A scaling rule in supercritical fluid chromatography. I. Theory for isocratic systems

Scaling is regularly done in chromatography either to transfer a successfully designed method of analysis developed in one system to another system, or to scale-up a separation method developed in analytical scale to preparative scale. For liquid chromatography there are well-tested guidelines for scaling, which makes it a routine job. For supercritical fluid chromatography (SFC), on the other hand, neither do we have any well-understood principles behind scaling nor do we know how far the strategies applied in LC could be applicable to SFC. In this article, we have addressed these issues and proposed a rule applicable for scaling isocratic methods between different SFC systems and column dimensions under commonly used operating temperatures and pressures. We have shown that the scale-up and method transfer techniques used in LC can be applied to SFC, provided we ensure that both the original and the target systems in SFC operate at the same average density. The current article will present the theory, discuss the extents of applicability of this rule, and outline its limitations. In an accompanying article implementation of this rule in various practical situations will be presented.