Triangular peak shape

The sample capacity is the maximum quantity of an analyte with which the phase can be loaded (Table 2.26). An overloaded column exhibits peak fronting, an asymmetrical peak which has a gradient on the front and a sharp slope on the back side. This effect can increase until a triangular peak shape is obtained, a so-called shark fin. Overloading occurs rapidly if a column of the wrong polarity is chosen. The capacity of a column depends on the internal diameter, the film thickness, polarity and the solubility of a substance in the phase. 

This form of the isotherm results in a linear rate of change of the capacity factor with mobile phase concentration and gives rise to a truly triangular peak shape. Knox also concluded that the efficiency of a peak under mass overloaded conditions... 

Knox and Piper (13) assumed that the majority of the adsorption isotherms were, indeed, Langmuir in form and then postulated that all the peaks that were mass overloaded would be approximately triangular in shape. As a consequence, Knox and Piper proposed that mass overload could be treated in a similar manner to volume overload. Whether all solute/stationary phase isotherms are Langmuir in type is a moot point and the assumption should be taken with some caution. Knox and Piper then suggested that the best compromise was to utilize about half the maximum sample volume as defined by equation (15), which would then reduce the distance between the peaks by half. They then recommended that the concentration of the solute should be increased until dispersion due to mass overload just caused the two peaks to touch. 

As columns are overloaded for preparative work, peak shape often deviates from the Gaussian shape typical of analytical work. In preparative work, the peaks can assume a triangular shape because the adsorption isotherm is nonlinear. A typical isotherm is shown in Figure 6-37, where CM is the concentration of sample in the mobile phase and Cs is the concentration of sample in the stationary phase. At low concentration of sample (CM) there is a linear adsorption isotherm which results in Gaussian peak shapes. At a point when either the sample adsorption in the stationary phase or the sample solubility in the mobile phase becomes limited, the isotherm becomes nonlinear, assuming either a convex or a concave shape. Convex isotherms are the most common and result in peak tailing. Conversely, concave isotherms cause fronting of the peaks. 

In quadmpole and ion trap spectrometers, it is customary to use the unit resolution definition, which means that each mass can be separated from the next integer mass (500 from 501, 2000 from 2001, etc.). The comparison and conversion between the different resolution definitions is not trivial, considering that they are strongly dependent on peak shape (Gaussian, triangular, trapezoidal, Lorent-zian, etc.).9... 

At a count efficiency of 0.2 cpm/dpm the 20 net counts represent 100 net decompositions/0.1 min. present in the most radioactive 150 pi increment of eluant. Finally, if one may assume that the eluted radioactivity peak shape is symmetrically triangular, the total radioactivity in the eluted peak is determined by multiplying the radioactivity in the center increment by one half the number of 150 pi increments in the eluted volume (100 X 4.5 ml X 1000 pl/ml = 1500 decompositions/ 0.1 min = 15,000 dpm). 150 pi X 2... 

If the sample size is increased, the shape of the peaks changes to rectangular (in the case of volume overload) or triangular (with mass overload) mixed forms and distorted peak shapes are also observed. Displacement effects can occur where a compound is pushed and concentrated by a following one that has a stronger affinity to the stationary phase. 

The peaks are roughly triangular in shape so their area is approximately ... 

Increases in mass resolution are not only accortpanied by a loss in ion transmission efficiency and hence signal intensity (Figure 2.15), but also by a change in peak shape from flat topped to triangular (Figure 2.14(b)).Moreover, the extremely narrow peaks at high mass resolution require an absolutely stable mass calibration (especially for isotope ratio applications). 

The first symptom of mass overload is seen as a broadening of the chromatographic peak as the mass of sample is increased. This is measured as a lowering of the efficiency (reduction in the number of theoretical plates) and increase in peak asymmetry, but as mass load is increased it often results in triangular shaped peaks which show typically a peak maximum at a reduced retention time and a tail which extends to the retention time of a peak resulting from an analytical load. Other, much more bizarre peak shapes can also be found. These represent cases where special interactions between the solute molecules and the stationary phase, the mobile phase or each other occur. 

In a well-tuned (adjusted) instrument, the shape of a mass spectral peak is approximately triangular (Figure 44.7a), but, in an instrument that is poorly tuned the peak will appear misshapen (Figure 44.7b). Usually, the cause of the skewing of the peak arises from incorrectly adjusted... 

The blast load is modeled as a triangular-shaped overpressure time curve. The blast overpressure rises instantaneously to the peak overpressure, B, then decays linearly with a blast pressure duration, T. The pressure is uniformly distributed over the surface of the plate and is applied perpendicular to the pane. 

In order to use the dynamic response charts based on a triangular shaped load, the bilinear pressure-time curve shown in Figure 3.7 can be simplified to an equivalent triangle. This equivalent load is computed by equating the impulse for each load shape and using the same peak pressure, Pt. The impulse, I, under the bilinear pressure-time curve is ... 

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