Chemical Analysis. Francis Rouessac
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k′ rather than by k alone.
This parameter takes into account the ability, great or small, of the column to retain each compound (capacity). When separations are being developed, k should not exceed 10. Ideally, k should be around five, otherwise the time of analysis is unduly long.
The expression capacity factor presents a possible confusion with the capacity of a column, which is the maximum solute mass the column may retain without being saturated. This factor is given by manufacturers when describing a column.
An experimental approach to the retention factor k
On the basis of Craig’s model, each molecule is considered as passing alternatively from the mobile phase (in which it progresses down the column) to the stationary phase (in which it is immobilized). The average speed of the progression down the column is slowed if the time periods spent in the stationary phase are long. Extrapolate now to a case that supposes n molecules of this same compound (a sample of mass mT). If we accept that, at each instant, the ratio of the nS molecules fixed upon the stationary phase (mass mS) and of the nM molecules present in the mobile phase (mass mM) is the same as that of the times (tS and tM) spent in each phase for a single molecule, the three ratios will therefore have the same value:
Take the case of a molecule that spends 75% of its time in the stationary phase. Its average speed will be four times slower than if it stayed permanently in the mobile phase. As a consequence, if 4 μg of such a compound has been introduced onto the column, there will be an average of 1 μg at all times in the mobile phase and 3 μg in the stationary phase.
Since the retention time of a compound tR is such that tR = tM + tS, the value of k is therefore accessible from the chromatogram
(1.27)
This important relation can also be written:
(1.28)
In light of Eqs. (1.16) and (1.18), the retention volume VR of a solute can be written:
(1.29)
or
(1.30)
This last expression linking the experimental parameters to the thermodynamic coefficient of distribution K is valid for ideal chromatography.
1.8 SEPARATION (OR SELECTIVITY) FACTOR
The separation factor α (Eq. (1.31)) enables the comparison of two adjacent peaks 1 and 2 present in the same chromatogram (Figure 1.7). It is defined by Eqs. (1.31) and (1.32).
By definition α is greater than unity:
or
The expression, connecting α to the Nernst distribution coefficients of the two solutes, shows that selectivity is dependent only on the value of these constants (intensity of interactions, temperatures) and does not depend on the column’s geometry (length and diameter) or its packing (diameter of particles and quantity of stationary phase). For nonadjacent peaks, the relative retention factor r is calculated in a similar manner to α, and cannot be less than 1.
1.9 RESOLUTION FACTOR
To quantify the separation between two compounds, the resolution factor R is calculated from the chromatogram (Figure 1.8):
(1.33)
For two adjacent peaks, this relationship involves two parameters: firstly, the difference between their retention times, tR(2) − tR(1), which corresponds to the distance between the two peaks, and, secondly, their half‐width at the base, ½ (ω2 + ω1) if we assume that each peak corresponds to an isosceles triangle (Figure 1.8).
Other expressions derived from the preceding ones and established with a view to replacing one parameter by another or to accommodating simplifications may also be employed to express the resolution. Therefore, Eqs. (1.34)–(1.36) are used quite often.
Equation (1.35) shows how resolution is affected by the efficiency, capacity factor, and selectivity factor. The chromatograms in Figure 1.9 present an experimental verification of this.