Mathematical Modelling of Size Exclusion Chromatography of Polymers

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
more » ... . Smaller molecules permeate more deeply into the pores of the stationary phase, thus delaying their elution as they spend more time in the column. 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 scaleup. 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, 12 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 o C. 200 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. iii Preface Two mathematical models of the size-exclusion chromatography process were developed for the purposes of scale-up. The first was a predictive model implementing Poisson and Gaussian distributions, and the second was a simplified version of the general rate model. Chapter 1 gives a brief history of the size-exclusion process and reviews how polymer properties are measured and how they affect polymer end uses. Present day scale-up procedures and their drawbacks are also defined in this chapter. Chapter 2 reviews the previous scientific literature on size-exclusion chromatography. This chapter describes the separation mechanism, as well as essential chromatography concepts such as: molecular weight distribution, polydispersity, retention, and efficiency. The importance of band broadening is also defined in this chapter. Chapter 3 details the type of column and polystyrene standards used in this investigation. It also details the methodology used to develop each mathematical model. The predictive model originates from the Poisson distribution that describes the molecular weight distribution of a specific polymer. The simplified general rate model was derived by performing mass balances on a section of the size-exclusion chromatography column. Differential equations of the rate model were solved using the finite volume method. Chapter 4 compares simulated and experimental results for unimodal and multimodal polystyrene standard samples. This chapter discusses the agreement between the simulated and experimental results. Chapter 5 proposes the main conclusions of this study and suggests future research work. The results from Chapter 4 are summarized and suggestions for future studies to strengthen key knowledge gaps are also provided. iv
doi:10.7939/r38s4k502 fatcat:v5rlklmqrjar5hliu5onsrjz6a