Impedance measurements instrumental limitations

Measurement science is one of the most active fields of chemistry today. Advances in microelectronics, computers, and sensing devices have accelerated the development of measurement instruments and techniques. Many of these innovations could be used for ocean measurements, although some of the new methods are not well known to ocean scientists. The use of new techniques of analytical chemistry for ocean science applications is impeded by limited interactions between ocean scientists and analytical chemists. Significant technical innovations will be required to make many of the new... 

Instrument limitations must be considered in the measurement of organic coatings because their resistivities are large, 1012 Q cm or more. The input resistance of common potentiostats is usually not more than 10n to 1012 ohms, and if the cell resistance approaches or exceeds the input resistance of the potenti-ostat, a significant fraction of the applied signal will pass across the input impedance and not the cell impedance. In these cases the collected data do not reflect just the impedance of the electrochemical interface, which is a fundamental assumption in almost all data analyses. In fact, the potentiostat input impedance in parallel with the stray capacitance associated with the potentiostat measuring leads will be obtained. 

Measurement of calibrated capacitors can also be used to determine instrument limitations. Figure 36 shows a plot of the variation in measured capacitance versus known capacitance for a commercial impedance analyzer system (110). 

Although EIS offers many advantages for diagnosing fuel cell properties, clear difficulties exist for applying impedance methods and fitting the data to the model to extract the relevant electrochemical parameters. The limitations of the EIS technique derive from the several requirements required to obtain a valid impedance spectrum, because the accuracy of EIS measurement depends not only on the technical precision of the instrumentation but also on the operating procedures. Theoretically, there are three basic requirements for AC impedance measurements linearity, stability, and causality. 

When following potential changes, eg electrochemical cell capacitance charging or discharging, ac impedance measurements, or electrochemical noise measurements, the bandwidth response of the measuring instrument may limit the application. 

Finally, methods of verification of obtained impedances and the modeling of experimental data are discussed. The last two chapters deal with applications of nonlinear measurements and instrumental limitations. 

The frequency range chosen in the above experiments was dictated by the limited electronics available in 1960 and the cumbersome experimental approach associated with it, which required that the impedance be measured independently at each frequency. The introduction of automated impedance analysis instruments removes this restriction and allows the experimenter to choose the most appropriate frequency range for a given experiment. This choice should be determined by the nature of the interfaces in the experiment and the time constants that are associated with them. For example corrosion studies, which often involve a slow aqueous diffusion process, generally have relatively large time constants (on the order of... 

An active null admittance measuring instrument that incorporates many of the advantages of the transformer ratio arm technique, while obviating many of the disadvantage of passive bridges, has been reported by Berberian and Cole [1969]. Figure 3.1.4 shows a form of this bridge modified to measure impedance and to remove some of the limitations of the earlier instrument (McKubre [1976]). 

With appropriate calibration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to zero concentration yield the intrinsic storage and loss moduli [Gr] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instrument provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 Hz. High frequency (20 to 500 K Hz) viscoelastic properties can be measured with another instrument, the high frequency torsional rod apparatus (HFTRA) (294). 

Another method of spatially resolving variations in impedance involves constructing regular arrays of small cells on a sample surface and performing conventional EIS measurements in them on a serial basis (138). This method does not require any special measurement equipment beyond that needed for conventional EIS measurement. However, as the cell size and working electrode area is reduced, the measured current will be reduced to the point where noise and instrument current resolution become factors. These factors limit how small a cell can be and determine the spatial resolution of the technique. This technique has been used to examine the changes in the EIS response on coil coated galva-... 

The operation of an oscilloscope can best be described by reference to Fig. 5, which shows a simplified layout of the controls of a commercial (Tektronix) digital instrument. The signal to be measured is applied to the input connector (BNC) of one of the vertical amplifier channels and must not exceed an upper limit of, typically, 400 volts if the scope input impedance is one megaohm and 5 volts for 50-ohm input impedance. The latter impedance is necessary for signal changes that occur rapidly, such as in the fluorescence decay measurements of Exps. 40 and 44. The lower limit of sensitivity is about 1 mV/division, so preamplification is sometimes needed if very low signal levels are to be measured. 

The best method to measure the double-layer capacitance is to use a phase-sensitive voltmeter. This instrument is sometimes incorporated into a frequency response analyzer, designed to make electrochemical impedance spectroscopy measurements, but it can also be used independently. In Part Two we devote a full section to the operation of such instruments and the analysis of results obtained by them. Here we shall limit the discussion to the measurement of capacitance. 

Since most electrochemical measurements relating to corrosion of metals are satisfied with a sensitivity of 1 jiV or 1 xA, modern instrumentation usually employs electronic operational amplifiers where the noise limits control the range of measurements. The function of the operational amplifier is to amplify the potential (Vg) applied at the input so that it can be displayed on a low impedance analogue or digital meter (V ) as shown in Fig. 1.1. The output potential of the operational amplifier is proportional to the source potential and is required to have sufficient input impedance to avoid polarisation of the potential source. 

For RF measurements, another class of instruments is available. Modem high-end network analyzers range up to 110 GHz. These instmments use reflexion measurements to determine ratios of inserted to reflected power. Because of the use of directional couplers, the lower frequency limit will typically not go below a few kHz. To obtain complex impedance values, a vector network analyzer (VNA) is needed, because scalar network analyzers give absolute values only. Measurements can be conducted very fast... 

As an example, Sanches et al. (2013a,b,c) developed methods and instrumentation that created an optimal broadband multisine signal in a given frequency range, by using other a priori information like the expected shape of the impedance spectrum. They were able to acquire an impedance spectrum about every 5 ms (1 kHz—1 MHz) and applied mathematical methods to identify nonlinearities and other limitations of the measurement system and also identify the object under test in the case of time-varying impedances. 

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