Using rheological monitoring to determine the gelation kinetics of chitosan-based systems

Belmiro P. M. Duarte; Maria J. Moura; Belmiro P. M. Duarte; Maria J. Moura

doi:10.3934/mbe.2023054

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 1176-1194. doi: 10.3934/mbe.2023054

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Research article

Using rheological monitoring to determine the gelation kinetics of chitosan-based systems

Belmiro P. M. Duarte ^{1,2
,
,},
Maria J. Moura ^1,2

1.
Department of Chemical and Biological Engineering, Coimbra Engineering Academy, Polytechnic Institute of Coimbra, Rua Pedro Nunes, Quinta da Nora, 3030–199 Coimbra, Portugal
2.
Centro de Investigação em Engenharia dos Processos Químicos e dos Produtos da Floresta, Department of Chemical Engineering, University of Coimbra, Rua Sílvio Lima, Pólo II, 3030–790 Coimbra, Portugal

Academic Editor: Yang Kuang

Received: 19 July 2022 Revised: 21 August 2022 Accepted: 22 August 2022 Published: 26 October 2022

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) ^[1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is formulated as a Dynamic Optimization problem and subsequently solved with a sequential approach. Parametric confidence regions are computed using the linear approximation of the covariance matrix at the optimum. Further, the parameters correlation matrix is also determined and used to qualitatively infer about the practical identifiability. The reaction order obtained for self-crosslinking kinetics is 1.3375 ± (0.0151) – approximately of first order –, and is 2.2402 ± (0.0373) for hybrid crosslinking (approximately of second order). In both cases we prove the error variance model is heteroskedastic and the model is identifiable. The approach proposed herein can be extended to other polymer systems.
- self-crosslinking,
- agent-based crosslinking,
- gelation kinetics,
- rheological monitoring,
- model fitting
Citation: Belmiro P. M. Duarte, Maria J. Moura. Using rheological monitoring to determine the gelation kinetics of chitosan-based systems[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 1176-1194. doi: 10.3934/mbe.2023054

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Abstract

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) ^[1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is formulated as a Dynamic Optimization problem and subsequently solved with a sequential approach. Parametric confidence regions are computed using the linear approximation of the covariance matrix at the optimum. Further, the parameters correlation matrix is also determined and used to qualitatively infer about the practical identifiability. The reaction order obtained for self-crosslinking kinetics is 1.3375 ± (0.0151) – approximately of first order –, and is 2.2402 ± (0.0373) for hybrid crosslinking (approximately of second order). In both cases we prove the error variance model is heteroskedastic and the model is identifiable. The approach proposed herein can be extended to other polymer systems.

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