18


December 2010


Figure 7. Experimental design for the 3-D retention model and its control. Red circles represent the twelve input experiments for the 3-D model, the light blue circles the validation experiments and the dark blue (tG 55ºC and MeOH in eluent B) and green (tG


= 22 min, T = = 45 min, T =


50ºC and MeOH:AN [80:20 V/V] in eluent B) circles optimum conditions for comparison (see Fig. 11 and 10 respectively).


Figure 6. 3-D Resolution space showing the tG – T (MeOH) plane. Red coloration within the resolution space indicates operating regions with Rs, crit> 1.5, whereas blue coloration indicates operating regions associated with co-elution or poor resolution. Predicted


# Peak name 1 Nicotine


2 Benzylamine 3 Procainamid 4 Terbutaline 5 Salbutamol 6 Amilorid


7 Trimethylbenzyalamine 8 Pindolol 9 Phenol


10 Benzylalcohol 12 Quinoxaline 11 Quinine


13 Oxprenolol


14 Chloropheniramine 15 ARC-68397 16 ARD-12495


17 Diphenhydramine 20 Remacemide 21 Desipramine 22 Nortriptyline


11.697 13.893 14.721 16.700 17.017 20.877 21.970 23.482 23.788 24.528 26.818 29.010 29.960


0.07 0.10 0.08 0.09 0.09 0.10 0.10 0.10 0.17 0.16 0.14 0.12 0.12 0.13 0.11 0.12 0.12 0.12 0.12 0.12


3.576 5.698 6.272 7.805 8.214 9.546 9.857


Actual


tR[min] W (½ ht) tR[min] % error W (½ ht) 3.572 5.702 6.269 7.811 8.215 9.555 9.875


0.11


-0.07 0.05


11.676 13.898 14.702 16.664 16.979 20.870 22.003 23.471 23.799 24.541 26.835 29.025 29.958


-0.08 -0.01 -0.09 -0.18 -0.18 0.04


-0.13 -0.22 -0.22 -0.03 0.15


-0.05 0.05 0.05 0.06 0.05


-0.01 Mean error in % 0.09


Table 2. Comparison of the predicted and experimental retention times, peak width and resolution using a binary mobile phase composition of MeOH, tG


below a baseline separation of Rs,crit By setting the Rs,crit


: 30 min and T: 40ºC. Average precision of predictions > 99.9%. > 1.5.


> 1.5 in the resolution map,


robust regions within the Design Space can be easily identified. The resolution map shown in Fig. 6 highlights that the separation (Rs,crit


has an extended robust region (shown in red) when MeOH is used in eluent B


> 1.5)


3.4 Validation of the 3-dimensional resolution model (the Cube)


The validity of the accuracy of the 3-D cubic retention model was determined by comparing the predicted and experimental retention times from the three validation runs in the 3-D design space, as shown in Fig.7. The


0.06 0.07 0.06 0.06 0.06 0.07 0.07 0.07 0.12 0.11 0.11 0.09 0.09 0.10 0.09 0.09 0.09 0.09 0.09 0.09


accuracy of the predicted retention times was excellent for the three validation experiments of the model, i.e., better than 99% accurate (deviations are in average less than 0.2%) as can be seen for the binary mobile phase composition using MeOH and a tG


of 30 min


and a T of 40ºC (see Table 2 for a typical result from one of the validation exercises). The average difference between predicted and experimental retention times is approximately 6 sec and the largest deviation is 14 sec.


Retention modelling with 99.9% accuracy in tR has the additional advantage that it allows the chromatographer a much higher degree of flexibility, in that the effect of changing operating parameters inside of the cube model can be quickly evaluated in order to test the robustness and improve the chromatography without the need for costly and time consuming method revalidation activities.


Fig. 8 illustrates the corresponding separation plane with 100% eluent B2 (organic modifier is AN). The separation throughout the plane is poor, indicating that no combination of the operating parameters (tG


and T) can afford


acceptable resolution. Evaluation of slices of the tG


-T planes throughout the cubic model visually shows that baseline resolution for the 22 compounds is only possible with an eluent B, which is rich in MeOH (i.e. > 80% B1) (see Fig.6). Hence, it is quickly established that it would be a waste of time and money to attempt to use AN in eluent B in this separation.


3.5 Robustness of the 3-dimensional


resolution model (the Cube) Fig. 9 illustrates that there are other additional robust regions within the design space for the separation for this complex separation, for example the use of the operating a ternary mobile phase composition containing (B1:B2)(80:20 V/V).


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