Impedance frequency dependence

Impedance-frequency dependence and equivalent circuit for a t5q>ical electrochemical cell... 

Other more complicated forms of impedance-frequency dependencies can be revealed when a combination of diffusion process and homogeneous bulk solution reaction or recombination of electroactive species is considered [34]. In the case of homogeneous bulk solution and electrochemical reaction, the corresponding charge-transfer impedance Z can be simplified by a kinetic resistance R. Another parameter, —critical frequency of reaction or recom-... 

Neufeld, P. and Queenan, E. D., Frequency Dependence of Polarisation Resistance Measured with Square Wave Alternating Potential , Br. Corros. J., 5, 72-75, March (1970) Fontana, M. G., Corrosion Engineering, 3rd edn., McGraw-Hill, pp 194-8 (1986) Dawson, J. L., Callow, L. M., Hlady, K. and Richardson, J. A., Corrosion Rate Determination By Electrochemical Impedance Measurement , Conf. On-Line Surveillance and Monitoring of Process Plant, London, Society of Chemical Industry (1977)... 

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

Figure 5 presents the capacitance-frequency dependence from impedance spectroscopy measurements for CS48 and CS15 in acidic and organic medium. In the low frequency region (from ImHz to lOOmHz) nearly a complete penetration of the ions into the pores is allowed and the quite stable values indicate the domination of the capacitive behavior at the electro 1 ytc/carbon interface. All the curves show a typical drop of... 

The IV measurements on molecules and monolayers have been carried out almost exclusively using direct current (DC) frequency-dependent alternating current (AC) impedance measurements have rarely been performed, even though a rich spectroscopy may reveal itself, if the IV measurements were followed as a function of frequency v. 

For capacity measurements, several techniques are applicable. Impedance spectroscopy, lock-in technique or pulse measurements can be used, and the advantages and disadvantages of the various techniques are the same as for room temperature measurements. An important factor is the temperature dependent time constant of the system which shifts e.g. the capacitive branch in an impedance-frequency diagram with decreasing temperature to lower frequencies. Comparable changes with temperature are also observed in the potential transients due to galvanostatic pulses. 

Important electrical informations about OLEDs, such as charge transport, charge injection, carrier mobility, etc., can be obtained from bias-dependent impedance spectroscopy, which in turn provides insight into the operating mechanisms of the OLED [14,15,73,75 78]. Campbell et al. reported electrical measurements of a PLED with a 50-nm-thick emissive layer [75], Marai et al. studied electrical measurement of capacitance-voltage and impedance frequency of ITO/l,4-Mv-(9-anthrylvinyl)-benzene/Al OLED under different bias voltage conditions [76], They found that the current is space-charge limited with traps and the conductivity exhibits power-law frequency dependence. 

Fig. 5.9 Frequency dependence of impedance of fresh electrodes of different Ru content in 5 M NaCl at room temperature at OCP. 

A constant phase element (CPE) rather than the ideal capacitance is normally observed in the impedance of electrodes. In the absence of Faradaic reactions, the impedance spectrum deviates from the purely capacitive behavior of the blocking electrode, whereas in the presence of Faradaic reactions, the shape of the impedance spectrum is a depressed arc. The CPE shows power law frequency dependence as follows129 130... 

It should also be mentioned that capacitors were then added in parallel with the resistors in equivalent circuit elements because the frequency-dependent experimental electrical impedance data had a component that was 90° out of phase with the resistor. 

Frequency dependent complex impedance measurements made over many decades of frequency provide a sensitive and convenient means for monitoring the cure process in thermosets and thermoplastics [1-4]. They are of particular importance for quality control monitoring of cure in complex resin systems because the measurement of dielectric relaxation is one of only a few instrumental techniques available for studying molecular properties in both the liquid and solid states. Furthermore, It is one of the few experimental techniques available for studying the poljfmerization process of going from a monomeric liquid of varying viscosity to a crosslinked. Insoluble, high temperature solid. 

In the past, impedance or dielectric studies have been examined as an experimental technique to monitor the flow properties, effects of composition, and the advancement of a reaction during cure [1]. Until a paper by Zukas et al [2], little emphasis had been placed on the frequency dependence except to note the shift in position and magnitude of impedance maxima and minima. Furthermore, most measurements on curing systems reported results in terms of... 

In situ frequency dependent electromagnetic-impedence measurements provide a sensitive, convenient, automated technique to monitor the changes in macroscopic cure processing properties and the advancement of the reaction in situ in the fabrication tool. This chapter discusses the instrumentation, theory, and several applications of the techniques, including isothermal cure, complex time—temperature cure, resin film infusion, thick laminates, and smart, automated control of the cure process. 

Frequency-dependent measurements of the materials dielectric impedance as characterized by its equivalent capacitance, C, and conductance, G, are used to calculate the complex permitivity, e = d — id, where co = 2nf, f is the measurement frequency, and C0 is the equivalent air replacement capacitance of the sensor. 

PROCESSING TOOL n frequency/time frequency dependent frequency/time molecular models impedance measurement molecular mobility models data base... 

The first two quantities calculated from S(t, y) depended on measurements of times the second two depend on measurements of amplitudes. From the amplitude of the reflection from the top surface of the cell the impedance, and hence the density, can be found using eqns (8.58) and (8.59). The impedance is plotted in Fig. 9.4(c). Finally, knowing the thickness and the impedance of the cell, the attenuation can be deduced from the amplitude of the echo from the interface between the cell and the substrate the weaker this echo, the greater the attenuation. The attenuation calculated from (8.60), neglecting frequency dependence, is plotted in Fig. 9.4(d). It is also possible to calculate the frequency dependence of the attenuation using (8.70) (Daft et al. 1989). 

The Capacitance of the Double Layer. It has been seen that the impedance of the double layer is frequency dependent Taking a frequency of 1 kilocycle, and a capacitance value of 50 pF cm, one has... 

It is easily argued that, if the voltage measured by the detector D equals zero, the impedance of the cell must be equal to the impedance of the series combination, i.e. Z = Rs and Z" = (coCs) 1. Usually, the values of Rs and Cs needed to balance the bridge vary with the applied frequency as a consequence of the fact that the cell impedance has a frequency dependence different from that of a simple RC series combination. 

Figure 8.8 Series RC circuit (a) circuit (b) current-voltage relationships (c) frequency dependence of impedance Z and phase angle .

The variables are frequency-dependent and represent Y (admittance), Z (impedance), V (voltage), and I, or i (current). The relationship between angular (on) and linear (F) frequency is o) 2nF. Both the admittance and the impedance are complex numbers, consisting of real and imaginary parts. Thus for admittance... 

In Chapters 6 and 7, we discussed potentiometric and amperometric sensors, respectively. The third basic electrochemical parameter that can yield sensory information is the conductance of the electrochemical cell (Fig. 8.1). Conductance is the reciprocal of resistance. It is related to current and potential through the generalized form of Ohm s law (C.l). If the measurement is done with AC signal conductance (G) becomes frequency-dependent conductance G(co) and the resistance R becomes impedance Z( (o). 

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