Calculated from capacitance data

Hence, association constants of metal ions in such SAMs, determined from changes in the charge-transfer resistance of solution redox couples, are similar to those calculated from capacitance data. 

Figure 96 DC conductivity, calculated from capacitance data measurements, vs hydration level h of the lysozyme powder. Left panel dc conductivity a normalized by the dc conductivity co of the dry sample. Right panel dc conductivity vs hydration level in a double-logarithmic scale. Solid lines show the slopes, corresponding to the critical exponents 1.3 and 2.0 for 2D and 3D percolation, respectively. Reprinted, with permission, from [592].

Fig. 3 Compact-layer capacitance versus electrode charge curves, C -i(a), for mercury electrode in aqueous NaF solutions calculated from the data in Fig. 2 with the use of Eqs. (20) and (21a), for each electrolyte concentration, 0.916 M (V), 0.1 M (A), 0.01 M (solid line in Fig. 3a) and 0.001 M (solid line in Fig. 3b). Solid lines for lower concentrations were obtained with the use of the error bars in Fig. 2 for the corresponding curves. The error bars are small at the two higher concentrations and are not shown.

The parallel capacitance calculated from the data of Figure 7.16 is not a pure double-layer capacitance, it is too frequency-dependent. It must be due to redox or sorption processes at the platinum surface, or the fractal surface of black platinum. Under optimum conditions, it is possible to obtain capacitance values of the order of 50 pF/mm at 20 Hz (Schwan, 1963). 

The capacitance of the cluster was calculated from a fit of the experimental data at 90 K to be 3.9 x 10 F. This value, which is very sensitive toward residual charges and nearby background charges, is close to the value of the microscopic capacitance, which was determined earlier by temperature-dependent impedance measurements [21]. Furthermore these results are found to be in good agreement with the capacitance data obtained on the above-mentioned gold nanoclusters on a XYL-modified Au(l 1 1) surface [13,22]. 

A similar conclusion arises from the capacitance data for the mercury electrode at far negative potentials (q 0), where anions are desorbed. In this potential range, the double-layer capacitance in various electrolytes is generally equal to ca. 0.17 F Assuming that the molecular diameter of water is 0.31 nm, the electric permittivity can be calculated as j = Cd/e0 = 5.95. The data on thiourea adsorption on different metals and in different solvents have been used to find the apparent electric permittivity of the inner layer. According to the concept proposed by Parsons, thiourea can be treated as a probe dipole. It has been cdculated for the Hg electrode that at (7 / = O.fij is equal to 11.4, 5.8, 5.1, and 10.6 in water, methanol, ethanol, and acetone, respectively. 

The behavior of a resistor in parallel with an ideal capacitor (see above) is recovered when n is 1 (Q = C). When n is close to 1, the CPE resembles a capacitor, but the phase angle is not 90°. The real capacitance can be calculated from Q and n. When n is zero, only a resistive influence is found. For all impedance spectra shown in this work, fitting with a single RC circuit was found to be sufficient, i.e., n was in all cases larger than 0.9. Figure 11.10 shows that a good accordance of measuring data and fit function is evident. 

Sahai and Sverjensky [63] calculated TLM parameters for 26 sets of charging curves taken from literature. The following procedure was used. The for given material was calculated from selected tritium-exchange or infrared data or estimated from crystallographic data. The ApKa was calculated from Eq. (5.51). Inert electrolyte binding constants (asymmetrical binding allowed, cf. Section 2) and the inner capacitance (outer capacitance was assumed to be 0.2 C m" ) were fitted numerically. The same authors [64] claimed a correlation between the equilibrium constants of reactions (5.46) and (5.47) and the dielectric constant of the adsorbent, i.e. 

Figure 17. Surface state density as a function of bias potential calculated from the capacitance data.

This simulation reproduces the essential features of the experimental data. A calculated capacitance for the tightly packed part of the surface-bound membrane (Cbl) can be obtained by treating Calk and Clip in series. The resistance can be similarly calculated from Ralk and Ru. The calculated values of 0.52 fiF/cm2 and 1325 ft cm2 are in good agreement with literature values for natural membranes (47-48). The best curve fit for the coverage factor, 0, was 0.97, which indicates formation of a relatively complete membrane by the detergent dialysis approach. 

The capacitance of the cluster/substrate-junction was calculated to be 3.9 x 10 F. This value is in agreement with the value of the cluster capacitance previously determined by temperature-dependent impedance measurements. These results are, furthermore, in good agreement with capacitance data obtained from self-assembled gold nanoparticles on a dithiol-modified Au surface, reported by Andres and coworkers.Here tunneling spectroscopy has been performed on 1.8 nm Au particles which were grown in the gas phase and a cluster-substrate capacitance of 1.7 X 10 F was obtained. Thus, the small capacitance enables the observation of Coulomb blockade phenomena at room temperature. 

With other biological macromolecules (19, 20), the number of adsorbed molecules was usually calculated from the linear dependence of the capacitance on t / using Equation 1, over the whole range of adsorption. The surface concentration of hormones could also be inferred directly from the calculated number of charges transferred between the electrode and an electroactive group, like S-S, of the adsorbed molecules, each one containing only one S-S (21, 22). This method could not be used for proteins, where only part of the S-S are available for the electrode reaction,as seen for prothrombin but in this case of proteins, the method of exploitation of the data presented above is very useful and quite new. 

Fig. 48. DLTS measurement time constant t (inverse of rate window) versus the inverse temperature of the peak in the electron emission spectrum at that r for a typical sample. The activation energy of 0.94 eV is the slope of the raw data without the 2kT correction (see text). The circles are from DLTS spectra the triangles are calculated from directly recorded capacitance transients.

The aforementioned work from the laboratories of Scheller " and Halad-jian does indicate that the mercury-adsorbed cytochrome c molecules are denatured under neutral pH conditions. Details of the extent of this denaturation are, however, not clear. The effective electrode surface area occupied by a directly adsorbed cytochrome c molecule has been calculated from both differential capacitance and radiochemical data. The value of... 

Fig. 2 Capacitance versus electrode charge curves for the mercury electrode in aqueous NaF solutions recalculated from the data in Fig. 1. The error bars were calculated from those in the capacitance versus potential curves (Fig. 1) that were assumed to have the precision of 0.1 pF cm for the two highest concentrations,...

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