Peak Capacity in Chromatography SIR: The outstanding feature of chromatography is its capacity to separate a large number of components in a single analysis, Although much theoretical work has been directed toward a fuller understanding of the efficiency of the process, the “peak capacity,” that is the maximum number of resolvable peaks, has only recently been examined ( I ) . Giddings (I) has shown that for elution chromatography carried out under normal conditions the peak capacity, n, is given approximately by :
n
=
1
+ (N1l2/4)In (VJV,)
.
/
(1)
where N is the plate number and V,, V , are the retention volumes of the first and last peaks. In gel permeation chromatography, V,/V,, thus, the peak capacity is uniquely defined by the ratio (total solvent volume)/ (volume of moving solvent) in the column, which is normally 2.3 f:0.3. Therefore, peak capacity of gel filtration is severely limited compared to that of other forms of chromatography where the ratio V,jV, is set only by operational conditions such as permissible analysis time and detector sensitivity. The treatment of Giddings ( I ) assumed that the ratio (peak width)/(retention volume) was the same for all peaks. Considerable improvement in peak capacity can be achieved if it is arranged that all peaks are of the same width, for example, by gradient elution in liquid chromatography or temperature programming in gas chromatography. This is demonstrated in Figure 1. Under these conditions the peak capacity is
n’
= (~1”2/4)[(~~/V -u 11 )
(2)
where N is obtained from the first peak assumed to be eluted with a uniform eluent or at constant temperature, Comparison of Equations 1 and 2 shows that the use of gradient elution or temperature programming increases the peak capacity by a factor of F = [(V,/V,) - ] j In (VJV,) or alternatively decreases the plate requirement for a given peak capacity by a factor of F2. For V,/V, = 10, 20, and 50, the (1) J. C. Giddings, ANAL.CHEM., 39,1027 (1967).
gel filt-ration
Figure 2. Peak capacity as a function of number of plates in gel filtration as well as in elution chromatography at regular or gradient elution plate requirement is reduced by 15, 40, and 150 times, respectively. The time of analysis is directly proportional to the required plate number; thus, it is also reduced by the same factor. The advantageous effect of employing gradient elution or temperature programming is illustrated in Figure 2. It is apparent from the present considerations that the goal of fast chromatographic separation can best be approached in liquid chromatography by employing gradient elution, whereby a large number of components may often be separated with modest column performance as has been demonstrated by the fast analysis of nucleic acid constituents (2). RECEIVED for review July 27, 1967. Accepted September 21, 1967. Work supported by grants from the National Institutes of Health (HE-03558-10 and FR 00356-01) and the National Aeronautics and Space Administration (SAR-NGR07-004-067 and NsG-192-61).
C.G. HORV~TH S. R. LIPSKY W -e+
Figure 1. Chromatograms with adjoining peaks (a)
Section of Physical Sciences Yale University School of Medicine New Haven, Conn. 06510
Regular elution
(b) Gradient elution N = 400, Y J V , = 4
(2) C. G. Horviih, B. Preiss, and S. R. Lipsky, ANAL.CWEM., 39, 1422 (1967). VOL. 39, NO. 14, DECEMBER 1967
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