Page 20 - Multidimensional Chromatography

Introduction 9
The fraction of the peaks resolved (s/m) also represents the probability, p, that a
component will be separated as a single peak, so that:
2m
n
P exp (1.4)
The values of n and the corresponding N which are necessary to resolve 50–90% of
the constituents of a mixture of 100 compounds are listed in Table 1.5, thus making
clear the limitations of one-dimensional chromatography. For example, to resolve
over 80 % of the 100 compounds by GC would require a column generating 2.4 mil-
lion plates, which would be approximately 500 m long for a conventional internal
diameter of 250 m. For real mixtures, the situation is even less favourable; to
resolve, for example, 80 % the components of a mixture containing all possible 209
7
polychlorinated biphenyls (PCBS) would require over 10 plates.

1.4 TWO-DIMENSIONAL SEPARATIONS

A considerable increase in peak capacity is achieved if the mixture to be analysed
is subjected to two independent displacement processes with axes z and y orientated
at right angles, and along which the peak capacities are, respectively, n z and n y . For
the orthogonality criterion to be satisfied, the coupled separations must be based on
different separation mechanisms; the maximum peak capacity is then n z n y
(Figure 1.3), and the improvement in resolving power is spectacular. Thus, a peak
capacity of 200 in the first dimension and one of 50 in the second, as is quite possible
4
in comprehensive two-dimensional (2D) GC, yields a total peak capacity of 10 ,
which would require in one dimension a plate number (30) of approximately 4 10 8
4
plates in a 250 m id column of 80 km in length! The peak capacity of 10 of the
two-dimensional system would permit resolution of 98 of the 100 components in the
mixture discussed above, and in principle 200 of the 209 PCBs. If, however, the two
separations are correlated, as for example, might hold for the separation of the
polycyclic aromatic hydrocarbons (PAHs,) naphthalene, phenanthrene, chrysene,
etc., by normal phase HPLC coupled to non-polar GC, there is little improvement
over either method applied singly, and the retention pattern in two dimensions is

Table 1.5 Peak capacity and corresponding plate numbers required to resolve a given
fraction of a 100-component mixture
Fraction of peaks resolved Required peak capacity Number of theoretical plates
0.5 290 250000
0.6 390 460000
0.7 560 950000
0.8 900 2430000
0.9 1910 10950000