Peak-tangent method

In the peak-tangent (P- T) method a common tangent is drawn to two neighboring maxima or minima, and the distance to the intermediate extremum value is measured parallel to the ordinate ( i, 2 h Fig 2-24). This method can be applied satisfactorily if a linear background is present, but most of the time it is better to check whether a higher order will give more exact results. 

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Figure 2-24. Peak-tangent method (PT method), where tn is proportional to the concentrations of peak P ,.

The height of the peak and area of the peak ai e traditionally used for calibration techniques in analytical chemistry. Peak maximum can also be evaluated by the height of a triangle formed by the tangents at the inflection points and the asymptotes to the peak branches. We propose to apply the tangent method for the maximum estimation of the overlapped peaks. 

Our calculations show that the systematic errors for the evaluation of the triangle height are lower then for the peak height and peak ar ea. It is to be noted that tangent method allows estimating of the latent peak in the overlapped signals when peak area and peak maximum determination is impossible. 

To sum up, in some instances the proposed tangent method and procedure of systematic error correction allows excluding the necessity of mathematical or chemical resolution of overlapped peak-shaped analytical signals. 

Tangents Method. The tangents on either side of the peak are drawn through the inflection points until the baseline. For an ideal Gaussian peak the resulting base line interval Wi, is equal to 4or. Equation (1) becomes with the width (Wb) ... 

The efficiency of a column, N, is a number that describes peak broadening as a function of retention and is dependent on the entire chromatographic system. The most common method for calculating N is the tangent method. 

Calculate the IBW (4 a) using the tangent method as shown in Figure 4.19b. An IBW of -60 pL was found for this HPLC. Figure 4.20 shows a chart plotting column efficiencies of 150-mm long 3-pm columns of various inner diameters versus retention factors (k) on an HPLC system with a 60-pL IBW. Note that efficiency loss from instrumental dispersion can be severe for small inner diameter columns where peak volumes are smaller. Note that peaks of low k are affected more by system dispersion since peak volumes are proportional to k. 

The peak width is measured in the same time units as retention time. The factor / depends on how the peak width is measured. It is, for example, 16 for the tangent method, S.S4S for the half-heigfrt method, and 25 for the 5[Pg.13]

For quantitative measurement, all methods are suited which evaluate the signal directly, such as the peak-peak, peak-tangent, and peak-zero methods (Sec. 2.6.1.1-2.6.1.3). However, if derivatives need to be compared, the signals must be normalized, which means that the concentration must be identical or it must be eliminated. 

A) Ideal conditions linear trend of residual current B) Evaiuation of wave heights under nonideal conditions C) Evaluation of peak currents with strongly curved residual current, a) Tangent method b) Evaluation with French curve (5)... 

In the case of perfect symmetric peaks, the retention time can be determined directly from the peak maximum method, which is the simplest and most common. The peak maximum method is useful for determination of retention time if the skewness ratio is 0.7-1.3 [15]. The skewness ratio is defined as the ratio of tangent slope to the peak leading part and tangent slope to the peak tailing part whereas both tangents are drawn in the inflexion points. In such cases the skewness ratio is our of this interval, Ir is obtained from the first-order moment method or the Conder and Young method. Between these two methods, Conder and Young is recommended [16] ... 

A major disadvantage of manual methods is that the accuracy of each measurement relies on the individual performing the calculations and on where the tangents or baselines are drawn, which may differ from one peak to the next within an analysis. If strip-chart recorders are used, all the peaks must be contained on the chart paper. This severely limits the dynamic range of solute composition that can be analyzed. In addition, the chart speed must be fast enough so that, for measurements based on peak width, narrow peaks are wide enough for accurate measurement. 

Figure 5 shows the influence of IPN component ratio on Tg. Each sample was of IPN 1 type, prepared by the simultaneous method. Increasing the amount of 23G lowered the Tg of the IPN. This result also suggests that these IPNs show a good ability to mix. The Tg of IPN containing 70% of 23G was shown to be about 0 C, just like IPN 2 synthesized by the sequential method. The structure of 70%-23G-IPN can be considered to be cured phenolic resol in a continuous poly 23G phase. So, the loss tangent peak of IPN 2 at 0°C was attributed to the structure of 23G rich IPN such as 70%-23G-IPN. 

A typical record obtained for the separation of a mixture of alcohols by this method is shown in Fig. 4-10, and an idealized portion of the curve is shown in Fig. 4-11. The first curve indicates the remarkable efficiency of this method for separating compounds. A quantity equivalent to the theoretical plate previously defined for fractional distillation may be determined with these columns. A triangle is drawn whose sides are tangents to the sides of the peak corresponding to the... 

According to the above reactions, removal of carbonate groups from the mineral surface should result in the reduction of the intensity of carbonate peak as shown in Fig. 4.33. On the other hand, adsorption and surface precipitation of oleate can take place on the dolomite surface leading also to similar reductions. A new peak at 1351 cm when the oleate concentration reaches about 10 mol/1 can be clearly seen in Fig. 4.33b and the intensity of this peak increases with the increase in the oleate concentration, where precipitation of calcium and magnesium oleates is likely to occur both on the particle surface and in the bulk. The peak heights of both the carbonate and the oleate (7co and 7oi) in the spectra were measured. Bulk precipitation using a common tangent baseline method (Willis et al., 1987) and the ratio Ico/Ioh is plotted in Fig. 4.34. This plot also... 

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