The Tag-Along Effect

This effect results in a long plateau on the rear part of the elution profile of the second component when the colmim is strongly overloaded and the loading factor of the first component is much larger than the loading factor of the second one. Like the displacement effect, the tag-along effect is a consequence of the competition between the molecules of the two components for interaction with the stationary phase. At constant concentration, the second component is less retained in the presence of a finite concentration of the first one than when it is alone. 

At the end of the mixed zone, the concentration Ci tends toward 0 and the con-centration of the second component toward C, given by Eq. 8.13b. The limit of the velocity associated with the concentration C2 is 

Band Profiles of Two Components with the Ideal Model 

This velocity is always higher than the velocity associated with the same concentration C on a continuous rear profile of the pure component 2, i.e., in the third zone of the chromatogram. This latter velocity is given by Eq. 7.7 or 8.32  

Accordingly, a concentration plateau appears on the rear of the second component profile, at the concentration Cf given by Eq. 8.13b [5,14,15,27]  

---

Figure 10.3b shows that in intermediate cases, when the concentration of the two components is similar, both the displacement and the tag-along effects appear simultaneously and the band profiles of both components are strongly influenced by the presence of the other component. 

Especially for feed mixtures with different ratios of the single components, the elution order must be considered. The major component should elute as the second peak, because in this case the displacement effect can be used to ease the separation (Chapter 2.6.2). If the minor component elutes as the second peak the tag-along effect reduces the purity and loadability of the system. 

One of the main advantages of equilibrium theory is the capability to predict some fundamental phenomena that occur in multi-component chromatography such as the displacement effect and the tag-along effect (Chapter 2.6.2). Another application is the use as short-cut methods for preliminary process design. As no effects causing band spreading are included, it is not possible to predict the system behavior exactly. 

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]. 

It is convenient to choose the length of the plateau on the rear of the second component profile as a measure of the intensity of the tag-along effect. We shall define... 

As with the displacement effect, the intensity of the tag-along effect depends essentially on the ratio of the two loading factors. When the loading factor for... 

Thus, for a given value of the relative composition of the feed, the intensity of the tag-along effect, like the intensity of the displacement effect, depends strongly on the ratio of the two column saturation capacities. Note, however, that the solution of the ideal model for a binary mixture that is discussed in this chapter assumes that the Langmuir competitive model is valid. But the Langmuir competitive model is truly valid only if 5,1 = qsg-... 

Significant or even large differences between band profiles calculated with the two finite difference methods arise for aU mixture compositions at low column efficiencies. Such differences also arise at high efficiencies, when the relative concentration of the second component is low, i.e., when the tag-along effect is important [6-8]. In this last case, the only significant differences between the profiles calculated with the different methods are in the steepness of the shock layers in the mixed zone and in the retention time of the second component front [6-9,28]. The numerical problems have been discussed above, in Sections 11.1.3 and 11.1.4, and examples shown in Figures 11.5 and 11.6. 

In Figure 12.4c, the displacer concentration has been further lowered to 46.4 mg/mL, the watershed of the second component (Figure 12.4c). Therefore, the displacer front moves too slowly for the isotachic train to include the bands of the first two components, and in the case of this figme, the train begins with the third component. The first two bands are eluted as overloaded elution bands. The plateau on the top of the second band is the result of the tag-along effect between the first and second bands, as in Figure 8.6b. It has nothing to do with the displacement or the injection plateau. 

There is no competition between the two components. Accordingly, the elution band profiles of the two components are the same, whether a given amoimt of each component is injected pure or as a mixture. They recognized that this assumption is inexact when the resolution between the bands is moderate (i.e., lower than 2). Due to the large influences of the displacement and the tag along effects on the band profiles, this assumption is unrealistic for bands having a resolution of the order of 1. 

The optimum loading factor is higher in gradient elution than in isocratic elution, because the band compression diminishes the tag-along effect of the more retained component. Accordingly, the average concentration of the collected... 

There are additional effects occurring during the elution of a binary mixture at higher concentration depending on the specific thermodynamics described by the isotherms and their coefficients as well as the relative mass ratio of the two components in the mixture. Two of the most prominent effects are the displacement effect and the tag-along effect (Guiochon et ah, 2006). Both are ruled by the competition of the more and the less retained molecules with the interaction sites of the adsorbent. Depending on the mass load and the composition of the feed, it results in quite different elution profiles. 

---