Specific resistance, electrolytes

Silver sulfide, when pure, conducts electricity like a metal of high specific resistance, yet it has a zero temperature coefficient. This metallic conduction is beheved to result from a few silver ions existing in the divalent state, and thus providing free electrons to transport current. The use of silver sulfide as a soHd electrolyte in batteries has been described (57). 

Table 5. Specific resistance (Q/cm)of aqueous electrolyte containing MEM and 3 molLT1 ZnBr2 (taken from Ref. [68])...

The electrocatalytic activity of MIEC cathodes also depends strongly on the properties of the electrolyte, as shown by Liu and Wu [109], The electrode polarization resistances, RE, or area specific resistance (ASR) measured by the electrochemical... 

Side length of a square electrode Specific resistivity of the electrolyte... 

For micro PS a decrease in the specific resistivity by two or three orders of magnitude is observed if the dry material is exposed to humid air [Ma8] or vapors of polar solvents, e.g. methanol [Be6]. This sensitivity of PS to polar vapors can be used to design PS-based gas sensors, as discussed in Section 10.4. This change in resistivity with pore surface condition becomes dramatic if the pores are filled with an electrolyte. From the strong EL observed under low anodic as well as low cathodic bias in an electrolyte it can be concluded that micro PS shows a conductivity comparable to that of the bulk substrate under wet conditions [Ge8]. Diffusion doping has been found to reduce the PS resistivity by more than five orders of magnitude, without affecting the PL intensity [Ell]. 

The voltage losses in SOFCs are governed by ohmic losses in the cell components. The contribution to ohmic polarization (iR) in a tubular cell" is 45% from cathode, 18% from the anode, 12% from the electrolyte, and 25% from the interconnect, when these components have thickness (mm) of 2.2, 0.1, 0.04 and 0.085, respectively, and specific resistivities (ohm cm) at 1000°C of 0.013, 3 X 10, 10, and 1, respectively. The cathode iR dominates the total ohmic loss despite the higher specific resistivities of the electrolyte and cell interconnection because of the short conduction path through these components and the long current path in the plane of the cathode. 

The separator resistance is usually characterized by cutting small pieces of separators from the finished material and then placing them between two blocking electrodes. The separators are completely saturated with the electrolyte. The resistance (Q) of the separator is measured at a certain frequency by ac impedance techniques. The frequency is chosen so that the separator impedance is equal to the separator resistance. To reduce the measurement error, it is best to do multiple measurements by adding extra layers. The average resistance of single layer is determined from multiple measurements. The specific resistivity, ps cm), of the separator saturated... 

Tortuosity is a long-range property of a porous medium, which qualitatively describes the average pore conductivity of the solid. It is usual to define x by electrical conductivity measurements. With knowledge of the specific resistance of the electrolyte and from a measurement of the sample membrane resistance, thickness, area, and porosity, the membrane tortuosity can be calculated from eq 3. 

Figure 53. Idealized half-cell response of a thin solid electrolyte cell, (a) Cell geometry including working electrodes A and B and reference electrode (s). (b) Equivalent circuit model for the cell in a, where the electrolyte and two electrodes have area-specific resistances and capacitances as indicated, (c) Total cell and half-cell impedance responses, calculated assuming the reference electrode remains equipotential with a planar surface located somewhere in the middle of the active region, halfway between the two working electrodes, as shown in a.

Suppose the solution-filled space between the electrode and the tip of the Luggin capillary is of length L and the current on the electrode is /. The resistance of the electrolyte column is (1/k)(L/A) where K is the specific resistivity of the electrolyte between the tip of the capillary and the electrode, L is the length of the electrolyte column, and A is the cross-sectional area of the gap. The current I is iA. If one can consider the electrode-Luggin distance as a small cylinder of solution (Fig. 7.38), then ... 

The Solution Resistance. The size of this quantity will depend on the concentration of the electrolyte and the dimension of the cell. Consider a column of electrolyte, cylindrical in shape, with a cross-sectional area (A) of 2 cm2 and a length (L) of 1 cm, containing a 0.1 M salt solution. The specific resistance of such a solution will be about 0.01 ohm cm-1. Since the solution resistance R = (1/k)(L/A), R = (l/0.01)(l/2) = 50 ohms. 

The use of solvents that favor association of electrolytes, for example, dimethoxyethane and tetrahydrofuran. This is the reason for their much higher specific resistances than the other solvents containing similar amounts of electrolyte (Table 12.1). 

With this choice of geometiy and conductivities the area specific resistance is ASRo 0.35 ohm cm2 at T = 900°C. The ASRo is quite sensitive to temperature, mainly due to the change of the electrolyte conductivity with temperature [3], Once the ASRo is known, the ohmic losses can be evaluated using Ohm s law ... 

The impedance is dependent on temperature, as can be seen in Figure 4, which shows the area specific resistance (ASR) of a cell as a function of cell temperature for different gas flow rates. For the same cell temperatures, lower ASR was observed for increasing gas flow rates due to the increased gas diffusion near the electrodes that effectively reduced the overpotential resistances [4], Because the anode and cathode are often conductive, the impedance of the cell is dependent largely on the thickness of the electrolyte. Using an anode supported cell structure, a YSZ electrolyte can be used as thin as 10-20 pm or even 1-2 pm [32, 33] as compared to 0.5 mm for a typical electrolyte supported cell [26],... 

For rx = 0.05 cm, and a potential error not to exceed 2 mV, the specific resistance of the electrolyte must be less than 200 fi-cm for currents of 10 /iA. This approximate calculation indicates that the errors in potential due to iR drop will be 200 mV when the specific resistance of the electrolyte is 104 fi-cm. 

The solution iR drop at the DME will also be time-dependent because rt, the drop radius, is a function of time. For this reason a stationary hanging-mercury-drop electrode (HMDE) is to be preferred or the vertical orifice (Smo-ler) DME can be used (see Figure 5.14). The tip of a platinium-wire quasireference electrode can be placed as close as 0.1 drop diameter (about 0.003 cm) because the drop grows in the downward direction.7 This gives nearly complete compensation in an electrolyte with a specific resistance of 15,000 Q-cm for a cell with total resistance of about 105 12. The effect of the polargrams of placing the quasi-reference electrode at different distances from the electrode surface is shown in Figure 6.3. 

Optimum geometry in voltammetry with microelectrodes. In electrolytes of specific resistance of 100-12 cm or less, the geometry is not very critical. The working electrode should be placed between the counter and reference electrodes and is ordinarily an appreciable distance (> 1 cm) from both. At small, nearly spherical electrodes, all points on the surface of the electrode will be essentially equidistant from the counter electrode and the current density will be almost uniform over the surfaces of the microelectrode. 

TABLE 7.6 Solubilities of Tetraaikylammonium Salt Electrolytes and Specific Resistances of the Solutions at 25°C... 

Rc is the specific resistance of the cell (electrolyte + interfacial resistances). 

Conductivity, Electrical Conductometry and Conductometric Titrations. Electrical conductivity is thequality or ability of a substance to transmit electrical energy. If it deals with the conductivity of an electrolyte in solution, it is then called electrolytic conductivity. Conductometry deals with analyses by measuring electrolytic conductivity, based on the fact that ionic substances in many solvents conduct electricity. Conductometric titrations are quantative analysis based on the fact that with the addn of the titrating agent to a soln being titrated, the specific conductivity (reciprocal of specific resistance in mhos) changes at a different rate before and after the end point (Comp with Potentiometric Analysis) Refs 1 )Kirk Othmer 4 (L 949), 325-33 (Conductometry) 2)W.G.Berl, Edit, "Physical Methods... 

The magnitude of this resistance depends on the nature, the dimensions and the temperature of the electrolyte. Its value at a given temperature can be calculated from the specific resistance of the electrolyte q (i. e. from the resistance... 

In this case the losses in voltage due to the resistance of the electrolyte cannot be calculated by the usual method i. e. from the specific resistance of the solution, the spacing of the electrodes and the area of their surfaces this difficulty is caused by the presence of gas bubbles suspended in the solution these bubbles decrease the actiial cross section between the electrodes, i. e. the area covered by the lines of force, and consequently the resistance of the bath rises. The decrease of conductance of the electrolyte caused by suspended bubbles is more marked when the current is higher, the height of electrodes greater (as bubbles accumulate mainly at the upper end of the electrode), the electrolytic cell narrower and the movement of the electrolyte slower. The amount of bubbles in one unit of volume also depends on the viscosity and the temperature of the electrolyte. 

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