Electrochemical analog circuits

R2 with a large capacitor. This will in effect lower the impedance of the source load, giving rise to a corresponding increase in amplification. The capacitor can favorably be implemented as a symmetric 2-electrode PEDOT PSS electrochemical capacitor. 

An interesting variation of this circuit is the cascode amplifier shown in Fig. 9.13. Here, the drain load is exchanged for a constant-current generator. Theoretically this gives infinitely high impedance thus yielding a very high level of amplification. 

---

An electrochemical cell is a type of electrical circuit. As such, it may be modeled with an electrical analog circuit. The potentiometric cell can be considered to be an electrical potential applied to a capacitor and a resistor in series. The capacitor represents the interface between the electrode and the solution, the applied potential is the solution Eh, and the resistor represents the heterogeneous kinetics of the aqueous redox species. The term "heterogeneous kinetics" denotes electron transfer between different phases, in this case aqueous species and the noble-metal electrode. The time required for the capacitor to equilibrate with the applied potential depends on the size of the capacitor and the electrical current. 

Still in Hsu et al. work, electrochemical impedance was used to analyze the reaction kinetics and interfacial characteristics of an anode in DMFC [142]. Several analogy-circuit models are proposed (Fig. 8.11). The new model incorporates CPEs rather than conventional capacitors in the equivalent-circuits taking into account the porous structure of the anode, particularly that in the CL and at the anode/... 

While introducing this new way of obtaining electroanalytical data, we will need to rely on the analogies between an electrochemical cell (or sample) and an electrical circuit made up of resistors and capacitors assembled in order to mimic the current-voltage behaviour of the cell. All the time, though, we need to bear in mind that the ideas and attendant mathematics are for interpretation only, although they are fundamentally very simple. 

For dissociative electron transfer, an analogous thermochemical cycle can be derived (Scheme 2). In this case the standard potential includes a contribution from the bond fragmentation. Using equations (40) and (41) one can derive another useful expression for BDFEab-, equation (42). While direct electrochemical measurements on solutions may provide b. b, for example, of phenoxides and thiophenoxides (Section 4), the corresponding values for alkoxyl radicals are not as easily determined. Consequently, these values must be determined from a more circuitous thermochemical cycle (Scheme 3), using equation (43). The values of E°h+/h io a number of common solvents are tabulated elsewhere. Values of pKa in organic solvents are available from different sources. " A comparison of some estimated E° values with those determined by convolution voltammetry can be found in Section 3. 

Virtually all energy transductions in cells can be traced to this flow of electrons from one molecule to another, in a downhill flow from higher to lower electrochemical potential as such, this is formally analogous to the flow of electrons in a battery-driven electric circuit. All these reactions involving electron flow are oxidation-reduction reactions one reactant is oxidized (loses electrons) as another is reduced (gains electrons). 

Figure 28 A typical Nyquist plot obtained from a nickel electrode polarized to low potentials (0.2 V versus Li/Li+) in PC solutions (1 M LiBF4 in this case). The equivalent circuit analog of 4 R C circuits in series and their separate Nyquist plots (four semicircles) are also shown. The frame in the lower right represents a typical fitting between the experimental data and this equivalent circuit analog [34]. (With copyright from The Electrochemical Society Inc.)...

Figure 18 Various models proposed for the surface films that cover Li electrodes in nonaqueous solutions. The relevant equivalent circuit analog and the expected (theoretical) impedance spectrum (presented as a Nyquist plot) are also shown [77]. (a) A simple, single layer, solid electrolyte interphase (SEI) (b) solid polymer interphase (SPI). Different types of insoluble Li salt products of solution reduction processes are embedded in a polymeric matrix (c) polymeric electrolyte interphase (PEI). The polymer matrix is porous and also contains solution. Note that the PEI and the SPI may be described by a similar equivalent analog. However, the time constants related to SPI film are expected to be poorly separated (compared with a film that behaves like a PEI) [77]. (With copyrights from The Electrochemical Society Inc., 1998.)...

Figure 4. Charge trapping on a metalized semiconductor powder, as an analog to a short-circuited electrochemical cell.

Because the chief electrochemical variables are all analog quantities (at least in the ranges of normal interest), our first concerns are with circuitry for controlling and measuring voltages, currents, and charges in the analog domain. The circuit elements best suited to these jobs are operational amplifiers. We must explore their properties before we can understand the way in which the amplifiers are assembled into instruments. 

Figure 3. DC circuit analog to simulate scaling according to electrochemical...

Historically, the Warburg impedance, which models semi-infinite diffusion of electroactive species, was the first distributed circuit element introduced to describe the behavior of an electrochemical cell. As described above (see Sect. 2.6.3.1), the Warburg impedance (Eq. 38) is also analogous to a uniform, semi-infinite transmission line. In order to take account of the finite character of a real electrochemical cell, which causes deviations from the Warburg impedance at low frequencies. 

---