Cell internal resistance determination

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

If the potential of the Daniell cell is to be determined accurately, we have already seen that the measurement has to be made at zero current. In order to ensure zero current, the internal resistance of the voltmeter shown in Figure 3.1 must be vast, as discussed in the previous chapter. The voltmeter operates in much the same way as a switch or circuit breaker does reaction (in this case, cell discharge) would occur but for the incorporation of the voltmeter in the circuit. 

The thermal energy generated or absorbed by an electrochemical cell is determined first by the thermodynamic parameters of the cell reaction, and second by the overvoltages and efficiencies of the electrode processes and by the internal resistance of the cell system. While the former are generally relatively simple functions of the state of charge and temperature, the latter are dependent on many variables, including the cell history. 

Many putative receptors for anti-dsDNA on the membrane of various cell types have been noted. Some workers found a 30-kDa protein involved in the binding and internalization of [3H]DNA via receptor-mediated endocytosis (B12, B13). Other possible receptors include nucleosomes on human leukocytes (R8), Fc receptors on human T cells (A6), DNA on mouse and human mononuclear cells (06), a 94-kDa protein on several cells lines (J2), DNase-resistant target on human fibroblasts and PK 15 cells (K9), membrane determinant precisely resembling DNA in murine renal tubular cells (Zl), Hp8 on human and murine tubular cells (Z2), ribosomal P protein on rat and human glomerular mesangial cells (S30, S31), brush border myosin 110 kDa on rat hepatoma cells, and a diverse set of membrane proteins on a series of human tumor cell lines (R3). 

According to Appendix 1 the cell voltage is determined by the electrochemical potentials of the electrons at the terminal leads under the above assumptions. Their difference is proportional to the difference of the jue - values at x = 0 and x = L up to constant resistance contributions stemming from processes in or at the electrode. This internal jue difference is given by (cf. Eq. (71))... 

The conductivity cell is modified from a conventional type. It is made of borosilicate glass, which resists the attack of anhydrous chlorine and bromine trifluorides, and is equipped with two smooth platinum electrodes to minimize electrode corrosive effects. These electrodes are approximately 12x25 mm. in size, held 1.5 mm. apart with borosilicate glass spacers. The arrangement of electrodes and leads is shown in Figure 1. An internal thermocouple well leads from the top of the cell to a point near the electrodes and contains a copper constantan thermocouple. The cell constant is determined by measuring the cell resistance... 

Figure 22-1 An electrolytic cell for determining (a) Current = 0.00 mA. (b) Schematic of cell in (a) with internal resistance of cell represented by a 15.0 n resistor and fiappued increased to give a current of 2.00 mA.

High-energy batteries with a lithium anode are classified < with regard to the type of their ionic conductor. This can be a fast solid Li -ion conductor, a fused lithium salt, a lithium-potassium-salt eutectic mixture, or a non-aqueous lithium salt solution. If inorganic solvents are used, e.g. SOj, SOClj, SOjClj, the solvent itself is the depolarizer and then a solid catalytic electrode is needed, e.g. carbon. The type of ionic conductor determines the internal resistance of the cell and the working temperature range and hence the possible technical applications. 

The internal resistance of the cell is temperature-independent, = 0. From Eqs. (5.60) and (5.61) functions are found, whose sign determines the cell stability for these two limiting cases ... 

The operation of the cell is associated with various irreversibilities and leads to various potential losses. In the case of electrodes the total resistance comprises of the internal resistance, contact resistance, activation polarization resistance, and concentration polarization resistance. Internal resistance refers to the resistance for electron transport, which is usually determined by the electronic conductivity and the thickness of the electrode structure. Contact resistance refers to the poor contact between the electrode and the electrolyte structure. All resistive losses are functions of local current density. However, one can minimize the overpotential losses by appropriate choice of electrode material and controlling the micro-structural properties during manufacturing process. 

R. Kohlrausch improved the torsion electrometer of Dellmann and used it to show 2 that the electromotive forces of Grove and Daniell cells, and of a cell of silver in a solution of sodium chloride and potassium cyanide and copper in copper sulphate solution, agreed with the electrometric potential differences of the open cells. Kohlrausch proved Ohm s law for the internal resistance of a Daniell cell. He then determined the single potential differences in the Daniell cell. With a condenser of zinc and copper plates he found the potential difference 4-17 (electrometer reading). To find the contact potential of the zinc and copper sulphate solutions, he spread these over filter paper on glass plates and connected these with the corresponding metal plates. He found hardly any potential difference. The two poles of the Daniell cell gave a potential difference =4 51. 

This impedance was acquired using an internal resistance of commercial measuring equipment of 10 2. As the cell impedance was less than 0.1 Q, a lower sense resistor was desirable. The authors used and calibrated a shortening bar as a 0.1245 2 sensing resistor, determined its characteristics, and subtracted its impedance to obtain the pure impedance of the battery. The result is shown in Fig. 16.4 (right). In these measurements long commercial cables with crocodile clips were replaced by short cables bolted to the cell terminals. It is also recommended to use coaxial cables or twisted cable pairs in which currents flow in opposite directions, decreasing the inductive effect [693, 694]. 

In order to have a more accurate prediction of the thermal behavior of the battery cell in any environmental condition, the proposed thermal model should be extended to become an electrothermal model. This approach is needed for an accurate determination of the internal resistance and for the estimation of the state of charge (see Figure 11.13). Based on this approach, there will continuously be an interaction between the electrical and the thermal models. 

The internal resistance of the fuel cell is influenced by the thickness of the electrolyte fUm between the electrodes. Other factors that are important for conductivity include the position of the diaphragms that determine the distance between the electrodes, the concentration of the electrolyte and the average length of the electrolyte paths. The resistances of the various diaphragms to electrolyte solutions are listed in Table 4.2. The resistance of the electrolyte decreases with increasing temperature. 

Figure 6.2 Typical polarization curves that can be recorded from a BES. OCV, open cell voltage OCV, open cell voltage used to determine current-dependent internal resistance. Sections A, activation overpotentials are the dominant voltage loss in this region B, current-dependent voltage loss...

The current interrupt method can be used to determine the ohmic resistance of a fuel cell. A resistor is used to close the circuit, which enables the cell to give a stable potential and current output. Subsequently, the external resistor is removed and the instantaneous potential change is used for the calculation of the ohmic resistance by means of Ra = A V/I [36]. EIS is a more sophisticated technique to characterize BES [40]. It entails applying an alternating potential with set amplitude on a set cell potential. The results are analyzed by fitting the data to an equivalent circuit with the potentiostat software and internal resistance is determined from a Nyquist plot. However, the use of EIS has not been widely applied in BES research and therefore no consensus yet exists on frequency range, amplitude, and interpretation of the data with the equivalent circuit [10, 12, 40, 73-75]. 

The zinc and manganese dioxide electrode reaction kinetics in alkaline electrolyte are faster than the same reactions in the Leclanche and zinc chloride electrolyte. These differences in reaction rate determine the differences in cell performance. The alkaline cell delivers superior capacity, higher-rate discharge capability, lower internal resistance, lower leakage, and longer shelf life. Alkaline cells have excellent high-rate... 

---