64 August / September 2019
in industry is to use an empirical approach, although even here there are some general rules that will help establish a more robust methodology. Guillarme suggested the following;
The rules are;
• the stationary phase chemistry in the target system should be identical to the original system
• the ratio between the column length (L) and the particle diameter (dp) of the target system should be the same as the original system (the L/dp rule)
• the ratio between the injection volume and the column void volume in both the systems should be the same
• the reduced linear velocity in both the systems should be the same. Conclusion
Figure 1: A schematic plot showing a ‘Pressure drop across the column’ contour plot showing effect of column pressure and temperature. The shaded area represents the conditions for a different physical state.
pressure drops at higher MeOH concentrations or pressures. This is counter to most of the recent SFC literature recommendations which stress relationships between density and retention. Changes in viscosity, not density, explains both pressure drops and changes in diffusion coefficients with pressure and modifier concentration. Unfortunately, viscosity data are nearly non-existent.”
This presents an interesting perspective though as it suggests that if the density is not considered that there is a non-linear relationship with other parameters, and ultimately the retention time. The final consequence of this non-linearity is that the analytical system may be susceptible to small perturbations. Thus it is probably this term that needs to be considered the most when transferring methods as it can be impactful on the retention times. Unfortunately, it is not feasible to measure the density within a chromatographic system. Most commercial systems at best will have one or two pressure sensors placed at one end or both ends of the column, and from this a nominal density could be calculated. To determine a pressure or a calculated density reading along the column assumes that the pressure drops evenly per unit length, which may not be the case. Figure 1 highlights the issue. In this figure the outlet pressure of the column is plotted against the temperature, with the pressure drop across the column represented by the contour lines. It can be seen that small differences in the experimental arrangement can result in either increase or decreases in the pressure which will result in retention time variability.
Scaling strategies
There are a range of numerical models that can be used to aid scale-up and can also be used to determine the stability of the assay performance. These models include the Equilibrium Dispersive model, the Lump-Kinetic and general rate models. These models do need experimental input data to allow a degree of characterisation of the analytical system, however they are typically only employed in an academic environment. A common approach to optimising a method
As with all method transfer and method scale up it is important to be aware of the impact that each parameter can have on the analytical performance. The challenge with SFC is that the flexibility of the technology results in a greater potential for instabilities to be built into the analysis, and this will ultimately result in challenges for the separation scientist. As with all chromatography the solution is to ensure that the operators have a thorough understanding of the practical and theoretical aspects of using a supercritical fluid. In particular a thorough understanding of the subtle interplay between co-solvent, pressure, temperature, diffusion and viscosity is key to ensure the development of robust methodologies.
References
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4. D. Asberg, M. Enmark, J. Samuelsson, T. Fornstedt, J. Chromatogr. A. 1374 (2014) 254-260
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6. R.J. Smith, D.R. Taylor, S.M. Wilkins, J. Chromatogr. A 697 (1995) 587. 7. Chromatography Today, Aug/Sept. 2018, 44-46 8. G. Guiochon, A. Tarafder, J. Chromatogr. A, 1218 (2011), pp. 1037-1114
9. K. De Klerck, D. Mangelings, Y. Vander Heyden, J. Pharm. Biomed. Anal., 69 (2012), pp. 77-92
10. L.C. Harps, J.F. Joseph, M.K. Parr, J Pharm. Biomed. Anal., 162 (2019) 47-59;
11. C. West, A. Bouet, S. Routier, E. Lesellier, J. Chromatogr. A. 1269 (2012) 325-335
12. A. Kristl, P. Lokošek, M. Pompe, A. Podgornik, J. Chromatogr. A, 1597 (2019) p89-99
13. D. McCalley, TRAC, 63 (2014) p31-p43 14. C. Wang, Y. Zhang, J. Chromatogr. A. 1281 (2013) 127-134
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16. T. Berger, Chromatography Today, Feb/Mar 2019, 28-31
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