Page 121 - Multidimensional Chromatography

Coupled-Column Liquid Chromatography 113

behaviour, termed the General Elution Problem (4) is common to all forms of liquid
chromatographic systems in which a mixture of various components, having a large
spread of k values, is eluted under isocratic conditions. A solution for solving this
problem is to change the band migration rates during the course of separation by a
gradient elution under precisely controlled conditions. A chromatographic separa-
tion can be considered complete when the column produces as many peaks as there
are components in the analysed sample (5). In order to describe the effectiveness of
most separation systems to resolve a multicomponent mixture, Giddings introduced
the concept of peak capacity (6), which is defined as the maximum number of peaks,
, that can be fitted into the available separation space with a given resolution which
satisfies the analytical purpose. Peak capacity can be expressed by the following
equation (6):

1 N r ln (1 k i ) (5.3)
1 2

where N is the number of theoretical plates, r is the number of standard deviations
which equal the peak width (r 4) when the resolution (R s ) 1, and k i is the
capacity factor of the last eluted peak in a series.
Theoretically, under gradient elution conditions, HPLC systems yield peak capac-
ities which are calculated to be in the range 100–300. These values would be ade-
quate to resolve components in a mixture where the number of analytes is smaller
than the peak capacity of the system. However, peak capacity is an ideal number
and expresses the maximum number of resolvable analytes which exceeds the real
number by some factor determined by operational conditions, such as the allowable
separation time (components in a complex mixture are usually not uniformly dis-
tributed and appear randomly, overlapping each other). In other words, often the
information obtained from the chromatogram is not the true recognition of all indi-
vidual analytes in complex multicomponents samples, but gives an indication of
sample complexity based on the number of observed peaks (7). Davis and Giddings
(8) developed a statistical model of component overlap in multicomponent chro-
matograms by which it was estimated that one never expects to observe more than
37% of the theoretically possible peaks with uniform spacing. This percentage, cor-
responding to the number of visible peaks, P, in a chromatogram can be estimated by
the following equation:

P m exp ( m ) (5.4)

where m is the number of components in a multicomponent mixture and is the
peak capacity.
By assuming that (selectivity of the chromatographic system) can be rewritten
as follows:
m (5.5)