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11.2.3 Retention factor

One of the most important parameters in chromatography is theretention factor,

k(previously calledcapacity factorand represented by the symbolk^0 ). It is simply the

additional time that the analyte takes to elute from the column relative to an

unretained or excluded analyte that does not interact with the stationary phase and

which, by definition, has akvalue of 0. Thus:

k¼tRtM

tM

¼t

(^0) R
tM
ð 11 : 3 Þ
It is apparent from this equation that if the analyte spends an equal time in the
stationary and mobile phases, itstRwould equal 2tMand itskwould be 1, whilst if
it spent four times as long in the stationary phase as the mobile phasetRwould equal
5 tMso thatkwould equal 5tMtM/tM¼4. Note thatkhas no units.
If an analyte has akof 4, it follows that there will be four times the amount of
analyte in the stationary phase than in the mobile phase at any point in the column
at any time. It is evident, therefore, thatkis related to the distribution coefficient
of the analyte (equation 11.1), which was defined as the relative concentrations of
the analyte between the two phases. Since amount and concentration are related by
volume, we can write:
k¼t
0
R
tM

¼MS

MM

¼KdVS

VM

ð 11 : 4 Þ

whereMSis the mass of analyte in the stationary phase,MMis the mass of analyte in

the mobile phase,VSis the volume of stationary phase andVMis the volume of mobile

phase. The ratioVS/VMis referred to as thevolumetric phase ratio,b. Hence:

k¼Kdb ð 11 : 5 Þ

Thus the retention factor for an analyte will increase with both the distribution

coefficient between the two phases and the volume of the stationary phase. Values

ofknormally range from 1 to 10. Retention factors are important because they

are independent of the physical dimensions of the column and the rate of flow of

mobile phase through it. They can therefore be used to compare the behaviour of

an analyte in different chromatographic systems. They are also a reflection of the

selectivity of the system that in turn is a measure of its inherent ability to discriminate

between two analytes. Such selectivity is expressed by theselectivityorseparation

factor,a, which can also be viewed as simply the relative retention ratio for the two

analytes:

¼kA

kB

¼KdA

KdB

¼

t^0 RA

t^0 RB

ð 11 : 6 Þ

The selectivity factor is influenced by the chemical nature of the stationary and

mobile phases. Some chromatographic mechanisms are inherently highly selective.

Good examples are affinity chromatography (Section 11.8) and chiral chromatog-

raphy (Section 11.5.5).

437 11.2 Chromatographic performance parameters