Capacitance measurements, differential

The variation of the integral capacity with E is illustrated in Fig. V-12, as determined both by surface tension and by direct capacitance measurements the agreement confrrms the general correctness of the thermodynamic relationships. The differential capacity C shows a general decrease as E is made more negative but may include maxima and minima the case of nonelectrolytes is mentioned in the next subsection. 

It measures differential pressures. A thin diaphragm separates two chambers (see Fig. 1.28). One of the two chambers is kept at a constant pressure. A pressure difference causes the bending of the diaphragm which forms, together with a fixed electrode, a capacitor. The change in capacitance is measured by a very sensitive capacitance meter (measurement of AC 10 19 Farad are possible). 

Figure 3 also contains an example of an ISER-flrel plot for a simple specifically adsorbed species, bromide on silver (solid curve). This plot was extracted from bromide coverage-potential data, obtained from differential capacitance measurements, along with the corresponding potential-dependent intensity of the SERS bromide-surface stretching mode at ca. 160 cm"1 (19.). In this case, the maximum (i.e. unity) value of 0r>1 corresponds to a close-packed bromide monolayer, ca. 1.4 x 10"9 mol cm 2. Again, the ISER-0t 1... 

Adsorption of putidaredoxin on gold electrodes has been studied using dynamic spectroscopic ellipsometry and differential capacitance measurements [307]. In Ref. 307, a method for the measurement of metal surface optical perturbation during protein adsorption at a constant potential has been described. The method is based on the concept that the charged transition layer develops between the electrode substrate and the adsorbate. 

Adsorption of glycosidic surfactants at Hg electrode was studied by means of differential capacitance measurements... 

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)... 

Actually, the electrochemistry of diamond dates back to the paper [11], A current-voltage curve of crystalline diamond electrode was first taken there, as well as the differential capacitance measured at the diamond/electrolyte solution interface. The diamond electrodes turned out to be photosensitive, and their photo-electrochemical behavior was compared with their semiconductor nature. 

Relaxed interfaces cannot be polarized unless special precautions are taken. Capacitances can of course be obtained as derived quantities by differentiating the surface charge with respect to the surface potentieil if changes In the latter are known, which is possible if the Nemst equation applies. We now discuss direct capacitance measurements on reversible interfaces. To start with, the response of such an interface to an applied field has to be considered. The basic problem is that not only are double layers built up, but also charge transfer across the interfaces takes place and diffusion of charge-determining ions to or from the surface starts to play a role. With regard to these physical processes only the sum-effect is measured, and this sum has to be divided into its parts to obtain the capacitance. Distinctions can be made because the three constituents mentioned react in a different way to the frequency of the external field. 

The Integration should start at a reference potential E (p.z.c.) where a° = 0, which coincides with the electrocapillary maximum, e.c.m. Small errors In the establishment of this value lead to an Integration constant In [3.10.61. Generally, the results of the two ways of obtaining a° agree with an accuracy that Is enviable for those working with disperse systems. Double differentiation of electrocapillary curves and comparison with directly measured differential capacitances is more critical but can be achieved within less than 0.2 pF cm", seel). 

As with metals, the Helmholtz layer is developed by adsorption of ions or molecules on the semiconductor surface, by oriented dipoles or, especially in the case of oxides, by the formation of surface bonds between the solid surface and species in solution. Recourse to band-edge placement can be sought through differential capacitance measurements on the semiconductor-redox electrolyte interface [29j. 

Nanjundiah C, McDevitt S F, Koch V R. Differential capacitance measurements in solvent-free ionic liquids at Hg and C interfaces. J. Electrochem. Soc. 1997. 144, 3392-3397. 

Differential capacitance measurements were used to determine the extent that DMSA adsorbsonto the metal surface as a function of its concentration in solution. In this approach the metal-solution interface is modelled as a resistor and capacitor in series and if the diffuse part of the double layer is neglected, the measured capacitance can be expressed as ... 

Table 3 lists some ionization properties of functionalized gold-thiol monolayers and relevant alkylsiloxane monolayers together with the appropriate bulk values. Monolayers with carboxylate terminal groups show abnormal wetting behaviour, which makes it difficult to determine accurately their surface pKa values308. Apart from contact angle titration, other methods were also used to study proton transfer equilibria at the mono-layer surfaces, such as quartz crystal microbalance (Table 3, line 1), measurements of the adhesion force between the monolayer deposited at the surface of an AFM tip and the same monolayer deposited on the substrate (chemical force microscopy, Table 3, lines 3, 4, 15), FT-IR spectroscopy (Table 3, line 7), adsorption of polyelectrolytes (Table 3, line 5) and differential capacitance measurements (Table 3, lines 12, 13). 

The differential capacitance is the more useful quantity, in part because it is precisely measurable by impedance techniques (see Chapter 10). As we will see in Section 13.3, capacitance measurements have played crucial roles in the formulation of structural models for the double layer. 

There is a variation on the "Zerbst technique in which the current and capacitance are measured direedy and plotted against one another. [91] No differentiation of the experimental data is required, but one must measure both current and capacitance. It is one of many pulsed MOS capacitance measurement variations that have been developed over the years. For a detailed review of the... 

Figure 14. Relative decrease in differential capacit ance of cytochrome c solutions at the dropping mercury electrode as a function of time. Differential capacitance measurements obtained near the point of zero charge, -700 mV vs. SCE. Solutions contained 0.1 Af KCl. Cytochrome c concentrations are (1) 0.38/LtM, (2) 0.76/xM, (3) 1.54/xM, and (4) 3.10 fiM. Adapted from reference (93) with permission.

Differential capacitance measurements by Niki et for cytochrome C3 from D. vulgaris, strain Miyazaki, were consistent with irreversible, diffusion-limited adsorption for 4-s drop times above a concentration of 10 fiM. The surface excess of cytochrome C3 was calculated to be 0.92 x 10 " mole/cm. Niki etal also investigated the a.c. polarographic behavior of cytochrome C3 at the reversible half-wave potential. The capacitive peak height was frequency independent while the resistive peak height decreased with increasing frequency to a value of zero above 2000 Hz. These results were fit to a Laitinen-Randles equivalent circuit yielding an n value of... 

---