Double admittance

Horton and Price (H11) have obtained acoustic-admittance data for a series of double-base and composite propellants with different burning-rate characteristics. They examined the effects of pressure at various frequencies... 

When transient techniques are employed for fundamental research on these and other subjects, the effect of double-layer charging has to be accounted for in the analysis procedures. It has been observed frequently that at solid—solution interfaces, this process does not obey the capacitive behaviour predicted by double-layer theories. For example, the doublelayer admittance, Fc, cannot be represented by Yc = jciCd, but rather follows the relation [118]... 

Formulations of the general expressions for YF (s) and of some limiting cases can be found in ref. 53. It is to be noted that this faradaic admittance is connected in parallel to the double-layer admittance Yc (s). The latter may well be influenced by the presence of the adsorbed intermediate. Nevertheless, the quite specific frequency dependence of Yf can be applied to detect the presence of a mechanism of the type discussed here [53, 132]. 

One assumes that the double layer admittance is that of a pure capacitor. Thus its value should be independent of frequency. The graphical variation of Y with Y" is shown schematically in Fig. 11.9. More details may be found in Ref. 9. 

The admittance response at 1 kHz has also been interpreted in terms of the behavior at residual defects in anodic films. This interpretation is based on electron optical characterization, which shows that anodic films contain a distribution of preexisting defects associated with substrate inclusions and mechanical flaws (96,102). In aggressive environments, pits nucleate from these defects and propagate into the metal substrate. In this model, pits are distinct from anodic film flaws, and both can contribute to the measured admittance. Measurements of anodic films exposed to chloride solutions showed that the dissipation factor increased with time, but the capacitance remained nearly constant. Under these conditions, pit propagation at a flaw led to a pit area increase, which increased the resistive component of the admittance, resulting in an increased dissipation factor, but no increase in the capacitance. Measurements at 100 kHz were reflective of the electric double layer and not the components of the oxide film. 

Immittance — In alternating current (AC) measurements, the term immittance denotes the electric -> impedance and/or the electric admittance of any network of passive and active elements such as the resistors, capacitors, inductors, constant phase elements, transistors, etc. In electrochemical impedance spectroscopy, which utilizes equivalent electrical circuits to simulate the frequency dependence of a given elec-trodic process or electrical double-layer charging, the immittance analysis is applied. 

The selection of impedance or admittance for presentation of experimental results and data analysis is dependent on the type of equivalent electric circuit. For instance, for the analysis of -> charge-transfer processes and -> double-layer charging, the impedance may be preferred, while for the resonance circuits (e.g., in piezometric systems) the admittance may offer advantages. 

In ac impedance measurement at ITIES, admittance due to the transfer of supporting electrolyte ions is significant even in the middle of the potential window, as was first suggested and treated quantitatively by Samec et al. [35]. This imposes a difficulty in accessing double layer capacitance from the admittance, particularly when the transfer of supporting electrolyte ions is not reversible. There is no straightforward way to deconvolute the admittance ascribable to double layer capacitance and that ascribable to ion transfer admittance [30]. A nonlinear least-squares... 

Because of the relaxation of double layers, the resistive and capacitive components of the impedance Z(co) vary with frequency the former leads to K( o), the latter yields elw). The quantity Z(cu) or, for that matter, the admittance Y a) is usually measured in an impedance spectrometer. Quite generally, the Impedance may be written as... 

The characteristic angular frequency for the blocking circuit is o c = 1/ReC, the same as is found for the admittance of the blocking circuit. At the characteristic angular frequency, the real part of the capacitance is equal to half the double-layer capacitance, and the imaginary part is equal to minus one-half of the double-layer capacitance. The complex-capacitance plot for tire blocking circuit traces a semicircle. 

Example 16.1 Admittance of Dielectrics Example 16.2 Complex Capacitance of Dielectrics Example 16.3 Evaluation of Double-Layer Capacitance... 

The next step, after all experimental parameters have been given their correct values, is usually a calibration. A dummy cell is used, consisting of electronic components that imitate the behaviour of the real cell as closely as possible. The simplest one, which also is in many cases a completely adequate one, is shown in Fig.5. It consists of a capacitance (double layer capacitance) in parallel with a resistance (charge transfer resistance), and then, in series with this circuit, another resistance (solution resistance). The admittance of the dummy cell is recorded in an ordinary experiment and the transfer function, T(u), of the instrument is set equal to the ratio of the calculated, 0( )5 to the measured, ym( )) admittance of the dummy cell i.e. 

RCSUB Corrects cell admittance arrays for the non-faradaic effects ohmic resistance and double-layer capacitance. Uses data provided by the FITl-FITALL sequence and the formula... 

Measured (A) In-phase ( ) and quadrature (0) faradaic admittance polarograms at 1367 Hz. (B) Cot polarogram at 1367 Hz. (C) Faradaic admittance magnitude spec-trim near low frequency peak potential [at -1.605 V vs. Ag/Agl/(1.0 M TBAI, CH3CN)]. (D) Cot spectrum at -1.605 V vs. reference electrode. (ET Same as (B), except after interactive refinement of double-layer admittance subtraction. (F) Same as (A) after refinement of double-layer admittance subtraction. 

In Section 7.5, we analyze the double layer charge in a solution as a function of the perpendicular distance from the solid surface. No double layer formations are considered in the Maxwell—Wagner theory (Section 3.5.1). However, in wet systems and in particular with a high volume fraction of very small particles, the surface effects from counter-ions and double layers usually dominate. This was shown by Schwan et al. (1962). By dielectric spectroscopy, they determined the dispersion for a suspension of polystyrene particles (Figure 3.10). Classical theories based on polar media and interfacial Maxwell—Wagner theory could not explain such results the measured permittivity decrement was too large. The authors proposed that the results could be explained in terms of surface lateral) admittance. 

The metal and the electroljrte also determine the DC half-cell potential, modeled by the battery B. If there is no electron transfer. Ret is very large and the battery B is decoupled, the electrode is then polarizable with a poorly defined DC potential. But if there is an electrode reaction. Ret has a lower value and connects an additional admittance in parallel with the double layer admittance. This current path is through the faradaic impedance Zf, and the current is the faradaic current if. Faradaic current is related to electrode reactions according to Faraday s law (Section 7.8). The faradaic impedance may dominate the equivalent circuit in the lower Hz and sub-Hz frequency range and at DC. The faradaic impedance is modeled by a complete Cole-like series system. It consists of the resistor Ret... 

EIS data are analysed by fitting them to an equivalent electrical circuit model consisting of resistors, capacitors, and inductors. The working electrode interface undergoing an electrochemical reaction is analogous to an electronic circuit and can be characterised as an electrochemical system in terms of equivalent circuit. Typical circuits are shown in Figs. 1.10, 1.11, 1.12 and 1.13 where is admittance (ohm-cm ),Cf is double-layer capacitance and a is the exponents [114]. (/ .E Reference Electrode and W Working Electrode)... 

Figure 2. Frequency(F) and admittance (Y) changes observed under double potential steps (+0.98 Vand 4), 3 V). a) no insertion in thin polymer layer, b) large insertion in moderately thick polymer, c) no insertion measured. (Reprintedfrom J. Electroanal Chem., 476, Lagjrost, Tanguy, Aeiyach, Lacroix, Jouini, Chane-Ching, and Lacaze, Polymer chain encapsulation followed by a quartz crystal microbalance during electropolymerization of bithiqphene-J3-cyclodextrin hot-guest compounds in aqueous solution, pp. 1-14, Copyright 1999 with permission from Elsevier Science).

Fig. 5 Adsorption/desorption behavior of double- or single-stranded DNA at mercury electrodes (at weakly alkaline pH s), (a) scheme of AC polarographic curves of DNA obtained with DME. (a) dsDNA, low ionic strength (b) dsDNA, moderate ionic strength (c) ssDNA (el) bacl round electrolyte p.z.c. See text for more details, (b) AC admittance curves measured at HMDE. (a, b) ssDNA (c, d) dsDNA (a, c) initial potential —0.5 V, potential scanned from positive to negative values (b, d) initial potential —1.7 V, potential scanned from negative to positive values [E. Jelen and P. Belusa, unpublished] see text for more details.

Rs and Cm can be obtained from the measurement in the presence of the supporting electrolyte only if the distance between the Luggin capDlaiy and the working electrode is the same. One can also determine these parameters in the presence of the electroactive species R at high frequencies and Cm by interpolation of the Fj plot versus the potential before and after the faradaic peak. An example of such an interpolation is shown in Fig. 4.6, where the in-phase (real part) ac current propor-tirnial to the real part of the total admittance is displayed for Cd " reduction in dimethylsulfoxide (DMSO) [150]. Similar measurements of the out-of-phase (imaginary) part make it possible to determine the double layer capacitance in the presence of the redox reaction. 

As can be seen from Eig. 5.3 and the preceding discussion, one simple Eq. (5.51) describing the faradaic admittance in the presence of one adsorbed species, in combination with the double-layer capacitance, can produce many different complex plane plots and electrical equivalent circuits. It should be stressed that the kinetic equations with physically possible rate parameters in Eqs. (5.25) and (5.26) may not give all the behaviors, i.e. impedance plots, found by arbitrarily allocating values to the circuit elements. 

The total impedance of the pore walls consists of the faradaic and the doublelayer impedances. They are connected in parallel, Eq. (9.22) therefore, the faradaic admittance, Tf,toi> and double-layer admittance, fan niust be added in series ... 

As pointed out by de Levie, however, the most important weakness in the model is the assumption that the current distribution is normal to the macroscopic surface, that is a neglect of the true current distribution. For a rough surface, the lines of electric force do not converge evenly on the surface. The double layer will therefore be charged unevenly, and the admittance will be time and frequency dependence. 

---