System peaks Separation factor

The time-dependent structure factor S k,t), which is proportional to the intensity I k,t) measured in an elastic scattering experiment, is a measure of the strength of the spatial correlations in the ordering system with wavenumber k at time t. It exliibits a peak whose position is inversely proportional to the average domain size. As the system phase separates (orders) the peak moves towards increasingly smaller wavenumbers (see figure A3.3.3. 

At this point, it is important to stress the difference between separation and resolution. Although a pair of solutes may be separated they will only be resolved if the peaks are kept sufficiently narrow so that, having been moved apart (that is, separated), they are eluted discretely. Practically, this means that firstly there must be sufficient stationary phase in the column to move the peaks apart, and secondly, the column must be constructed so that the individual bands do not spread (disperse) to a greater extent than the phase system has separated them. It follows that the factors that determine peak dispersion must be identified and this requires an introduction to the Rate Theory. The Rate Theory will not be considered in detail as this subject has been treated extensively elsewhere (1), but the basic processes of band dispersion will be examined in order to understand... 

A highly versatile method for enantiomer analysis is based on the direct separation of enantiomeric mixtures on nonraceinic chiral stationary phases by gas chromatography (GC)6 123-12s. When a linearly responding achiral detection system is employed, comparison of the relative peak areas provides a precise measurement of the enantiomeric ratio from which the enantiomeric purity ee can be calculated. The enantiomeric ratio measured is independent of the enantiomeric purity of the chiral stationary phase. A low enantiomeric purity of the resolving agent, however, results in small separation factors a, while a racemic auxiliary will obviously not be able to distinguish enantiomers. 

In this equation i represents the first eluting peak of a peak pair and j the last eluting peak. Hence, by definition a is always larger than unity. Sometimes a is called the separation factor, which is somewhat unfortunate terminology because separation is influenced by other factors than just a (see section 1.3). a is the chromatographic parameter that is most directly related to the selectivity of the phase system. In this book, therefore, the word selectivity will often be associated with a. Using eqns.(1.7) and (1.10) we can write two other equations for a, . 

Resolution, like the separation factor, differs for each specific component pair and therefore fails as a global criterion of separation. For analytical separations, more universal criteria have evolved, such as plate height, number of plates, rate of generation of plates, and peak capacity (Chapter 5). While these indices differ somewhat from one component to another, they effectively establish a ballpark figure of merit for different systems and different conditions of operation. 

The aim of any chromatographic system is to resolve a number of components in a sample mixture, i.e. to ensure that individual peaks do not overlap or coincide. To achieve this you need to consider several important factors capacity factor, separation factor or selectivity, column efficiency and asymmetry factor. 

Separation performance can be expressed by the separation factor a, which is only dependent on the retention times of the two enantiomers, or by the resolution factor Rs which also takes into account the breadth of the chromatographic peaks. The higher these factors are, the better separation is. Remarkable selectivities have been obtained, for instance with an enantiomeric mixture of the dipeptide JV-acetyl-Trp-Phe-O-Me (non-covalent system, Rs= 17.8) [141] and... 

When the critical pair is separated, so are all other peaks in the chromatogram. If the critical pair is not the last two peaks in the chromatogram the separation time will be tR(l + nk) where n is the ratio of the retention factor of the last peak to elute in the chromatogram to the retention factor of the second peak of the critical pair. The fastest separation is obtained when tR is minimized. This will be the case if the following criteria are met. The minimum useful value for the resolution of the critical pair is accepted. The separation system is optimized to maximize the separation factor (a) for the critical pair. The retention factor for the critical pair is minimized (k 1 -5). The column is operated at the minimum value of the plate height, Hmin, corresponding to Uopt. 

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