Theory, chromatography separation factor

There is considerable discussion in the literature regarding the adsorption mechanism of ions from aqueous solutions onto RPLC stationary phases [87-90]. It has been shown that, under certain conditions, organic ions are adsorbed as ion pairs [87,89,91], and that, under other conditions, they may be adsorbed as separate ions. In this case, the model derived by StMUberg [92] may be useful. In his theory of the retention mechanism in ion-pair chromatography, StMilberg focused on the derivation of the isotherm of the amphiphilic compoimd, that is, the counter-ion used in this technique to adjust the retention factors of the sample components and their separation factors e.g., the cation tetrabutulammonium). The counter-ion (Br, Cl , H2PO4 ) may not be strongly associated with the cation in a mobile phase that is a mere aqueous buffer. Other cations, rmder other experimental conditions may adsorb as true ion pairs, in which case the isotherm behavior is quite different. 

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... 

The peak recorded in a chromatogram represents the distribution of molecules in a band as it elutes from the column, the overall broadness being conveniently m sured in terms of the width of the peak. A number of independent factors such as sample-injector and detector characteristics, temperature and column retention processes, contribute to the dispersion of molecules in a band and band broadening. The cumulative effect of small variations in these factors is described in statistical terms as the variance, cr, in the elution process. Classical chromatography theory considers that the separation process takes place by a succession of equilibrium steps, the more steps in a column the greater the column efficiency with less band broadening (variance) occurring, therefore... 

In almost all cases, the experiments yielded values a> 1. The heavier isotope is enriched in the solution phase and is eluted first. The theory of isotope separation by elution chromatography and the procedure for the calculation of the separation factor from experimental data was elaborated by Glueckauf. For the case of displacement chromatography the theory was developed by Kakihana and Oi. 

CEC is a miniaturized separation technique that combines capabilities of both interactive chromatography and CE. In Chapter 17, the theory of CEC and the factors affecting separation, such as the stationary phase and mobile phase, are discussed. The chapter focuses on the preparation of various types of columns used in CEC and describes the progress made in the development of open-tubular, particle-packed, and monolithic columns. The detection techniques in CEC, such as traditional UV detection and improvements made by coupling with more sensitive detectors like mass spectrometry (MS), are also described. Furthermore, some of the applications of CEC in the analysis of pharmaceuticals and biotechnology products are provided. 

Although many have contributed to the theory of HPLC, only the summary by Kaizuma, H., Myers, M.N. and Giddings, J.C., J. of Chromatog. Sci., 8, 630 (1970) will be discussed now. Refer to the van Deemter section in Chapter 20, p. 217, to help you compare the theories of gas-liquid chromatography (GLC) and HPLC. In order to get the best separations, band broadening must be held to a minimum. The major factors that contribute to this are summarized in equation 19-1. 

We will state or derive a bare minimum of the equations most useful for understanding and describing how the most easily measured or controlled variables affect separations in chromatography. Many of the factors in these equations can be derived or calculated from more fundamental parameters, such as diffusion coefficients of analytes in the two chromatographic phases, column dimensions, or variables defined in the statistical theory of random variation. Such details are covered in more advanced texts. 

Indeed, the 30-plus year progress of liquid chromatography is a history of the development of packing materials. The particle size directly influences the column efficiency and thus further affects the separation results. The underlying theory is the van Deemter equation, which is the empirical formula that shows the relationship between linear velocity (flow rate) and plate height (column efficiency). From the van Deemter equation we can know that, as the particle diameter decreases, there is a significant gain in efficiency even when the flow rates are increased. When the particle size was reduced to sub-2 (jim, the analytical process was speeded up by a factor of nine without compromise of efficiency, or in other words, the efficiency was increased by a theoretical ninefold for a similar run time (22). 

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