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K3 < Ki
Thus, again from equation (2), it follows that those parts of the solute band containing high concentrations of solute will move more rapidly through the column than those parts of the solute band that contain low concentrations of solute. The resulting elution curve will take the form of that shown in figure (3c). This peak shape is often called an adsorption peak, this term arose during the development of GC and is not really an appropriate term for use In LC.
The major cause of peak asymmetry In LC Is sample overload and this occurs mostly in preparative and semi preparative LC. There are two forms of sample overload, volume overload and mass overload. Volume overload results from too large a volume of sample being placed on the column and this effect will be discussed later. It will be seen that volume over load does not, In itself, produce asymmetric peaks unless accompanied by mass overload. Mass overload which, as discussed above, is accompanied by a distortion of the normally linear isotherm, can cause very significant peak asymmetry and, in fact, seriously impair the resolution obtained from the column.
It has already been stated that, in order to achieve the separation of two substances during their passage through a chromatographic column, the two solute bands must be moved apart and, at the same time, must be kept sufficiently narrow so that they are eluted discretely. It follows, that the extent to which a column can constrain the peaks from spreading will give a measure of its efficiency. It is, therefore, desirable to be able to measure the peak width and obtain from it, some value that can describe the column performance.
Because the peak will be Gaussian in form, the peak width at the points of inflexion of the curve (which corresponds to twice the standard deviation of the curve) will be determined. At the points of inflexion (2),
(v - 2nv + n(n-1))
Thus, at the points of inflexion,
Hence, v2-2 nv + n(n-l) = 0 and
It is seen that the points of inflexion occur after n- Vn and n+ Vn plate volumes of mobile phase has passed through the column. Thus the volume of mobile phase that has passed through the column between the inflexion points will be,
Thus the peak width at the points of inflexion of the elution curve will be 2Vn plate volumes which, in milliliters of mobile phase will be obtained by multiplying by the plate volume i.e.,
The peak width at the points of inflexion of the elution curve is twice the standard deviation and thus, from equation (3) it is seen that the variance (the square of the standard deviation) is equal to (n), the total number of plates in the column. Consequently, the variance of the band (o2) In milliliters of mobile phase is given by,
Now, o2 = n(vm + Kvs)2
n + Vn-n+Vn = 2Vn
Peak Width = 2-/n(vm + Kvs)
Vr = nCvmg + Kvs)
it follows, that the variance of the peak is inversely proportional to the number of theoretical plates in the column and the larger the number of theoretical plates, the more narrow the peak, and the more efficiently the column has constrained the band dispersion. As a consequence the number of theoretical plates in a column is given the name Column Efficiency. It is, therefore, important to be able to measure the efficiency of any column and this can be carried out in a very simple manner Let the distance between the injection point and the peak maximum (the retention distance on the chromatogram) be ó cm and the peak width at the points of inflexion be x cm
A Chromatogram Showing the Separation of Two Solutes
Then as the retention volume is n(vm + Kvs) and twice the peak stanaara deviation at the points of inflexion is 2Vn(vm + Kvs),
Ret.Distance ó n(vm+Kvs) Vn men' PeakWidth ~x_2Vn(vm+Kvs)~ 2
Equation (5) allows the efficiency of any solute peak, from any column, to be calculated from measurements taken directly from the chromatogram. The various characteristics of the chromatogram that have so far been considered are shown in figure (5) which is an extension of the chromatogram shown in figure (3) In Chapter 2.
The Position of the Points of Inflection
Since the measurement of efficiency is important for evaluating the quality of a column, it is necessary to know the position of the points of inflection in order to measure the peak width. The inflection points are ill defined on the chromatogram and it is necessary to know at what fraction of the peak height they occur. This fraction will be the same as the ratio of the value of the solute concentration after (n - Vn) plate volumes of mobile phase has passed through the column, to the solute concentration after (n) plate volumes of mobile phase has passed through the column.
Thus, if (f) is the fraction of the height (h) at which the points of inflection occur,then (3),
f _ xm(n-/n)
Now,lfX<<l, l0ge(,_x) = _x.^j^j?