Development of novel models for predicting mechanical properties of hydrogels based on network graph theory

• Main Author: You, Hao
• Other Authors: Lam Khin Yong
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Engineering; Hydrogel; Solid mechanics; Moddling
• Online Access: https://hdl.handle.net/10356/181142
• Institution: Nanyang Technological University

This thesis delves into the development of advanced models for hydrogels, polymeric materials known for their high water content and ability to swell in aqueous environments. Hydrogels exhibit a wide range of properties, from soft and rubbery to tough and resilient, making them invaluable in various applications such as tissue engineering, drug delivery, and biomedical devices. Despite their versatility, understanding and predicting the mechanical behavior of hydrogels remain challenging due to their complex network structure. Traditional constitutive models based on single polymer chains often oversimplify hydrogel mechanics, neglecting factors like network topology, network defects, entanglement, and hidden length. As a result, there is a pressing need for advanced modeling approaches that can capture the complex network structure. This study addresses this gap by developing new models that incorporate network graph approaches and deep learning techniques for predicting the mechanical properties of hydrogels, considering their complex network structure. To address these challenges, this thesis proposes three novel models aimed at capturing the unique characteristics of hydrogel mechanics from the perspective of polymer network structures, as briefly summarized below. The first model extends the classic self-avoiding walk (SAW) chain model by incorporating loop probabilities, thereby advancing the understanding of the mechanical behavior of polymer networks with network defects, particularly in hydrogels. By incorporating loop probabilities to account for network defects like looped and entangled chains, this model provides predictions of stress-strain responses in various hydrogel configurations, including bulk hydrogels and thin films. It sheds light on the stiffness-toughness conflict, strain-softening and hardening phenomena, and thickness effects observed in hydrogels. Through integration with the Arruda-Boyce model, the framework allows the adjustment of the Kuhn length, facilitating the modeling of strain-softening and hardening phenomena in both soft regular and highly entangled hydrogels. Validation against experimental stress-stretch curves of ultrathin hydrogel films and soft regular and highly entangled hydrogels confirms the accuracy and reliability of the proposed model. Overall, this research contributes to uncovering the underlying physical principles of empirical models like the Gent model, providing insights into hydrogel mechanics and enabling precise predictions of mechanical properties in various hydrogel configurations, thus enhancing their applicability in diverse fields. The second model modifies the traditional single-chain-based Arruda-Boyce model by integrating network robustness analysis, effectively addressing the predictions of swelling behavior and the Mullins effect in hydrogels with unconventional network topologies. This model represents an advancement in understanding hydrogel behavior by characterizing damage properties across different polymer network topologies. It captures the impact of hidden length and entanglement on hydrogel swelling and hysteresis, revealing insights into the swelling resistance of highly entangled hydrogels and the stress-stretch hysteresis behavior. Validation against experimental data confirms the model's capability to capture swelling and damage behaviors in hydrogels. Parameter studies elucidate the role of entanglements and hidden lengths in hydrogel swelling and hysteresis, highlighting the differences between highly entangled and soft regular hydrogels. Specifically, highly entangled hydrogels exhibit superior swelling resistance due to entanglements, while soft regular hydrogels demonstrate distinct stress-stretch hysteresis patterns influenced by hidden lengths. These insights contribute to improved design strategies for hydrogels with tailored mechanical properties, enhancing their applicability in diverse applications. The third model develops a methodology to anticipate the elasticity of hydrogels with inhomogeneous polymer networks characterized by varying polymer densities and structures, pose significant challenges due to their complex configurations. To tackle these challenges, we employ a combination of community detection algorithms and deep learning neural networks. Community detection facilitates the transformation of discrete network images into continuous density distribution images, enabling the identification of regions with similar polymer densities for mechanical property analysis. Specifically, parameters from the discrete network model, such as node density, chain modulus $C_1$, and bulk modulus $K$, are translated into RGB values of the density distribution images. This encoding enables the application of transfer learning approaches, particularly those tailored for image recognition, to analyze the network structures. Evaluation of five transfer learning units: VGG16, ResNet50, DenseNet121, Xception, and EfficientNetB7, reveals that DenseNet121 demonstrates superior performance in predicting hydrogel elasticity. The neural network is trained to uncover the relationship between the mesoscale structures of the material samples and their elasticity. Validation of the accuracy and efficiency of the network's predictions is conducted through cross-validation. This methodology integrates advanced image processing, discrete network modeling, finite element analysis, community detection, and deep learning to address the challenge of predicting the effective moduli from mesoscale polymer network images. In summary, the main contribution of this thesis is the development of three new models that enhance the comprehension and prediction of mechanical properties in hydrogels with network structures. The first model, utilizing SAW statistics, offers a comprehensive framework for understanding the impact of network defects on mechanical behavior. Based on the first model for network defects, the second model further employs network robustness analysis to forecast swelling behavior and the Mullins effect in hydrogels with unconventional topologies. Lastly, the third model combines community detection and deep learning to anticipate the elasticity of inhomogeneous polymer networks, thereby enhancing computational efficiency compared to the first two proposed models. These models contribute to advancements in polymer mechanics, introducing fresh perspectives, tools, and methodologies to advance the understanding and application of these materials across diverse domains.