Mathematical Modelling of Size Exclusion Chromatography of Polymers

  • Author / Creator
    Gregory Afacan
  • Size-exclusion chromatography (SEC) is a valuable liquid chromatography tool for the analytical or preparative fractionation of proteins and polymers. SEC separates macromolecules according to differences in their hydrodynamic volumes. It does not rely on any binding between the solutes and the stationary phase. As the solutes travel through a packed SEC column, larger molecules are less prone to entering the pores of the stationary phase and thus have shorter retention times. Smaller molecules permeate more deeply into the pores of the stationary phase, thus delaying their elution as they spend more time in the column. To date, imprecise scaling correlations and trial and error methods are used for the scale-up of liquid chromatography. In early design stages, it is practical to simulate liquid chromatography processes using rate models. This cuts costs and time associated with physical experiments and mitigates any errors when relying on trial and error methods for scale-up.
    In this work, two mathematical models of the SEC process have been developed. The first is a predictive model that generates separate elution profiles for various molecular weights contained within a specified molecular weight distribution (MWD), which can be described by the Poisson distribution. These elution profiles resemble a Gaussian distribution, and added together, form the final chromatographic profile. The second method is a mathematical rate model considering various mass transfer effects using a lumped kinetic model where all sources of mass transport resistances were combined into the mass transfer coefficient. As an experimental base for the analysis, 13 polystyrene standards of varying molecular weights were selected. The experiments were performed using three linear columns (PLgel Olexis, 13 μm gel particles, and 300 mm × 7.5 mm) at 145 oC. Two hundred microliters of a polymer solution were injected into the columns at a flow rate of 1.0 mL/min of trichlorobenzene (TCB). The accuracy of each model was verified by comparing the predicted and simulated results to the experimental data. Both models accurately predicted the retention times and peak shapes of unimodal and multimodal polystyrene standard samples.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
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