Four-electrode systems

A well-defined polarization of an ITIES can be accomplished by means of a four-electrode system with two couples of current-supplying (counter) and potentialmeasuring (reference) electrodes, which are connected to phases (w) and (o) in the... 

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. 

Three-electrode control systems are widely available in the market and there are also four-electrode systems for double working electrodes. The construction is either integral or modular. It is perfectly possible to construct the necessary electronics in-house and, in this case, modular construction is suggested as being more flexible. Operational amplifiers and other components of high quality should be used, particularly for kinetic applications. The elements of a bipotentiostat (independent control of two working electrodes) and a galvanostat are described in ref. 139. 

Three or four-electrode systems together with the use, when appropriate, of a Luggin capillary solve most of the problems of uncompensated resistance in solution. However, at times positive feedback... 

Masada, T., et al. 1989. Examination of iontophoretic transport of ionic drugs across skin Baseline studies with the four-electrode system. Int J Pharm 49 57. 

Srinivasan, V., W.I. Higuchi, and M.H. Su. 1989. Baseline studies with four electrode system The effect of skin permeability increase and water transport on the flux of a model uncharged solute during iontophoresis. J Control Release 10 157. 

Electron-conductor separating oil-water (ECSOW) system — For studying the -> electron transfer (ET) at the -> oil/water interface, the ECSOW system was devised, in which the oil and water phases are separated by an electron conductor (EC), as shown in the Figure. Specifically, the oil and water phases are linked by two metal (e.g., Pt) electrodes that are connected by an electric wire. The ET across the EC phase can be observed voltammetrically in a similar manner to the oil/water interface, i.e., by controlling the potential difference between the two phases using a four-electrode potentiostat (see -> four-electrode system). Because ion transfer (IT) across the EC phase cannot take place, the ECSOW system is useful for discrimination between ET and IT occurring at the oil/water interface. 

Four-electrode system — For electrochemical measurements with the -> interface between two immiscible electrolyte solutions (or the oil/water interface), the four-electrode system is used. In potentiostatic measurements such as cyclic voltammetry, two reference elec-... 

Four-electrode system — Figure. Electronic circuit of a four-electrode potentiostat (X, potential input Y, current output RE1 and RE2, reference electrodes CE1 and CE2, counter electrodes PF, positive feedback circuit for IR drop compensation)... 

Positive feedback circuit — Electronic circuit incorporated in a -> potentiostat, which is used for the - IR drop compensation. Through this circuit, a part of the voltage at the current output of a potentiostat is positively fed back to the potential input, so that the - IR drop can be automatically compensated for. However, note that the positive feedback makes the system unstable and occasionally leads to oscillation. See also - four-electrode system. 

The measuring cell was made of PTFE and had a four-electrode system connected to its outer cylinder. One pair of electrodes served as terminals for the measuring amplifier, and the outer pair was connected to the current supply through a 10-MO wire-wound resistor (the sample resistance was much less than 10 MQ). The measuring cell was carefully shielded from electric and magnetic fields and from mechanical vibrations. 

Errors Due to "Stray" Impedances Three- and Four-Electrode Systems... 

Although in principle, a four-electrode system may be used to eliminate series resistance (connection) errors, this will rarely be found beneficial in measuring the surface... 

Electrodes are the most important part of an impedance-measuring system (Geddes 1972). They determine the sensitivity field (Section 10.5), which determines the contribution of each small voxel to the overall result. Three- and four-electrode systems are more complicated because, as we shall see, they introduce volumes of negative sensitivity because they measure transfer impedance. 

FIGURE 10.10 Skin surface electrode systems. Monopolar systems are usually not ideally monopolar, see text below. The three- and four- electrode systems measure transfer immittance. Electrode functions M, measuring CC, current carrying R, reference PU, pick up. 

If we look at a simple example of a DC resistance measurement with a four-electrode system, the sensitivity will be computed in the following manner ... 

Sensitivity calculations can be utilized equally well for two-, three-, and four-electrode systems. In each case, you must identify the two CC electrodes used for driving an electrical current through the... 

In a rotating field as from a four-electrode system with potentials = Vo sin (ot and Vy = Vg cos cot applied to the x and y electrode pairs, the magnitude of the maximum field. Eg, and the potential differences remain constant in the midregion of the symmetric electrodes. 

Bioimmittance is measured in vivo or in vitro. The tissue may be kept alive and perfused under ex vivo conditions. Bioimmittance can be measured with two-, three- or four-electrode systems. With four electrodes, one electrode pair is current carrying and the other pair picks up the corresponding potential difference somewhere else in the tissue. If the measured voltage is divided by the applied current, the transfer impedance is calculated. If no voltage is measured, the transfer impedance is zero. This is equivalent to the bioelectricity case in which a signal from the source, such as the heart, is transferred to the skin surface electrodes. Zero transfer impedance does not mean the tissue conducts well, only that no signal transfer occurs. With the bioimpedance two-electrode technique, the transfer factor is eliminated because current application and signal pickup occur at the same site, which means that measured impedance reflects tissue electrical properties more directly. 

Equations (6.29—6.35) are the basic equations for three- and four-electrode systems according to the model of two ideal dipoles. Notice that all these analytical models presuppose ideal dipoles that is, electrode sphere radii are much smaller than dipole length, distance between dipoles is much larger than dipole lengths, and infinite homogeneous isotropic medium. 

Figure 6.16 Four-electrode system with current density and reciprocal current density lines. Sensitivity is illustrated at one point, the dot product therefore, the sensitivity there is small because the two current density vectors are almost perpendicular to each other.

Make a comparison between the two-electrode system (resistance of two hemispheres far away from each other according to Eq. (6.1) is R = p/ira) and the four-electrode system of Eq. (6.35). 

Figure 7.2 Metal dependence of polarizability, (a) Four-electrode system in 0.9% saline, (b) Equivalent electric circuit for the loaded PL) electrode pair. B is the unloaded PU signal output from six different metals as shown in Figure 7.3 as registered with 750 kohm load...

If the effect of the zones proximal to the current carrying electrodes and the polarization impedance of the electrodes themselves are to be reduced, the four-electrode system is preferred. Such four-electrode systems correspond to a two-port, four-terminal network equivalent (see Section 8.1). Because there are two ports, these systems actually measure transfer parameters between the ports. This means that if for instance impedance is measured to 0 O, this does not necessarily imply high-conductivity tissue, but rather no signal transfer from CC to PU electrodes. 

As a four-electrode system, the measured segment is determined by the position of the two PU electrodes R and R, or more exact by the position of their electrolyte/salt bridge... 

Figure 7.26 Four-electrode system, tubular in vitro version.

Four-electrode systems are commonly used on humans both with skin surface electrodes or on probes meant for different body cavities. It could also be used by implantable devices... 

Figure 7.28 Four-electrode system, in vivo version. Equipotential lines are dashed. The position of the PU electrodes determines the tissue segment measured and the size of the proximal zones...

Sometimes more specialized results can be achieved by using more than four electrodes Rabbani et al. (1999) combined two orthogonal four-electrode systems to achieve a more localized zone of measurement sensitivity in what he called focused impedance measurements. Kwon et al. (2012) showed that a system using 16 miniature electrodes was able to outperform the four-electrode system in sensitivity and impedanee estimation. With this method, they were also able to recover anisotropic properties from the measured object. 

Quadro-polar Tetra polar Four-electrode system... 

A one-port (dipolar) electrode system measures immittance. The two electrodes function both as CC and PU electrodes. A two-port four-electrode system measures transmittance (transfer immittance) for example, with current injected in one port and voltage recorded at the other port (the black box, Section 7.1). The electrode pairs of current injection and voltage recording may be interchanged if the reciprocity theorem is valid, the transmittance is the same. For the reciprocity theorem to be valid, there are no constraints on geometry, only on, for example, system linearity as outlined in Section 8.1.3. The reciprocity theorem is not based on geometry but on network theory, and is therefore treated in Section 8.1. 

A very general box is the four-terminal type with two ports. Figure 8.1(a). This is the box corresponding to the four-electrode systems described in Section 7.10.3 two pickup (PU) electrodes in the electrical field generated by two current-carrying (CC) electrodes. 

Second, the model of Figure 3.1 is predominantly a dielectric model with dry samples. In bioimpedance theory, the materials are considered to be wet, with double layer and polarization effects at the metal surfaces. Errors are introduced, however, that can be reduced by introducing three- or four-electrode systems (Section 7.10). Accordingly, in dielectric theory, the dielectric is considered as an insulator with dielectric losses in bioimpedance theory, the material is considered as a conductor with capacitive properties. Dry samples can easily be measured with a two-electrode system. Wet, ionic samples are prone to errors and special precautions must be taken. 

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