An entropy spring model for the Young’s modulus change of biodegradable polymers during biodegradation |
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| Authors: | Ying Wang Xiaoxiao Han Jingzhe Pan Csaba Sinka |
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| Institution: | 1. Institute of Health and Biomedical Innovation, Queensland University of Technology, 60 Musk Avenue, Kelvin Grove, 4059 Brisbane, Australia;2. Department of Experimental Trauma Surgery, Klinikum Rechts der Isar, Technical University Munich, Ismaninger 22, 81675 Munich, Germany;3. Institute for Advanced Study, Technical University Munich, Lichtenbergstrasse 2a, 85748 Garching, Munich, Germany;4. Department of Orthopaedic Surgery, Koenig-Ludwig Haus, University of Wuerzburg, Brettreichstr. 11, 97074 Wuerzburg, Germany;5. Department of Materials and Department of Bioengineering, Institute of Biomedical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom;1. Federal Center of Technological Education of Rio de Janeiro – CEFET/RJ, Av. Maracanã, 229, Rio de Janeiro, RJ, Brazil;2. Université de Nantes, Institut de Recherche en Génie Civil et Mécanique, Saint-Nazaire, France;1. Centro de Biomateriales e Ingeniería Tisular, Universitat Politècnica de València, 46022 Valencia, Spain;2. CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Valencia, Spain;1. Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, International Research Center for Implantable and Interventional Medical Devices, Beihang University, Beijing 100191, China;2. Beijing Key Laboratory for Optimal Design and Evaluation Technology of Implantable & Interventional Medical Devices, China;3. National Research Center for Rehabilitation Technical Aids, Beijing 100176, China |
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| Abstract: | This paper presents a model for the change in Young’s modulus of biodegradable polymers due to hydrolysis cleavage of the polymer chains. The model is based on the entropy spring theory for amorphous polymers. It is assumed that isolated polymer chain cleavage and very short polymer chains do not affect the entropy change in a linear biodegradable polymer during its deformation. It is then possible to relate the Young’s modulus to the average molecular weight in a computer simulated hydrolysis process of polymer chain sessions. The experimental data obtained by Tsuji Tsuji, H., 2002. Autocatalytic hydrolysis of amorphous-made polylactides: Effects of L-lactide content, tacticity, and enantiomeric polymer blending. Polymers 43, 1789–1796] for poly(L-lactic acid) and poly(D-lactic acid) are examined using the model. It is shown that the model can provide a common thread through Tsuji’s experimental data. A further numerical case study demonstrates that the Young’s modulus obtained using very thin samples, such as those obtained by Tsuji, cannot be directly used to calculate the load carried by a device made of the same polymer but of various thicknesses. This is because the Young’s modulus varies significantly in a biodegradable device due to the heterogeneous nature of the hydrolysis reaction. The governing equations for biodegradation and the relation between the Young’s modulus and average molecular weight can be combined to calculate the load transfer from a degrading device to a healing bone. |
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