Capacitive conductivity cells

Ion chromatography (see Section 7.4). Conductivity cells can be coupled to ion chromatographic systems to provide a sensitive method for measuring ionic concentrations in the eluate. To achieve this end, special micro-conductivity cells have been developed of a flow-through pattern and placed in a thermostatted enclosure a typical cell may contain a volume of about 1.5 /iL and have a cell constant of approximately 15 cm-1. It is claimed15 that sensitivity is improved by use of a bipolar square-wave pulsed current which reduces polarisation and capacitance effects, and the changes in conductivity caused by the heating effect of the current (see Refs 16, 17). 

As already indicated conductimetric measurements are normally made with alternating current of frequency 103Hz, and this leads to the existence of capacitance as well as resistance in the conductivity cell. If the frequency of the current is increased further to 106 — 107 Hz, the capacitance effect becomes even more marked, and the normal conductivity meter is no longer suitable for measuring the conductance. 

Variations of resistance with frequency can also be caused by electrode polarization. A conductance cell can be represented in a simplified way as resistance and capacitance in series, the latter being the double layer capacitance at the electrodes. Only if this capacitance is sufficiently large will the measured resistance be independent of frequency. To accomplish this, electrodes are often covered with platinum black 2>. This is generally unsuitable in nonaqueous solvent studies because of possible catalysis of chemical reactions and because of adsorption problems encountered with dilute solutions required for useful data. The equivalent circuit for a conductance cell is also complicated by impedances due to faradaic processes and the geometric capacity of the cell 2>3( . 

A simple conductivity probe is shown in Fig. 3.20 (KPG). This probe can be used for both rough and precise measurements, but when used for precise measurements of low conductances it may give rise to capacitance effects. To avoid large capacitances, the leads to the conductivity cell should be situated as far apart as possible (see, e.g. Fig. 3.15), and they must be screened. 

The conductivity of a solution is measured using an AC bridge with a two-elec-trode conductance cell on one arm (Fig. 5.40(a)) a balance is sought, manually or automatically, by adjusting the variable resistance and capacitance in another arm of the bridge. Usually AC voltage of a few volts and 1 kHz is applied to the cell. The impedance caused by the double-layer capacity at the electrodes does not affect the measured values of conductivity. In some cases, the conductance is measured with a four-electrode cell, as shown in Fig. 5.40(b). For practical methods of measurement, see the reviews in Ref. [25],... 

A method of avoiding the effect of potential differences arising at the electrodesolution interface is to take advantage of the capacitive behavior of the double layer at the electrode surface to make ac (alternating current) contact with the solution. To understand how this may be accomplished, it is necessary to consider a basic model of a conductance cell and examine its behavior under the influence of ac excitation. A review of ac circuit principles at a level sufficient for understanding the behavior of conductance cells and the instrumentation for conductance measurement is presented. The reader who desires a more thorough study of this topic is directed to material contained in the references [4-7]. 

At relatively low applied frequencies, a conductance cell may be represented as the double-layer capacitance Cs in series with the solution resistance R, as shown in Figure 8.8a. When a sinusoidal voltage es is applied to the series RC circuit, the instantaneous current i is the same in every part of the circuit and is given by... 

A high-frequency limit for the applied potential is encountered above several kilohertz where the impedance of the conductance cell again begins to deviate from the resistance R. Since the solution medium itself is a dielectric situated between two parallel charged surfaces, it can assume the characteristics of a capacitor placed in parallel across the solution resistance as shown in Figure 8.9a. The magnitude of this capacitance is given by... 

We can understand how this is carried out by considering the waveforms of Figure 8.13a. At frequencies for which parallel capacitive components of the conductance cell impedance are negligible, sinusoidal excitation of the cell produces the waveforms of A, where es, eR, ec, and i have the same significance as previously discussed. In order to measure the real component of the impedance, the magnitude of the correlation integral cc must be determined. 

The values of specific capacitance and cell resistance obtained with symmetric two-electrode capacitors built with a-Mn02/CNTs composite electrodes are presented in Table 8.3. The addition of nanotubes to a-Mn02 causes a drastic decrease of cell resistance and an increase of specific capacitance referred to the mass of a-Mn02 H20. However, when the specific capacitance is referred to the total mass of the composite electrode material, to be realistic, a CNTs loading higher than 10-15 wt% does not improve the electrodes performance. Therefore, 10-15 wt% of CNTs conducting additive seems to be an optimal amount both on the point of view of electrodes capacitance... 

Capacitance probe, conductivity cell, float gauge,... 

The inductance L is fixed, while the capacitance C is the sum of several separate capacitances that of the conductance cell, Cx, that of a separate variable tank capacitor incorporated in the oscillator, Cj (if present) and stray capacitances due to leads, etc., Q. Also present in some methods is a precision air capacitor Cp graduated directly in capacitance units (generally picofarads), used when the equipment is operated in a null mode. In this mode the precision air capacitor is used to bring the frequency /to the same value in each measurement, and the change in reading of the precision air capacitor is then equal in magnitude to the change in capacitance of the cell. 

The nature of the tracer dictates the detection system. For the liquid phase, quite often the tracers (e.g., NaCl, H2S04, etc.) are such that the detection probe is directly inserted into the reactor and continuous monitoring of the concentration at any fixed position is obtained by means of an electrical conductivity cell and a recorder. In this case, no external sampling of liquid is necessary. If the tracer concentration measurement requires an analytical procedure such as titration, etc., sampling of the liquid is required. For the solid phase, a magnetic tracer is sometimes used. The concentration of a solid-phase tracer can also be measured by a capacitance probe if the tracer material has a different dielectric constant than the solid phase. In general, however, for solid and sometimes gas phases, some suitable radioactive tracer is convenient to use. The detection systems for a radioactive tracer (which include scintillation counters, a recorder, etc.) can be expensive. Some of the tracers for the gas, liquid, and solid phases reported in the literature are summarized in Table 3-1. 

The solution conductivity was measured using a Yellow Springs Instrument conductivity meter (YSI Model 34) with a high pressure conductivity cell (cell constant of 0.0044 cm ). The high pressure cell consisted of ten stacked, stainless steel disc electrodes (10-mm diameter discs), insulated with Teflon washers. The meter is particularly well suited for use with this type of cell because capacitance errors are minimized by the active circuit and electrode over-potential is eliminated by measurement potentials of less than 1 volt. 

All types of cells show the same general response to the alternating current flow. When the amplitude of the sinusoidal potential applied is less than the potential required for an electrochemical reaction, the conductivity cell can be represented approximately by the scheme shown in Figure 8.4. The frequency independent metal-salt interfacial capacitance (the double-layer capacitance) is charged and discharged according to the variation of the potential. 

At potentials sufflciently high for the occurrence of the reaction, the charge transfer across the interface may be represented by the impedance Zr in parallel with the doublelayer capacitance Cs. Figure 8.5 is thus an approximate representation of the conductivity cell during that part of each cycle in which the potential exceeds the potential of the reaction. 

Figure 8.5. Representation of a conductivity cell when the applied potential exceeds the potential for reaction. Re - ohmic resistance, Cj - double layer capacitance, Z, - impedance due to the electrode reaction.

Figure 8.6. Complete representation of a conductivity cell. Re - ohmic resistance, Cs - double layer capacitance, Rw - Warburg s resistance, Cw - Warburg s capacitance, - resistive component due to the finite rate of electrode reaction, Cq — stray capacitance.

Fig. 6.5 Schematic diagram of a conductivity cell (a) and its impedance representation as an equivalent circuit (b). Capacitances Ci and C2 are at the electrode I solution...

Many fuel specifications require the use of static dissipator additive to improve safety in fuel handling. In such cases the specification defines both minimum and maximum electrical conductivity the minimum level ensures adequate charge relaxation whereas the maximum prevents too high a conductivity, because this can upset some capacitance-type fuel gauges in aircraft (ASTM D-2624, ASTM D-4308, IP 274). The standard test methods (ASTM D-2624, IP 274) employ an immersible conductivity cell and field meter intended for measuring the conductivity of fuel in storage tanks. 

We have already noted above that in analyzing excitable systems one has, more often than not, to deal with a parabolic equation with a nonlinear source. In this section we will concern ourselves with an excitable medium of a different type, where the signals are transmitted in the neuron network not by the local currents but by the nervous impulses traveling along the axons. The propagation speed of the activity wave will, if this transmission mode is possible at all, depend not only on the signal transmission speed but also on the other characteristics of nerve cells such as cell body capacitance, conductance, etc. 

Electrical conductivity cell. Impedance is a measure of the total opposition to the flow of a sinusoidal alternating current in a circuit containing resistance, inductance, and capacitance. Inductance and capacitance together are called the reactive part of the circuit. The changes in impedance that occur in a microbial culture can be measured by placing two metal electrodes into the culture medium and introducing an alternating potential into the circuit. 

Driven by the alternating current, the conductivity cell now has capacitances between the electrodes, across the double layer presented by the solution-electrode interface and between the wires of the connecting cable. Additional resistances and inductances in the wire leads and connections further complicate... 

Measurement Principles. The equipment used for measuring conductance usually consists of a conductivity sensor, a measuring attachment, and a temperature-compensation unit. Conductance values are obtained by establishing either the current flow between a set of electrodes subjected to a constant AC voltage, or the current induced in the secondary coil of a transformer connected to the primary coil by the electrolyte of interest. Capacitive coupled cells have been developed as well, but because of their expensive construction they are no longer of interest (98)-[101]. 

Schematic of a simple immersion conductivity cell for rapid measurements of solution conductivity is shown in Figure 3.16, and schematic of an experimental setup for such measurements is shown in Figure 3.17. The cell consists of two tetragonal platinized (electrochemically covered by fine Pt powder) platinum electrodes positioned in parallel on a distance of a few millimeters. The platinized platinum has a true surface area much higher than the geometrical surface area of the electrode and, therefore, increases the EDL capacitances, and CED +). The setup consists of a digital bridge, a...

C. Capacitance (variable) to balance capacitance as well as resistance of conductance cell. 

Several studies have been conducted regarding the electrostatic properties of interdigitated electrodes, leading to the development of mathematical equations for their capacitance and cell constant values [6,7,8,9,10]. The cell constant c [1/cm] is defined as the proportionality between the measured media resistance and its specific resistivity ... 

For one percent of cells in the suspension, the permittivity increment becomes only A6p 25. The sensitivity of this method for cell detection depends on the 4 power of the cell diameter. In the case of cells with radius R,. 1 pm, permittivity constant = 8.85 1(F F/cm, membrane thickness 8 = 5 nm, membrane permittivity = 6, membrane conductivity for "live" cell Ombr = 10 S/cm, effective capacitance of cell membrane / 5-... 

The ionic conductivity of a solvent is of critical importance in its selection for an electrochemical application. There are a variety of DC and AC methods available for the measurement of ionic conductivity. In the case of ionic liquids, however, the vast majority of data in the literature have been collected by one of two AC techniques the impedance bridge method or the complex impedance method [40]. Both of these methods employ simple two-electrode cells to measure the impedance of the ionic liquid (Z). This impedance arises from resistive (R) and capacitive contributions (C), and can be described by Equation (3.6-1) ... 

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