Isothermal retention times, predicting

Using temperature and retention factor data for 50 and 60°C, we can compute the coefficients A and B in Equation 4.5 for this example, and then apply them to higher temperatures in order to predict isothermal retention times and retention factors. These data can then be used to predict how far the peak will move during each discrete temperature step in our example. A spreadsheet program was used to calculate this data as shown in Table 4.4. The values for k and iR are for isothermal elution at the indicated temperamre step. The values for Zt are the total distances the peak has moved at the end of the indicated step. The last entry for Zt shows that the peak has been eluted from the column (z, = 10.0 m) in just less than 5 min during the 90°C temperature step. 

Although PTGC was used as early as 1952 for the separation of alkyl chlorides, the technique did not achieve general acceptance until after the fundamental work of Dal Nogare and co-workers (27-29) and the activities of Martin and co-workers (30), who first made commercial PTGC equipment available and showed how one could predict retention times based on isothermal data by the use of graphical methods. 

This approach is valid for more complex isotherms only when the i.e., ternary interaction effects can be neglected and the adsorbate-adsorbate interactions in the ternary system are the same as these interactions between the same components in the corresponding binary systems. The validity of this assumption was confirmed for the mixtures of fructose and dextran T6, of fructose and dextran T9, and of dextran T6 and dextran T9, by comparing the predicted and the measiued retention times obtained for the ternary system [111]. 

The apparent plate munber can be calculated from the experimental profiles [27]. However, this number depends on the fractional height at which the bandwidth is measured. The value of Nth is calculated from the profiles predicted, under the same experimental conditions, by the ideal model. Finally, Nion is derived from the band profiles recorded in linear chromatography, e.g., with a very small sample size, using the relationships valid for Gaussian profiles. From Eqs. 7.24 and 7.26, we can derive the band width at half height, Wi/2, and the retention time of the band profile, ty, obtained with an infinitely efficient column. In the case of a Langmuir isotherm, we obtain [31]... 

In the former case [32], the production rate of 99% pme enantiomers from the racemic mixture of R- and S-2-phenylbutyric acid was maximized as a function of the sample size and the mobile phase composition. The calculations were based on the column performance and the equilibrium isotherms of the two components (bi-Langmuir isotherms. Chapter 3). The separation was performed on immobilized bovine serum albumin, a chiral stationary phase, using water-methanol solution as the mobile phase. The retention times decrease with increasing methanol content, but so does the separation factor. For this reason, the optimum retention factor is around 3. Calculated production rates agree well with those measured (Table 18.4). The recovery yield is lower than predicted. 

Type of data used in the estimation. The minimum requirement is the availability (from experimental measures or from published data) of the retention time of the analytes in GC columns having the same stationary phase used in the 2D GC xGC set object of the estimation, assuming a variation of retention with temperature similar for all the compounds. In order to obtain higher prediction accuracy, retention times should be measured at least at three different temperatures in the isothermal mode. If RI values are used, reference n-alkanes should be run under the same conditions. If the objective is optimisation, several runs are also required in the specific GCxGC set to be optimised, in order to correct errors related to column geometry or to the use of stationary phases from different batches. 

The programing procedure usually involves three stages. An initial isocratic period is introduced to efficiently separate the early eluting peaks with adequate resolution. The isocratic period is followed by a linear increase in column temperature with time, which accelerates the well-retained peaks so that they also elute in a reasonable time and are adequately resolved. The effect of linear programing can be calculated employing appropriate equations and the retention times of each solute predicted for different flow rates (see Programmed Temperature GC, p. 1918). To do this, some basic retention data must be measured at two temperatures and the results are then employed in the retention calculations. The temperature program often ends with a final isothermal period. This is usually... 

In reality it is neither practical nor desirable to step the column oven temperature in 10° increments every minute, nor does the stepwise model predict elution times with sufficient accuracy for our purposes. If we now imagine instead that the oven temperature increases in 1° steps every 6 s or even better in 0.1° increments every 600 ms, we can approach a true linear temperature program rate of 10°C/minute as is encountered in modem gas chromatographic systems. Our isothermal retention data at 50 and 60°C are still valid, and we could calculate the peak positions for each 0.1°C step in a tabular format. The problem is that even this small a step is still too large for accurate prediction of programmed-temperature retention times. Instead, we must to turn to calculus and consider an arbitrarily small step size (dt). A simplified relationship of a single-step linear temperature program to elution time can be expressed as follows [13] ... 

These mathematical models enable prediction of isothermal or temperature-programmed retention times with very good accuracy, and so chromatographers can estimate the effects of changing conditions on peak elution sufficiently well to provide a good basis for optimization. These models do not take into account any of the band-broadening processes that determine peak shapes, and therefore alone they cannot predict peak resolution, Trennzahl or separation number, or any other measurement of chromatographic quality. 

The prediction of GC retention data is based mostly on the retention index introduced by Kovats. The measured retention time for an isothermal chromatogram is dependent on the flow rate of the eluent gas and the column temperature. To be able to compare the retention under different column conditions, the retention of n-alkanes is measured under the same conditions. The retention index of an n-alkane is defined as the number of C-atoms times 100. n-Hexane, for example, has an retention index of 600. The retention times of all other solutes are converted to retention indices according to... 

Laboratory measurements of the losses of CO2 and C02 from a surrogate unsaturated zone atmosphere to unsaturated sediments indicate the presence of an adsorbed C phase that can retard C02 transport in the unsaturated zone. Measured losses of CO2 from the atmosphere were 8 to 17 times greater than those predicted by calcite equilibrium calculations. Modeled predictions of C02 transport in a cross section near buried low-level radioactive waste support the presence of the adsorbed C phase distribution of P C02 was more accurately simulated using a model of C02 retention based on measured CO2 -loss isotherms than with a model based on calcite equilibrium control. Failure to account for the adsorbed C phase can lead to substantial errors when using models to estimate C transport and exchange in the unsaturated zone. 

---