Valley-to-peak ratio

TABLE 21.4 Peak Resolution Parameters Valley-to-Peak Ratios, v, and Peak Separation Parameters, P, for Batch 52 Gel... 

The final step in the process of standardizing our columns was to try and maintain the high quality of columns from batch to batch of gel from the manufacturer. This was done by following the basic procedures outlined earlier for the initial column evaluation with two exceptions. First, we did not continue to use the valley-to-peak ratios or the peak separation parameters. We decided that the D20 values told us enough information. The second modification that we made was to address the issue of discontinuities in the gel pore sizes (18,19). To do this, we selected six different polyethylenes made via five different production processes. These samples are run every time we do an evaluation to look for breaks or discontinuities that might indicate the presence of a gel mismatch. Because the resins were made by several different processes, the presence of a discontinuity in several of these samples would be a strong indication of a problem. Table 21.5 shows the results for several column evaluations that have been performed on different batches of gel over a 10-year period. Table 21.5 shows how the columns made by Polymer Laboratories have improved continuously over this time period. Figure 21.2 shows an example of a discontinuity that was identified in one particular evaluation. These were not accepted and the manufacturer quickly fixed the problem. 

The quality of the eventually selected separation depends on the appropriateness of the criterion and it is therefore important to select the criterion well. This selection consists of several steps. The first is to select what is called an elemental criterion. which describes the separation quality of two substances, the second is to derive from the elemental criterion value a global criterion. There are two types of elemental criteria. They have been called p- and. v-criteria. The p criteria compare in some way the height of the peaks with the valley in between them. Several variants have been proposed. Two of them are shown in Fig. 6.3 (the valley-to-peak ratio F, . = 1 — v/hi and the... 

Fig. 6... Two elemental p criteria (a) peak-valley ratio. P = f/g (b) valley-to-peak ratio, />,.= — where represents either /ii or /ij depending on the substance of main interest.

Examples of optimizations in HPLC using the simplex approach can be found in [28,84]. In [28] the mobile phase composition for the chiral separation of (6/ )- and (65)-leucovorin on a BSA (bovine serum albumin) stationary phase is optimized by means of a variable-size simplex. Three factors were examined, the pH of the mobile phase buffer, the ionic strength of the buffer and the percentage of 1-propanol in the mobile phase. Table 6.19 shows the experimental origin, the initial step size and the acceptable limits for the factors. The criterion optimized is the valley-to-peak ratio (Section 6.2). The points selected and the results are pre.sented in Table 6.20 and... 

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. 

Two positional-shape criteria have been developed [1 l],the valley-to-peak ratio ... 

The simulated chromatograms for 10% 2-propanol and three different concentrations of surfactant are given in Fig. 8.17, The disagreement among the positional and positional-shape criteria is due to the retention behavior of peaks 13-15. As the concentration of surfactant decreased from 0.12 to 0.10 M (Fig. 8.17a and 8.17b), the valley-to-peak ratio improved, and the overlapped fractions decreased to a lesser extent. The positional resolution however became worse. A further reduction in the concentration of CTAB decreased both the positional and positional-shape resolution (see peaks 9-10 and 13-15). 

CTAB-2-propanol mobile phases, according to different criteria (a) separation factor, (b) valley-to-peak ratio, and (c) overlapped fi-actions. Reprinted from Ref. 11 with permission of Elsevier. 

Remarkably, typical I(V) characteristics of an Au-(nitroaniline OPE)-Au device at 60 K are shown in Figure 4.13. Positive bias corresponds to hole injection from the chemisorbed thiol-Au contact and electron injection from the evaporated contact. Unlike previous devices that also used molecules to form the active region, this device exhibits a robust and large NDR with a valley-to-peak ratio (PVR) of 1030 1. The NDR effect from the system was observed up to 260 K. Beyond that temperature, however, no NDR was observed. More recently room temperature NDR has been seen in the nanopores containing the SAM of the nitro OPEs (Figure 4.14a), but even larger PVRs of 7 1 have been observed at room temperature with the dinitrobiphenylene compound (Figure 4.14b). ... 

In our early evaluations, three parameters were utilized for the resolving power of the columns (3,4,7). These were the valley-to-peak height ratio, v, the peak separation parameter, P, and the parameter mentioned earlier, Djcr. The valley-to-peak height ratio is defined as... 

Figure 4.2 Three definitions for peak-valley ratios as elemental criteria to quantify the extent of separation between a pair of adjacent peaks in a chromatogram, (a) Peak-valley ratio (P eqn.4.3) according to Kaiser, (b) median peak-valley ratio (Pm eqn.4.4) according to Schupp and (c) (opposite page) the valley-to-top ratio (P eqn.4.5) according to Christophe. 

The peak-valley ratios vary from zero for separations where no valley can be detected, to unity for complete separation. It ought to be noticed that a P value equal to zero does not necessarily imply that two solutes elute with exactly the same retention time (or k value). There is a threshold separation below which the presence of two individual bands in one peak only leads to peak broadening or deformation, without the occurrence of a valley. In these cases Rs values are indeed not equal to zero, because by definition (eqn.1.14) Rs is proportional to the difference in retention times. 

For practical evaluation FO is a very unattractive criterion. Its variation with At and with the peak area ratio A is similar to that of the peak-valley ratio Pv. Pand Pmare similar to each other in all respects. Pm may be obtained from the chromatogram slightly more easily than P, because it only requires location of the peak tops, and not of the valleys. To calculate Rs from the chromatogram an estimate of N is required. S can be estimated very easily, using only the retention times of individual peaks. 

The applicability of the Kalman filter requires an accurate knowledge of the response of each component and an efficient procedure for background removal. Background subtraction has recently been treated with cubic splines polynomials(5,6] as smoothing interpolators between peak valleys and this has proved to be efficient for baseline resolution particularly for very low signal-to-noise ratios [7]. 

The role of the mass analyser is to separate ions emerging from the ion source according to their mass (w/z ratio). The separating capability or mass resolution, R, of the analyser is measured in terms of its ability to resolve ions to less than a 10% valley between peaks ... 

Fignre 16.1 Explanation of the discrimination factor dg. Measured is the ratio of the distance between the apex of the smaller peak and the valley to the height of the smaller peak... 

Initially developed at Columbia University, flash chromatography is an air pressure driven hybrid of medium pressure and short column chromatography which has been optimized for particularly rapid separations. The resolution is measured in terms of the ratio of retention time (r) to peak width (w, w/2). It is measured by baseline resolution in the valley between the peaks and the distance from peak to peak. Sample size can be increased dramatically if less resolution is required. This innovative work by the Columbia University team demonstrated that column performance was quite sensitive to the rate of elution, and the best performance was accomplished with relatively high eluent flow rates. 

Tucker B, King J (1984) Dependence of sediment-filled valley response on input amplitude and valley properties. Bull Seismol Soc Am 74 153-165 Zhu TJ, Heidebrecht AC, Tso WK (1988) Effect of peak ground acceleration to velocity ratio on ductility demand of inelastic systems. Earth Eng Struct Dyn 16 63-79... 

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