Microelectrodes equivalent circuit

Fig. 13. (a) Sketch of the microelectrode configuration used to investigate the distribution of grain boundary properties, (b) Typical impedance spectrum calculated for a model sample (inset) consisting of 24 cubic grains and two microelectrodes on adjacent grains. An equivalent circuit consisting of two serial RC-elements (inset) can be used to fit the spectrum. 

Fig. 28. (a) Sketch of current lines of the dielectric displacement current between a contact needle and a counter-electrode indicating the influence of the stray capacitance, (b) Equivalent circuit (including the stray capacitance) representing microelectrode measurements on single crystals and the two simplified subcases for ohmic and non-ohmic microelectrodes. 

Fig. 42. (a) Impedance spectrum obtained on a 30 pm LSM microelectrode at a temperature of approx. 800 °C. The inset shows the equivalent circuit used to fit the data, (b) Electrode resistance Rti as a function of the microelectrode diameter at a temperature of approx. 800 °C. The solid line is a linear regression of the resistance data and shows the proportionality of Rd to the inverse of the square of the microelectrode diameter. 

Peck et al. [153] carried out an experiment, which to date remains unique, on electrodes in the superconducting state. Unfortunately, instead of voltammetry, they used the less direct method of impedance measurements in the frequency range 10 -10 Hz. They studied two TBCCO microelectrodes (Tc 112 and 119K) and also (in test experiments) platinum and glassy carbon. All these electrodes were cathodically polarized under potentiostatic conditions (so that the amplitude of potential modulation was substantially lower than its constant component). The equivalent circuit included Cdi and the parallel polarization resistance. The nature of... 

First, we consider the properties of a microelectrode in contact with a solution of pure electrolyte in the absence of a dissolved or immobilized redox active analyte. The objective is to understand the fundamental behavior of microelectrodes in the absence of an electroactive analyte and to discuss strategies for optimizing the electrode s temporal response. The existence of the double-layer capacitance (see Chapter 1) at the working electrode complicates electrochemical measurements at short timescales. Figure 6.1.1.1 is an equivalent circuit of an electrochemical cell where Zp is the faradaic impedance corresponding to the... 

An ac impedance technique based on changes in solution resistance is also available and has been appUed to enzyme-coated microelectrodes (64). In this case, a sinusoidal potential is applied between the electrode and the auxiliary electrode. The measured sinusoidal current is sent to a frequency response analyzer that monitors the change of the real impedance with distance to the substrate. Using equivalent circuits, a theoretical approach curve can be obtained and fitted to the experimental solution resistance profiles with distance. 

Figure 7.7. Basic equivalent circuit for metal microelectrode.

When the analysis, using a microelectrode to pass the current, was extended to striated muscle by Katz (1948), it became clear that muscle was anomalous in that the membrane capacity was substantially larger than in nerve fibres. In frog sartorius muscle fibres appeared to be about 5 yF/cm of fibre surface. In time it became clear that this was due to the extensive membranes of the transverse tubular system in muscle fibres. Several studies using A.C. impedance methods were undertaken to define the equivalent circuit of the morphologically complex membranes in a muscle fibre (Falk Fatt, 1964 Schneider, 1970 Valdiosera, Clausen Eisenberg, 1974). 

Figure 14.22 Electrical impedance spectroscopy for detection of Salmonella suspensions using interdigitated microelectrodes in (a) Dl water and (b) PBS with the cell concentrations in the range of i(y to Iff cfu/ml, along with water and PBS as controls, together with their fitting spectra and the equivalent circuits. Frequency range 1 Hz to 100kHz. Amplitude 50mV. From Ref [57] with permission from Elsevier...

The influence of Qiis significant in rapid voltametry measurement. The equivalent circuit in Fig. 2 can be regarded as a simple RC circuit with a time constant, t = Qii s, especially when no redox material exists R = oo). In other words, the ctirrent signal response flattens due to the limitation imposed by the time constant dtiring a fast sweep. However, for the microelectrode, z = pa where p is the specific resistance of the solution and a is the radius of the electrode. Hence, unlike with the use of an ordinary electrode, fast sweep is possible. 

Figure 4.10. Electrical equivalent of microelectrode (adapted from Amatniek, 1958, Figure 12, p. 9). (a) Basic system, (b) model of microelectrode and single cell penetrated by electrode, (c) electrical circuit model of (b), (d) lumped parameter equivalent of (c).

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