Retention time calculation Integration

An automated procedure to measure peak widths for peak capacity measurements has been proposed.35 Since peak width varies through the separation, the peak capacity as conventionally measured depends on the sampling procedure. The integral of reciprocal base peak width vs. retention time provides a peak capacity independent of retention time, but requires an accurate calculation of peak width. Peak overlap complicates automation of calculation. Use of the second derivative in the magnitude-concavity method gives an accurate value of the standard deviation of the peak, from which the base peak width can be calculated. 

Both new and experienced users can take advantage of software to lead them through instrument set-up and data acquisition. Automated quantitation routines are available to calculate compound amounts in samples. These routines offer complete flexihihty to generate custom report formats. By integrating retention time information and internal or external cahhration curves can he calculated. Quantitation data can he exported to popular spreadsheet programs. 

Although recorders and integrators are used in some older systems, generally in modern ion exchange chromatography results are stored in computer. Retention time and peak areas are the most useful information. Retention times are used to confirm the identity of the unknown peak by comparison with a standard. In order to calculate analyte concentration peak areas are compared with the standards which is in known concentration [10]. 

Strip-chart recorders are still the least expensive option, but areas and retention times have to be manually calculated from the tracing. The more expensive integrators, using small memories, give us a time-noted trace followed by a report of areas (or peak heights) versus retention times. The computer requires much more memory to store the one point per second (or more) required for an HPLC run. However, it has much more flexibility in manipulation, redisplay, calculation, and report generation. Data processing will be covered in detail in Chapter 14. 

The most accurate measurements of peak areas are those obtained by means of electronic data reduction with integrators or computers. The vast majority of laboratories now have electronic or computer methods for determining peak areas. Two main features are required for electronic processing of chromatographic data accurate digitization of the analog signal and software. The software is required for the detection of peaks, correction for baseline drift, calculation of peak areas, retention times, and concentrations of components in the sample, and production of the final report.5... 

Besides the traditional type of chart recorder, chart integrators, or "printer-plotters" as they are often called, may be used. Printer-plotters automatically calculate the percentage of each component in the total mixture and print this out in the form of a list of retention times and percentages. But, unless a correction factor is applied to each component, these values, which are based on the characteristic response of the detector, are not normally accurate to within more than a 10-20% variation. 

The retention time tr can no longer be calculated as L/Rv (Eq. 10.2) because v is not constant. Below we write v as v(x) to show that it varies with distance x down the column. To get tr we must sum up (integrate) all the small time elements dt needed for a component to pass through each thin slice dx of column. We have... 

Calibration Chromatograph successive 2- to 5-p,L portions of the Standard Preparation until the relative response factor, F, is constant (i.e., within a range of approximately 2%) for three consecutive injections. If using graphic integration, adjust the instrument to obtain at least 70% maximum recorder response for the hexadecyl hexadecanoate peak. Measure the areas under the major peaks occurring at relative retention times of approximately 0.60 (a-tocopheryl acetate) and 1.00 (hexadecyl hexadecanoate), and record the values as As and Aj, respectively. Calculate F by the formula... 

Six 50-mg blank hair samples were extracted by SFE and the noise was integrated for the ion used for quantification (m/z = 355 for codeine, 369 for ethylmorphine, 383 for 6-MAM, and 397 for morphine) in a retention time window of tj + 0.5 min. The LOD and LOQ were determined (n = 6) using lUPAC methods. For each substance the standard deviation of the blank value (Sg) was determined. The mean area converted from the noise was calculated as concentration equivalent based on a calibration graph. The LOD is defined as 3Sg and the LOQ as lOSg. 

Integrators are manufactured by many companies (for example Hewlett-Packard, Spectro Physics, Varian). Many integrators plot the chromatography mn, record the retention times of peaks, calculate the areas under the peaks automatically and print this data at the end of the mn. 

Elution Time, Eq. 8.47. The retention time of the first shock cannot be calculated in closed form. It is derived as the lower boimdary of the finite integral of the two profiles of the first component (in the first and second zones), such that this integral corresponds to the mass of first component injected. 

Figure 10.11 Overloaded chromatograms of a pure compound (kg = 5) calculated according to the three different schemes. Langmuir isotherm, Ly = 10%, L = 25 cm. (a) N = 300 theoretical plates, m = 15. Integration increments Forward-backward scheme, h = 500 ftm, T = 4.0 s backward-forward scheme, h = 600 im, r = 0.4 s forward-backward +i, h = 250 Jim, T = 1.0 s. Retention times ideal model, 335 s forward-backward scheme, 372 s backward-forward scheme, 352 s forward-backward +i, 360 s. (b) Same as (a), but N = 5000 theoretical plates, m = 250. Integration increments forward-backward scheme, h = 30 Jim, T = 0.24 s backward-forward scheme, h = 36 jim, r = 0.024 s forward-backward +i, h = l5 Jim, T 0.060 s. Reproduced with permission from M. Czok and G. Guiochon, Anal. Chem., 62 (1990) 189 (Figs. 4 and 5). 1990, American Chemical Society.

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