Stochastic model for gel permeation separation of polymers

The stochastic theory of chromatography developed by Giddings and Eyring and by McQuarrie is applied to gel permeation chromatography (GPC) by first recasting their assumptions to fit the GPC process and secondly by making specific assumptions about the molecular size dependence of the rate constants λ1 and λ2 for entrapment and elution of a polymer molecule, respectively. The model assumes that: (1) a monodisperse sample is injected; (2) molecules behave independently within the column; (3) no molecular diffusion occurs; (4) the polymer molecules are unperturbed random coils; (5) entrapment sites in the bed are identical; (6) λ1 is proportional to the probability Pe that the square of the polymer end‐to‐end distance is less than the square of the average pore radius in the bed; (7) λ2 is constant. The calculated difference in retention times, tR‐to (where tR is the retention time for a molecule of arbitrary molecular size and to is the retention time for a molecule whose size totally precludes entrance into the pores of the bed), is shown to be proportional to Pe. The model as thus applied is based on only one parameter. The theory is tested by examining the ratio Pe/(tR − to)exp, predicted to be constant, for narrow polystyrene fractions in the molecular weight range 1.1 × 104 – 8.9 × 105. Chromatographs were obtained by Moore and Arrington by using a θ solvent and a single column packed with a porous glass bed having a sharp distribution of pore sizes. Ratio values ranged from 0.046 to 0.073 with an average value of 0.058 ± 0.009. This relative constancy demonstrates semiquantitative utility of the model for gaining insight into the GPC process.