Elution of a Narrow Band with Competitive Langmuir Isotherms

3 Elution of a Narrow Band with Competitive Langmuir Isotherms 

The difference between the elution of a narrow band and the elution of a wide band, discussed in the previous section, is that in the former case the injection plateau has eroded during elution and, therefore, tR,2 (Eq- 8.19) is larger than (Eq. 8.23a), making Eq. 8.36 no longer valid at z = L. After the injection plateau has disappeared, the heights of the two concentration shocks decrease continuously. Accordingly, the velocities of these shocks decrease and the solution of the problem becomes more complex. We will show that the first shock continues to move faster than the second shock and that the two bands eventually separate. 

Band Profiles of Two Components with the Ideal Model 

The solution of the problem is long and complex. However, its derivation follows the same line as the one presented in the previous section, the simpler case of a wide rectangular injection pulse. The essential features of the solution are similar in both cases. They originate from the competition that takes place between the two components when they interact with the stationary phase. The major features, such as the displacement and the tag-along effects, are common to both solutions. Accordingly, it does not seem necessary to reproduce here the details of the derivations, which can be foimd elsewhere [12,14,15]. 

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. 

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