Theory, chromatography column efficiency

Golshan-Shirazi, S. and Guiochon, G., Theory of optimization of the experimental conditions of preparative liquid chromatography optimization of column efficiency, Anal. Chem., 61, 1368, 1989. 

Displacement Development A complete prediction of displacement chromatography accounting for rate factors requires a numerical solution since the adsorption equilibrium is nonlinear and intrinsically competitive. When the column efficiency is high, however, useful predictions can be obtained with the local equilibrium theory (see Fixed Bed Transitions ). 

The efficiency of a column is a number that describes peak broadening as a function of retention, and it is described in terms of the number of theoretical plates, N. Two major theories have been developed to describe column efficiency, both of which are used in modern chromatography. The plate theory, proposed by Martin and Synge,31 provides a simple and convenient way to measure column performance and efficiency, whereas the rate theory developed by van Deemter et al.32 provides a means to measure the contributions to band broadening and thereby optimize the efficiency. 

The process of band broadening (Figure 2.1) is measured by the column efficiency or the number of theoretical plates N, equation (2.24)), which is equal to the square of the ratio of the retention time to the standard deviation of the peak. In theory, the value of N for packed columns has only a small dependency on k and may be considered to be a constant for a particular column. Column efficiency in open-tubular systems decreases markedly with increased retention. For this reason open-tubular liquid chromatography systems must be operated at relatively low kf values (see section 2.5.S.2). 

The rate theory of chromatography describes the shapes and breadths of elution bands in quantitative terms based on a random-walk mechanism for the migration of molecules through a column. A detailed discussion of the rate theory is beyond the scope of this text. We can, however, give a qualitative picture of why bands broaden and what variables improve column efficiency. ... 

For all these reasons, the mathematical aspects of the theory become much more complex. The mathematics of nonlinear chromatography are so complex that even for a single solute, there is no analytical, closed-form solution available, except with two simplified models, the ideal model and the Thomas model [120]. The ideal model is based upon the assumption of an infinite column efficiency. Its solutions are discussed in detail in Chapters 7 to 9. The Thomas model is based upon the assumptions that there is a slow Langmuir adsorption-desorption kinetics and that there are no other nvass transfer resistances, nor any axial dispersion. The system of equations of this model has been solved by Goldstein [121], and this general solution has been simplified for pulse injection by Wade et al. [122]. In aU other cases, the problem must be solved numerically. The Thomas model is discussed with other kinetic models in Chapter 14 and 16. 

As discussed already in Chapter 2 (Section 2.2.6), Giddings [10] has developed a nonequilibrium theory of chromatography and showed that the influence of the kinetics of mass transfers can be treated as a contribution to axial dispersion. As illustrated in Chapter 6, this approximation is excellent in linear chromatography, as long as the column efficiency exceeds 20 to 30 theoretical plates. 

So far liquid column chromatography has been dealt with in respect of details of technique and equipment involved. The present chapter discusses theory that relates performance of an LC column to its various parameters. The aim of this discussion is to understand conditions which give high column efficiency, good resolution and quick analysis. 

Theory of chromatography column efficiency expanded Chromatography simulation software for method development Capillary gas chromatography (GC) columns updated and expanded Headspace, thermal desorption, and purge and trap GC analysis Fast gas and hquid chromatography... 

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 many chiral separations, it is often a struggle to adequately resolve the enantiomers and achieve adequate separation ratios. In such cases, the above procedure may be essential to achieve the minimum analysis time. In addition, the time would be much extended, the column longer, and the efficiency that was needed, would be much greater. The same type of approach can be used for reversed phase systems employing water which, if in a binary mixture, will associate with the other solvent and produce a ternary mixture. Unfortunately, the procedure becomes extremely involved and its discussion is more appropriate to a text on chromatography theory and, consequently, is outside the scope of this book. 

Figure 3.5 Plots of Cp (peak capacity) as a function of k value for the last-detected peak, for several values of column efficiency N (also taken as that for the last peak), calculated from Plate Theory taking into account variation of peak width with retention time. Adapted from Scott, http //www.chromatography-online.org/, with permission.

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