Summary
Some porous packings used in chromatography have been claimed to be fractals with a scale of sizes a<l<L, where a is a molecular size and L is the size of the largest pores. For a fractal porous packing, the excluded volume for molecules in solution in the vicinity of the packing surface is directly related to Df, the fractal dimension of the pore surface (2<Df<3). Since retention in size exclusion chromatography is itself directly related to this excluded volume, the fractal nature of the packing provides a model of retention in this technique. According to this model there is a linear relationship between log Rs and log(1-Kd), where Rs is the hydrodynamic radius of the solute macromolecules and Kd the distribution coefficient. The fractal dimension is derived from the slope of this plot. Size exclusion chromatographic retention data have been analyzed according to the model. It is found that some HPLC packings are fractals with fractal dimensions ranging from about 2.15 to 2.6, depending on the material. Such a large range of Df values indicates large variations in the selectivities and domains of applications of the different packings. For some classical gel filtration chromatographic gels, the fractal retention model does not seem to apply.
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Brochard, F., Ghazi, A., Le Maire, M. et al. Size exclusion chromatography on porous fractals. Chromatographia 27, 257–263 (1989). https://doi.org/10.1007/BF02260458
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DOI: https://doi.org/10.1007/BF02260458