Martin's rule revisited. Its molecular sense and limitations

The linear relation ln k' = Bn + ln A between the retention factor k' in liquid adsorption chromatography (LAC) and the number of repeat units n within a homologous series of oligomers is called Martin's rule. This empirical relation was supported by the retention behavior of the homologous series of different classes of oligomers but had no theoretical justification. In this paper, it is demonstrated that Martin's rule is a consequence of the general theory of liquid chromatography and the molecular sense of coefficients B and A is clarified: B is the Gibbs energy of the repeat unit of the long polymer chain adsorbed at the wall surface, and A is a combination different parameters which characterize the column and the adsorption correlation length H. The theory predicts the deviations from the linear dependence under conditions of weak adsorption between repeat units and stationary phase when H is close to radius of gyration Rg. Experimental data for retention volumes and selectivity of poly(ethylene glycol)s are given for normal and reversed-phase LAC on different columns in acetone-water and methanol-water as mobile phases. These data show excellent agreement between the theory and experiments. It is shown that Martin's rule holds under special conditions, which are theoretically defined by the relation H > Rg/1.5.