Equivalent circuit conducting polymers

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.

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.)...

When the polymer flhn is oxidized, its electronic conductivity can exceed the ionic conductivity due to mobile counterions. Then, the film behaves as a porous metal with pores of limited diameter and depth. This can be represented by an equivalent circuit via modified Randles circuits such as those shown in Figure 8.4. One Warburg element, representative of linear finite restricted diffusion of dopants across the film, is also included. The model circuit includes a charge transfer resistance, associated with the electrode/fllm interface, and a constant phase element representing the charge accumulation that forms the interfacial double... 

FIGURE 8.4 Equivalent circuit for describing EIS of conducting polymers. 

Greszczuk et al. [252] employed the a.c. impedance measurements to study the ionic transport during PAn oxidation. Equivalent circuits of the conducting polymer-electrolyte interfaces are made of resistance R, capacitance C, and various distributed circuit elements. The latter consist of a constant phase element Q, a finite transmission line T, and a Warburg element W. The general expression for the admittance response of the CPE, Tcpr, is [253]... 

The film grown on an electrode surface has a duplex structure with a thin, compact first layer that is directly on the electrode surface and a porous second layer contacting the electrolyte. An equivalent circuit can be used to represent the electrical properties of this film. The components of an equivalent circuit can be determined by impedance spectroscopy. Therefore, this method has become one of the key methods for the characterization of conducting polymers. 

Figure 11.17 Equivalent circuit of the conducting polymer fUm on an inert electrode surface. The model assumes a compact film on the metal surface with semiconducting properties in the neutral state (/ 5( and C q) and a porous film towards the electrolyte with electron resistance and ion resistance and a Faraday capacitance Cp. is the electrolyte resistance.

The final step required to demonstrate the validity of the polymer grid triode implementation of local contrast enhancement is to show that it computes the center-surround difference in Eq. 2. The equivalent circuit of the PGT demonstrated previously (3, 4) is that of two coupled diodes connected back-to-back, like that of a bipolar transistor (5). This is achieved by using semiconducting polymer in layers (2), (3 and (4). For the prototype array sketched in Figure 2c, layer (2) was fabricated with a material with sufficient conductivity to make an ohmic contact to the grid so that the equivalent circuit is simplified to a diode in series with a resistor. In the initial experiments, polyvinylcarbazole (PVK) was used for this resistor layer (2). In forward bias,... 

An overview on the topic of IS, with emphasis on its application for electrical evaluation of polymer electrolytes is presented. This chapter begins with the definition of impedance and followed by presenting the impedance data in the Bode and Nyquist plots. Impedance data is commonly analyzed by fitting it to an equivalent circuit model. An equivalent circuit model consists of elements such as resistors and capacitors. The circuit elements together with their corresponding Nyquist plots are discussed. The Nyquist plots of many real systems deviate from the ideal Debye response. The deviations are explained in terms of Warburg and CPEs. The ionic conductivity is a function of bulk resistance, sample... 

Fig. 3.12a-d Schematics of the structures of polymer films grown on smooth (a) and rough (b) surfaces, the proposed equivalent circuit (c), and a boundless section with miciopoies (d). is the uncompensated ohmic resistance, 2 is the impedance which is attributed to the conductivity path along the long chains and long micropores, 2 represents the impedance of the short chains with short micropores connected to the long pores. (From [66], reproduced with the permission of Elsevier Ltd.)... 

FIGURE A5 A typical complex plane impedance plot that would be obtained for a system such as a conducting polymer. Inset An equivalent circuit for the conducting polymer electrolyte system [89]. 

However, in order to fit the data accurately in the instances in which biofilms spanned the gap, it was necessary to add an extra resistor, representing an additional conductive pathway, in parallel to the RC model that described the controls without biofilms (Fig. 7.6b dotted line). This equivalent circuit method has been previously employed to measure conductivity of nanostructured films [51, 52] and conducting polymers [53] and serves to separate electronic and ionic conductivity in mixed conductors [49]. The need to include this extra conductance in the circuit model demonstrates that the biofilm is electronically conductive. Additional experiments in the absence of acetate further confirmed that the measured conductance is an intrinsic property of biofilm and does not arise from the charge transfer occurring at the biofilm/anode interface. 

This leads to describing the mixed conduction characteristics of an electroactive polymer in terms of a simple equivalent circuit. A particularly appealing representation uses the concept of a transmission line. This type of approach has been advocated by a number of researchers, such as Rubinstein,Buck, and Albery et and... 

FIGURE 1.72. (a) General equivalent circuit representing an electroactive polymer film exhibiting redox conduction. Each individual circuit element corresponds to a particular kinetic/transport/structural property of the polymer, (b) Approximate equivalent circuits and associated Nyquist plots for various simplified limiting situations encountered in practice. Approximation (i) is valid when / ct is very low, / ps = = 0, the redox site... 

FIGURE 1.82. Schematic representation of the equivalent circuit ladder network corresponding to Fletcher porous electrode model for electronically conducting polymers (see Refs. 68, 69). The specific equivalent circuit representation of the interfacial impedance element is also illustrated. 

We extend the analysis and consider the entire ladder network in terms of distinct R and C circuit elements. The impedance x can be represented by a resistance Ri, which defined the resistance of counterions in the pore electrolyte. Furthermore the impedance element z, which is that of the solid polymer, is replaced by a Randles equivalent circuit (see Fig. 1.84), where there is a parallel arrangement of a resistor Rj. and a capacitor Q in series with a resistor Ra- Hence we see that the pore solution is modeled in terms of a simple resistor, whereas the solid polymer is a binary composite medium. TTie latter assumption can be justified as follows. From a macroscopic viewpoint (and this has been demonstrated experimentally), the electronic resistance of the polymer is due to two contributions the first, Ra, from regions of high structural order the second, R, from regions of low structural order. Hence Ra is smaller than R. From a microscopic point of view, the polymer may exhibit two fundamentally different types of conduction. As noted in... 

Hence at low and very low frequencies, the impedance response of the ladder network is the same as that in Fig. 1.83 except that the impedance is divided by a factor N (related to the thickness of the film) and the locus of impedance points is shifted along the real axis in the first quadrant of the complex plane by a factor (iV/3)(f g + R + R ). A further point should be noted At high frequencies a second semicircle can also be observed, which is due to the intrinsic conduction properties of the solid polymer. At these frequencies interfacial behavior can be neglected. We can describe the network in terms of a randies equivalent circuit with parallel components C /N and NR and a series component NR. The latter quantities are defined as... 

Capacitive humidity sensors commonly contain layers of hydrophilic inorganic oxides which act as a dielectric. Absorption of polar water molecules has a strong effect on the dielectric constant of the material. The magnitude of this effect increases with a large inner surface which can accept large amounts of water. An example of this type of dielectric is porous j8-alumina. Colloidal ferric oxide, certain semiconductors, perowskites and certain polymers have also been used. /1-alumina is characterized by ionic conductance. Materials of this type can be characterized by a complex resistance composed of real (ohmic) as well as capacitive terms. The behaviour of such solids can be symbolized by a model and an associated equivalent circuit as given in Fig. 5.8. 

It is assumed that the IPMC is composed of an IP film sandwiched between two perfectly conductive metal electrodes. The linearized PNP model is used to describe the dynamics of the electric potential and the concentration of the mobile counterions within the polymer. In the case of the fiat electrodes, by solving the partial differential equation based on the PNP model, the equivalent circuit, which is composed of the following lumped capacitances - the double-layer capacitance, Cj, the bulk capacitance Q, and the bulk conductance, Si (see Fig. 6a) - can be obtained (Aureli and Porfiri 2012). 

The chemical (electroless) plating process for plating the metal electrodes, which has been described previously, is typically repeated several times, in order to increase the thickness and hence the electric conductivity of the electrode layers. The sequential plating steps result in a dendrite-like structure in the electrode layer this structure penetrates into the ionic polymer, as shown in Fig. 4. In such a case, the interface between the IP and the electrode is rough. Further, the equivalent circuit of the IPMC is a distributed circuit composed of a capacitance, C(r), and a conductance, S(r), as shown in Fig. 6b (Aureli and Porfiri 2012). 

Liu Y Zhao R, Ghafifari M et al (2012) Equivalent circuit modeling of ionomer and ionic polymer conductive network composite actuators containing ionic liquids. Sens Actuators A 181 70-76... 

Fig. 5 Simple electrical equivalent circuit diagrams, (a) Each capacitor represents one electrode -which could each, for example, be two sheets of conducting polymer. The contact resistance Rc represents the sum of electrical contact resistances at both electrodes. is the electrolyte or separator resistance. The other two resistors, shown in (b), represent loss of charge due to parasitic reactions. In the literature, typically the equivalent circuit either describes only one electrode or lumps both electrodes into one capacitance. Often, solution and contact resistances are also lumped together...

Physieal models and equivalent circuit representations for conducting polymer actuators and sensors are presented, including mechanical, electrical, and electromechanical descriptions. The underlying concept of most models is that strain is proportional to charge density, and sense voltage is proportional to stress. Dynamics are determined by the rate of charge transfer, as well as the mechanical properties of... 

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