Staircase frontal analysis

Figure 2.2 Classical boundary conditions of common chromatographic problems, (a) Elution of a rectangular pulse, (b) Multiple gradient elution of a rectangular pulse, (c) Staircase frontal analysis, (d) Displacement. Dotted line component 1. Shaded line component 2.

Figure 14.7 Staircase frontal analysis of (+)-and (-)- Troger s base, (a) (+) enantiomer,...

Figure 14.8 Dependence of the apparent column efficiency on the concentration. Efficiency derived from self-sharpening fronts obtained in staircase frontal analysis of (-)-Trdger s base, 1 at 50°C 2 at 40°C 3 at 30°C and of (+)-Tr6ger s base at 30°C. Reproduced with permission from A. Seidel-Mor-genstem, S.C. Jacobson and G. Guiochon, J. Chromatogr., 637 (1993) 19 (Fig. 6)...

There are two possibilities for performing a frontal chromatography experiment for the purpose of the determination of equilibrium isotherms. The step-series method uses a series of steps starting from C = 0 to C +i. After each experiment, the column has to be reequilibrated and a new step injection with a different end concentration C +i can be performed. In the staircase method, a series of steps is performed in a single run with concentration steps from 0 to Q, Q to C2,.. ., C to C +i. The column does not have to be reequilibrated after each step and, therefore, the staircase method is faster than the step-series method. Both modes of frontal analysis give very accurate isotherm results. 

Frontal analysis in the staircase mode requires two pumps, one connected to a bottle with pure mobile phase and one connected to a bottle with the analyte to be investigated dissolved in the pure mobile phase. Initially, only mobile phase is present in the column and the staircase is obtained by successive abrupt step changes at the inlet of the column. In each step the analyte concentration in the mobile phase is increased and the stationary phase will consequently adsorb successively more analyte [109], see Figure 9. 

Figure 9. The principle of the frontal analysis technique. In the uper part of the figure a theoretic staircase is shown with 10 steps, showing the increment of solute in the stationary phase. A new step starts every 40 mL and is shown in the figure by a vertical line. In the lower part of the figure the corresponding isotherm is shown. The following values have been used VT = 2 mL, a = 120, b = 0.4 mM 1. Vs = 0.4 mL. The illustration was used with kind permission from Gustaf Gotmar [111].

Figure 17 shows a section of two individual overlaid staircase chromatograms resulting from single component frontal analysis of (S) and (R)-2-phenylbutyric acid, respectively. At the first step up to 30.5 mM the enantiomers are clearly separated from each other, at the second step up to 61.0 mM they are still separated and even at the third step up, to 91.5 mM it is still a very small tendency for separation. This figure indicates that the chiral capacity is somewhat higher than 90 mM. 

Figure 3.37 Typical experimental chromatograms obtained in the determination of equilibrium isotherms by chromatographic methods, (a) Frontal analysis staircase. FACP on the diffuse rear boundary after the last frontal step, (b) ECP. Data recorded with an HP 1090 (Hewlett-Packard, Palo Alto, CA) liquid chromatograph. Reproduced with permission from S. Golshan-Shirazi and G. Guiochon, Anal Chem., 60 (1988) 2630 (Figs. 1 and 2), ( )1988 American Chemical Society.

Equation 16.9 is general and is applicable to the profile of each step in the "staircase" profiles obtained in conventional binary frontal analysis. When a binary mixture is introduced as a step into an empty column (Cj = 0 and cj = C , / = 1,2), Eq. 16.9 becomes... 

This value is in agreement with the one derived from band profiles calculated with the equilibrium-dispersive model [9]. The time given by Eq. 16.20 provides useful information regarding the specifications for the experimental conditions under which staircase binary frontal analysis must be carried out to give correct results in the determination of competitive isotherms. The concentration of the intermediate plateau is needed to calculate the integral mass balances of the two components, a critical step in the application of the method (Chapter 4). This does not apply to single-pulse frontal analysis in which series of wide rectangular pulses are injected into the column which is washed of solute between successive pulses. 

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