Fitting of the Chromatogram

In order to identify the correct isotherm model, the analysis has to be repeated for several potential candidate models. In each case realistic initial estimates for the free parameters have to be provided in order to facilitate convergence of the nonlinear optimization procedure required. A drawback of this curve fitting approach is that all errors of the assumed column and plant models have an effect on the quality of the isotherm parameters estimated. Thus, this approach is in particular recommended to get relatively fast a first idea about the thermodynamic properties of the chromatographic system investing only small amounts of sample. 

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Modeling and Determination of Model Parameters 6.57.9 Curve Fitting of the Chromatogram... 

Thus, assuming that the number of peaks that can be fitted into the chromatogram between the dead time and the time for the complete elution of the last peak is (r), then... 

When a model has been obtained, it is necessary to evaluate the fit of the model, by comparing for each of the points the experimental value obtained for the response and the value predicted with the model. Important differences indicate that the model is not adequate and that a more complex model (see below) may be needed. To have still more confidence in the model, validation can be carried out. This requires that new chromatograms be obtained at different x-values from those obtained with the experimental design. Again the experimental and predicted response values are compared. 

Equation 31 -2 tells us that we can achieve faster separations by using short columns, higher-than-usual carrier gas velocities, and small retention factors. The price to be paid is reduced resolving power, caused by increased band broadening and reduced peak capacity (that is, the number of peaks that will fit in the chromatogram). 

Figure 4.33 Top. Simultaneous fitting to a competitive bi-Langmuir model of the chromatograms obtained with a large (50.7 mg) and a moderate (10.14 mg) sample of the racemic mixture of 1-indanol. Bottom. Comparison of the FA adsorption data points (s)rmboIs) and the best competitive bi-Langmuir isotherms obtained by the inverse method (lines) for the racemic mixture. Reproduced with permission from A. Felinger, D. Zhou, G. Guiochon, f. Chromatogr. A, 1005 (2003) 35 (Figures 7 and 8).

Figure 12.16 Adsorption isotherms and displacement chromatogram for 3,4-dihydroxyphenyl, 2-hydroxyphenyl, and 4-hydroxyphenyl acetic acids. (Left) Adsorption isotherms measured by frontal analysis on a 250 x4.6 mm column packed with 10 tm Partisil ODS-2 from 0.1 M phosphate buffer, pH 2.12 at 25°C. The soUd Unes are a least-squares fit of the data points to the Langmuir isotherm. (Right) Displacement chromatogram, carrier 0.1 M phosphate buffer, pH 2.12 displacer n-butanol at 0.97 M. Flow rate 0.05 mL/min at 25°C. Feed 1.5 mL of 30, 35, and 45 mg of 3,4 dihydroxy-, 4-, and 2-hydroxyphenylacetic acids, respectively. Fraction size, 0.15 mL. Fraction 40 marks 12 mL of eluent volume. Reproduced with permission from Cs. Horvath, A. Nahum and J.H. Frenz, J. Chroniatogr. 218 (1981) 365 (Figs. 6 and 7).

Muller and Schmid (1984) buUt on the earlier work of Gj0s and Gustavsen by introducing CP mixtures into a low resolution ECNI-MS ion source via a GC fitted with a 15 m capillary coluirm [58]. The appearance of the chromatogram is remarkably similar to what is generated today by most laboratories. 

Now to our subject. Modern software programs offer many options for the manipulation of the chromatogram, e.g. automated baseline subtraction, programmed change of integration parameter, auto-zero functions and auto scale, automated calibration for non-linear signal-to-concentration ratio, etc. It is worth while knowing these options and how to use them as they fit. 

If we are interested in improving the overall resolution of a complex sample (containing many bands), a more useful index of separation is the peak capacity PC—equal to the number of bands with baseline resolution (R, 1) that can be fit between the beginning (usually to) and end of the chromatogram. For gradient elution, peak capacity is given by (24)... 

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