Theoretical considerations on size-exclusion chromatography

At the present time (1988), it seems that there is no satisfactory theory of the size-exclusion chromatography, perhaps only because we lack a good model. We shall begin with a summary of the classical theory and later we shall run into a difficulty when trying to interpret this theory. 

It is classically assumed that, in the column, the molecules lie either in the interstitial space, where they are swept along by the liquid, or in the pores where the liquid stagnates. It is assumed that at any moment, we have a concentration equilibrium. Then, we have to evaluate the partition coefficient P. We understand that, owing to size effects the molecule may occupy only a part of the 

P — oocupiable volume of the pores/total volume of the pores. 

For reasons of simplicity, the molecules will be represented by spheres of diameter 2r and the pores as cylinders of diameter 2r0 (see Fig. 1.17). 

In Fig. 1.18, we represented ln(r/r0) as a function of P. The number P varies linearly with respect to the elution volume (see Section 1.6.1) and ln(r/r0) can be considered as a linear function of InM, where M is the molecular mass of the polymer. The curve of Fig. 1.18 has therefore to be compared to the calibration curves 14 and 15. Thus, it can be understood that by mixing three or four types of grains, with different porosities, it is possible to make columns which can separate polymers for very different values of the molecular mass. However, a question arises. In the model described above, what is the effective radius r of the polymer molecule Is it the square root R of the mean square end-to-end distance or the square root Ra of the mean square radius of gyration, or another length Let us now examine this problem. 

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