Problems with reliable measurement

It is now clear that electrochemical measurements can often have significant advantages over the classical spectroscopic approaches. Amperometry can be more specific therefore, lower detection limits are often feasible. Because electrochemical detectors do not require optical carriers, they can be much less expensive than UV absorption or fluorescence detectors. This is especially true when one considers that electrochemical detectors are inherently tunable without the need for such things as monochrometers or filters. On the other hand, there can be significant problems with reliability, and, more often than not, there is a lack of acceptance by chemists weaned on Beer s law. Amperometric methods in biochemistry are just beginning to be commercialized, and it is now almost certain that they will come into widespread use. 

The terms batch equilibration [653], pH drift method [654], addition method [552], solid addition method [655], powder addition method (cited in [656] after [654]), potentiometric titration [234] ( sic —in the present book, the term potentiometric titration is reserved for a different method, described in Section 2.5), and salt addition [573] ( sic —in the present book, the term salt addition is reserved for a different method, described later in this section) refer to the same method, which is now described. A series of solutions of different pHs is prepared and their pHs are recorded. Then, the powder is added and the final pH is recorded. The addition of a solid induces a shift in the pH in the direction of the PZC. The pH at which the addition of powder does not induce a pH shift is taken to be the PZC. Alternatively, the PZC is determined as the plateau in the pHfln, (pH ,.,., .j) curve. The method assumes that the powder is absolutely pure (free of acid, base, or any other surface-active substance), which is seldom the case. Even with very pure powders, the above method is not recommended for materials that have a PZC at a nearly neutral pH. Namely, the method requires accurate values of the initial pH, which is the pH of an unbuffered solution. The display of a pH meter in unbuffered solutions in the nearly neutral pH range is very unstable, and the readings are not particularly reliable. The problem with pH measurements of solutions is less significant at strongly acidic or strongly basic pHs (see Section 1.10.3). The above method (under different names) became quite popular, and the results are referred to as pH in the Method columns in the tables in Chapter 3. The experimental conditions in the above method (solid-to-liquid ratio, time of equilibration, and nature and concentration of electrolyte) can vary, but little attention has been paid to the possible effects of the experimental conditions on the apparent PZC. The plateau in the pH, , (pH, ,, ) curve for apatite shifted by 2 pH units as the solid-to-liquid ratio increased from 1 500 to 1 100 [653]. Thus, the apparent PZC is a function of the solid-to-liquid ratio. 

The problems with the pH measurements discussed in Section 4.3.1 make the determination of PZC by titration much more difficult than at low ionic strengths. Special procedures related to pH measurements at high ionic strengths are seldom addressed in publications reporting PZCs obtained by titration. Very likely, most titration results available in the literature were obtained by means of standard procedures recommended only for low ionic strengths. Other standard experimental methods used in studies of pH-dependent surface charging must also be combined with a reliable pH measurement, but potentiometric titration is more sensitive to problems with pH measurements than are other methods. 

Detailed Evaluation Detailed evaluation is performed by measuring the capture efficiency, either by using the actual contaminant or by using a tracer gas. (In principle, it is possible to use particles as tracers, but gases are usually used as tracers.) The most reliable evaluation is to use the process-generated contaminant, since there are always problems with a tracer, due to the difficulties of feeding the tracer to the source in the same way and in a similar amount as the generated contaminant. ... 

The concentration of the transferred ion in organic solution inside the pore can become much higher than its concentration in the bulk aqueous phase [15]. (This is likely to happen if r <5c d.) In this case, the transferred ion may react with an oppositely charged ion from the supporting electrolyte to form a precipitate that can plug the microhole. This may be one of the reasons why steady-state measurements at the microhole-supported ITIES are typically not very accurate and reproducible [16]. Another problem with microhole voltammetry is that the exact location of the interface within the hole is unknown. The uncertainty of and 4, values affects the reliability of the evaluation of the formal transfer potential from Eq. (5). The latter value is essential for the quantitative analysis of IT kinetics [17]. Because of the above problems no quantitative kinetic measurements employing microhole ITIES have been reported to date and the theory for kinetically controlled CT reactions has yet to be developed. 

With this modification the conditioning of matrix A is significantly improved and cond AR) gives a more reliable measure of the ill-conditioning of the parameter estimation problem. This modification has been implemented in all computer programs provided with this book. 

Modem LP solvers can solve very large LPs very quickly and reliably on a PC or workstation. LP size is measured by several parameters (1) the number of variables n, (2) the number of constraints m, and (3) the number of nonzero entries nz in the constraint matrix A. The best measure is the number of nonzero elements nz because it directly determines the required storage and has a greater effect on computation time than n or m. For almost all LPs encountered in practice, nz is much less than mn, because each constraint involves only a few of the variables jc. The problem density 100(nz/mn) is usually less than 1%, and it almost always decreases as m and n increase. Problems with small densities are called sparse, and real world LPs are always sparse. Roughly speaking, a problem with under 1000 nonzeros is small, between 1000 and 50,000 is medium-size, and over 50,000 is large. A small problem probably has m and n in the hundreds, a medium-size problem in the low to mid thousands, and a large problem above 10,000. 

Most problems with solid fat content determination arise from inconsistencies in sample preparation. As noted above, the solids content is dependent on the temperature history of the sample, so deviations from the tempering protocols can lead to inaccuracies. The time required to measure a sample is not expected to lead to extensive crystallization or melting, but care should be taken to start the measurement as soon as possible after the oil is removed from the tempering block. Several instruments can be fitted with a thermostatic control for the sample in the coil, and this should be used if it is reliable. It is recommended that the NMR tubes be capped, particularly for the long tempering times required for stabilizing fats. 

When voltammetry measurements are made in nonaqueous solvents, the problems of an adequate reference electrode are compounded. Until the 1960s the most common reference electrode was the mercury pool, because of its convenience rather than because of its reliability. With the advent of sophisticated electronic voltammetric instrumentation, more reliable reference electrodes have been possible, especially if a three-electrode system is used. Thus, variation of the potential of the counter electrode is not a problem if a second non-current-canying reference electrode is used to monitor the potential of the sensing electrode. If three-eleetrode instrumentation is used, any of the conventional reference electrodes common to potentiometry may be used satisfactorily. Our own preference is a silver chloride electrode connected to the sample solution by an appropriate noninterfering salt bridge. The one problem with this system is that it introduces a junction potential between the two solvent systems that may be quite large. However, such a reference system is reproducible and should ensure that two groups of workers can obtain the same results. 

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