Chromatographic Retention

Retention parameters are measured in terms of times, mobile-phase volumes or retention factors (k) (previously called capacity factors: k'). If the flow rate is constant, the volumes are proportional to times, e.g. tR (time) is analogous to VR (volume).

If a mixture is chromatographed, the time taken for a component to be eluted from the column, the (total) retention time (tR), is measured from the moment of injection to the appearance of the peak maximum. This, together with the width of the peak measured at the baseline (w) or at half peak height (wh), and the elution of an unretained peak, are important parameters in chromatography and are illustrated in Figure 2, which shows the separation of a two-component mixture eluting with retention times (tR^ and (tR)2, with an unretained component (retention time, tM).

The retention volume (VM) of an unretained peak (where VM = FxtM) is also called the mobile-phase volume and equals the volume (both inter- and intra-particle) available to the mobile phase in the column.

The adjusted retention time/volume (tR/VR) is the total elution time/volume minus the retention

Figure 1 The general elution problem.

Unretained component

Time

Figure 2 Separation of a two-component mixture showing retention parameters. See text for details.

time/volume of the mobile phase:

The unretained peak, which has no affinity for the stationary phase and does not exhibit exclusion, passes through the column at the same speed as the mobile phase. A substance which shows affinity for the stationary phase moves through the column more slowly than the mobile phase and is said to be retained. The ratio of the two velocities is known as the retardation factor (R):

^ rate of movement of retained peak rate of movement of mobile phase

A retained component spends time in both the mobile phase (tM) and the stationary phase (tS) and retention time tR is given by:

The time spent in the stationary phase is dependent on the distribution coefficient (Kc) such that tS = KcVS. If CS and CM are the concentrations of a component in the stationary phase and mobile phase respectively, the distribution constant is given by:

the stationary phase (a high distribution coefficient) moves slowly through the column. Components of a mixture are, therefore, separated only if their distribution coefficients differ. Using volumes rather than times we can write:

which is the fundamental equation for chromatogra-phy, neglecting the effects of nonlinearity of the sorption isotherm and band broadening.

In adsorption chromatography the stationary-phase volume is replaced by the surface area (AS) of the stationary phase, and the distribution coefficient is changed to the adsorption coefficient (KA).

An alternative expression (the retention factor: k) for the distribution of a sample component is in terms of the relative number of moles (n) of a component in the stationary and mobile phases, such that:

amount of solute in the mobile phase

amount of solute in mobile + stationary phases

The rate of movement of a component through the column is inversely proportional to the distribution constant, i.e. a substance with a high concentration in

Substituting the retention factor into the equation: VR = Vm + KcVs gives VR = Vm(1 + k) [14]

or using retention times:

and on rearrangement:

This last expression is widely used as a simple way of expressing retention from values easily measured from the chromatogram, and without the need to measure flow rates. Since:

we can write:

Hence the retention time is directly proportional to the column length and inversely proportional to the linear flow rate of the mobile phase.

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