Modeling chain-end scission using the Fixed Pivot technique

Chain-end scission of polymer molecules is the breakage of a fixed-size oligomer or monomer from either end of the macromolecule. A common example is the generation of the glucose monomer from the hydrolysis of starch by glucoamylase. Modeling the dynamics of chain-end scission from first principles by considering each molecular size is challenging due to the large number of differential equations to be solved. The Population Balance Modeling (PBM) is a helpful framework as it could be formulated to lump a few molecular sizes together. However, it is then not obvious how to accurately account for the temporal evolution of the low molecular weight species, which is often of the greatest industrial interest. Here, the Fixed Pivot (FP) technique - one of the methods to solve PBM equations - was appropriately modified to address this difficulty. By treating the lower molecular size range as a discrete domain in conjunction with a continuous domain in the upper ranges, the modified FP technique not only retains its original strengths, but also captures accurately the distribution of oligomers including the monomer. The results, which were obtained at a fraction of computational expense, benchmarked very well against the exact solutions for a polymer with a broad size distribution at different Degrees of Polymerization up to ~O(10⁵). To facilitate wider adoption, guidelines on choice of pivots and observations of the performance of the modified FP technique are also deliberated.