Logarithmic response

The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can cause large errors. (Recall that an... 

Controlled potential methods have been successfully applied to ion-selective electrodes. The term voltammetric ion-selective electrode (VISE) was suggested by Cammann [60], Senda and coworkers called electrodes placed under constant potential conditions amperometric ion-selective electrodes (AISE) [61, 62], Similarly to controlled current methods potentiostatic techniques help to overcome two major drawbacks of classic potentiometry. First, ISEs have a logarithmic response function, which makes them less sensitive to the small change in activity of the detected analyte. Second, an increased charge of the detected ions leads to the reduction of the response slope and, therefore, to the loss of sensitivity, especially in the case of large polyionic molecules. Due to the underlying response mechanism voltammetric ISEs yield a linear response function that is not as sensitive to the charge of the ion. 

Robins, I., Ross, J.F. and Shaw, J.E.A., The logarithmic response of palladium-gate metal-insulator-silicon field-effect transistors to hydrogen, Journal of Applied Physics, 60(2), 843, 1986. 

For this solution to be valid, the data must be collected for a sufficient time to establish the presence of a logarithmic response in the tail. 

The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can thus cause large errors. (Recall that an uncertainty of 1 mV corresponds to a relative error of 4% in the concentration of a monovalent ion.) Since potential measurements are seldom better than 0.1 mV uncertainty, best measurements of monovalent ions are limited to about 0.4% relative concentration error. In many practical situations, the error is significantly larger. The main source of error in potentio-metric measurements is actually not the ISE, but rather changes in the reference electrode junction potential, namely, the potential difference generated between the reference electrolyte and sample solution. The junction potential is caused by an unequal distribution of anions and cations across the boundary between two dissimilar electrolyte solutions (which results in ion movement at different rates). When the two solutions differ only in the electrolyte concentration, such liquid junction potential is proportional to the difference in transference numbers of the positive and negative ions and to the log of the ratio of the ions on both sides of the junction ... 

Accordingly, the electron gas develops a singular logarithmic response... 

One should not see the potentiometric mode as an alternative but as a complement to the amperometric mode. The potentiometric mode offers the possibility of performing measurements on non-redox active species, e.g., not detectable amperometrically in aqueous solutions. Another advantage is the increased selectivity of the potentiometric response compared to the Faradaic response. The logarithmic response is also useful when the species of interest is in low concentrations. Since the tip is passive, only substrate generation-tip detection experiments are possible. However, the tip does not alter the concentration profile of the chemically or electrochemically generated species. The potentiometric micropipette tips have very small dimensions, typically 1 /xm or less, and the shielding is minimal. 

This logarithmic response means that one will only obtain rate increments that are useful in synthesis by going to quite high pressures (see Fig. 7.1). The pressure range 5-20 kbar is normally used for organic synthesis. However, eqns... 

A Gran plot converts a logarithmic response to a linear plot. 

Amplifiers with a logarithmic response have use in liquid scintillation counting for compression of the higher energy part of the jS-spectrum. 

Note that brightness is a subjective (mental) response to a visual stimulus. Brightness, for points of light against a dark background, is approximately a logarithmic response to light intensity. 

The magnetoelastic sensor has been used to detect Mycobacterium tuberculosis (M. TB), the cause of tuberculosis (TB) and the world s second most common cause of morbidity and mortahty from infectious disease. The sensor was immersed in a culture medium of M. TB. The growth and reproduction process produced changes in viscosity and density of the culture medium and, consequently, altered the resonant frequency of the sensor. The device showed logarithmic response proportional to the M. TB concentration in the range 10 -10 cells/mL (Pang et al. 2008). 

Detectors with Enhanced Gas Sensitivity. One frequent complaint regarding the use of potentiometric gas and ion-selective membrane electrodes for analytical purposes is lack of precision owing to the logarithmic response of such devices. Thus, uncertainty in measured potentials of ilmV will result in i-4% precision for sensors with slopes of 5 9 mV/decade and —8% for those devices based on response to divalent ions (e.g., the above sulfite and SO2 gas sensors). One novel approach suggested in the literature for enhancing response slopes of potentiometric sensors is to use several membrane electrode cells in series (28, 29). This arrangement results in response... 

Chemresistors based on a hexafluoroisopropanol-substituted polythiophene (HFIP-PT)/SWCNT hybrid system were shown to be highly sensitive and selective for DMMP. The fast and reproducible response was observed for HFIP-PT/SWCNT hybrid sensor, which gave an 8% conductance change upon exposure to even very low (0.6 ppm) concentration of DMMP. Moreover, the sensor displays a linear logarithmic response to analyte concentration over two decades of concentration (Figure 12.26). 

If the amplitude of the amplifier output is normalized to unity, then this signal represents the sample absorption in per cent. If, furthermore, the amplifier has a logarithmic response (so-called balanced detectors are such devices), then the signal output is ln(/ //o), or log(/i//o), and thus is directly proportional to the absorbance A (see Equations (6.1) and (6.2)). Thus, an unknown absorber particle density N can easily be derived from the signal, provided the absorption cross-section a is known. Alternatively, one can calculate the absorption cross-section if the absorber particle density is predetermined. 

Thus electrochemical transducers dominate in the construction of microbial biosensors. Amperometric sensors offer greater sensitivity, since their response is linear as opposed to the logarithmic response of potentiometric sensors. This was described in detail by Mascini and Memoli [260] who compared microbial sensors based on amperometric and potentiometric electrodes with the yeast Saccharomyces for the determination of glucose. 

Given the logarithmic response of the probe, its best precision is obtained when the partial pressure to be measured is equal to the reference pressure. The oxygen pressure used as a reference in the electrochemical cell can be fixed, in various ways but two reference media are utilised in practice air and metal-oxide couples (19) ... 

These sensitivities provide numerical measures for the contribution of the th reaction when 9j is associated with the parameter of the corresponding rate expression, namely, with the rate constant kj for the isothermal case or with the preexponential factor Aj for a nonisothermal model. It is more convenient to deal with nondimensional, or logarithmic, measures of sensitivities (Bukhman et al, 1969 Frank, 1978 Gardiner, 1977). Thus, the rth logarithmic response sensitivity of rate constant kj is given by... 

The set of logarithmic response sensitivities for all rate constants is referred to as a sensitivity spectrum. The highest absolute values of the sensitivities in the spectrum pinpoint the most important reactions in the kinetic scheme for determining the chosen set of responses. The lowest absolute values of sensitivities, however, do not necessarily identify unimportant reactions. Let... 

---