The Displacement Effect

The interaction between the bands of different components of the feed eluted successively is due to the competition between these components for interaction with the stationary phase. Although the results of these band interactions are often important and can be spectacular rmder certain circumstances, their origin can be traced to the fact that the differences between the equilibrium constants of the two components are rather small. For example, if we have a 1 1 binary mixture of two components with a competitive Langmuir isotherm and a value of the relative retention x = fl2/ i = 1-2, which is not imusual in practice, the proportion of the second component in the stationary phase at equilibrium is only 20% larger than the proportion of the first component. Under such conditions, the molecules of the component present in large excess in the feed may crowd those of the other component out of the stationary phase, whether the major component is the more or the less retained one. Thus, the interactions that take place between these two components result in an important displacement effect of the first component, at the front of the second component band, and/or in a significant tag-along effect exhibited by the second component band. In this section, we discuss the former, the displacement effect. 

We note for further reference that one of the properties of the competitive 

Langmuir isotherm is that the selectivity of the chromatographic system for the two components  

Band Profiles of Two Components with the Ideal Model 

This effect is fundamental in displacement chromatography (see Chapter 9) and explains the displacement of the band of one component by another band and the eventual formation of an isotachic train. 

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Dielectric loss The dielectric loss factor represents energy that is lost to the insulator as a result of its being subjected to alternating current (AC) fields. The effect is caused by the rotation of dipoles in the plastic structure and by the displacement effects in the plastic chain caused by the electrical fields. The frictional effects cause energy absorption and the effect is analogous to the mechanical hysteresis effects except that the motion of the material is field induced instead of mechanically induced. 

In contrast, in Figure 10.3c, the minor component is less retained than the major one. The component present in large excess in the sample displaces the other component out of the stationary phase, and the displacement effect of the first component, at the front of the second component band is observed. The first component elutes from the column sooner as if it were injected separately on the column. 

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. 

For each successive step, the profile of the second component exhibits an intermediate plateau at a concentration that is intermediate between the initial plateau concentration and the feed concentration in the new step, while, simultaneously, the first component profile exhibits an intermediate plateau with a concentration that is greater than the feed step. This is the result in frontal analysis of the displacement effect, itself the result of competition. Upon arrival at the column exit of the second component front (whose plateau concentration is equal to the feed concentration, the first component concentration undergoes a drop to the feed concentration. Note that the concentrations of both components converge simultaneously to the feed composition. The first step of a two-component frontal analysis has been studied experimentally and theoretically by Carta et al. [107], for the breakthrough of two amino acids, and by Zhu et al. [73] for the breakthrough of 2-phenylethanol and 3-phenylpropanol (Figure 4.22). 

We can now give a description of what happens when the sample size is decreased by reduction of the injection band width, tp. When tp becomes smaller than the threshold given in Eq. 8.36, the feed concentration plateau has vanished before elution, the second component concentration behind the second shock is lower than Cj, and its velocity decreases. Thus, the top concentration plateau in the first component profile, which is caused by the displacement effect, begins to erode. This erosion is rapid (it is complete when zj in Eq. 66 of Ref. [14,15] is equal to L). When this plateau has also disappeared, the two concentration discontinmties begin to slow down progressively, the distance between them increases regularly, and, eventually, the second shock will be eluted at a time for which C, as given by Eq. 8.41a, is equal to 0. This time is such that... 

One will note, comparing Figures 8.4 to 8.7, the progressive widening of the bands, and the dilution of the feed in the mobile phase. This effect is more important for the second component than for the first one because the latter has been somewhat concentrated by the displacement effect. 

In elution chromatography, the intensity of the displacement effect is conveniently measured by the ratio [27]... 

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. 

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-... 

As demonstrated in Chapter 8, the retention time of the end of the second component tail is constant and equal to 2 the retention time of the second component under linear conditions. The retention time of the band front decreases with increasing sample size. Therefore, as the sample size increases, the band spreads, and its front moves forward, driving the displacement of the first component. Consider the production of the second component. As the sample size increases, the production rate for the second component increases. With increasing sample size, the displacement effect creates a first component tail which penetrates into the front shock layer of the second component. At this point, the peld begins to decrease, while the production rate continues to increase and a mixed band is generated. When the tail penetrates too deeply into the second component band, the production rate begins to drop. 

Figures 16.6 to 16.7 is dramatic. The profiles are much broader, the influence of the nonlinear behavior of the phase equilibrium is considerably reduced, and the intensity of the displacement effect of the first component by the second one is much reduced. As a consequence, there is almost no separation.

Finally, the dependence of the production rate on the separation factor is complex since No, 7, x, and X depend on a, [21]. x varies rapidly with a when the relative concentration of the second component is large, and the displacement effect is dominant [2], Nevertheless, it can be shown that at constant pressure AP, the maximum production rate obtained with an optimized column is approximately proportional to [(a — l)/a] [28]. For a given i.e., nonoptimized) column, the production rate is proportional to [(a - T)/ ]y, with y between 2 and 3, depending on the importance of the difference between the given and the optimum columns [28]. 

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