Warburg component

For a constant phase process, as a diffusion process, the plot is represented as a straight line with one slope (see Figure 8.22) [75], This is evident from Equation 8.86, because when Z, is plotted versus Zr, the Warburg component is represented as a straight line with a unitary slope. 

AC impedance spectroscopy also has seen extensive utility in the study of the hole injection or recombination process depicted in Fig. 14. An equivalent circuit for this process is illustrated in Fig. 17 it does resemble the circuit in Fig. 16(a), except for the Warburg component [84]. Early studies [85-88] utilized the recombination resistance parameter, / r, that was extracted from model fits of the measured AC impedance data. This parameter was seen to be inversely related to the hole injection current, thus signifying that it is indeed related to the recombination process. However, the challenge is to differentiate... 

The diffusion impedance at semiconductor electrodes has been considered recently [105]. This author described the applicability of AC impedance spectroscopy for the study of electron capture and hole injection processes at n-CaAs-H20/C2H50H-methyl viologen, p-InP-aq. KOH-Fe(CN)6l -GaAs-H2S04-Ce +, and -InP-aq. KOH-Fe(CN)6 interfaces. In the case of electron capture processes, a Randles-like equivalent circuit was found to be applicable [105]. On the other hand, no Warburg component was present in the hole injection case when the reverse... 

The grain boundary and electrode features are associated with Warburg components of 3 x 10 cm s and 1.3 x lO S cm s respectively. The known properties of the zirconia phase do not, however, fit such an interpretation the resistivity, extrapolated from higher temperature is at least lO Qcm. This would suggest... 

The second circuit [Fig. 5.25(1 )] was proposed by Hladky et al. [13]. to take into account a diffusion-limited behavior corresponding to a Warburg component which can be described by Eq. (5.26). The exponent n in Eq. (5.26) can vary between 0.5 and 0.25 depending on the smoothness of the metallic surface that is 0.5 for highly polished surfaces and 0.25 for porous or very rough materials [14]. R and C in Eq. (5.26), are the resistance and capacitance associated with the distributed R-C line of infinite length. 

Figure 7.28 illustrates the complex-plane presentation of simulated data corresponding to the model circuit in Fig. 7.256 when R = 10 O, = 100 kfl, Cdi = 40 jiF, and the exponent n of the Warburg component = 0.4. Figure 7.29 shows the same data in a Bode representation. 

The impedance with its components R and C is known as the Warburg diffusion impedance, and constant as the Warburg constant. In the equivalent circuits for electrochemical reactions, a Warburg impedance is represented by the symbol -W- as shown in the lower part of Fig. 12.15b. 

Since the ion transfer is a rather fast process, the faradaic impedance Zj can be replaced by the Warburg impedance Zfy corresponding to the diffusion-controlled process. Provided that the Randles equivalent circuit represents the plausible model, the real Z and the imaginary Z" components of the complex impedance Z = Z —jZ " [/ = (—1) ] are given by [60]... 

Redox potentials were also used to arrange the electron carriers in their correct order. This procedure was applied to the cytochromes by Coolidge (1932). There were however serious difficulties. Electrochemical theory applies to substances in solution the values obtained are significantly affected by pH and the concentrations of the different components. Of the members of the electron transport chain only the substrates NAD+, NADP+, and cytochrome c are soluble. The other components were difficult to extract from tissue particles without altering their properties. Further, it was hard to determine their concentration and to decide on appropriate values for pH and oxygen concentration. Nevertheless, mainly from work by Ball (1938), at the time in Warburg s laboratory, an approximate order of redox potentials was drawn up ... 

Figure 7. (A, top) Simple battery circuit diagram, where Cdl represents the capacitance of the electrical double layer at the electrode—solution interface (cf. discussion of supercapacitors below), W depicts the Warburg impedance for diffusion processes, Rj is the internal resistance, and Zanode and Zcathode are the impedances of the electrode reactions. These are sometimes represented as a series resistance capacitance network with values derived from the Argand diagram. This reaction capacitance can be 10 times the size of the double-layer capacitance. The reaction resistance component of Z is related to the exchange current for the kinetics of the reaction. (B, bottom) Corresponding Argand diagram of the behavior of impedance with frequency, f, for an idealized battery system, where the characteristic behaviors of ohmic, activation, and diffusion or concentration polarizations are depicted.

Pure NADP+ was isolated from red blood cells in 1934 by Otto Warburg and W. Christian, who had been studying the oxidation of glucose 6-phosphate by erythrocytes.13 They demonstrated a requirement for a dialyzable coenzyme which they characterized and named triphosphopyridine nucleotide (TPN+, but now officially NADP+ Fig. 15-1). Thus, even before its recognition as an important vitamin in human nutrition, nicotinamide was identified as a component of NADP+. 

Nicotinic acid was prepared in 1867 by oxidation of nicotine. Although it was later isolated by Funk and independently by Suzuki in 1911-1912 from yeast and rice polishings, it was not recognized as a vitamin. Its biological significance was established in 1935 when nicotinamide was identified as a component of NAD+ by von Euler and associates and of NADP+ by Warburg and Christian.3 Both forms of the vitamin are stable, colorless compounds highly soluble in water. 

If the reaction rate is controlled by transport phenomena, then the resulting impedance can be explained by a component that depends on the conditions of transport. The best-known example is the so-called Warburg impedance Zw, valid for semi-infinite diffusion37,38 ... 

EIS data analysis is commonly carried out by fitting it to an equivalent electric circuit model. An equivalent circuit model is a combination of resistances, capacitances, and/or inductances, as well as a few specialized electrochemical elements (such as Warburg diffusion elements and constant phase elements), which produces the same response as the electrochemical system does when the same excitation signal is imposed. Equivalent circuit models can be partially or completely empirical. In the model, each circuit component comes from a physical process in the electrochemical cell and has a characteristic impedance behaviour. The shape of the model s impedance spectrum is controlled by the style of electrical elements in the model and the interconnections between them (series or parallel combinations). The size of each feature in the spectrum is controlled by the circuit elements parameters. 

The terminal component of the respiratory chain is cytochrome c oxidase, which reduces dioxygen to two molecules of water. This cytochrome was discovered as the Atmungsferment by Warburg already in the 1920s and shown by him to be a heme protein in 1929 [2], an achievement for which he was awarded the Nobel Prize for Physiology or Medicine in 1931. The electron donor of the oxidase, cytochrome c, had been found earlier by Keilin (see [3]), as had one of the oxidase heme components, cytochrome a, whereas Keilin did not observe the dioxygen-reacting cytochrome fl3 until 1939. Keilin had before this discovery maintained that the oxidase is not a heme but a copper enzyme, and we now know that it also contains two... 

It should be noted that if one or both of the partial reactions are at least partially controlled by the diffusion of reacting species, then the expression describing the impedance becomes more complex because of participation of the component called Warburg impedance at low frequencies. Under such circumstances, selection of an optimum frequency becomes critical for the impedance measurement at low frequencies. 

Figure 8.6. Complete representation of a conductivity cell. Re - ohmic resistance, Cs - double layer capacitance, Rw - Warburg s resistance, Cw - Warburg s capacitance, - resistive component due to the finite rate of electrode reaction, Cq — stray capacitance.

The EIS response depends on the flhn thickness and morphology, applied potential, and, obviously, the nature of the components of the hybrid system. The hydro-phobic nature of the polymer, the level of doping within the film, and the size of ions in contact with the polymer surface are factors to be considered for studying the response of such materials. In short, the kinetics of the overall charge transfer process should take into account (1) electron hopping between adjacent redox sites (Andrieux et al., 1986) usually described in terms of a Warburg diffusion impedance element (Nieto and Tucceri, 1996) and (2) double-layer charging at the metal-flhn interface, represented in terms of a double-layer capacitance element. 

The Warburg impedance has a minimum at 1/2. The mass-transfer impedance is a vector containing real and imaginary components that are identical, that is, the phase angle (p = atan(Z" v/Z w) = atan(-l) = 5°. The faradaic impedance is shown in Fig. 11(b) (dashed line). On the complex plane plot, it is a straight line with a slope of 1 and intercept The total electrode impedance consists of the solution resistance, R, in series with the parallel connection of the double-layer capacitance, Qi,... 

---