Dual rail transmission line

FIGURE 1.13. (a) Classical single-rail transmission line, one rail assumed to exhibit zero resistance. Resistive line can correspond to either electron hopping or counterion transport, (b) Dual-rail transmission line both electronic and ionic resistance are finite. 

FIGURE 1.14. A more sophisticated dual-rail transmission line representing charge percolation in an electroactive polymer film. 

FIGURE 1.54. Schematic representation of dual-rail transmission line for electroactive polymer films. The / is resistance for electron hopping, Rj is resistance for counterion transport Cp is the distributed Faradaic capacitance, and denotes the uncompensated solution resistance. 

Figure 1.82 shows the model circuit which takes the form of a diagonally connected discrete ladder network or in simple terms, a dual-rail transmission line of finite dimension. The essential problem is to replace the general impedance elements x, y, and z by suitably arranging such passive circuit elements as resistors and capacitors that adequately represent the microscopic physics occurring within an electronically conducting polymer. 

Randles model are used to describe the frequency dependence of diffusion and the capacitive impedance observed in the intermediate and low frequency ranges. A dual transmission line model has been proposed by including ionic and electronic resistance rails connected in parallel with a capacitance Cp (Fig. 6.5). The model has been used to define the electrochemical behavior of polyaniline, and the capacitance was explained as a result of oxidation and reduction of the pol5mier. Ionic (i i) and electronic (Rg) resistances are used to describe hindered motion of ions and electrons in the system, respectively. The impedance behavior has been found to be dependent on the ratio of the two resistances. 

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