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Pan Z, Brassart L. A reaction-diffusion framework for hydrolytic degradation of amorphous polymers based on a discrete chain scission model. Acta Biomater 2023:S1742-7061(23)00346-X. [PMID: 37343906 DOI: 10.1016/j.actbio.2023.06.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Revised: 06/06/2023] [Accepted: 06/15/2023] [Indexed: 06/23/2023]
Abstract
Hydrolytic degradation of polymers involves the scission of long chain molecules, leading to molecular weight reduction and mass loss. The precise degradation response however depends on the scission probability of individual bonds along the polymer backbone. In particular, bonds near the chain ends are considered to be more susceptible to hydrolysis than inner bonds. In this paper, we incorporate a discrete chain scission model that can handle arbitrary bond scission probabilities within a continuum reaction-diffusion framework. Overall hydrolysis kinetics (including autocatalysis) is described independently of the chain scission model. By decoupling the description of the chain scission mechanism from kinetics, our framework enables the identification of the chain scission mechanism from molecular weight reduction and mass loss curves commonly reported in experimental degradation studies. We further propose a reduced continuum model which is better suited for large-scale simulations while retaining the predictive capability of the full discrete-continuum model. The model capability is illustrated in representative case studies based on experimental data from the literature for different materials and geometries. STATEMENT OF SIGNIFICANCE: Many models have been proposed to predict the evolution of molecular weight and mass loss in biodegradable polymers undergoing hydrolytic degradation. However, existing models remain limited in their ability to describe the degradation mechanism, autocatalytic kinetics and short chains diffusion simultaneously. Moreover, existing models often rely on empirical relations and a large number of fitting parameters. Here, we propose a conceptually simple discrete-continuum mathematical framework with a small number of parameters which all have a clear physical meaning. Model calibration against experimental data is simplified, and further provides insights into the degradation mechanisms at play, namely random scission, chain-end scission, or a combination of both. The framework can serve as a basis for future generalisations, including a description of evolving crystallinity, or other degradation mechanisms, such as thermal oxidation or photo-degradation.
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Affiliation(s)
- Zhouzhou Pan
- Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
| | - Laurence Brassart
- Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK.
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Wang J, Wang T, Luo Z, Zhou Y. Analytical and Numerical Simulations of Depolymerization Based on Discrete Model: A Chain‐end Scission Scenario. AIChE J 2022. [DOI: 10.1002/aic.17854] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Jiang Wang
- Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites Shanghai Jiao Tong University Shanghai PR China
| | - Tian‐Tian Wang
- Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites Shanghai Jiao Tong University Shanghai PR China
| | - Zheng‐Hong Luo
- Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites Shanghai Jiao Tong University Shanghai PR China
| | - Yin‐Ning Zhou
- Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites Shanghai Jiao Tong University Shanghai PR China
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Ahamed F, Song HS, Ho YK. Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose. Biotechnol Bioeng 2021; 118:1898-1912. [PMID: 33547803 DOI: 10.1002/bit.27705] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Revised: 02/03/2021] [Accepted: 02/04/2021] [Indexed: 11/09/2022]
Abstract
Consolidated bioprocessing (CBP) of cellulose is a cost-effective route to produce valuable biochemicals by integrating saccharification, fermentation and cellulase synthesis in a single step. However, the lack of understanding of governing factors of interdependent saccharification and fermentation in CBP eludes reliable process optimization. Here, we propose a new framework that synergistically couples population balances (to simulate cellulose depolymerization) and cybernetic models (to model enzymatic regulation of fermentation) to enable improved understanding of CBP. The resulting framework, named the unified cybernetic-population balance model (UC-PBM), enables simulation of CBP driven by coordinated control of enzyme synthesis through closed-loop interactions. UC-PBM considers two key aspects in controlling CBP: (1) heterogeneity in cellulose properties and (2) cellular regulation of competing cell growth and cellulase secretion. In a case study on Clostridium thermocellum, UC-PBM not only provides a decent fit with various exometabolomic data, but also reveals that: (i) growth-decoupled cellulase-secreting pathways are only activated during famine conditions to promote the production of growth substrates, and (ii) starting cellulose concentration has a strong influence on the overall flux distribution. Equipped with mechanisms of cellulose degradation and fermentative regulations, UC-PBM is practical to explore phenotypic functions for primary evaluation of microorganisms' potential for metabolic engineering and optimal design of bioprocess.
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Affiliation(s)
- Firnaaz Ahamed
- Chemical Engineering Discipline, School of Engineering, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, Selangor, Malaysia
| | - Hyun-Seob Song
- Department of Biological Systems Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska, USA.,Department of Food Science and Technology, Nebraska Food for Health Center, University of Nebraska-Lincoln, Lincoln, Nebraska, USA
| | - Yong Kuen Ho
- Chemical Engineering Discipline, School of Engineering, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, Selangor, Malaysia.,Monash-Industry Palm Oil Education and Research Platform, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, Selangor, Malaysia
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Singh M, Kumar A, Shirazian S, Ranade V, Walker G. Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation. Pharmaceutics 2020; 12:pharmaceutics12121152. [PMID: 33260899 PMCID: PMC7760032 DOI: 10.3390/pharmaceutics12121152] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2020] [Revised: 11/19/2020] [Accepted: 11/24/2020] [Indexed: 11/16/2022] Open
Abstract
The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.
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Affiliation(s)
- Mehakpreet Singh
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland; (S.S.); (V.R.); (G.W.)
- Correspondence:
| | - Ashish Kumar
- Pharmaceutical Engineering, Faculty of Pharmaceutical Sciences, Ghent University, 9000 Gent, Belgium;
| | - Saeed Shirazian
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland; (S.S.); (V.R.); (G.W.)
- Laboratory of Computational Modeling of Drugs, South Ural State University, 76 Lenin Prospekt, 454080 Chelyabinsk, Russia
| | - Vivek Ranade
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland; (S.S.); (V.R.); (G.W.)
| | - Gavin Walker
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland; (S.S.); (V.R.); (G.W.)
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Singh M, Singh R, Singh S, Walker G, Matsoukas T. Discrete finite volume approach for multidimensional agglomeration population balance equation on unstructured grid. POWDER TECHNOL 2020. [DOI: 10.1016/j.powtec.2020.08.022] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Ahamed F, Singh M, Song HS, Doshi P, Ooi CW, Ho YK. On the use of sectional techniques for the solution of depolymerization population balances: Results on a discrete-continuous mesh. ADV POWDER TECHNOL 2020. [DOI: 10.1016/j.apt.2020.04.032] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Compartmental approach for modelling twin-screw granulation using population balances. Int J Pharm 2020; 576:118737. [DOI: 10.1016/j.ijpharm.2019.118737] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2019] [Revised: 09/20/2019] [Accepted: 09/25/2019] [Indexed: 11/22/2022]
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Singh M, Ismail HY, Matsoukas T, Albadarin AB, Walker G. Mass-based finite volume scheme for aggregation, growth and nucleation population balance equation. Proc Math Phys Eng Sci 2019; 475:20190552. [PMID: 31824226 DOI: 10.1098/rspa.2019.0552] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 10/02/2019] [Indexed: 11/12/2022] Open
Abstract
In this paper, a new mass-based numerical method is developed using the notion of Forestier-Coste & Mancini (Forestier-Coste & Mancini 2012, SIAM J. Sci. Comput. 34, B840-B860. (doi:10.1137/110847998)) for solving a one-dimensional aggregation population balance equation. The existing scheme requires a large number of grids to predict both moments and number density function accurately, making it computationally very expensive. Therefore, a mass-based finite volume is developed which leads to the accurate prediction of different integral properties of number distribution functions using fewer grids. The new mass-based and existing finite volume schemes are extended to solve simultaneous aggregation-growth and aggregation-nucleation problems. To check the accuracy and efficiency, the mass-based formulation is compared with the existing method for two kinds of benchmark kernels, namely analytically solvable and practical oriented kernels. The comparison reveals that the mass-based method computes both number distribution functions and moments more accurately and efficiently than the existing method.
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Affiliation(s)
- Mehakpreet Singh
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland
| | - Hamza Y Ismail
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland
| | - Themis Matsoukas
- 8H Thomas, Department of Chemical Engineering, Pennsylvania State University, PA 16802, USA
| | - Ahmad B Albadarin
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland
| | - Gavin Walker
- Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland
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Ahamed F, Song HS, Ooi CW, Ho YK. Modelling heterogeneity in cellulose properties predicts the slowdown phenomenon during enzymatic hydrolysis. Chem Eng Sci 2019. [DOI: 10.1016/j.ces.2019.05.028] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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