Calculated elution profile

Fig. 17. The resolution of a HPLC-UV-VIS datamatrix obtained for a 6-component system by Iterative Target Transformation Analysis (ITTFA). calculated elution profile, true elution profile. From B. G. M. Vandeginste, W. Derks and G. Kateman, Anal. Chim. Acta 173, 261 (1985). Reproduced by permission of Elsevier Science Publishers, Amsterdam...

The adsorption isotherm parameters obtained in paper IV were validated in two step (1) the experimental perturbation retention data were compared with the calculated retention data using the adsorption isotherm parameters, and (2) by using them with computer simulation programs to calculate elution profiles. The simulated profiles were compared with the experimental profiles using the calculations of the overlap (see section 3.6) as evaluation... 

As the overall aim of parameter determination is the (simulation-based) prediction of the process behavior the final decision about the suitability of the isotherm equation can only be made by comparing experimental and theoretical elution profiles (Section 6.6). Depending on the desired accuracy, this may involve iteration loops for the selection of isotherm equations or in some cases even the methods (Fig. 6.16). In this context it should be remembered that, according to the model equations (e.g. Eq. 6.47), the migration velocity and thus the position of the profiles is a function of the isotherm slope. Therefore, it is most important for the reliability of process simulation that the slopes of the measured and calculated elution profile fit to each other. If the deviations are unacceptable, another isotherm equation should be tested. 

Figure 4. Calculated elution profile to simulate a protein separation on Sephadex G-7S using equation (12). This simulation is based on parameter values for a 30 x 1.5 cm column with a flowrate of 1.77 ml/min and a longitudinal diffusivity of 0.01 cm2/min. The ratio of mobile phase volume to pore volume was 0.9, and the sample volume was 0.17 ml. Capacity factors for each of the solutes are 0, 0.5, and 1.1, respectively.

In Figure 16 the elution profiles for samples from each group of seven plates are included together with the overall composite peak from the total charge. The calculations assumed a column efficiency of 5000 theoretical plates. The elution... 

The intersection of these two lines with the line defined by the mixture chromatograms gives the scores of the pure elution profiles (0.360, 0.070) and (0.325, -0.166) resulting in the chromatograms given in Fig. 34.18. Knowing the pure elution profiles, the spectra are easily calculated by solving eq. (34.3). 

The aim of all the foregoing methods of factor analysis is to decompose a data-set into physically meaningful factors, for instance pure spectra from a HPLC-DAD data-set. After those factors have been obtained, quantitation should be possible by calculating the contribution of each factor in the rows of the data matrix. By ITTFA (see Section 34.2.6) for example, one estimates the elution profiles of each individual compound. However, for quantitation the peak areas have to be correlated to the concentration by a calibration step. This is particularly important when using a diode array detector because the response factors (absorptivity) may considerably vary with the compound considered. Some methods of factor analysis require the presence of a pure variable for each factor. In that case quantitation becomes straightforward and does not need a multivariate approach because full selectivity is available. 

FIGURE 15.2 Experimentally measured (---------) and theoretically calculated (...) eluting peak profiles... 

Fig. 16a-c. Resolution of GC-MS spectra obtained for mixtures of 1-pentanol, toliKne and butyl-acetate. a. the elution profile, b. the mas spectra measured for scans 126 to 143. c. the calculated pure mass spectra from scans 126 to 143 compared to the pure mass spectra. From J. H. Chen and L. P. Hwang, Anal. Chim. Acta 133,277 (1981). Reproduced by permission of Elsevier Science Publishers, Amsterdam... 

Figure 5. Composite MWD diagram showing the calculated distributions of four of the five master fractions obtained from preparative chromatography of organosolv aspen lignin (fraction number 4 to 1 from left to right). The Mw values for the master fractions from left to right are 1,110, 1,310, 2,420, and 8,050, respectively. The insert shows the elution profile of organosolv aspen lignin from the YMC preparative /z-Styragel column (5 x 200 cm). The 30 fractions collected were pooled into the five master fractions shown.

Without prior incubation in aqueous NaOH solution. d After 300 h at 170 gL-1 in 1.0 M ionic strength aqueous 0.40 M NaOH. e Calculated from Sephadex GlOO/aqueous 0.10 M NaOH elution profiles monitored at 320 nm. 

Calculated as the difference between fraction II of the native starch and fraction I ofthe debranched starch GPC elution profiles... 

Expansion behavior according to the Richardson-Zaki equation provides reassurance that the particles behave properly. The next factor to determine is dispersion. A pulse of a tracer is passed through the bed and monitored after leaving the expanded bed. The dispersion is calculated by comparing the shape of the elution profile with that of the original plug of liquid. Often acetone or phenol is used as a tracer and is monitored using UV. 

What does exist, however, is GPC, which separates the molecules in a polymer on the basis of molecular size (weight). The large molecules elute from the column earlier than small molecules and from this elution profile both the weight-average molecular weight (size) and the molecular weight (size) distribution can be calculated. 

As an example, consider a data matrix consisting of 10 rows (labelled from 1 to 10) and eight columns (labelled from A to H), as in Table 4.10. This could represent a portion of a two-way HPLC-DAD data matrix, the elution profile of which in given in Figure 4.15, but similar principles apply to all multivariate data matrices. We choose a small example rather than case study 1 for this purpose, in order to be able to demonstrate all the steps numerically. The calculations are illustrated with reference to the first two PCs, but similar ideas are applicable when more components are computed. 

For polymer systems without UV activity the combination of a RI detector with a density (D) detector can be used. The working principle of the density detector is based on the mechanical oscillator method. Since this detector yields a signal for every polymer, provided that its density is different from the density of the mobile phase, this detector can be regarded as universal [29,30,36]. The separation of mixtures of polystyrene and polybutadiene by SEC with dual den-sity-RI detection is presented in Figs. 7 and 8. In a first set of experiments, the response factors of both polymers in both detectors have to be determined. Then from the intensity of each slice of the elution curves in both detectors, the mass distribution of both polymers across the elution volume axis can be calculated. As can be seen in Fig. 7, a separation into the component peaks is obtained due to the fact that the molar masses of PS and PB are sufficiently different. For both components the individual elution profiles can be determined and using corresponding calibration curves for PS and PB the individual MMDs can be calculated. The same information can be extracted from an experiment where the molar masses of the components are similar and SEC separation does not work (see Fig. 8). Again the individual mass distributions are obtained and the MMDs for PS and PB can be determined. 

Figure 5.13 shows overloaded elution profiles obtained for three different injection volumes of solutions of the same concentrations of the two enantiomers of PA (dashed lines). The solid lines in these figures show the band profiles numerically calculated for a concentration dependent mass transfer coefficient k( (main figure), a low concentration value of (upper inset) and a high concentration value of kf (lower inset). For the r-enantiomer, the best fit of the data is obtained using the concentration dependent rate constant, while for the o-enantiomer the best fit is obtained using a constant value of k equal to 35/min (low concentration value). 

Fig. 5.13. Example of overloaded elution profiles from the frontal analysis runs described in Fig. 5.8 and Fig. 5.12. D,L-PA was injected at sample volumes of 240, 160 and 80 p at a sample concentration of 1 g/L and a temperature of 40°C. Experimental data dotted lines. Numerical calculations solid lines. (A) L-PA, main figure = 117.3 C " "/min, upper...

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