Four-electrode measurements

With four-electrode measurements effected from the surface, an average soil resistivity over a larger area is obtained. The resistivity of a relatively localized layer of earth or pocket of clay can only be accurately measured by using a spike electrode. Figure 3-18 gives dimensions and shape factors, Fg, for various electrodes. 

When materials have very high conductivities, one needs to use four-electrode measurements to avoid limitations from the in-plane resistance of the electrode... 

When low resistance values (< 10kf2) are being measured, series resistance errors may arise from the leads connecting the electrodes to the "resistance meter" or from the contact resistances between the electrodes and the test material. Both may be eliminated by using "four-electrode" measuring systems where the electrodes and leads used for current and potential connection are completely separate. Obviously, the meter must be one designed for four-terminal measurement and will employ the "fixed current.measured potential" system. 

Fig, 1.3 AV Plus DX (St. Jude Medical, Model 1368). Vertical arrows show the different dimensions along the lead horizontal arrows show the distance between the four electrodes. Measurements in millimeters (courtesy of St. Jude Medical)... 

The electrical properties of microporous membranes in 1 mM KCI solution was investigated in the frequency range 1 mHz to 1 kHz by Martinsen et al. (1998a), using a four-electrode measuring cell (Figure 3.11). 

Impedance is typically measured in a two-electrode configuration where the electrolyte is compressed between two blocking (steel, platinum) or nonblocking Li-electrodes (Qian et al. [2(X)2]). Analysis of electrolyte impedance in the presence of electrode impedance is complicated and usually assumes that the electrolyte is responsible for the highest frequency region of the spectrum, about IkHz. To improve confidence in the conductivity estimation, measurements with several layer thicknesses should be performed. To remove the effect of the electrode impedance in a test setup, four-electrode measurements have also been proposed (Bruce et al. [1988]). Typically, two pseudoreference electrodes made of Li-foil strips are pressed through a cavity in the middle of circular main electrodes to the surface of the polymer electrolyte under test. 

Figure 2.15 illustrates an improved four-electrode measuring system which utilizes commercially available operational amplifiers (Ferris and Rose, 1972). The sample chamber used with this system is shown schematically in Figure 2.16. 

Figure 10.6 illustrates a cell for use in four-electrode measurements of electrolyte impedance. The working electrodes are platinum. The sensing electrodes are also platinum, but are platinized. They are recessed from the main cell by salt bridges. It is possible to obtain four sample sizes by changing the relative positions of the two sensing electrodes. A detailed description of this cell appears in Schwan and Ferris (1968). 

The goal of the "ideal" four-electrode measurement is to minimize these additional artifacts to keep the measured impedance Z e sured dose as pos-... 

In complex cases of four-electrode measurement in highly resistive media with metal "pseudo-reference" electrodes the contact impedance may become significant, resulting in confounding results and equivalent circuits consisting of inductive, capacitive, and resistive elements related to an instrumental artifact and not to a physical condition of a studied system [15]. One therefore has... 

Y. Yoon, A. C. Mount, K. M. Hansen, D. C. Hansen, Electrolyte conductivity through the shell of the eastern oyster using a four-electrode measurement,]. Electiochem. Soc.,2009,156, 2, pp. 169-176. 

Resistances in and of electrolytes are exclusively measured with low or audio frequency ac so as not to falsify the results with polarization effects. Measurement is mainly by four electrodes, which eliminates voltages due to the grounding field resistances of the measuring electrodes. 

The most commonly applied indirect method of measuring soil resistivity using the four-electrode arrangement of Fig. 3-14 is described further in Section 24.3.1. The measured quantities are the injected current, /, between the electrodes A and B, and the voltage, t/, between the electrodes C and D. The specific soil resistivity follows from Eq. (24-41). For the usual measuring arrangement with equally spaced electrodes a = b,ii follows from Eq. (24-41) ... 

Measurement of resistivity The most usual method of measuring soil resistivity is by the four-electrode Wenner method. Figure 10.48 indicates the basic circuit. The mean resistivity is given by... 

Measurement of resistance As previously mentioned, the four-electrode resistivity meters can be used to measure resistances. For this purpose the... 

The measurement of resistance to remote earth of a metallic structure is normally carried out with a four-electrode instrument. The connections are shown in Fig. 10.52. A current / is passed between the structure and a remote electrode. The potential difference V is measured between the structure and a second remote electrode. In this way the ohmmeter records the resistance of the structure to earth, i.e. V/I. The spacing of the electrode from the structure is important and must be such that the remote potential electrode lies on the horizontal part of the resistance/distance curve, as shown in Fig. 10.52. Generally speaking, a minimum distance of 15 m from the structure is necessary for the potential electrode to lie on the flat part of the curve, with the current electrode usually at least twice the distance of the potential electrode. 

FIGURE 32.2 Scheme of a four-electrode system for polarization measurements at an ITIES comprising a potentiostat (POT), two reference electrodes connected to the cell by means of Luggin capillaries (REl, RE2), and two counter electrodes (CEl, CE2). The planar ITIES is formed at the edge of a round hole in a glass barrier between the spaces for the aqueous (water) and the organic (org) phases. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

The electrochemical cell for the polarographic measurements had a four-electrode configuration equipped with a microsyringe, and was connected to a computer-assisted data-acquisition system [7]. On the other hand, the cyclic voltammetric measurements that are also assisted by a computer data-acquisition system were carried out using a gel electrode that contains the aqueous phase [8]. The cell structure was as follows ... 

Field measurement of soil resistivity using the Wenner four-electrode method... 

Direct shear test of soils under consolidated drained conditions pH of soil for use in corrosion testing Field measurement of soil resistivity using the Wenner four-electrode method Optimum S03 in portland cement... 

Fig. 11 The scattering properties of a five branches - four electrodes molecular bridge, (a) Detailed atomic structure of the molecule. A central perylene branch was included to mimic an internal measurement branch, (b) EHMO-ESQC calculated T12(E) transmission coefficient (plain) and predicted T12(E) transmission coefficient (dashed), applying the intramolecular circuit rules discussed for the four molecular fragments given in Fig. 12. The dashed (dotted) line is the Ti2(E) variation for the single molecular branch, as presented in the inset, to show the origin of the destructive interference...

Fig. 21 The variation of the balancing tunneling current of the four branches four electrodes monomolecular Wheatstone bridge connected as presented in (a). In (b), the dashed line is for the current intensity 7W (in absolute value) measured by the ammeter A and deduced from the standard Kirchoff laws calculating each molecular wire tunneling junction resistance of the bridge one after the other from the EHMO-ESQC technique. In (b), Hie full line is the same tunnel current intensity but obtained with the new intramolecular circuit rules discussed in Sect. 2. (c) The resistance of the branch used to balance the bridge as a function of its rotation angle. The minimum accessible resistance by rotation is 78 MQ for the short tolane molecular wire used here...

In a real experiment one uses at least four electrodes (see Fig. 12.2), one counter and one reference electrode on each side, and measures the difference in potential between the two reference electrodes. In principle each reference electrode could be referred to the vacuum scale using the same procedure that was outlined in Chapter 2. However, in practice the required data are not available with sufficient accuracy. Of course, the voltage between the two reference electrodes characterizes the potential difference between the two phases uniquely. It can be converted to an (estimated) scale of inner potential differences by using the energies of transfer of the ions involved. 

The overpotential is directly determined by measuring the potential difference between the working and reference electrodes in an arrangement such as that of Fig. 10.9. (In a four electrode cell the potential difference must be measured between the two reference electrodes.) Frequently a potentiostat is used to impose a known overpotential and the current flowing in the cell is measured as a function of ij. 

In general it will be necessary to measure via impedance measurements using a four electrode cell. A schematic diagram of the cell which would be used for such measurements is shown in Fig. 10.15. The expected behaviour will be as described in Eqn (10.3) except that Warburg impedances can arise from either or both phases. An example of an impedance spectrum of the H2O/PVC interface is shown in Fig. 10.16. The application of a constant overpotential will, in general, lead to a slowly decaying current with time due to the concentration changes which occur in both phases, so that steady state current potential measurements will be of limited use. 

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