Integral capacitance

The temperature dependence of the inner-layer properties has been studied by Vaartnou etal.m m over a wide interval, -0.15°C < T< 50°C. The inner-layer integral capacitance Kh a curves have been simulated using the Parsons308 and Damaskin672,673 models. The experimental Kj, T dependence has a minimum at T = 20°C. The influence of the potential drop in the metal phase has been taken into account. 

This is the integral capacitance, and it is generally used for electrical capacitors where the capacity is constant and independent of the potential. This constancy of capacity may not be the case with electrified interfaces and in order to be prepared for this eventuality, it is best to define a differential capacity C thus... 

Define the following terms used in Section 6.5 (a) electrocapillary measurements, (b) ecm, (c) Lippmann equation, (d) integral capacitance, (e) differential capacitance, and (1) potential of zero charge. (Gamboa-Aldeco)... 

We are therefore in a position to compare Faradaic and non-Faradaic currents and at 10-5 M they are of comparable magnitude (using Cj 20/xFcm-2). However, ic decays with t1/3 whereas iF increases with t1/6. This is, of course, an important reason for the sampling of current towards the end of drop life, which is used, for example, in the pulse polarography techniques. Pulse techniques are also useful when the integral capacitance, Ci, varies with potential in these cases graphical elimination of ic can be difficult. 

To avoid confusion we should point out that CqC as defined above is the differential capacitance. The integral capacitance per unit area is differential capacitance is easier to measure. 

Except in special cases, the differential capacitance Cd is the most useful magnitude (see Fig. 1.9) since it is that measured with impedance techniques, although the integral capacitance is of interest as average data [13, 19]. 

Each of those potential drops can be written in terms of the corresponding integral capacitance C (see Eq. 1.78),... 

For the differential capacitance (which in the limit of low potential is equal to the Integral capacitance) we obtain... 

Note that in some equations this K, may occur together with K. the integral capacitance of the Stem layer. 

Figure 10.19 Schematic plot of surface species, charge (cr), and potential tfr) relationships versus distance from the surface, used in the triple-layer model. Integral capacitances C and C2 are assigned to regions between the 0 and /3 and the fi and d planes, respectively. Electrolyte ions are adsorbed at the plane. Reprinted from Adv. Colloid Interface ScL 12,...

The surface protonation equilibria are interpreted according to the constant-capacitance model of Schindler and Stumm (1987). The two model parameters, the intrinsic constant pK x (intr.) at zero surface charge and the integral capacitance of the flat electric double layer C( = 2 Fm"2) are determined from titration curves. The methods of the acidimetric titration of kaolinite suspensions are discribed by Wieland (1988). 

The output voltage of the circuit in Fig. 6.1.8b is independent of Cp. This result assumes infinite amplifier gain, a condition that is usually met with sufficient accuracy. Equation (10) suggests that arbitrarily high sensitivity can be achieved by simply lowering the integrating capacitance Cint. Since, however, the closed-loop... 

The variation in Q with E causes us to define an integral capacitance, Q (sometimes denoted K), which is the ratio of the total charge density, at potential E to the total potential difference placing it there. That is,... 

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