Analytical Solutions of the Ideal Model

The elution of a strong solvent shock of finite amplitude causes the effect known, in thin-layer chromatography, as demixion. The solvent front is eluted before the limit retention time of the strong solvent at infinite dilution and it is extremely sharp. The components eluted before the solvent front are eluted im-der isocratic conditions in the pure weak solvent. The sudden breakthrough of the strong solvent constitutes an extremely steep gradient of the strong solvent inside the column. It is accompanied with the very rapid elution of numerous components that are poorly or not resolved. Such a situation must be avoided in analytical applications. 

The approach described in the previous subsection remains valid. However, the characteristic lines issued from the boimdary condition have now a more complex equation. If the boundary condition is C(x = 0, t) = Co/(f), the equation of the characteristic line corresponding to concentration C will be 

Band Profiles of Single-Components with the Ideal Model 

We assume that the injection profile, or boimdary condition for Eq. 7.1, is a rectangular pulse of width fp and height Cq. The area of the injection pulse is proportional to the sample size. It is given by 

In the case of the Langmuir isotherm [q — aC/ l-f hC), a, b, numerical coefficients], the equations giving the velocity associated with a concentration (Eq. 7.3) 

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A possibility to reduce the influence of column efficiency on the results obtained by the ECP method is to detect the position of the peak maximum only, which is called the peak-maximum or retention-time method. Graphs like Fig. 6.23 are then achieved by a series of pulse injections with different sample concentrations. The concentration and position of the maximum is strongly influenced by the adsorption equilibrium due to the compressive nature of either the front or the rear of the peak (Chapter 2.2.3). Thus, the obtained values are less sensitive to kinetic effects than in the case of the ECP method. The isotherm parameters can be evaluated in the same way as described in Section 6.5.7.6, but the same limitations have to be kept in mind. For some isotherm equations, analytical solutions of the ideal model can be used to replace the concentration at the maximum (Golshan-Shirazi and Guiochon, 1989 and Guiochon et al., 1994b). Thus, only retention times must be considered and detector calibration can be omitted in these cases. 

Golshan-Shirazi, S., Guiochon, G. Experimental characterization of the elution profiles of high concentration chromatographicbands using the analytical solution of the ideal model, Anal. Chem., 1989, 61, 462 1-67. 

This section summarizes the analytical solutions of the ideal model with a Langmuir competitive isotherm in the different cases identified . 

Golshan-Shirazi and Guiochon have investigated the optimization of the experimental conditions using the analytical solution of the ideal model [20-24]. In the case of touching bands, the recovery yield is practically total ( 100%). Therefore, the same experimental conditions assure the maximum production rate for both components. Their assumptions are limited to the following two ... 

The analytical solution of the ideal model for linear isotherms to the following constraints for complete separation of a two-component feed mixture (A and B) ... 

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