An entropy spring model for the Young’s modulus change of biodegradable polymers during biodegradation

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.