Calculated elution profile separation

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.

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. 

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. 

Here c ( ), csim ( ) are the experimental and simulated responses at time t. When the experimental and simulated elution profiles coincide perfectly the overlap is 100% and when they are totally separated the overlap is 0%. In papers III-VI, the accuracy of the parameters was validated by calculating the overlap. We suggest that an overlap of more than 90% could be considered as good. A high overlap validates that both right isotherm model and right column model have been chosen. 

Figure 6.30 shows the very close agreement between these methods for this enantiomer system. Especially when considering the effort necessary to measure the multi-component isotherms, IAS theory or its extensions may provide a good estimate for the component interaction in the case of competitive adsorption. Therefore, it is advisable to simulate elution profiles using the IAS theory after singlecomponent isotherms have been measured. These calculations should then be compared with a few separation experiments to decide if measurements of the multi-component isotherm are still necessary. 

Since the equations giving the rear diffuse profiles of the two components in the mixed zone and of the second component in the third zone where it is pure are the same for a narrow or for a wide injection band, it seems logical to begin here the description of the chromatogram. Equations 8.25 to 8.29 and 8.33 apply to both cases. By contrast, the retention times of the two concentration shocks, tRg and tRg, and the elution profile of the pure first component between the two shocks are different and must be calculated separately. 

The analytical solution obtained for this model is not trivial as it is in the case of the elution and breakthrough problems. Accordingly, it is most useful for the investigation of separation carried out rmder linear or quasi-linear conditions. In such cases, it provides a useful starting point for further studies. Figure 17.9 shows a comparison between the experimental and the calculated concentration profiles along the column train of an SMB unit. It shows that the condition of ideality can be relaxed (see later. Section 17.4) and that the solution of the ideal... 

Both methods use a low-capacity cation exchanger as a stationary phase and a dilute mineral acid such as hydrochloric or nitric acid as a mobile phase. Although stationary phases and eluents have changed over the years, the principal difference between the methods is the same up to the present day. For his hypothetical experiments. Small kept constant the volume of the stationary phase, the ion-exchange capacity of the separator colunm, the selectivity coefficients for sodium and potassium relative to the hydronium ion, and the injection volume. With these values and the known acid concentration in the mobile phase, it is possible to calculate the elution volumes of sodium and potassium. To further simplify the calculation of the elution profiles, the chromatographic peaks are assumed to be symmetrical, so that they can be described by a Gaussian curve. One can further assume that the membrane-based suppressor system exhibits a very small dead volume and, therefore, subtracts negligibly from the efficiency of the separator column, which is estimated to be 3000 theoretical plates. 

Diffusion and mass transfer effects cause the dimensions of the separated spots to increase in all directions as elution proceeds, in much the same way as concentration profiles become Gaussian in column separations (p. 86). Multiple path, molecular diffusion and mass transfer effects all contribute to spreading along the direction of flow but only the first two cause lateral spreading. Consequently, the initially circular spots become progressively elliptical in the direction of flow. Efficiency and resolution are thus impaired. Elution must be halted before the solvent front reaches the opposite edge of the plate as the distance it has moved must be measured in order to calculate the retardation factors (Rf values) of separated components (p. 86). 

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