Peak maximum

A chromatographic peak may be characterized in many ways, two of which are shown in Figure 12.7. The retention time, is the elapsed time from the introduction of the solute to the peak maximum. The retention time also can be measured indirectly as the volume of mobile phase eluting between the solute s introduction and the appearance of the solute s peak maximum. This is known as the retention volume, Vr. Dividing the retention volume by the mobile phase s flow rate, u, gives the retention time. 

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. 

Table 13.11 Multiplying factors to obtain the momentary peak (maximum r.m.s. or dynamic) values of the short-circuit currents including the sub-transient d.c. component at different power factors (FI/Xl)...

Table 28.1 Momentary peak (maximum r.m.s.) current ratings, asymmetrical, for switchgear and metal-enclosed bus systems, based on ANSI-C-37/20C...

The dead point is the position of the peak maximum of an unretained solute. It is not the initial part of the dead volume peak as this represents a retarded portion of the peak that is caused by dispersion processes. The importance of employing the peak maximum for such measurements as dead volume and retention volume will be discussed in later chapters of the book that deal with peak dispersion. 

The peak maximum is the highest point (the apex) of the peak. 

The retention time (tr) is the time elapsed between the injection point and the peak maximum. Each solute will have a characteristic retention time. 

The corrected retention volume (V r) is the volume of mobile phase passed through the column between the dead point and the peak maximum. It will also be the retention volume minus the dead volume. 

The peak height (h) is the distance between the peak maximum and the baseline geometrically produced beneath the peak. 

Once the elution-curve equation is derived, and the nature of f(v) identified, then by differentiating f(v) and equating to zero, the position of the peak maximum can be determined and an expression for the retention volume (Vr) obtained. The expression for (Vr) will disclose those factors that control solute retention. 

The retention volume of a solute is that volume of mobile phase that passes through the column between the injection point and the peak maximum. Consequently, by differentiating equation (10), equating to zero and solving for (v), an expression for the retention volume (Vr) can be obtained. 

Equating to zero and solving for (v), then at the peak maximum,... 

It is seen that the peak maximum is reached after (n) plate volumes of mobile phase have passed through the column. Thus, the retention volume in ml of mobile phase will be obtained by multiplying by the plate volume, (vm + Kvg). 

If the mobile phase is a liquid, and can be considered incompressible, then the volume of the mobile phase eluted from the column, between the injection and the peak maximum, can be easily obtained from the product of the flow rate and the retention time. For more precise measurements, the volume of eluent can be directly measured volumetrically by means of a burette or other suitable volume measuring vessel that is placed at the end of the column. If the mobile phase is compressible, however, the volume of mobile phase that passes through the column, measured at the exit, will no longer represent the true retention volume, as the volume flow will increase continuously along the column as the pressure falls. This problem was solved by James and Martin [3], who derived a correction factor that allowed the actual retention volume to be calculated from the retention volume measured at the column outlet at atmospheric pressure, and a function of the inlet/outlet pressure ratio. This correction factor can be derived as follows. 

Another serious error can occur if it is known that there are two peaks which are unresolved, and the retention time of the maximum of the envelope is taken as the mean retention time of the two isomers. This measurement can only be true if the peaks are absolutely symmetrical and the two peaks are of equal height. The effect of different,proportions of each isomer on the retention time of the composite envelope is shown in Figure 3. It is seen that the position of the peak maximum of the composite envelope is significantly different from the mean of the retention times of the individual peaks. 

Furthermore, in the example given, the peaks were considered to be truly Gaussian in shape. Asymmetric peaks can distort the position or the peak maximum of the envelope to an even greater extent. In general, the retention time of a composite peak should never be assumed to have a specific relationship with those of the unresolved pair. 

Higher concentrations of solute move through the system more rapidly, thus reducing the retention time of the peak maximum which produces a peak with a sharp front and a sloping tail. 

Higher concentrations of solute move through the system more slowly displacing the peak maximum to a later retention time and, thus, a peak is produced with a sloping front and a sharp back. 

Let the distance between the injection point and the peak maximum (the retention distance on the chromatogram) be (y) cm and the peak width at the points of inflexion be (x) cm. If a computer data acquisition and processing system is employed, then the equivalent retention times can be used. 

The concentration of solute at the peak maximum is approximately twice the average... 

The peak measured for a plate number determination contains additional information about the packing quality of a column. The same peak may also be used to quantify information about the shape as well. The peak width on both sides of the perpendicular through the peak maximum is measured at a height of 10% of the maximum height (see Fig. 14.2). The quotient of the back by the front part of the peak is defined as the asymmetry factor (AF) ... 

Scheitel-. vertical peak, maximum (Anat.) parietal, -ausschlag, m. amplitude. -Knie,/ vertical line, -punkt, m. vertex zenith. 

The oxygen peak maximum shifted monotonically with burnoff time, rising from 531.05 eV for pristine NG7 to 534.0... 

Fig. 50. Yield for chain scission as a function of strain rate for different fractions of polycarbonate (PC) in benzyl alcohol/dioxan (90 10 v.v) at 20 °C. A normal PC with Mp = 417000 B normal PC with Mp = 321000 C normal PC with Mp = 256000 D PC with weak bonds, Mp = 217000 Mp molecular weight at peak maximum sc critical strain rate for chain scission (extrapolated from the linear portion of the degradation curve)...

Figure 5.39 c shows the O Is spectmm obtained during electrochemical O2 pumping in vacuum at Uwr 1.1V. The spectmm clearly proves massive electrochemically controlled O2 backspillover onto the Pt catalyst surface with a concomitant shift of the broad Ols spectmm peak maximum to -530 eV. 

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