Conducting polymers transmission line model

Figure 16. General transmission-line model for a conducting polymer-coated electrode. CF is the faradaic pseudo-capacitance of the polymer film, while Rt and Rt are its electronic and ionic resistance, respectively. R, is the uncompensated solution resistance.

M.R. Warren and J.D. Madden, Electrochemical switching of conducting polymers A variable resistance transmission line model, J. Electroanal. Chem., 590 (1), 76-81 (2006). 

Farajollahi M et al (2015) Non-hnear two-dimensional transmission line models for electrochemically driven conducting polymer actuators. lEEE/ASME Transactions on Mechatronics, Vol. 21, 2016... 

Warren MR, Madden JDW (2006a) A structural, electronic and electrochemical study of polypyrrole as a function of oxidation state. Synth Met 156(9-10) 724—730 Warren MR, Madden JDW (2006b) Electrochemical switching of conducting polymers a variable resistance transmission line model. J Electroanal Chem 590(1) 76-81 Wing Yu Lam J (2011) Influences of growth conditions and porosity on polypyrrole for supercapacitor electrode performance. UBC, Vancouver, BC, Canada Wu Y et al (2007) Soft mechanical sensors through reverse actuation in polypyrrole. Adv Funct Mater 17(16) 3216-3222... 

Dielectric materials such as silicon nitride, silicon dioxide, polymers and glass are normally used for the fabrication of solid-state nanopore devices [25]. The pore conductance may be expected to be frequency-dependent, perhaps similar to the transmission line model by de Levie (for closed pores) [40] [41]. For simplicity (and since the DC case is much more common), this aspect is typically ignored. In simple terms, a nanopore device as shown in Fig. 14 A can then be represented by a combination of solution (or access) resistance R the frequency-independent pore resistance Rp re and a device capacitance Cp (or alternatively a constant-phase element (CPE)), cf. the... 

W. J. Albery, A. R. Mount, 2nd transmission-line model for conducting polymers, J. Electro-anal. Chem., 1991, 305, pp. 3-18. 

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. 

The electrode layers formed using die physical loading method are usually relatively thicker (more than 10 pm in thickness), and the composite layers are composed of nanoparticles of the electrode material and the ionic polymer. These layers are both electronically and ionically conductive. The impedance for such electrodes is assumed to be similar to diat of porous electrodes. Levie (1963, 1964) was the first to develop a transmission line circuit (TLC) model of the porous electrode consisting of the electrolyte resistance and the double-layer capacitance. Subsequently, a number of authors proposed modified TLC models for the impedance of porous electrodes on the basis of Levie s model. Bisquert (2000) reviewed the various impedance models for porous electrodes. The composite electrode layers prepared by the physical loading method could be successfully represented by the impedance model for porous electrodes, as shown in Fig. 6d this model is composed of the double-layer capacitance, Cj, the Warburg diffusion capacitance, W and the electrolyte resistance, 7 (Liu et al. 2012 Cha and Porfiri 2013). 

A single homogeneous phase representation, where a combination of double-layer capacitance and diffusion-controlled Faradaic process is responsible for oxidation reduction of the polymer, resulting in appearance of "transmission line" in the equivalent circuit model. The large capacitances exhibited by conducting polymer electrodes are usually attributed to the double-layer capacitance and pseudocapacitance originating from the redox process of the polymer. 

For the same geometry, Paasch found for a transmission line like the one in Fig. 2 for the porous model of the conducting polymers " ... 

Then, the two models give equivalent results. This calculation was also given by Buck without the electroneutrality hypothesis (i.e. Cp 0). The transmission line approach is often called the porous model of a conducting polymer as electrons are supposed to cross the polymer (phase 1) and ions are supposed to move into pores, filled by electrolyte, represented by the second branch of the transmission line. It is noticeable that the transmission line approach allows more complicated kinetics to be tested for a two-species problem, e.g. charge transfer in parallel to the capacity Ce(x) and C,- (x), or diffusion of the ion in the ionic pores , i.e. to introduce complex impedances instead of the real resistance p and/or p2, of the pure capacitances Ci and/or C2. It also allows position-dependent parameters to be introduced to mimic concentration gradients in the polymer [Cj(x) constant]. 

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