Conductance equivalent circuit

According to this model, the SEI is made of ordered or disordered crystals that are thermodynamically stable with respect to lithium. The grain boundaries (parallel to the current lines) of these crystals make a significant contribution to the conduction of ions in the SEI [1, 2], It was suggested that the equivalent circuit for the SEI consists of three parallel RC circuits in series combination (Fig. 12). Later, Thevenin and Muller [29] suggested several modifications to the SEI model ... 

Figure 13. Schematic presentation of a small segment of polyheteromicrophase SEI (a) and its equivalent circuit (b) A, native oxide film B, LiF or LiCl C, non conducting polymer D, Li2CO, or LiCO, R GB, grain boundary. RA,/ B,RD, ionic resistance of microphase A, B, D. Rc >Rqb charge-transfer resistances at the grain boundary of A to B or A to D, respectively. CA, CB, CD SEI capacitance for each of the particles A to D.

Variations of resistance with frequency can also be caused by electrode polarization. A conductance cell can be represented in a simplified way as resistance and capacitance in series, the latter being the double layer capacitance at the electrodes. Only if this capacitance is sufficiently large will the measured resistance be independent of frequency. To accomplish this, electrodes are often covered with platinum black 2>. This is generally unsuitable in nonaqueous solvent studies because of possible catalysis of chemical reactions and because of adsorption problems encountered with dilute solutions required for useful data. The equivalent circuit for a conductance cell is also complicated by impedances due to faradaic processes and the geometric capacity of the cell 2>3( . 

A simple equivalent circuit diagram for a two-electrode contactless conductivity measurement is shown in Figure 7.8. The impedance is given by... 

To a first approximation, the BLM can be considered to behave like a parallel plate capacitor immersed in a conducting electrolyte solution. In reality, even such a thin insulator as the modified BLM (designated by and R, in Fig. 108) could block the specific adsorption of some species from solution and/or modify the electrochemical behavior of the system. Similarly, System C may turn out to be a semiconductor(l)-insulator-semiconductor(2) (SIS ) rather than a semiconductor(l)-semiconductor(2) (SS ) junction. The obtained data, however, did not allow for an unambiguous distinction between these two alternative junctions we have chosen the simpler of the two [652], The equivalent circuit describing the working (Ew), the reference (Eg), and the counter (Ec) electrodes the resistance (Rm) and the capacitance (C of the BLM the resistance (R ) and capacitance (Ch) of the Helmholtz electrical double layer surrounding the BLM as well as the resistance of the electrolyte solution (RSO ) is shown in Fig. 108a [652],... 

Here, we concentrate on cell 1 and assume negligible electrode effects. If a constant current is switched on, both a faradaic as well as a displacement current flows (cf. Section I). Hence the actual current can be ionic/electronic or capacitive, the relative proportions depending on the electronic (creon) and ionic (crion) conductivities and the dielectric constant. Correspondingly, the elements are, as long as creon and crion are summed locally, in parallel (oo denotes the bulk and / , = ReonRtJ Re(m + 70) and the equivalent circuit is given by (cf. also Eq. (5))... 

The phenomena important in electrolytic conductance have been discussed96 and are represented by the electrical equivalent circuit of a conductance cell shown in Figure 6.24a. 

Figure 6.24 (a) Electrical equivalent circuit for a conductance cell (b) AC bridge with the cell impedance balanced by a series R-C combination (c) AC bridge with the cell impedance balanced by a parallel R-C combination (see Table 6.7). 

A physical insight into eqs. (2)-(5) is gained by considering the equivalent circuit shown in Figure 4, which displays the same frequency response defined in eqs. (2)-(5). The membrane capacitance per unit area Cjj, appears in series with the access impedances p and Pa/2, while the term CTfl (1-1.5p) provides for the conductance of the shunting extracellular fluid. Hence the time constant T which determines the frequency where the impedances l/(jjCmR and (p + Pa/2) are equal is given by eq. (5). 

There are several models for the equivalent circuit of the electrolyte under an applied voltage, the simplest one is a resistor and a capacitor in parallel (see Figure 4.48). Applying this circuit, the real and imaginary parts of the complex impedance are obtained from the measured conductance and the capacitance using the relations [30,75] ... 

The complications and sources of error associated with the polarization resistance method are more readily explained and understood after introducing electrical equivalent circuit parameters to represent and simulate the corroding electrochemical interface (1,16-20). The impedance method is a straightforward approach for analyzing such a circuit. The electrochemical impedance method is conducted in the frequency domain. However, insight is provided into complications with time domain methods given the duality of frequency and time domain phenomena. The simplest form of such a model is shown in Fig. 3a. The three parameters (Rp, Rs, and C d,) that approximate a corroding electrochemical inter-... 

Figure 4.33. Equivalent circuit of a catalyst layer [8]. (Reproduced by permission of the authors and of ECS—The Electrochemical Society, from Lefebvre MC, Martin RB, Pickup PG. Characterization of ionic conductivity within proton exchange membrane fuel cell gas diffusion electrodes by impedance spectroscopy.)...

Conductive polymers are not used in fuel cells. However, the equivalent circuit of conductive polymers is similar to that of catalyst layers, which may help to understand impedance spectra in fuel cells. In general, the electric circuits of... 

Figure 4.37. Equivalent circuit of conducting polymers [10]. (Albery WJ, Mount AR. Dual transmission line with charge-transfer resistance for conducting polymers. J Chem Soc Faraday Trans 1994 90 1115-9. Reproduced by permission of The Royal Society of...

Figure 4.38. Equivalent circuits of conducting polymers with a Randles circuit [12]. (Reprinted from Journal of Electroanalytical Chemistry, 420, Ren X, Pickup PG. An impedance study of electron transport and electron transfer in composite polypyrrole plus polystyrenesulphonate films, 251-7, 1997 with permission from Elsevier and from the authors.)...

---