Conductivity measurements element impedance

Traditionally, the instrument of choice for accurate conductance measurements that are relatively free of capacitance effects has been the ac Wheatstone bridge illustrated in Figure 8.14. The details of operation and the derivation of the balance condition of the ac bridge are presented in considerable detail elsewhere [16,17], The balance condition is exactly analogous to that of the dc bridge except that impedance vectors must be substituted for resistances in the arms of the bridge when reactive circuit elements are present. 

The Rb based on the sample cannot be calculated correctly, since the electric charge transfer resistance and the electric double layer in an electrode interface are also detected as a resistance, even if bias voltage is impressed to the measurement cell in order to measure the ionic conductivity. For the ionic conductivity measurement, a dc four-probe method, or the complex-impedance method, is used to separate sample bulk and electrode interface [4]. In particular, the complex-impedance method has the advantage that it can be performed with both nonblocking electrodes (the same element for carrier ion and metal M) and blocking electrodes (usually platinum and stainless steel were used where charge cannot be transferred between the electrode and carrier ions). The two-probe cell, where the sample is sandwiched between two pohshed and washed parallel flat electrodes, is used in the ionic conductivity measurement by complex-impedance method as shown in Figure 6.1. 

Electrical Measurements. Both ac and dc conductivity measurements were made on elemental sulfur and P4S3. The ac measurements were made with an Electro Scientific Industries model 290A impedance bridge in conjunction with a model 860A generator/detector at frequencies of 0.1, 1.0, and 10.0 kHz. A compensating variable capacitor was used either in series or in parallel with the variable resistance arm of the bridge. The... 

The transport time of conduction band electron across a 10-pm thick nanocrystalUne titania film is typically a few milliseconds while for good cells the recombination time is in the range of seconds. This explains why practically all the injected electrons reach the current collector before they recombine. These time constants or resistances can be measured by impedance spectroscopy, which provides a powerful tool for analyzing the circuit elements of nanocrystalUne solar cells [56,57]. 

In view of the success of the 3-element model for the quantitative description of the variation of the low-frequency conductivity of resin-solution columns with the solution concentration, it is logical to inquire whether the same model can explain the electrical behavior of these or similar systems at high frequencies, at which the admittance of the system as a whole and/or of the model elements is appreciable. In other words, the question is asked Can the 3-element model describe the change of the complex impedance of these systems with the frequency of the alternating current used to measure the impedance ... 

Example 3.5 Evaluation of Chi-Squared Statistics Consider that, for a given measurement, regression of a model to real and imaginan/ parts of impedance data yielded = 130. Measurements were conducted at 70 frequencies. The regressed parameters needed to model the data included the solution resistance and 9 Voigt elements, resulting in use of 19 parameters. Under assumption that the variances used in the evaluation ofxf were obtained independently, evaluate the hypothesis that the x value cannot be reduced by refinement of the model. 

Greszczuk et al. [252] employed the a.c. impedance measurements to study the ionic transport during PAn oxidation. Equivalent circuits of the conducting polymer-electrolyte interfaces are made of resistance R, capacitance C, and various distributed circuit elements. The latter consist of a constant phase element Q, a finite transmission line T, and a Warburg element W. The general expression for the admittance response of the CPE, Tcpr, is [253]... 

For applications requiring a large sensing surface area, such as those measuring permittivity and conductivity of tissue, an interdigital capacitor was introduced as the capacitive element in an LC circuit. The change in capacitance resulted in a variation of the impedance and resonant frequency of the LC sensor, which can be interpreted as alterations in the permittivity and conductivity of tissue. The sensor was implanted into the phantom tissue and a saturation depth was achieved such that data were only collected from the tissue layer of interest (Yvanoff and Venkataraman 2009). 

The electrode impedance, Zei- resulting from this polarization is written as a complex function z i=zo( dielectric interface. and the exponent n is usually taken to be This is equivalent to a constant phase element in series with the bulk dieleetric properties of a material. The expression for the measured conductance Gmeas (in Sie-... 

Figure 1.62. (a) Diagrammatic view of the correlation circuit for photoconductivity cross-correlation measurement in (CH) on broadband microstrip lines, (b) Corresponding circuit diagram. The switches are modeled using the approximation of lumped elements with a static capacitance Cg and a resistor having a time-dependent conductance G(/) in parallel. Z is the characteristic impedance of the transmission lines. (Reprinted with permission from ref. 149)... 

If an analyte affects one or more of these equivalent circuit parameters and these parameters are not affected by interfering species, then impedance methods can be used for analyte detection. arises primarily from the electrolyte resistance and is analytically useful mainly in conductivity sensors. The Warburg impedance, which can be used to measure effective diffusion coefficients, is seldom useful for analytical applications. The equivalent circuit elements in Figure 14.1 that are most often useful for analyte detection are and Qi. 

The same authors used magnetic beads coated with a bio-recognition element for the specific separation and concentration of cells prior to impedance measurement. After separation and resuspension of bacterial cells in low conductivity 0.1 M mannitol solution, the concentrated sample was uniformly spread on the surface of IDpE. The impedance sensor detected a minimum of 7.4 x 10" and 8.0 x 10 cfu/ml of E. coli 0157 H7 in pure culture and ground beef samples, respectively. The concentration of bacterial cells attached to nanoparticle-antibody conjugates in the active layer of IDpE above the surface of electrodes was achieved with the help of a magnet placed underneath the electrode chip. This improved the sensitivity of the biosensor by 35% as compared to no use of the magnet. These experiments were performed on an open chip [54]. 

---