Adjacent peaks

Intensity classification is often based on image histogram which shows different peaks, each corresponding to one region and adjacent peaks are likely to be separated by a valley. The problem posed is to determine thresholds corresponding to these valleys [Fig 04]. 

Coupling constant J (Section 13 7) A measure of the extent to which two nuclear spins are coupled In the simplest cases It IS equal to the distance between adjacent peaks in a split NMR signal... 

Resolution. The degree of separation or resolution, Rs, of two adjacent peaks is defined as the distance between band peaks (or centers) divided by the average bandwidth using 14), as shown in Fig. 11.3. 

Although not apparent at this time, it will become clear that two adjacent peaks from solutes of different chemical type, or significantly different molecular weight, are not likely to have precisely the same peak widths (i.e., exhibit the same efficiency). Nevertheless, in most cases, the difference will be relatively small and, in fact, likely to be negligible. As a consequence, the widths of closely adjacent peaks will, at this time, be assumed to be the same. 

The analysis can be performed for several values of the relative peak height n, using the appropriate values of f(n) taken from Table I. Thus several estimates of Ed are obtained and either an average of them is calculated with its standard deviation, or provided a dependence of Ed on n is encountered, conclusions on the variability of Ed with coverage are drawn. As an alternative, only the half-widths of the peak are treated, as long as the experimental data are not distorted by some adjacent peak. Obviously, more information is obtained in such a case. The ratios of the half-widths taken at various values of n and compared with those given in Table I represent a criterion for the fit of the value of the desorption order. Since the estimates of Ed are free of contributions of fcd, the Tm relations can be used to estimate grossly the value of fcd, similarly as in Section V.C.2.b. 

Fiq. 4. Conditions for resolution of two adjacent peaks on a desorption curve according to Carter (88). Tm and Tm are the temperatures at maximum desorption rate for the first and second peak, respectively. T and T are the temperatures at maximum desorption rate for the first and second peak, respectively. Te and Te are the temperatures at 1/e = 37 per cent of the maximum desorption rate for the first and second peak, respectively. 

There are three main reasons for this choice. Firstly, it becomes more and more difficult to obtain recordable, molecular-ion signals from un-derivatized carbohydrates as their M, increases significantly above 3000. Secondly, the mass spectrometers that have been used in all high-mass-carbofiydrate studies published at the time of writing this article are not capable of very sensitive analysis above —3800 mass units (see later). Thirdly, at masses >4000, it is usually not practicable to work at the resolution necessary for adjacent peaks to appear as separate signals in the spectrum. To do so would require that the source and collector slits be narrowed to such a degree that there would be an unacceptable loss in sensitivity. Thus, spectra acquired at mass >4000 are usually composed of unresolved clusters. 

For manual optimization methods the peak separation function, P, is easy to determine and can be calculated as shown in Figure 4.30 (479). The chromatographic response function for the chromatogram is then simply the sum of the In P values for the n adjacent peak pairs. 

Two polymorphs of (/q-penicillaminc are known [2], with the existence of these being confirmed using infrared spectroscopy and X-ray crystallography. It was reported that Form I has a minimum between its IR peaks at 1078 and 1101 cm-1 that are less intense than the adjacent peaks at about 1050 and 1160 cm-1, while Form II has an absorption peak at 1092 cm-1 which is more intense than the adjacent peaks at about 1050 and 10160 cm 1 [2],... 

FIGURE 3.13 Dependence on the resolution of two adjacent peaks from the separation selectivity, column efficiency, and capacity factors of peaks. Curves were calculated by keeping values of two parameters constant at the starting value and varying the third parameter. 

Resolution may be calculated from a chromatogram as the difference between the retention times divided by the average of the peak widths at the baseline for two adjacent peaks. 

A calculated value for resolution greater than 1.5 indicates that the adjacent peaks exhibit baseline resolution the signal has fully returned to the baseline from the first peak before the second peak begins. Often, a minimum acceptable resolution of 2 is used in method development to ensure that acceptable resolution is maintained, even as the method is transferred among instruments, analysts and laboratories. 

From the data presented above, use adjacent peak pairs to calculate selectivity (a) and resolution (Rs). 

A common but very important goal in HPLC is to obtain adequate separation of a given sample mixture. To achieve this goal, we need to have some quantitative measure of the relative separation or resolution achieved. The resolution, Rs, of two adjacent peaks 1 and 2 is defined as equal to the distance between the center of two peaks, divided by average peak width (see Fig. 15.3) ... 

When a wave, such as that on the sea, travels in a particular direction, we can characterize it by a number of parameters - the velocity of travel, its amplitude (the height of the waves), its wavelength (distance between adjacent peaks), and its frequency (the number of waves per unit time). The simplest form of wave to consider is a sine wave, the equation for... 

In a compound having the structure > CHb - CHa2 - two signals will be expected in the NMR spectrum because of the influence of two equivalent protons, the signal for the proton b will appear as a triplet and the distance between any two adjacent peaks will be the same as shown (Fig. 15.13)... 

Quadrupole analyzers generally are operated at so-called unit resolution normally restricting their use to typical low resolution (LR) applications. [111,112] At unit resolution adjacent peaks are just separated from each other over the entire m/z range, i.e., R = 20 at m/z 20, R = 200 at m/z 200, and R = 2000 at m/z 2000 (Fig. 4.37). 

The goal of most HPFC analysis is the separation of one or more analytes from other components in the sample in order to obtain quantitative information for each analyte. Resolution (RJ is the degree of separation of two adjacent analyte peaks, and is defined as the difference in retention times of the two peaks divided by the average peak width (Figure 6). As peak widths of adjacent peaks tend to be similar, the average peak width can be equal to the width of one of the two peaks. 

Efficiency or plate count (N)—an assessment of column performance. N should be fairly constant for a particular column and can be calculated from the retention time and the peak widths. Selectivity (a)—the ratio of retention k ) of two adjacent peaks. Sample capacity— the maximum mass of sample that can be loaded on the column without destroying peak resolution. Capacity factor k )—a measure of solute retention obtained by dividing the net retention time by the void time. 

For example, to determine the empirical formula of di-n-octylphthalate, the daughter spectrum of the containing molecular ion (392) was obtained (Figure 7). The relative peak areas of adjacent peak pairs at m/z 149 and 150 is 2 1. This indicates that the M+1 ion is twice as likely to lose a atom as retain it. Thus the ratio of the number of carbon atoms lost to those retained is 2 1. Since the identified phthalate substructure contains 8 carbons, the unknown compound (di-n-octylphthalate) must contain 24 carbon atoms. These data, along with the molecular weight of 390 as determined from the conventional Cl mass spectrum of the unknown was fed into the empirical formula generator and the output was one empirical formula C24H38O4. 

Modem isotope ratio mass spectrometers have at least three Faraday collectors, which are positioned along the focal plane of the mass spectrometer. Because the spacing between adjacent peaks changes with mass and because the scale is not linear, each set of isotopes often requires its own set of Faraday cups. 

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