Modeling chain-end scission using the Fixed Pivot technique

Ho, Yong Kuen; Doshi, Pankaj; Yeoh, Hak Koon; Ngoh, Gek Cheng

doi:10.1016/j.ces.2014.05.035

Cited by 27 publications

(38 citation statements)

References 35 publications

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“…[10][11][12] Importantly,aprevious study has shown that the yield of the head-totail configuration is high in alkene polymers. [10,11] In this work, we investigate the depolymerization mechanism of chain-end scission based on at ypical poly(alpha-methylstyrene) (PAMS) model. The depolymerization mechanism varies with the moleculars tructures and experimental conditions.…”

Section: Introductionmentioning

confidence: 99%

Depolymerization of Free‐Radical Polymers with Spin Migrations

Wang

Dai

et al. 2015

ChemPhysChem

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The mechanism of depolymerization is one of the most essential issues in chemical engineering and materials science. In this work, we investigate the depolymerization reactions of three typical free-radical poly(alpha-methylstyrene) tetramers by using first-principles density functional theory. The calculated results show that these reactions all need to overcome the energy barriers in the range of 0.58 to 0.77 eV, and that breaking the C-C bond at the chain end leads to the dissociation of alpha-methylstyrene monomers from the polymers. Electronic-structure analysis indicates that the reactions occur easily at the CR3 unsaturated end, and that the frontier molecular orbitals that participate in the reactions are mainly localized at the unsaturated ends. Meanwhile, spin population analysis presents the unique net spin-transfer process in free-radical depolymerization reactions. We hope the current findings can contribute to understanding the free-radical depolymerization mechanism and help guide future experiments.

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Section: Introductionmentioning

confidence: 99%

Depolymerization of Free‐Radical Polymers with Spin Migrations

Wang

Dai

et al. 2015

ChemPhysChem

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“…The matrix F (stationary in time) operates on

S

such that the i ‐th element of vector L contains the sum of all species with DP = i . Here, p and q are the meshing parameters representing the number of pivots in the discrete and continuous regions, respectively (Ho et al, ). Since mass should be conserved, the first moment of the distribution ( ξ = 1) is a constant.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…The form of Eqs. – is a result of the FP approximation for chain‐end scission developed by Ho et al () where

n_{i j}

is given as follows:

n_{i j} = \int_{x_{i}}^{x_{i + 1}} [\frac{x_{i + 1} - v}{x_{i + 1} - x_{i}}] δ (v - [x_{j} - v_{m}]) d v + \int_{x_{i - 1}}^{x_{i}} [\frac{v - x_{i - 1}}{x_{i} - x_{i - 1}}] δ (v - [x_{j} - v_{m}]) d v

…”

Section: Case Studymentioning

confidence: 99%

“…In addition, as soluble starch was employed by the authors, a relatively narrow distribution with a polydispersity index (

PD = {\overset{M}{true}}_{w} true/ {\overset{M}{true}}_{n} = 1.32

) commonly found in the starch literature (Breuninger et al, ) was used to characterize h ( v ) in Table . Meshing was done according to the guidelines given by Ho et al () where the values of the meshing parameters p and q were chosen to be [ p , q ] = [51, 149]. This value of p is the minimum required for a total number of pivots = 200.…”

Section: Case Studymentioning

confidence: 99%

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Interlinked population balance and cybernetic models for the simultaneous saccharification and fermentation of natural polymers

Doshi

Yeoh

et al. 2015

Biotech & Bioengineering

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Simultaneous Saccharification and Fermentation (SSF) is a process where microbes have to first excrete extracellular enzymes to break polymeric substrates such as starch or cellulose into edible nutrients, followed by in situ conversion of those nutrients into more valuable metabolites via fermentation. As such, SSF is very attractive as a one-pot synthesis method of biological products. However, due to the co-existence of multiple biochemical steps, modeling SSF faces two major challenges. The first is to capture the successive chain-end and/or random scission of the polymeric substrates over time, which determines the rate of generation of various fermentable substrates. The second is to incorporate the response of microbes, including their preferential substrate utilization, to such a complex broth. Each of the above-mentioned challenges has manifested itself in many related areas, and has been competently but separately attacked with two diametrically different tools, i.e., the Population Balance Modeling (PBM) and the Cybernetic Modeling (CM), respectively. To date, they have yet to be applied in unison on SSF resulting in a general inadequacy or haphazard approaches to examine the dynamics and interactions of depolymerization and fermentation. To overcome this unsatisfactory state of affairs, here, the general linkage between PBM and CM is established to model SSF. A notable feature is the flexible linkage, which allows the individual PBM and CM models to be independently modified to the desired levels of detail. A more general treatment of the secretion of extracellular enzyme is also proposed in the CM model. Through a case study on the growth of a recombinant Saccharomyces cerevisiae capable of excreting a chain-end scission enzyme (glucoamylase) on starch, the interlinked model calibrated using data from the literature (Nakamura et al., Biotechnol. Bioeng. 53:21-25, 1997), captured features not attainable by existing approaches. In particular, the effect of various enzymatic actions on the temporal evolution of the polymer distribution and how the microbes respond to the diverse polymeric environment can be studied through this framework.

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“…Such a hybrid formulation was employed due to the challenges involved in solving chain‐end scission via the fundamental continuous model, and thus the authors approximated the chain‐end scission by a negative growth process. Ho et al showed that such an approximation of chain‐end scission by a negative growth process is not necessary: by treating the lower molecular size range as a discrete domain in conjunction with a continuous domain in the upper ranges using the continuous fundamental model, the fundamental continuous model for chain‐end scission can be tackled successfully using a modified FP technique. The ability to achieve this, which was previously deemed intuitively unattainable by Vanni, leads to the possibility of this work, as discussed next.…”

Section: Introductionmentioning

confidence: 99%

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

Doshi

Yeoh³

2017

Can J Chem Eng

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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.

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Modeling chain-end scission using the Fixed Pivot technique

Cited by 27 publications

References 35 publications

Depolymerization of Free‐Radical Polymers with Spin Migrations

Depolymerization of Free‐Radical Polymers with Spin Migrations

Interlinked population balance and cybernetic models for the simultaneous saccharification and fermentation of natural polymers

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

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