Electrode resistance contribution from diffusion

Because the Adler model is time dependent, it allows prediction of the impedance as well as the corresponding gaseous and solid-state concentration profiles within the electrode as a function of time. Under zero-bias conditions, the model predicts that the measured impedance can be expressed as a sum of electrolyte resistance (Aeiectroiyte), electrochemical kinetic impedances at the current collector and electrolyte interfaces (Zinterfaces), and a chemical impedance (Zchem) which is a convolution of contributions from chemical processes including oxygen absorption. solid-state diffusion, and gas-phase diffusion inside and outside the electrode. 

Impedance Spectroscopy. Impedance spectroscopy has been carried out on devices with WO3 as the cathodic electrochromic layer, counter electrodes of iridium oxide, polyaniline or Prussian blue, and polymers as electrolytes (Katsube et al [1986], Friestad et al [1997]). The equivalent circuit for a whole device becomes very complicated. In the works quoted above simplified, Randles-type circuits were used for the two electrochromic layers, while the ion conductor was modeled by a pure resistance, or neglected. Extraction of device parameters from the data fitting was reported. However, it is clear that in many cases it will be difficult to distinguish the contributions from the different layers in a device, in particular if the migration impedances, ion diffusion impedances, etc. are of the same order of magnitude. When it comes to characterizing electrochromic devices, impedance spectroscopy is a very time-consuming process, since a spectrum down to low frequencies should be taken at a number of equilibrium potentials. Thus we believe that transient current measurements in many cases offer a faster alternative that sometimes allows a simple determination of diffusion coefficients. 

It is seen that the contribution from the concentration polarisation, Rp.diff + Rp.canrer IS dominating. In an electrode-supported cell, the limitation of gas diffusion through the support is a cell-relevant resistance, whereas Rp,comvr... 

An ideal unpolarized cell would have R = 0 and infinite current an ideal polarized cell would have a fixed R independent of and thus a constant current. Reality is somewhere in between There are several sources of "polarization" that can be considered as finite contributions to the overall resistance R > 0 (or better, the impedance Z). The IR drop, from whatever source, is also called the overpotential t] (i.e., IR > 0), which always decreases the overall E remember that R is always a function of time and E. The causes of polarization are (1) diffusion-limited mass transfer of ions from bulk to electrode (2) chemical side reactions (if any), and (3) slow electron transfer at the electrode between the adsorbed species to be oxidized and the adsorbed species to be reduced. 

For n = 1-e, where 0electrode surface roughness or distribution/accumulation of charge carriers. For n = 0.5 e, where 0< < 0.1, the CPE is related to diffusion, with deviations from Fick s second law. For n = 0 e, where 0inductive energy accumulation. Therefore, the CPE is a generalized element. Several factors can contribute to the CPE surface roughness, varying thickness or composition, non-uniform current distribution, and a distribution of reaction rates (non-homogeneous reaction rates on the electrode surface) [3],... 

The expression for R(9) contains three contributions. The first is the resistance of the bulk electrolyte. The second is due to the bubble diffusion region. As discussed in Section 3.4, this contribution is almost constant. The third comes from the shielding effect of the bubbles growing on the electrode surface. This contribution is a function of 0. A possible ansatz for R(9) is (see also Fig. 3.11 and the corresponding discussion) ... 

The impedance spectrum of polymer and gel electrolyte appears as a depressed semicircle in the frequency region between 100 kHz and 0.1 Hz, which can be analyzed using the Cole and Cole [1941] approach, as described in Section 2.I.2.3. Typically, polymeric, plasticized, and gel Li-ion conductors show abnormally low conductivity as compared to that expected from self-diffusion coefficients calculated using other methods such as PMFG-NMR (Clericuzio et al. [1995]). In addition to the usual attribution of this effect to ion association, the incomplete removal of the electrode impedance effect during analysis can contribute to an apparent increase in the electrolyte resistance. 

This electrochemical model was shown to be consistent with the experimental results and, as expected, the diffusion potential was found to make a significant contribution to the overall cell potential because of the significant difference in mobility for the electrons and cations. In contrast, changing the cation from Li" " to Cs had little effect on the diffusion potential. One of the experimental advances in this study was the use of boron-doped diamond electrodes, which have the advantage of slowly eroding in the flame and therefore resisting surface contamination better than Pt electrodes. 

Pulse voltammetry techniques are characterized by a succession of potential steps. During the sequential potential steps, the rates of current decay of the capacitive (If.) and the faradaic currents (7p) are essentially different (specifically, while 4 in Equation 2.1 decays exponentially with time. Ip decreases as a function of t 2, characteristic of a diffusion-controlled electrochemical reaction). In this way, the rate of decay of If. is significantly faster than that of Ip, and thus I. is negligible at a time of 57 uQ after the potential step is imposed (where 7 uQ is the time constant, Tj-gy, for the electrochemical cell having values from microseconds to milliseconds, and R is the uncompensated resistance between reference and working electrodes). Consequently, Ip is the main contribution to the measured current I when its value is measured at the end of a potential step. The detection limits of these techniques therefore fall around 10 M making them suitable for quantitative analysis. 

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