Orientation of Rigid Macromolecules during Hydrodynamic Chromatography Separations

We have recently reported the successful separation of xanthan polysaccharide macromolecules by hydrodynamic chromatography. We show here that kinetic theory calculations of the orientation of rodlike macromolecules by flow in porous media can be used to intepret the experimentally observed chromatographic separations. Xanthan is a rigid rodlike molecule approximately 1 jum in length and 40 A in diameter, yet it is found experimentally to elute from the chromatography column at the same volume as a 0.153-μm diameter latex sphere. To relate the physical dimensions of the xanthan molecule to its “apparent hydrodynamic volume” as determined from chromatography experiments, we begin by modeling the molecule as a rigid dumbbell. Elongational strain rates and shear rates characteristic of flow through a packed bed of impermeable 25 μm spheres are calculated and subsequently used to obtain the orientational distribution function for the dumbbell in elongation and shear. The projection of the distribution function in the direction of flow is evaluated to determine an effective radius (or cross section) for the oriented dumbbell. In elongation the effective diameter is 0.14 μm; in shear the effective radius is 0.22 μm. These values compare favorably with the experimentally determined value of 0.153 μm. The analysis predicts the effects of flow rate and packing diameter on the separations of nonspherical particles by hydrodynamic chromatography. In addition, the analysis provides a framework for investigating the maximum size rigid macromolecule that can pass through a porous media of given characteristics. The success of these order-of-magnitude calculations suggests that a more detailed analysis of the orientation in the complex two-dimensional flow field in a pore will prove fruitful.