Displacement chromatography displacer, definition

Experimental work of Kalasz et al. resulted in the statement of the characteristics and basic rules of displacement chromatography. They conceived properties of the fully developed displacement train, factors affecting displacement development, efficacy of separation, analysis of displaced fractions, determination of displacement diagrams from Langmuirian isotherms, as well as selection of the column, carrier, and displacer for displacement chromatography. Concentration of the sample is a particular feature of displacement chromatography. However, the displacer in the carrier is also definitely concentrated through the development of the displacement train. 

Rhee et al. developed a theory of displacement chromatography based on the mathematical theory of systems of quasi-linear partial differential equations and on the use of the characteristic method to solve these equations [10]. The h- transform is basically an eqmvalent theory, developed from a different point of view and more by definitions [9]. It is derived for the stoichiometric exchemge of ad-sorbable species e.g., ion exchange), but as we have discussed, it can be applied as well to multicomponent systems with competitive Langmuir isotherms by introducing a fictitious species. Since the theory of Rhee et al. [10] is based on the use of the characteristics and the shock theories, its results are comprehensive e.g., the characteristics of the components that are missing locally are supplied directly by this theory, while in the /i-transform they are obtained as trivial roots, given by rules and definitions. 

The application of the z-transform and of the coherence theory to the study of displacement chromatography were initially presented by Helfferich [35] and later described in detail by Helfferich and Klein [9]. These methods were used by Frenz and Horvath [14]. The coherence theory assumes local equilibrium between the mobile and the stationary phase gleets the influence of the mass transfer resistances and of axial dispersion (i.e., it uses the ideal model) and assumes also that the separation factors for all successive pairs of components of the system are constant. With these assumptions and using a nonlinear transform of the variables, the so-called li-transform, it is possible to derive a simple set of algebraic equations through which the displacement process can be described. In these critical publications, Helfferich [9,35] and Frenz and Horvath [14] used a convention that is opposite to ours regarding the definition of the elution order of the feed components. In this section as in the corresponding subsection of Chapter 4, we will assume with them that the most retained solute (i.e., the displacer) is component 1 and that component n is the least retained feed component, so that... 

Figure 15.2 Definition of the parameters of the shock layer and the SLT in displacement chromatography, in an isotachic train. Reproduced with permission from J. Zhu and G. Guiochon,. Chromatogr. A, 659 (1994) 15 (Fig. 2).

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