertical to the real axis. The rate-limiting process of this plot is that the ion diffuses to form a double layer. 

One such properly is the capacitance, which is observed whenever a metal-solution interphase is formed. This capacitance, called the double layer capacitance, is a result of the charge separation in the interphase. Since the interphase does not extend more than about 10 nm in a direction perpendicular to the surface (and in concentrated solutions it is limited to 1.0 nm or less), the observed capacitance depends on the structure of this very thin region, called the double layer. If the surface is rough, the double layer will follow its curvature down to atomic dimensions, and the capacitance measured under suitably chosen conditions is proportional to the real surface area of the electrode. 

If double-layer charging is the only process taking place in a given potential region (this would be the case for an ideally polarizable interphase) and one cycles the potential between two fixed values, the results should be such as shown in Fig. 2L(a). Plotting Ai = i - i = 2 i as a function of v, as shown by line 1 in Fig. 2L(b), one can obtain the value of the double-layer capacitance from the slope. If a faradaic reaction is taking place, a result such as shown by line 2, from which C can still be obtained (cf. Fig. 14G), might be observed. 

Figure 16. Schematic repmsentation of an electrochemical double layer at a mctal/elcctrolytc solution interface, (a) The jcllium double layer (with electron spill-over region contacts a layer of (ordered) solvent molecules, chemisorption of a negative ion is also shown, (b) Representation of the double layer capacitance as a series connection of the capacitance corresponding to the double layer of the metal surface, and the capacitance of (he Helmholtz layer al the solution side.

Figure 1. Impedance spectra (real vs. imaginary part) of an carbon aerogel and the corresponding equivalent circuit. The RC-circuit parallel to the double layer capacitance (circuit with dotted lines) corresponds to pseudocapacitances due to reversible redox-groups on the carbon surface [10]. The position x = 0 denotes the pore entrance of the cylindrical pore adjacent to the reference electrode. The corresponding frequencies are between 20 kHz and 8.25 mHz (region a to c).

FIGURE 7.3. Illustration of the instability window in electrocapiUary curve (a), excess surface charge density vs. potential curve (b) and double-layer capacitance vs. potential curve (c) in the absence (dashed lines) and the presence (solid lines) of the adsorpdon and partition of an ionic surfactant. Parameters used for calculation are the same as those in Figure 7.1. Shaded region shows the potential range where the system is thermodynamically unstable. Horizontal dashed lines in the middle of b and c represent the lines of zero surface charge and of zero capacitance, respectively. See text for parameters used for the calculation. Adapted in Figure 1 in Ref. [14]. 

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