Capacitance spectrum

Figure 6.3. Capacitance spectrum Ci(v) of the empty capacitor (lower curve) and ofnon-polar (N2) and polar (CO) sorptive gases at elevated pressures and T = 298 K, [6.8,6.13],...

In Fig. 6.22 the spectrum of the initial state is indicated by Vac. . It can be seen that within the first hour of the adsorption process the capacitance of the system increases with a shift of its maximum value to somewhat higher frequencies. This effect is possibly due to a primary adsorption process of the CO-molecules at locations in macro- and mesopores of the AC where, due to their permanent dipole moment (pco = 0.1 D), they add to both the capacitance and the resonance frequency of the loaded AC. Now microbalance measurements have shown that approximately 80 % of the total mass adsorbed during the whole process is adsorbed within the first hour. In view of this, the changes of the capacitance spectrum which were observed afterwards for nearly 40 h are doubtless due to an internal diffusion or dissoziation process of the CO molecules taking place without uptake of more molecules from the gas phase. 

Evacuation of He-gas (p < I Pa) and cooling down to ambient temperature (298 K). During the activation process polar molecules (H2O, CO, H2S, NOx etc.) are desorbed from the AC leaving unsaturated polar groups in the AC which form the capacitance spectrum with a maximum at ca 240 kHz, [6.3, 6.13]. 

Also for reproducible measurements normally several grams of a sorbent material are needed. That is, it is not easy to build capacitors which can handle sorbent probes in the mg range. Glues used often in designs of this kind normally penetrate some pores and change the capacitance spectrum of the sorbent. Hence these devices cannot be recommended. 

The capacitance spectrum (see Figure 4.6) depends mainly on the properties of the activated carbon. The equivalent capacitance reaches its maximum value at very low frequency when there is time for the ions to reach the entire available surface on the carbon. If a large surface area is at the bottom of deep, narrow pores (micropores), the equivalent capacitance drops rapidly as the frequency increases. 

Membrane thickness fluctuations were initially discussed in the local approach by Hladky and Gruen (HG) [102] in conjunction with their possible effect on membrane capacitance. They are directly related to the spectrum of 5-modes ... 

Curiously, fluorine incorporation can result in property shifts to opposite ends of a performance spectrum. Certainly with reactivity, fluorine compounds occupy two extreme positions, and this is true of some physical properties of fluoropolymers as well. One example depends on the combination of the low electronic polarizability and high dipole moment of the carbon-fluorine bond. At one extreme, some fluoropolymers have the lowest dielectric constants known. At the other, closely related materials are highly capacitive and even piezoelectric. 

A constant phase element (CPE) rather than the ideal capacitance is normally observed in the impedance of electrodes. In the absence of Faradaic reactions, the impedance spectrum deviates from the purely capacitive behavior of the blocking electrode, whereas in the presence of Faradaic reactions, the shape of the impedance spectrum is a depressed arc. The CPE shows... 

The crystal impedance is capacitive at frequencies below the fundamental wave and inductive at frequencies above the resonance. This information is useful if the resonance frequency of a crystal is unknown. A brief frequency sweep is carried out until the phase comparator changes over and thus marks the resonance. For AT quartzes we know that the lowest usable frequency is the fundamental wave. The anharmonics are slightly above that. This information is not only important for the beginning, but also in the rare case that the instrument loses track of the fundamental wave. Once the frequency spectrum of the crystal is determined, the instrument must track the shift in resonance frequency, constantly carry out frequency measurements and then convert them into thickness. 

The sample, a reverse-biased p-n or metal-semiconductor junction, is placed in a capacitance bridge and the quiescent capacitance signal nulled out. The diode is then repetitively pulsed, either to lower reverse bias or into forward bias, and the transient due to the emission of trapped carriers is analyzed. As discussed in the preceding section, for a single deep state with JVT Nd the transient is exponential with an initial amplitude that gives the trap concentration, and a time constant, its emission rate. The capacitance signal is processed by a rate window whose output peaks when the time constant of the input transient matches a preset value. The temperature of the sample is then scanned (usually from 77 to 450°K) and the output of the rate window plotted as a function of the temperature. This produces a trap spectrum that peaks when the emission rate of carriers equals the value determined by the window and is zero otherwise. If there are several traps present, the transient will be a sum of exponentials, each having a time... 

We have extended the technique of Relaxation Spectrum Analysis to cover the seven orders of magnitude of the experimentally available frequency range. This frequency range is required for a complete description of the equivalent circuit for our CdSe-polysulfide electrolyte cells. The fastest relaxing capacitive element is due to the fully ionized donor states. On the basis of their potential dependence exhibited in the cell data and their indicated absence in the preliminary measurements of the Au Schottky barriers on CdSe single crystals, the slower relaxing capacitive elements are tentatively associated with charge accumulation at the solid-liquid interface. 

The Relaxation Spectrum Analysis was carried out for a cell consisting of n-CdSe in a liquid junction configuration with NaOH/S=/S 1 1 1M as the electrolyte. Three parallel RC elements were identified for the equivalent circuit of this cell, and the fastest relaxing capacitive element obeys the Mott-Schottky relation. 

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