Non-Gaussian zones

We should add that while resolution and peak capacity are excellent criteria of merit for the separation of multicomponent mixtures into discrete zones, other criteria exist, some very general, for judging the efficacy of separation and purification in any separative operation (see Section 1.4). Various terms such as impurity ratio and purity index abound. Rony has developed a criterion termed the extent of separation [22]. Stewart, as well as de Clerk and Cloete, have shown that entropy can be formulated as a very general measure of separation power, as we might expect from the discussion of Section 1.6 [23,24]. An excellent discussion of separation indices, with an emphasis on non-Gaussian zones (below), is found in Dose and Guiochon [25]. 

A Gaussian zone is the model around which most discussions of zonal separation methods revolve. However, there are frequent departures from 

Peaks departing from Gaussians are often described by exponentially modified Gaussian (EMG) functions, a combination (via a convolution operation) of a Gaussian and an exponential function [27,28]. Other empirical functions have been used as well [29]. None of the above functions has a very sound theoretical footing, but they are nonetheless important for descriptive purposes. 

Finally, we note that some component zones do not acquire Gaussian shapes because the controlling processes are quite unlike those described above. This situation applies to some of the steady-state zones described in the following chapter. 

1( ) Find the second moment around the mean in the x coordinate system, ((x-f)2), for the Gaussian, c const -exp(-jr2/4Z 0-From integral tables one finds that 

---

Factors leading to non-Gaussian zones in separation systems were described generally in Section 5.9. One source of zone asymmetry identified was the variation of local solute velocity W with solute concentration, described as overloading. The way in which overloading causes zone asymmetry in chromatography is explained below. 

In a real chromatogram the peaks often have profiles that are non-Gaussian. There are several reasons for this. Besides the accepted approximations, such as invariance of the distribution coefficient K with concentration, there are irregularities of concentration in the injection zone at the head of the column. Furthermore, the speed of the mobile phase is zero at the walls and maximum at the centre of the column. The asymmetry observed in the peak shape is measured by a parameter called the skewing factor, which is calculated at 10% of the peak height (Fig. 1.4) ... 

---