Product resolution criteria

Figure 5.32 Initial phase selection diagrams for three possible ternary mobile phase systems applied to the separation of five diphenyl amines. Top (Initial) retention lines. Bottom (initial) response line. Criterion normalized resolution product (r eqn.4.19 drawn line) Also shown is the response surface using the product resolution criterion (IIeqn.4.18 dashed line). The required chromatograms are shown in figure 5.33 (a, b and c). Figure taken from ref. [576]. Reprinted with permission.

The non-linearity of the retention lines is apparent from this figure. The response lines have been drawn for two different criteria the normalized resolution product r (drawn line eqn.4.19) and the product resolution function FIRS (dashed line eqn.4.18). It is seen that the product resolution criterion would in fact have guided us to a completely different optimum at a composition of 24.1% methanol and 25.2% THF. The chromatogram that we would have obtained at this composition is shown in figure 5.33h. Clearly, this chromatogram is less attractive than the one of figure 5.33g. Obviously, the normalized resolution product is to be preferred to the resolution product itself (see the discussion in section 4.3.2). 

Structure determination of luciferin. Once a luciferin is obtained in a sufficient purity, the determination of luciferin structure should be attempted most of the important properties of luciferin are usually already obtained during the course of purification as a necessity. The structural study is considerably more straightforward than the extraction and purification, due to the availability of advanced methods, such as high-resolution mass spectrometry and various NMR techniques. If help or collaboration is needed in structure determination, the attractiveness of a luciferin will make it easy to find a good collaborator. However, the purified luciferin is usually an extremely precious material considering the effort spent in preparing it. To avoid accidental loss of the purified material, the chosen collaborator must have solid knowledge and experience in structure determination a criterion to be considered is that the person has successfully done the structure determination of at least one new natural product. 

Another method (ASTM D-4808) covers the determination of the hydrogen content of petroleum products, including vacuum residua, using a continuous-wave, low-resolution nuclear magnetic resonance spectrometer. Again, sample solubility is a criterion that will not apply to coal but will apply to coal extracts. More recent work has shown that proton magnetic resonance can be applied to solid samples and has opened a new era in coal analysis by this technique (de la Rosa et al., 1993 Jurkiewicz et al 1993). 

Because both Rs and Rs are proportional to VN, the normalized product of Rs values is equal to that of the S values, and both are independent of the number of plates. The normalized resolution product (r) will vary from zero, in the case where one or more pairs of peaks show no resolution, to one, if the resolution is equal for all the pairs of peaks in the chromatogram. Therefore, in choosing r as the optimization criterion the aim is to achieve an equal distribution of the peaks over the chromatogram. 

Nevertheless, the use of eqn.(4.32) may result in a slower optimization process than if a simple sum or product criterion were used. It is also unclear at the outset how the process would respond to chromatograms with the same value for Cp but widely different values f or C. In other words, the criterion cannot differentiate between a bad resol ution in a short time and a good resolution in a long time. 

In section 4.3.2 we have seen that the normalized resolution product criterion r aims at achieving a chromatogram in which all peaks appear at constant resolution intervals from the first one. If r is used instead of r, then the regular intervals start at an imaginary peak at t=t0. A chromatogram for which r = 1 is one of a series for which the constant intervals can be found. Once the absolute value of S, the number of peaks and the plate number are known, the chromatogram is defined unambiguously. 

If a product of peak-valley ratios is used as the optimization criterion, then two values would need to be used for every peak, one describing its resolution from the preceding peak in the chromatogram and the other one describing its resolution from the following peak. Because a product criterion is used, the weighting factors (g) will appear as powers in the product. If we assume the weighting factors to be positive, we may write... 

Figure 5.2 (a) Pseudo-isometric three-dimensional response and (b) iso-response contour plot for a two-parameter optimization problem. Parameters (in triangular representation) quaternary mobile phase composition. Criterion normalized resolution product (see section 4.3.2). O, is the location of the optimum. For further details see section 5.5.2. Figure taken from ref. [502]. Reprinted with permission. 

For the important case of the optimization of the mobile phase composition in reversed phase LC (RPLC), a typical two-dimensional response surface tends to be much less rugged, especially if the number of sample components is relatively small (n<10). A typical example is shown in figure 5.5. The selection of the normalized resolution product (r, eqn.4.19) as the criterion has also contributed to the smoother appearance of figure 5.5 relative to figure 5.1. Note that the criterion r has been recommended in chapter 4 for optimization processes in which the dimensions of the column are to be optimized after completion of the procedure (table 4.11). Therefore, the grid search approach is more appropriate for this kind of optimization than for optimization processes on the final analytical column. 

One method which can be used to establish the optimum conditions for the separation of a complex mixture (i.e., not only a pair) of compounds consists in searching for the maximum of a function denoted the chromatogram quality criterion. The evaluation of separation selectivity can be conducted with the aid of different criteria of chromatogram quality such as the sum of resolution, E 7 [6], the sum of separation factors, E 5 [2], and other sums and products of elementary criteria, selected examples of which are the resolution product, n Rs [7],... 

The individual properties studied were the selectivities, separation factors, valley-to-peak ratios and overlapped fractions. The two first criteria only consider the position of the chromatographic peaks, and the latter two their position and shape. The three latter functions may vary from 0 to 1. The combined function of resolution, r, is maximized to obtain the optimum mobile phase, and its proximity to unity indicates the quality of the separation. Since the product of all observed resolutions is used, coelution will effectively cause the criterion to drop to zero. Extremely long chromatograms with a number of unnecessarily large resolution values will also be represented by low criterion values. 

Speed is the most common HPLC optimization criterion. A method is considered optimized if it allows the separation of all relevant components with sufficient resolution in the shortest time possible. Such speed increase only translates into an economical benefit for the laboratory if it actually enables productivity increase of the respective lab. Labs with particularly high sample load are typical beneficiaries of this, but so are all labs that directly profit from knowing analytical results within hours or even minutes after receiving the samples in order to react on it. Productivity increase often requires optimization of the entire lab workflow which will include more than the analytical separation process. It is rather common that samples do not arrive in a ready to inject format and thus require sample preparation... 

Typically, resolution diagrams in MLC are complex, with several local maxima, frequently denoting interaction between factors. For this reason, reliable optimal conditions require considering all factors simultaneously, by applying an interpretive optimization strategy (i.e., based on the description of the retention behavior and peak shape of solutes). In this task, the product of free peak areas or purities has proved to be the best optimization criterion. An interactive computer program is available to obtain the best separation conditions in... 

The acceptance criterion for the resolution of GSI C-05 is that the plant designer shall select either the historic, conservative approach for predictions of decay heat employing the function described in ANS 5.0 (Proposed) or the recent, more realistic approach using the fission product decay heat function identified in ANS 5.1, in order to meet the requirements of 10 CFR 50.46. 

One of the most detailed criteria for the confirmation of contaminants comes from the European Commission Decision 2002/657/EC. This guideline applies to live animals and animal products [35], and confirmation is based on the accumulation of identification points (IPs). Any molecular spectrometric technique or combination of techniques can be used to obtain the minimum number of IPs necessary for the reliable identification of a compound (three or four IPs, depending on whether the compound is allowed or is banned). The number of IPs reached depends on the approach used, differentiating between MS, tandem MS, low-resolution (LR) and high resolution instruments. To qualify for the IPs reached, at least one ion ratio must be measured, and it must agree within specified tolerances. Moreover, the retention time (or relative retention time) of the analyte in the sample extract should correspond to that of the calibration solution, with a tolerance of 2.5% in LC—MS procedures. This criterion is a valuable tool for a rapid and easy comparison of MS techniques from the confirmation point of view. 

Instead of requiring the full behavioral sequence from flight to egg production to be the bioassay criterion, it maybe expedient to bypass, or short circuit, some of the steps in the process and focus upon critical steps, or indicator behaviors. This may result in little loss in resolution and great reductions in time and effort. Whenever such indicator behaviors are used, it is important to establish that the behavior is consistently displayed in the overall behavioral investigated, and not displayed in alternative behaviors. Additionally, results using indicator behaviors should be confirmed with bioassays using the complete behavioral sequence. 

Full spectrum search methods use, as the name implies, a fully digitized version of the spectrum. When used in this form, the spectra are usually stored at reduced resolution because at full resolution the storage overhead and the time required for processing become excessive. The matching of the unknown spectrum is usually based on a correlation criterion, such as the Dot Product between the library spectrum and the unknown. In practice, the only real advantage of this method is the availability of a digitized spectrum for display purposes. 

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