Conducting polymers impedance model

A similar equation hut containing the function coth was used hy Inzelt and L ng to descrihe the diffusional impedance of conducting polymers under reflective conditions [see Section III.6(ii) and Eq. (99)]. An electrical model containing this element accounted well for the impedance spectra, with a minimum number of free parameters. 

Ever since Feldberg s original model separating faradaic and capacitance current associated with a conducting polymer that behaves like a porous metal, " there have been various attempts to rationalize experimentally the nature of the current at a conducting polymer. Apart from impedance models, there has not been so much effort placed on modeling the system. Experimental efforts to examine processes at conducting-polymer-modified electrodes consisted of voltam-metry, " impedance, " and quartz crystal microbalance. However the... 

The bulk of EAP-based supercapacitor work to date has focused on Type I devices. Polypyrrole (PPy, Figure 9.4C) has been studied [147,151-153] for this application, with specific capacitance values ranging from 40 to 200 F/g. Garcia-Belmonte and Bisquert [151] electrochemically deposited PPy devices that exhibit specific capacitances of 100-200 F/cm with no apparent dependence on film thickness or porosity extensive modeling of impedance characteristics was used. Hashmi et aL [153] prepared PPy-based devices using proton and lithium-ion conducting polymer electrolytes. As is often observed, electrochemical performance suffered somewhat in polymeric electrolytes single electrode specific capacitances of 40-84 F/g were observed with stability of 1000 cycles over a 1 V window. 

Fletcher proposes adopting a porous electrode model, considering the conductive polymer film in contact with an aqueous electrolyte solution as consisting of a large number of identical, noninterconnected pores. The electrolyte solution is contained within the pores. The analysis then considers a single pore of uniform cross section. Three general impedance elements are considered the solution impedance x within the pore the interfacial impedance y between the solution within the pore and the pore wall and z, the internal impedance of the polymer. The latter quantities are assumed not to vary with distance inside the pore. 

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. 

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). 

In a recent study (Nguyen et al. 2014), starting with the diffusive impedance of a conducting polymer actuator, electrical, mechanical, and viscoelastic properties of a tri-layer conjugated polymer actuator are combined into an advanced mafliematical model, which describes the relationship between the eurvature of the actuator and an applied voltage, expressed as... 

Table 20.10 provides a compilation of ac impedance studies on conducting polymer films. The aspects under investigation include modeling of the ac impedance response of these materials [348-350,354,368.372], the separation of ionic and electronic contributions to the total conductivity [290,368], overdoping [352], the relative contribution of Faradaic and capacitive components to the total measured charge [221,351], the computation of diffusion coefficients associated with the oxidation of these polymers and the transport of dopant ions... 

Chambers and coworkers [72-74] also explored the properties of semiconductive sheets of polypyrrole treated paper and cloth, which they characterize as a parallel RC circuit. They too report that the capacitive part of the complex impedance of the sheets depends on the morphology of the poly pyrrole coating. Measured reflectivity plots for Salisbury screen (narrowband) and Jaumann (broadband) absorbers fabricated from sheets of polypyrrole-treated material are also presented in their article. The measured results agree well with their model calculations, indicating the potential utility of conductive polymer-treated fabrics in radar-absorbing structures. 

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]. 

It must be expected that a polymer material having a much lower conductivity than polyaniline will give impedance responses revealing the effect of the three time constants obtained in the model. The system investigated was chosen for this reason since pECBZ conductivity and redox capacity [94] correspond to DE = 10 7cm2,s 1 and therefore, for the same layer thickness (500nm), the diffusion time constant would be 0.025 s. Electron diffusion should therefore be detectable in the a.c. and even in the EHD frequency domain. 

Based on this framework, a Binary Friction Membrane Model (BFM2) was developed to account for coupled transport of water and hydronium ions in polymer electrolyte membranes. The BFM2 was cast in a general form to allow for broad applicability to the PFSA family of membranes. As a tool to determine the model parameters, a simplified Binary Friction Conductivity Model (BFCM) was derived to represent conditions found in AC impedance conductivity measurements. 

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... 

Usually, the starting point of model derivation is either a physical description along the channel or across the membrane electrode assembly (MEA). For HT-PEFCs, the interaction of product water and electrolyte deserves special attention. Water is produced on the cathode side of the fuel cell and will either be released to the gas phase or become adsorbed in the electrolyte. As can be derived from electrochemical impedance spectroscopy (EIS) measurements [14], water production and removal are not equally fast Water uptake of the membrane is very fast because the water production takes place inside the electrolyte, whereas the transport of water vapor to the gas channels is difiusion limited. It takes several minutes before a stationary state is reached for a single cell. The electrolyte, which consists of phosphoric add, water, and the membrane polymer, changes composition as a function of temperature and water content [15-18]. As a consequence, the proton conductivity changes as a function of current density [14, 19, 20). 

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