Modelling simultaneous chain‐end and random scissions using the fixed pivot technique

Abstract

In this study, for the first time we demonstrated that both random and chain‐end scissions of polymers can be simulated on a unified Fixed Pivot (FP) framework through an elegant implementation of a discrete‐continuous meshing strategy. Achieved using only a fraction of computational expense in solving the full set of exact equations, the FP solutions benchmarked very well against the exact solutions for a polymer with a broad size distribution typical of natural polymers at different degrees of up to ∼O(105). This is attained despite the use of an efficient computational technique to obtain the exact solutions. Moreover, new observations revealed an additional strength of the current meshing strategy, in that the number of the discrete partitions can be adjusted to improve the accuracy of the solution while retaining the total number of equations to be solved. The FP technique, which in the past was reported to over‐predict in cases of pure aggregation, also exhibits marginal over‐prediction for pure random scission. The source of this behaviour is further uncovered, leading to a revised guideline on the choice of the number of discrete pivots.

Population balance models for polymer upcycling: signatures of the mechanism in the molecular weight evolution

“…With the simplest cases of random and chain-end scission discussed, it is important to note that many processes are in fact combinations of the two. 30,38,56,68,[71][72][73] For example, in the polysaccharide/amylase system, there are three classes of enzymes that work together to depolymerize starches: aamylase catalyzes random cleavage, while band g-amylase catalyze chain-end cleavage. [74][75][76] The relative concentration and activity of these amylases can dramatically alter the evolution of the MWD.…”

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

“… Note : Readers are referred to the works of Ahamed et al (2019) and Ahamed (2020) for the formulation of the ML‐PBM including the balances of soluble products, enzyme‐polymer complex species, insoluble polymer species and surface‐adsorbed enzyme species, whereas Ahamed (2020), Ahamed et al (2020), Ho et al (2014), and Ho et al (2018) elucidate the numerical Fixed Pivot Technique (FPT) used to solve the depolymerization population balances over a mixed discrete‐continuous mesh. The descriptions of the key variables are given in the main text as well in the Nomenclature and explained in detail in the Supporting Information (cf.…”

Processive Depolymerization Catalysts: A Population Balance Model for Chemistry’s “While” Loop

“…Population balance models of depolymerization have been developed for non-processive mechanisms including chain-end scission, − in which small fragments are removed from the end of a polymer, and random scission, − in which random bonds along the polymer backbone are broken. Variations on these cases have also been developed, e.g., random scission models that preferentially cleave particular bonds, chain-end scission models that yield a distribution of fragments, and complex models (requiring simulation) that include chain end scission, random scission, and disproportionation reactions .…”