A plot of the detector response present at the column outlet as a function of
time is called a chromatogram (Fig. 31.6). The time from injection of the
sample until the peak elutes from the column is called the retention time, tr.
The amount of compound present for a given peak can be quantified by
measuring the peak height or area (most useful) and comparing it with the
response for a known amount of the same compound.
The aim of any chromatographic system is to resolve a number of
components in a sample mixture, i.e. to ensure that individual peaks do not
overlap or coincide. To achieve this you need to consider several important
factors: capacity factor, separation factor or selectivity, column efficiency and
Capacity factor, k':
This is a more useful measure of peak retention that
retention time, as it is independent of column length and flow rate. To
you need to measure column dead time, to
. This is the time it
takes an unretained component to
|Fig.31.6 Peak characteristics in a chromatographic separation, Le. a chromatogram. For symbols, see eqns [31.1] and [31.3].
pass through the column without any
interaction with the stationary phase. It is the time taken from the point of unretained component. The capacity factor for other components can then be
calculated according to the following equation:
Separation factor, α:
The separation factor, or selectivity, identifies when the
peaks elute relative to each other. It is defined for two peaks as the ratio of
the capacity factors (k'2
|⇒ Equation [31.2]
||tr,2 − to
||tr,1 − to
are the retention times of peak 1 and peak 2, respectively.
If two peaks are present the separation factor must be greater than one to
achieve an effective separation.
Column efficiency (plate number), N:
An additional parameter used to
characterize a separation system is the plate number, N
. It represents, in
general terms, the narrowness of the peak and is often calculated as follows:
where tr is the retention time of the peak and w0.5 is its width at one-half of
its height (Fig. 31.6).
For a compound emerging from a column of length L, the number of
theoretical plates, N, can be expressed as:
|⇒ Equation [31.4]
is the plate height (or height equivalent to a theoretical plate). In
general, chromatographic columns with larger values of N
give the narrowest
peaks and generally bftter separation.
Asymmetry factor, As:
The plate number, N
, assumes that the peak shape is
Gaussian, but in practice this is rare. It is more likely that the peak is
asymmetrical, i.e. it 'tails'. This is quantified using the asymmetry factor, As
calculated as shown Fig. 31.7.
A vertical line is drawn between the peak maximum and the base line. At
10% of the peak height, the width of the peak to the leading edge and the
trailing edge is measuted (a
in Fig. 31.7). The asymmetry factor is then
calculated as follows:
|⇒ Equation [31.5]
|Fig.31.7 Peak asymmetry.
In general, As
values between 0.9 and 1.2 are acceptable. If As
> 1 peak tailing
is in evidence; if As
< 1 peak fronting is evident. The practical impact of peak
tailing or fronting is that adjacent peaks are not as well separated as they would
be if they were symmetrical, leading to difficulties in peak quantitation.