Peak-fitting method

Application of the ECP method did not provide satisfactory results for the case of bicalutamide and anaesthetic gases. The main reason for that was the low number of theoretical plates of the columns (41 for bicalutamide, 84 for isoflurane and 91 for desflurane). Therefore, the adsorption isotherm parameters were also determined by peak-fitting method. It is a well-known method in chromatography for adsorption isotherm estimation.

In Chapter 3, section 3.2 the concept of the method was described with introducing the idea to apply it for estimation of the enantiomer isotherms from experiments with racemic mixtures. Before employing this method, one needs first to propose a model that would describe the process properly, and then to provide the values of all model parameters except the adsorption isotherms. Here the method applicability will be tested and validated using the example of bicalutamide and afterwards it will be applied for the anaesthetic gases. Since the use of the peak-fitting method requires adopting a column model in advance, its application also served here as evidence that the equilibrium dispersive model with assumed constant mobile phase velocity can be used for describing the gas-chromatographic process with diluted systems.

7.2.1 Peak-fitting method representation and validation using bicalutamide

The application of the peak-fitting method for chiral systems was first tested for bicalutamide. In general, possible difficulties when using racemic mixtures include inaccessibility of pure components, as well as detection issues. The latter is due to the fact that for most of the detectors intensity of signal of both enantiomers is equal. While this is a problem when applying other isotherm determination methods, for the peak-fitting it represents an advantage, because here the complete elution profile that contains both enantiomers is analysed. The fact that the signal from racemic mixture is equal to the signal of single enantiomers, makes the calibration easier and does not require pure components.

By simulating the elution profile with adopted column model and competitive Langmuir isotherm (eq. (2.33)) for different injection volumes and by applying the optimization routine for minimizing the objective function given by eq. (3.13) the isotherm parameters that provided the best fit were estimated. The first guesses used in the fitting procedure were the values obtained in the previous section from the binary-mixture ECP method.

The obtained values of the isotherm parameters H and b are given in Table 7.6 for both bicalutamide enantiomers.

7 Determination of adsorption isotherm parameters (only racemic mixtures available) 111

Table 7.6. Competitive Langmuir adsorption isotherm (eq. (2.33)) parameters of bicalutamide enantiomers at 25 ᵒC determined with the peak-fitting method.

Isotherm parameters S-Enantiomer (Component 1) R-Enantiomer (Component 2)

H [l/l] 0.29 4.98

b [l/g] 0.43 0.53

The competitive adsorption isotherms are shown graphically in Figure 7.9. From the figure the same can be concluded as by analysing the parameter values. The used column provides efficient separation of bicalutamide enantiomers with high selectivity.

Figure 7.9. Adsorption isotherms of bicalutamide enantiomers (S and R) at 25 ᵒC determined for a Chiralpak AD stationary phase. The isotherms are described by the competitive Langmuir model (eq. (2.33)) with the parameters given in Table 7.6.

Separation process for different injection amounts was simulated using the calculated parameters and compared to the experimental results. Four examples are given in Figure 7.10.

By observing the elution profiles, it can be stated that the matching between the experiments and simulation is very good, what means that the determined adsorption isotherms can be used for further predictions. The comparison of the experimental and theoretical profiles reveals that better matching is obtained for greater injected volumes. Larger deviations are observed in the peak shape, while the positions were correct, with only small difference for the 50 μl injection.

Even though the determined isotherm parameters provided good predictions by simulating elution profiles, they were estimated only from experiments with 1:1 mixture and therefore additional validation would be advantageous. As it was introduced in section 1.3, one of the reasons why bicalutamide was chosen as a reference substance, was that its single enantiomers were available for experiments. Therefore, to confirm the validity of the calculated isotherm parameters, they were used for simulating a chromatographic process with single enantiomers. Like for the tests with the mixture, the simulations were compared with experiments. While on one hand R-enantiomer was found not to be completely pure and it could only be concluded that the peak position was correct, on the other hand S-enantiomer was successfully employed for the method validation. Elution profiles resulting from pulse injections of S-enantiomer (first eluting component) are shown in Figure 7.11. It can be seen

112 7 Determination of adsorption isotherm parameters (only racemic mixtures available)

that the difference between the simulation and experimental profiles is very small and almost negligible.

Figure 7.10. Comparison of experimental (dotted line) and simulated (solid line) elution profiles of bicalutamide racemate for different injection volumes: a) 50 µl, b) 70 µl, c) 90 µl, d) 100 µl. Feed concentration was 19.2 g/l of racemic mixture and flowrate 2.5 ml/min.

Figure 7.11. Comparison of experimental (dotted line) and simulated (solid line) elution profiles of S-bicalutamide for different injection volumes: a) 50 µl, b) 70 µl, c) 90 µl, d) 100 µl. Feed concentration was 20 g/l and flowrate 2.5 ml/min.

7 Determination of adsorption isotherm parameters (only racemic mixtures available) 113

With these tests it could be concluded that the determined isotherm parameters can be considered as reliable, thus the described method can be applied to other racemic mixtures, even when no pure enantiomers are available for experiments.

7.2.2 Peak-fitting method application for isoflurane and desflurane

As for the demonstrational case of bicalutamide, in the case of isoflurane and desflurane the starting experiments included pulse injections of different amounts (shown previously in Figure 6.9 and Figure 6.10). These profiles were used for isotherm calculation. Taking the already calculated values of Henry constants (Table 6.3) and the first estimates from the ECP method (Table 7.5), the procedure for estimating the complete isotherm was performed. The values of the determined isotherm parameters are presented in Table 7.7.

Table 7.7. Competitive Langmuir adsorption isotherm parameters of isoflurane and desflurane enantiomers at 28 ᵒC determined by the peak-fitting method.

Isotherm parameters

Isoflurane Desflurane

S-Enantiomer (Component 1)

R-Enantiomer (Component 2)

S-Enantiomer (Component 1)

R-Enantiomer (Component 2)

H [l/l] 467.7 765.5 70.03 112.4

b [l/g] 17.6 39.3 1.91 5.03

The competitive Langmuir isotherms of S- (Component 1) and R-enantiomer (Component 2) of isoflurane and desflurane are shown in Figure 7.12. The isotherms are presented for the mobile-phase concentration range (0 - 0.03 g/l) that corresponds to the values in the elution profiles of both substances.

Figure 7.12. Adsorption isotherms of isoflurane (left) and desflurane (right) enantiomers (S – component 1 and R – component 2 for both substances) at 28 ᵒC on stationary phase based on modified γ-cyclodextrin (defined in section 6.1.2.1). The isotherms are described by the competitive Langmuir model (eq. (2.33)) with the parameters given in Table 7.7.

114 7 Determination of adsorption isotherm parameters (only racemic mixtures available)

As pointed out before, by comparing these isotherm parameters, determined by peak-fitting method, with those estimated by binary-mixture ECP method (Table 7.5), we can see that they follow the same pattern and that the corresponding values are in the similar ranges. In order to check if the values calculated now give better agreement with the experimental peaks, the simulated elution profiles are compared to the experimental ones, as it was done for bicalutamide. In Figure 7.13, it can be seen that for isoflurane there is a very good agreement between the experimental and simulated profiles for different injection amounts.

Figure 7.13. Comparison of experimental (dotted line) and simulated (solid line) elution profiles of isoflurane for different injection volumes: a) 1 µl, b) 3 µl, c) 4 µl, d) 5 µl. Injected pure racemic mixture in liquid phase.

Flowrate was 71 ml/min.

The same comparison for desflurane is shown in Figure 7.14. For desflurane the largest injection available from the experiments was the one of 1 μl and since the elution profiles resulting from even lower injection amounts are not relevant for the further process analysis, only this one was presented.

When analysing the simulated and experimental profiles in Figure 7.13 and Figure 7.14 it can be seen that they correspond well to each other. There are small discrepancies and it can be noticed that for all the cases they have the same form. This is mainly due to the fact that in the model used for simulations the same dispersion coefficient (and accordingly also NTP) was taken for both enantiomers. On the other hand, as reported in Table 6.3, it is known that these values are close to each other, but still larger for the S-enantiomer (first component).

Therefore, simulations predict slightly higher degree of dispersion for the first component and lower for the second component as it is in the reality.

7 Determination of adsorption isotherm parameters (only racemic mixtures available) 115

Figure 7.14. Comparison of experimental (dotted line) and simulated (solid line) elution profiles of desflurane for injection volume of 1 µl. Injected pure racemic mixture in liquid phase. Flowrate was 21 ml/min.

Since the differences between simulation and experiments are not significant, it can be concluded and that the matching is very good and that the calculated isotherms could be used for the correct prediction of the separation of the enantiomers of fluorinated anaesthetics.