Linear Nernstian systems

In this chapter, only the response of a reversible system will be described. Linear sweep ac voltammetry of a Nernstian system is considered. 

The cyclic voltammetric currents were normally not the main source of attention but rather the semi-integral Ij of the current was calculated from this the semi-differential or square root of time deconvolution dlj/dt. This dlj/dE were used for the clearest displays of results. The main difference in application of the latter pair depends on whether a potential ramp linear with time is applied at die working electrode surface i.e. hardware compensated at tte potentiostat if necessary for resistance between working counter electrodes. In this case using the linearly varying potential as an axis dlj/dt dl/dE are similar in shape either provides a suitable display. If uncompensated resistance remains then in Nernstian systems I is a function of the appropriate E (E ) suitable compensation via -i.R can be sqiplied post csqiture... 

In order to make the comparison between Ep and Ep/2 measurements summarized in Table 9, the two quantities were measured in separate experiments. A recent study by Eliason and Parker has shown that this is not necessary [57]. Analysis of theoretical LSV waves by second-order linear regression showed that data in the region of Ep are very nearly parabolic. The data in Fig. 9 are for the LSV wave for Nernstian charge transfer. The circles are theoretical data and the solid line is that described by a second-order polynomial equation. It was concluded that no detectable error will be invoked in the measurement of LSV Ep and Ip by the assumption that the data fit the equation for a parabola as long as the data is restricted to about 10 mV on either side of the maximum. This was verified by experimental measurements on both a Nernstian and a kinetic system. 

In this section, we discuss in detail how the selection of various experimental parameters affects each of these conditions. One of the first studies on EIS measurements in MXC applications by Strik et al. [29] covers some of these conditions very well, but we provide an expanded explanation here. While all these conditions are especially difficult to fulfill in a typical electrochemical cell, the conditions used in MXCs further exacerbate the problem. For example, it is known that polarization curves for microbial anodes exhibit nonlinear, Nernstian responses [30]. Thus, there are regions in the polarization curve where the system may not behave linearly even when small amplitudes are applied. The irreversibility of the enzymatic responses also leads to regions where finiteness is not met (Fig. 8.6). These cases would run also into difficulties in terms of the signal-to-noise ratio when small amplitudes are applied at potentials on the saturation region of the polarization curve. Similarly, as MXCs are biological reactors and can have changes in microbial responses due to small perturbations outside the conttol of researchers, conditions of both stability and causality are difficult to fulfill. 

In the case of clenbuterol, two sensors have been developed based on MIPs. The first report was on a flow chemiluminescence sensor based on the enrichment of nanogram amounts of clenbuterol by an MIP (methacrylic acid functional monomer, ethylene glycol dimethacrylate crosslinker), and the chemiluminescence reaction between potassium permanganate and formaldehyde in polyphosphate enhanced by clenbuterol. The system revealed linear response in the range of 1.0 x 1g/mL to 5.0 X 10 g/mL with a detection limit of 3.0 X 10 ° g/mL [434]. The other report covered an MIP-based poten-tiometric sensor based on the same MIP, which was reported to exhibit a Nernstian response in the rather wider, and yet higher range of 1.0 x 10" M to 1.0 X 10 M with an LOD of 7.0 X 10- M [377]. 

---