Handbook of Size Exclusion Chromatography and Related ...

The peak volume is also broadened by dispersion outside of the column, including
broadening of the sample band by the injector, injection volume, the detector cell,
detector time constant, and connecting tubing. Once an HPLC system has been
assembled, the extracolumn effects are constant factors that may or may not take
away from the quality of the separation obtained in the column, depending on the
column dimensions and the relative importance of each of the individual
extracolumn effects.
The volume in which a band elutes from an HPLC column VPV is defined as
four peak standard deviations s. The relationship between peak volume, retention
volume VE and efficiency of the peak N is given by the equation
VPV ¼ 4VE
N 1=2
(18)
in which VE (earlier described as Vi þ KDVP) can be expressed as a function of the
column volume as shown in Eq. (19):
VE ¼ 1 4 p (dc) 2 L(1 þ KD)ei
(19)
Substitution of Eq. (19) into Eq. (18) gives the following expression for the peak
volume:
VPV ¼ p (dc) 2 L(1 þ KD)eiN 1=2
(20)
It is clear from Eq. (20) that peak volumes are directly proportional to the volume
of the column and that samples elute with smaller peak volumes from the same
column when filled with a more efficient, that is, smaller size, packing material.
The more efficient the column, the narrower are the sample bands and the more
important is the effect of extracolumn band broadening. Wider columns provide
for more peak volume, and this reduces the importance of extracolumn band
broadening.
In ideal SEC, KD ranges from zero for a fully excluded solute to 1 for a fully
included solute. Unlike that in interactive liquid chromatography, in which
efficiency is roughly independent of the retention factor, the highest efficiency in
SEC is obtained for the smallest molecular weight compound that elutes last from
the column, that is, in the total mobile-phase volume. Larger compounds that are
partially excluded from the pores have broader peaks as a result of slower and
restricted diffusion into the pores. The relative importance of extracolumn band
broadening diminishes with increasing peak volume. Thus, in SEC, the
contribution of the system to extracolumn band broadening is best studied for a
small molecular weight solute that elutes in the total inclusion volume.
Sternberg (106) first showed that the variance of the chromatographic output
function can be written as the sum of the variances of the distributions of the
© 2004 by Marcel Dekker, Inc.