EIS Limitations

Although EIS offers many advantages for diagnosing fuel cell properties, clear difficulties exist for applying impedance methods and fitting the data to the model to extract the relevant electrochemical parameters. The limitations of the EIS technique derive from the several requirements required to obtain a valid impedance spectrum, because the accuracy of EIS measurement depends not only on the technical precision of the instrumentation but also on the operating procedures. Theoretically, there are three basic requirements for AC impedance measurements linearity, stability, and causality. 

To know whether or not a system is linear, we may use linear systems theory (LST) [37], LST is a good time-saving theory for testing whether a system is linear. The two basic tests are homogeneity and additivity. 

To achieve a steady-state environment, some actions must be taken before starting each impedance measurement for a PEMFC system. For example, Wagner [23] prepolarized the cell for at least 15 min at the measuring potential. The current densities before and after measurement were taken to prove the stability of the cell during measurement times. Guo et al. [38] operated a fuel cell at 0.6 V for 20 h to reach its steady-state operating current. Pickup et al. [34, 39] ran a H2/02 fuel cell for 30 min at 0.5 V before the impedance measurements were performed. In Gode et al. s work [40], the cell was mn galvanostatically for 1 h prior to the impedance measurement. 

The output of the system must be caused by the perturbing input. However, absence of linearity or stability does not prevent one from obtaining the output. It is necessary to assess the validity of the obtained impedance data, especially when a new system is being studied. 

For a linear system, the phase and amplitude of the impedance relate to each other. Consequently, if we know the frequency dependence of the phase we can calculate the amplitude of the impedance as a function of frequency. Similarly, we can deduce the frequency dependence of the phase from that of the amplitude of the impedance. The calculation can be achieved by the Kramers-Kronig (K-K) transforms. This is a useful check on the validity of a measured impedance spectrum. For information on K-K transforms, see Appendix C. 

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There are ill-defined limits on EI/CI usage, based mostly on these issues of volatility and thermal stability. Sometimes these limits can be extended by preparation of a suitable chemical derivative. For example, polar carboxylic acids generally give either no or only a poor yield of molecular ions, but their conversion into methyl esters affords less polar, more volatile materials that can be examined easily by EL In the absence of an alternative method of ionization, EI/CI can still be used with clever manipulation of chemical derivatization techniques. 

Gas-Fired water heaters are also made more efficient by a variety of designs that increase the recov-ei y efficiency. These can be better flue baffles multiple, smaller-diameter flues submerged combustion chambers and improved combustion chamber geometry. All of these methods increase the heat transfer from the flame and flue gases to the water in the tank. Because natural draft systems rely on the buoyancy of combustion products, there is a limit to the recovery efficiency. If too much heat is removed from the flue gases, the water heater won t vent properly. Another problem, if the flue gases are too cool, is that the water vapor in the combustion products will condense in the venting system. This will lead to corrosion in the chimney and possible safety problems. 

It is of course impossible for products to appear faster than the reactants are used up. Let us apply Eq. (4-25) to the situation at 430 nm, where e = 0 and [ = 1.33eP. If kjk] = 1.33, the reaction will follow first-order (not biexponential) kinetics at both wavelengths, the rate constants being ki at 540 nm and (ei/eP) i at 430 nm. Approximate adherence to Eq. (4-25) suffices within the usual error limits, as seems to be the case here. 

However, this equality does not hold in general. It holds if the factor ei(wu+com )s jn Eq (4.27) is omitted as if it were 1. The integrals over s and t are then trivial and the evolution matrices reduce to S-matrices (4.6). This limit is justified for non-adiabatic collisions [181], which occur at (< / + (OmkK < 1. 

Figure 7.1 Selective excitation of only one multiplet by a selective pulse transforms a 2D experiment into a ID technique. A selective pulse generates the transverse magnetization. The result is a trace of the corresponding 2D spectrum. (Reprinted from Mag. Reson. Chem. 29, H. Kessler ei al., 527, copyright (1991), with permission from John Wiley and Sons Limited, Baffins Lane, Chichester, Sussex P019 lUD, England.)...

CI-MS and EI-MS address the same compound class. Cl is used mainly when the molecule fragments so completely in El mode that no M+" ions are observed or when the problem is only knowledge of the molecular weight of the sample component. In fact, El and Cl are usually both carried out on the same sample, as the two ionisation methods produce complementary information of value for the determination of structure and MW of a compound. The detection limits of Cl tend to be better than El, as the latter technique divides the ion current between molecular and fragment ions. A few ng of sample may be detected. 

Table 6.13 lists the main characteristics of chemical ionisation. The use of Cl overcomes some of the limitations of EI-MS. CI-MS has the advantage of ease of interpretation and of being able to operate at higher input pressures. Cl restricts the fragmentation... 

FD-MS by itself provides only limited chemical information. Lattimer et al. [92] have also compared the analysis of extracted rubber vulcanisates by means of FD-MS and FAB-MS, using the aforementioned EI/FD/FT/FAB ion source. The systems investigated were neoprene/DOPPD, EPDM/(DOP, PBNA, paraffin wax), neoprene-SBR blend/(DOP, DOPPD, TDBHI). Certain compounds were observed by FD but not by FAB (wax, oil, isocyanurate antioxidant TDBHI). In FAB conditions some polymer additives suppress... 

Direct mass analysis of additives in bulk polymers is in principle an attractive methodology, albeit with many restrictions (Table 6.38). Early MS work has focused on direct thermal desorption of additives from the bulk polymer, followed by EI-MS [22,240], CI-MS [22,63] and FI-MS [22]. However, these traditional approaches are limited to polymer additives that are both stable and volatile at the higher temperatures,... 

Flow limitations restrict application of the DFI interface for pSFC-MS coupling. pSFC-DFI-MS with electron-capture negative ionisation (ECNI) has been reported [421], The flow-rate of eluent associated with pSFC (either analytical scale - 4.6 mm i.d. - or microbore scale 1-2 mm, i.d.) renders this technique more compatible with other LC-MS interfaces, notably TSP and PB. There are few reports on workable pSFC-TSP-MS couplings that have solved real analytical problems. Two interfaces have been used for pSFC-EI-MS the moving-belt (MB) [422] and particle-beam (PB) interfaces [408]. pSFC-MB-MS suffers from mechanical complexity of the interface decomposition of thermally labile analytes problems with quantitative transfer of nonvolatile analytes and poor sensitivity (low ng range). The PB interface is mechanically simpler but requires complex optimisation and poor mass transfer to the ion source results in a limited sensitivity. Table 7.39 lists the main characteristics of pSFC-PB-MS. Jedrzejewski... 

LC-MSn, generally requires some background information on the nature of the solutes. Compared with GC-MS with EI/CI, LC-MS does not offer the same identification possibilities, because of the different ionisation mechanisms. Nevertheless, LC-MS has become an invaluable tool to selectively quantify solutes, and to confirm structures or to elucidate structural characteristics. A drawback of LC-MS is that measurable organic compounds are very limited compared with compounds separable by LC alone. LC-MS places considerable constraints... 

Table 7.83 lists the main characteristics of TLC-FAB-MS/LSIMS. A key difference between EI/CI and FAB/LSIMS/LD is the fact that sampling in FAB and LSIMS is from a specified location that corresponds to the impact footprint of the primary particle beam. The natural compatibility of FAB, LSIMS and LD with the direct mass-spectrometric analysis of TLC plates is readily apparent. Most mass-spectrometric measurements are destructive in nature, but FAB and LSIMS are surface-sensitive techniques in which the material actually consumed in the analysis is sputtered only from the top few microns of the sample spot. The underlying bulk is not affected, and can be used for further probing. The major limitation of TLC-FAB depends on the capability of the compounds to produce a good spectrum. 

In the controlled (constant) potential method the procedure starts and continues to work with the limiting current iu but as the ion concentration and hence its i, decreases exponentially with time, the course of the electrolysis slows down quickly and its completion lags behind therefore, one often prefers the application of a constant current. Suppose that we want to oxidize Fe(II) we consider Fig. 3.78 and apply across a Pt electrode (WE) and an auxiliary electrode (AE) an anodic current, -1, of nearly the half-wave current this means that the anodic potential (vs. an RE) starts at nearly the half-wave potential, Ei, of Fe(II) - Fe(III) (= 0.770 V), but increases with time, while the anodic wave height diminishes linearly and halfway to completion the electrolysis falls below - / after that moment the potential will suddenly increase until it attains the decomposition potential (nearly 2.4 V) of H20 -> 02. The way to prevent this from happening is to add previously a small amount of a so-called redox buffer, i.e., a reversible oxidant such as Ce(IV) with a standard... 

This homogeneity value will become positive when the null hypothesis is not rejected by Fisher s E-test (F < Ei a)Vl)V2) and will be closer to 1 the more homogeneous the material is. If inhomogeneity is statistically proved by the test statistic F > Fi a>VuV2, the homogeneity value becomes negative. In the limiting case F = hom(A) becomes zero. 

In a self-reproducing, catalytic hypercycle (second order, because of its double function of protein and RNA synthesis) the polynucleotides Ni contained not only the information necessary for their own autocatalytic self-replication but also that required for the synthesis of the proteins Ei. The hypercycle is closed only when the last enzyme in the cycle catalyses the formation of the first polynucleotide. Hypercycles can be described mathematically by a system of non-linear differential equations. In spite of all its scientific elegance and general acceptance (with certain limitations), the hypercycle does not seem to be relevant for the question of the origin of life, since there is no answer to the question how did the first hypercycle emerge in the first place (Lahav, 1999). 

The cylindrical resonant cavity which operates in the TE0n mode is another very useful design. The Hi and Ei field lines of force for this cavity are shown in Fig. 9. One commercially available cavity of this type has a bottom which can be screwed in and out, thus changing the resonant microwave frequency over a limited range. 

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