Page 122 - Multidimensional Chromatography

114 Multidimensional Chromatography

where this equation shows that can be considered to be a kind of ‘saturation’ fac-
tor, expressing the ratio of components m to the hypothetical maximum number of
separable compounds , thus expressing the degree to which the separation space is
saturated (8), and assuming that m , we can replace the latter in equation (5.4),
thus obtaining the follow equation:

P exp( ) exp( ) (5.6)

and consequently we can write the following:

P exp( ) (5.7)

The dimensionless ratio P/ corresponds to the ratio between the number of visible
peaks, under the proposed chromatographic conditions, with the chromatographic
column having a peak capacity . Differentiation of equation 5.6 with respect to
gives the maximum possible value of the ratio P/ and shows this to occur at 1;
then, the maximum ratio P/ can be estimated by the following equation:

(P ) max exp( 1) 0.3679 (5.8)
which reveals that, as postulated above, the maximum number of visible peaks will
be equivalent to 37% of the capacity of the system peaks. Furthermore, the number
of single-component peaks which can be expected is given by the following:
(5.9)
S mP 1

where m, as above in equation 5.4, is the number of components in a multicompo-
nents mixture and P 1 is the probability that an analyte is eluted as a single-compo-
nent peak, which can be expressed as follows (8):

P exp( ) exp( ) exp( 2 ) (5.10)
Consequently, the corresponding number of single-component peaks is given by the
following:

S m exp( 2 ) (5.11)

As above, we can replace m by and thus equation 5.11 can be rewritten as follows:

S exp( 2 ) (5.12)

which can alternatively be presented as:
S/ exp( 2 ) (5.13)