Disordered biopolymer gels, such as those synthesized from polysaccharide and gelatin, play an important role in biomedical applications, particularly in tissue engineering. During the gelation process of these gels, polymer chains associate in the presence of gelling agents, forming physical cross-links known as the junction zones. In contrast to rubber-like networks, the resulting network comprises two main regions: the ordered region due to the junction zones and the amorphous region due to the unassociated chains. Under thermal fluctuations and/or external loading, the number and locations of junction zones can change leading to “zipping” (lengthening, i.e., expansion of the junction zones) and “unzipping” (shortening, i.e., shrinkage of the junction zones). This gives rise to intriguing features in biopolymer gels such as healing and damage-like energy dissipation. Despite the recognition of zipping and unzipping in such gels, the development of mathematical models that incorporate the microscopic mechanisms into the material’s macroscopic mechanical properties is still in its early stages. In this paper, we provide a systematic framework for such multiscale modeling. Several critical steps are taken to equip the eight-chain network model with a previously developed micromechanics model for a coil–rod structure, where the coil represents an unassociated chain and the rod represents a junction zone. Most importantly, for a network of coil–rod structures under zero stress, the rigidity induced by the rod leads to an end-to-end distance () for the coil–rod which is different from a classical result for a Gaussian coil: where is the Kuhn length and is the number of Kuhn segments in the coil. By relaxing the incompressible assumption in the original eight-chain model, is determined for the gel network, which depends on the length of the junction zone. Consequently, as the junction zone extends/shrinks following zipping/unzipping under an external load, an irreversible deformation can occur after unloading, consistent with experimentally observed “permanent set”. The extension/shrinkage of the junction zone is captured by statistical mechanics analysis in the grand canonical ensemble, which allows the exchange of segments between the coil and the rod, driven by the binding energy of polymer chain association. The model also includes explicit consideration of swelling and the influence of solvent molecules as a result of their mixing with the polymer chains in the gel network. With physically reasonable parameters, the proposed model is shown to provide good matching with experimental data on the uniaxial testing of alginate gels, revealing progressive unzipping during loading and partial re-zipping during unloading leading to the appearance of a permanent set. This formulation not only paves the way for more advanced studies of disordered biopolymer gels but also lays the groundwork for modeling hybrid gels that contain coil–rod structures as a component.

中文翻译：

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包含可变长度连接区的无序生物聚合物凝胶的多尺度力学模型


无序生物聚合物凝胶，例如由多糖和明胶合成的凝胶，在生物医学应用中发挥着重要作用，特别是在组织工程中。在这些凝胶的胶凝过程中，聚合物链在胶凝剂存在下缔合，形成称为接合区的物理交联。与橡胶状网络相比，所得网络包含两个主要区域：由于连接区而形成的有序区域和由于不相关链而导致的无定形区域。在热波动和/或外部负载下，接合区的数量和位置可以改变，导致“拉长”（拉长，即接合区的扩张）和“拉开”（缩短，即接合区的收缩）。这在生物聚合物凝胶中产生了有趣的特征，例如愈合和类似损伤的能量耗散。尽管人们认识到此类凝胶中的压缩和解压缩，但将微观机制纳入材料宏观机械性能的数学模型的开发仍处于早期阶段。在本文中，我们为这种多尺度建模提供了一个系统框架。采取了几个关键步骤，为八链网络模型配备了先前开发的线圈-杆结构的微力学模型，其中线圈代表不相关的链，杆代表连接区域。最重要的是，对于零应力下的线圈-杆结构网络，杆引起的刚度导致线圈-杆的端到端距离 ()，这与高斯线圈的经典结果不同：是库恩长度， 是线圈中库恩段的数量。 通过放宽原始八链模型中的不可压缩假设，确定了凝胶网络，这取决于连接区的长度。因此，当在外部负载下拉上/拉开拉链后，接合区会延伸/收缩，卸载后会发生不可逆的变形，这与实验观察到的“永久变形”一致。连接区的延伸/收缩通过大正则系综中的统计力学分析来捕获，这允许由聚合物链缔合的结合能驱动的线圈和杆之间的片段交换。该模型还明确考虑了溶胀以及溶剂分子与凝胶网络中的聚合物链混合所产生的影响。凭借物理上合理的参数，所提出的模型与藻酸盐凝胶单轴测试的实验数据提供了良好的匹配，揭示了加载过程中的渐进拉锁和卸载过程中的部分重新拉锁导致出现永久变形。该配方不仅为无序生物聚合物凝胶的更高级研究铺平了道路，而且还为模拟包含线圈-杆结构作为组件的混合凝胶奠定了基础。