Area under a peak

As you are no doubt aware, integrals are one of the key parameters in the interpretation of proton spectra and are pivotal in quantification. They measure the area under a peak and this is directly proportional to the number of protons (in the case of proton NMR) in that environment. Most software will automatically try to identify the peaks in your spectrum and integrate them for you. If you need to do it yourself, then it is a fairly trivial matter of defining the start and end point of the integrals of interest. The only complication is that you may need to tweak the slope and bias of the integral. This should be unnecessary if you have got the phase and baseline of your spectrum correct. If you find that you need to adjust slope and bias, we suggest that you go back and try to sort out baseline and phase a bit better. 

Second, the area under a peak is indicative of the number of hydrogens it represents. This, too, is important qualitative information, and so NMR spectrometer data systems are designed to determine... 

Since the technique is differential by nature, it is the area under a peak which is proportional to concentration, so the Osteryoung-Parry equation is merely an approximation. This explains why many workers prefer to work with peak area rather than say that peak height is proportional to concentration (equation (6.15)). In fact, there is usually a trade-off between several different experimental factors, which are listed in Table 6.6 below. 

The capacity or retention factor (k) is a measure of retention of a sample component. It should not be confused with the loading capacity of a column, which is expressed as milligrams of sample bound per milliliter of gel and represented by the area under a peak. The capacity factor may be calculated for any individual peak in a chromatogram. For example, the capacity factor for peak 2 in Figure B4.2.4 is derived from Equation B4.2.3, where Vjq is the elution volume of peak 2 and Vm is the volume of the mobile phase (i.e., the total bed volume). 

The area under a peak is directly proportional to the number of equivalent hydrogens giving rise to the signal. 

To relate the area under a peak to actual protein concentration many... 

The area under a peak is proportional to the number of hydrogens contributing to that peak. For example, in the methyl rm-butyl ether spectrum (Figure 13-19), the absorption of the ferf-butyl protons is larger and stronger than that of the methoxy protons because there are three times as many rm-butyl protons as methoxy protons. We cannot simply compare peak heights, however the area under the peak is proportional to the number of protons. 

The measurement of the area under a peak, proportional to the number of protons giving rise to that peak. (p. 577)... 

In the classical differential thermal analysis (DTA) system both sample and reference are heated by a single heat source. The two temperatures are measured by sensors embedded in the sample and reference. In the so-called Boersma system, the temperature sensors are attached to the sample pans. The data are recorded as the temperature difference between sample and reference as a function of time (or temperature). The object of these measurements is generally the determination of enthalpies of changes, and these in principle can be obtained from the area under a peak together with a knowledge of the heat capacity of the material, the total thermal resistance to heat flow of the sample and a number of other experimental factors. Many of these parameters are often difficult to determine hence, DTA methods have some inherent limitations regarding the determination of precise calorimetric values. 

Another method known as "differential scanning calorimetry (/) records the differential electrical energy necessary to maintain sample and reference at an equal and linearly increasing temperature. Here also it is claimed that the area under a peak is directly proportional to the energy absorbed or liberated in a transition and is unaffected by sample geometry, sample heat capacity, or such instrument operating parameters as scanning rate (/). 

On the other hand, measurement of peak intensities is not simply measurement of peak heights. First, the background should be extracted from the peaks. Second, the integrated intensity should be measured for quantitative analysis. It means that the total area under a peak should be measured. Three basic types of peaks are encountered when attempting quantitative phase analysis (Figure 2.26) ... 

In the differential-temperature loop, signals representing the sample and reference temperatures, as measured by the platinum-resistance thermometers, are fed to the differential-temperature amplifier via a comparator circuit, which determines whether the reference or the sample temperature is greater. The differential-temperature-amplifier output then adjusts the differential-power increment put into the reference and sample heaters in the direction and magnitude necessary to correct any temperature difference between them. A signal proportional to the differential power is also transmitted to the pen of a recorder, giving a curve of differential power versus time (temperature). The area under a peak, then, is directly proportional to the heat energy absorbed or liberated in the transition,... 

The determination of the area under a peak—i.e., the absolute intensity of a particular gamma energy—is not as straightforward as the assignment of energy, because the area under a peak includes contributions from other gammas. The methods that have been developed for the determination of the area can be classified into two groups methods that treat the data (i.e., counts per channel) directly, and methods that fit a known function to the data. 

Peak area area under a peak obtained from integration of the detector signal for a given component. Peak area is proportional to the number of molecules contained in an eluted band and hence may be used to calculate the proportion of each component in a mixture see integration, detector response factors and internal standard. 

A recorded plot from a typical experiment involving a mixture of three components might appear as shown in Fig. 2-27. The area under a peak is in many cases roughly proportional to the concentration of the component giving rise to it (to obtain accurate compositions of mixtures, known mixtures must be run), and the retention time is a characteristic of its chemical identity. If the aim of the experiment is to achieve a physical separation of the components, they can be condensed and collected after they have passed through the detector (Sec. 2.5.4). 

Given a number of conditions, the area under a peak in an NMR spectrum is proportional to the energy absorbed by each chemically distinct nucleus. It is thus an indication of the relative proportion of each nuclear population. Peak areas are especially useful in kinetic studies, where they can give a precise indication of the proportion of each chemical species present. For these quantitative studies, it is essential that no saturation occurs and that all the instrument conditions be kept constant. 

It has already been pointed out that the area under a peak on a differential thermal curve is approximately proportional to the amount of energy absorbed or evolved during a reaction... 

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