Chemical Analysis. Francis Rouessac

retention time t_R of an alkane having n atoms of carbon, minus the dead time t_M; a and b are numerical coefficients. The slope of the graph obtained depends on the overall performance of the column and the operating conditions of the chromatograph.

      This expression follows on from another linear relation seen in thermodynamics linking the variation in free energy and the equilibrium constant K (∆G = −RT ln K), for a homologous family of compounds in which each term differs from the preceding one by an additional CH₂ unit. Since K = kβ, ; thus log will increase with ln K for the homologous family: ln .

      2.10.2 Kovats Retention Index

      A compound (X) is now injected onto the column without changing the settings of the instrument. The resulting chromatogram will enable I_x, the Kovats retention index, to be calculated for X on the specific column employed: this is equal to 100 times the equivalent number of carbon atoms n_x of the ‘theoretical alkane’ having the same adjusted retention time as X. Two methods can be used to find the number n_x of equivalent carbons of X.

      The first is based on the Kovats relationship obtained above (Figure 2.17). This leads to a calculation of n_x (therefore I_x), using a spreadsheet, for example.

The second can be used to calculate I_x directly from the adjusted retention times of the two n‐alkanes (n and n + 1 C) that bracket compound X on the chromatogram:

(2.4)

      In contrast to the Kovats regression line, the retention indexes depend only on the stationary phase and not on the settings of the chromatogram. In particular, they do not depend on retention times.

In practice, to ensure that the experimental conditions for the two injections are uniform, compound X and the n−alkanes mixture are co‐injected (Figures 2.9 and 2.18).

The chromatogram that gives the Kovats relationship for a given stationary phase can also serve to evaluate expected column performance. For this, the separation number, also known as the trennzahl number (TZ), is calculated from Eqs. (2.5) or (2.6). The two retention times occurring in these relationships relate to two successive alkanes differing by one carbon number (n and n + 1 atoms) or to two compounds of the same type. The separation number indicates how many compounds could be separated reasonably well by the column in the arbitrary elution interval of these two compounds. The alkanes whose elution times are on either side of that of the analyte are chosen. For the chromatogram in Figure 2.18, TZ is around 30.

Figure 2.18 Kovats retention index (I = 100n_x) on a column in isothermal mode. The equivalent number of carbons n_x is found from the logarithm of the adjusted retention time t′_R(X) of X. The chromatogram corresponds to the injection of a mixture of four n‐alkanes and two aromatic hydrocarbons. The values in italics indicate the retention times given in seconds. By injecting this mixture periodically, the modifications to the Kovats indexes of these hydrocarbons enable us to track the column’s performance. With temperature programming, we can still plot this relationship using an adjusted formula, though this entails a reduction in precision.

(2.5)

      or

(2.6)

      There are tables of retention indexes of compounds currently in general use on the most common stationary phases. If several retention indexes of the same compound obtained on different stationary phases are available, then this unique collection of values could then characterize the compound with greater certainty. However, identification by retention index is not as reliable as using coupled techniques such as GC/MS (see Section 2.7.1), which require more expensive equipment.

It should be remembered that the above calculations for retention indexes imply that the measurements were made under isothermal conditions. With temperature programming, they still give good results when substituting retention times for the corresponding logarithms in Eq. (2.4).

      Retention time locking. It is obviously difficult to identify compounds whose retention times are very close and whose mass spectra are almost identical (certain forms of isomers). A current method consists in selecting an internal standard or a compound known to be present in all of the samples to be analysed. Through the use of computer software, the value of its retention time is locked for the different analyses, even if these are undertaken on different apparatuses. The effect of this is to conserve the retention times of the other compounds of the mixture, facilitating their identification. This approach, which avoids use of retention indexes, is possible with modern GC instruments and is known as Retention Time Locking (RTL).

      2.10.3 McReynolds Constants for Stationary Phases

To evaluate the behaviour of a stationary phase, a comparison of the Kovats indexes for five reference compounds belonging to different structural classes is made on the studied phase as well as on squalane, chosen as the reference phase for this calculation. The five indexes on a column using squalane, the only reproducible nonpolar phase since it is formed from a pure material, have been established once and for all (Table 2.2).

The five McReynolds constants for a given stationary phase are obtained (Eq. (2.7)) by