Films capacitance

P. G. Dargie, S. T. Hughes. A thick-film capacitive differential pressure transducer. Measurement Science and Technology, 5, 1994, pp. 1216-1220. 

The origin of the observed correlation was not established, and the relation was not interpreted as causal. It could be argued that a sustained elevated potential due to as-yet unknown microbial processes altered the passive film characteristics, as is known to occur for metals polarized at anodic potentials. If these conditions thickened the oxide film or decreased the dielectric constant to the point where passive film capacitance was on the order of double-layer capacitance (Cji), the series equivalent oxide would have begun to reflect the contribution from the oxide. In this scenario, decreased C would have appeared as a consequence of sustained elevated potential. 

Once the film capacitance is known, the dielectric constant of the layer can be determined by using Equation (4.10), provided that the thickness of the assembly is known. For self-assembled monolayers of long-chain alkane thiols, the experimentally determined dielectric constants fall in the range 23-2.6 and are consistent with a close-packed layer of alkane chains with essentially no penetration by electrolyte solvent or ions. 

The use of galvanostatic transients enabled the measurement of the poten-tiodynamic behavior of Li electrodes in a nearly steady state condition of the Li/film/solution system [21,81], It appeared that Li electrodes behave potentio-dynamically, as predicted by Eqs. (5)—(12), Section III.C a linear, Tafel-like, log i versus T dependence was observed [Eq. (8)], and the Tafel slope [Eq. (10)] could be correlated to the thickness of the surface films (calculated from the overall surface film capacitance [21,81]). From measurements at low overpotentials, /o, and thus the average surface film resistivity, could be measured according to Eq. (11), Section m.C [21,81], Another useful approach is the fast measurement of open circuit potentials of Li electrodes prepared fresh in solution versus a normal Li/Li+ reference electrode [90,91,235], While lithium reference electrodes are usually denoted as Li/Li+, the potential of these electrodes at steady state depends on the metal/film and film/solution interfaces, as well as on the Li+ concentration in both film and solution phases [236], However, since Li electrodes in many solutions reach a steady state stability, their potential may be regarded as quite stable within reasonable time tables (hours —> days, depending on the system s surface chemistry and related aging processes). 

The admittance in this region is modeled using either a film capacitance in series with the solution resistance or a parallel resistance and capacitance, which is in series with the solution resistance. This is treated as a parallel R-C combination whose magnitude, expressed as an impedance, is given by... 

The effective CPE coefficient representation in Figures 17.6 and 17.13 yields, for a = 1, information concerning the high-frequency capacitance of the system. In the case that a < 1, Figures 17.6 and 17.13 yield an effective CPE coefficient Qeg that can be related to the film capacitance through a model of the distributed time constants following Brug et al. ° ... 

Silicon piezoresistance Thin-film piezoresistance Ceramic capacitance Thin-film capacitance Ceramic piezoelectricity... 

Figure 183 (a) The admittance spectrum of a typical film in the low-frequency range the darkened squares are the measured data and the open squares are derived from (fc) the circuit model for low-frequency characteristics containing the interface admittance, Ri, Cj, and the film admittance, Rf, Cj. For the curve fit, the interface capacitance, C,, is 0.25 /xF and the interface resistance, R, is 1 kQ the film capacitance, C/, is 0.1 /xF and the film resistance, Rf, is 2.5 M 2. 

Jones, Jr., W. R. Johnson, R. L. Hyslop, I. Day, R., "Film Thickness Measurement of Five Fluid Formulations by the Mercury Squeeze Film Capacitance Technique," NASA Lewis Research Center, Cleveland, Ohio, 1976 February. 

The apparatus used in our study of thin liquid films is shown diagrammatically in Fig. 1 [16, 17, 85, 86]. There is a hole (0.5 mm in diameter) in the side of the Teflon chamber, which separates two aqueous solutions. The oil phase containing film-forming substances is introduced into the hole with the aid of a small syringe (ATP Inc., MI, USA). The film capacitance (Cm) and resistance were measured by a Multi-Function Analyzer (Sino-Jinke Electronics Co. Ltd, Tianjin, China). The thickness of thin liquid films, according to the parallel-plate formula, is given by... 

Figure 8 shows the formation of a thin liquid film in a crude oil/alkali system. When the crude oil is contacted with an alkaline solution, the film capacitance increases and reaches a stable value after several minutes. This implies that the film has another thinning mechanism after the gravity drainage. 

FIG. 8 Film capacitance of crude oil/alkali system as a function of time. Oil phase 30% Shengli crude oil/w-Cio aqueous phase 0.25 mol/L NaOH. 

We can see from Tables 1 and 2 that the alkali concentrations have no influence on the film capacitance of model oil systems. The sodium oleate formed by the reaction between the oleic acid and the alkali has a strong trend to partition into the aqueous solution, so it moves from the interface very quickly and has no effect on the interface. This may explain the results in Tables 1 and 2. The results in Table 3 show that the film capacitance of crude oil systems decreases with increasing alkali concentration below 0.06% NaOH. 

TABLE 1 Effect of Alkali Concentration on Film Capacitance in Modeling Oil (7.5 mmol/L Oleic Acid)/Alkali Systems... 

In Figure 10.11, represents the solution resistance, the paint film resistance, Cpf is the paint film capacitance, Q is the differential capacitance, Rp represents the polarization resistance, is the charge transfer resistance, and represents the diffusion layer resistance. The results indicated that the mass loss calculations agree with data obtained using the EIS [49]. 

Electrochemical impedance spectroscopy (EIS) provides indirect information about the surface phenomena of all kinds of electrodes [32]. The high-frequency part of impedance spectra of electrodes is usually attributed to surface phenomena such as Li-ion migration through surface films, surface film capacitance, and interfacial charge transfer [33]. However, it should be noted that EES provides very ambiguous information. A special skill, as well as experience, is needed for a reliable assignment of spectral features to the time constants of a complicated electrochentical system such as that of composite electrodes [34]. 

Itagaki et al. [120] used EIS to investigate the electrochemical properties of the rust film membrane formed on low alloy steels. The electrochemical impedance of the actual rust film membrane formed by wet-dry cycles showed the capacitive semicircle on Nyquist plot corresponding to a single time constant. The time constant of the capacitive semicircle was found composed of the rust film resistance and the film capacitance. The value of rust film resistance was shown to depend on the alloying elements in weathering steel and it was shown that the... 

In summary, two processes should be considered as indicated above when the polymer is reduced and can be represented by the equivalent circuit of Figure 3a. In this diagram, represents the solution resistance, Q refers to the double layer capacitance, Ri is the intrinsic resistance due to charge transfer of the redox process within the polymer film, W is the equivalent to the ionic diffiision at the film/electrolyte interphase, Q is the film capacitance, and Rf is the film resistance. In all cases, an electronic resistance component of the polymer film is considered to be connected in series with the solution resistance. Similar equivalent circuits were described in the literature for poly(2,5-di-(-2-thi yl)-thiophene) films earlier in the literature (25). The value of e electrical r istance of the polymer film varies considerably according to the applied potential to the polymer film, the film thickness and the electrol3rtic medium in which the measurement is taking place (26). Polymer film parameters are summarized in Table 1 for both oxidized and reduced states, respectively. 

The relaxation of the open circuit potential Fqc following an ILIT perturbation is a function of the thermal relaxation back to the initial isothermal condition and the kinetics of an electron-transfer relaxation that is characterized by the experimentally measured rate constant (see Sec. IV.D)—km is a function of the electron-transfer resistance (units ohm cm ), the film capacitance, C (units F/cm ), and the redox or pseudo- capacitance, (units F/cm ) (as before, the superscript i denotes the equilibrium value of the variable prior to the perturbation). The equivalent circuit for this relaxation, shown in Fig. 8, includes the area, a (units cm ), so that the circuit element Rf. /a has the units of ohms and a C and a have the units of farads. The electron-transfer resistance... 

In Figure 5.11, we described the interplay between electron transfer and mass transfer and how both are required to observe a current from a G. sulfurreducens biofilm. It is difficult to determine the role of mass transfer in biofilms simply from cyclic voltammograms usually, certain electrochemical setups are required to investigate mass transfer via electrochemical methods. In our case, we used a combination of EIS and RDEs to study electron transfer and diffusional processes in G. sulfurreducens biofilms respiring on electrodes [50]. We tested the hypothesis that the RDE can be used as an electrochemical tool that controls diffusional processes when EABs are studied. We determined the film resistance, film capacitance, interfacial resistance, interfacial capacitance, and pseudocapacitance of G. sulfurreducens biofilms as shown in Eigure 5.23. The details of the calculations and experimental procedures are given in the literature [50],... 

Figure 5.23 Equivalent circuit of G. sulfurreducens biofihn consisting of the film resistance, film capacitance, interfacial resistance, interfacial capacitance, and pseudocapacitance. Reproduced with permission from Ref. [50]. Copyright 2014 Wiley Periodicals, Inc. See insert for...

In the long-time period the potential should vary in a linear manner with time. The slope of the latter plot yields the film capacitance Cp directly. 

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