Gels: Energetics, Singularities, and Cavitation
Gels: Energetics, Singularities, and Cavitation
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DOI：
10.1007/s10659-023-10000-5
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发表时间：
2023-03
影响因子：
2
通讯作者：
M. Calderer;Duvan Henao;Manuel A. Sánchez;Ronald A. Siegel;Si-Mon Song
中科院分区：
文献类型：
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作者：
M. Calderer;Duvan Henao;Manuel A. Sánchez;Ronald A. Siegel;Si-Mon Song
本文研究了凝胶的平衡奇异构型，并解决了有关凝胶能量学的公开问题。我们将凝胶建模为不可压缩、不可混溶和饱和的固体聚合物和溶剂的混合物，这些混合物在分子水平上保持化学作用。我们假设凝胶的能量由其聚合物网络的弹性能加上Flory-Huggins混合能组成。后者包括各组分的熵能加上聚合物和溶剂之间的相互作用能，以及与温度有关的Flory参数，它编码了溶剂的性质。特别是，促进混合区的良好溶液在阈值以下被发现，而相分离区在该临界值以上发展。我们证明了空洞和奇点是在后一种情况下产生的。我们发现两类主要的奇点：(I)干燥的溶剂，水可能通过边界离开凝胶区域，在凝胶中心留下一个暴露的聚合物核心；(Ii)空化，响应边界上的牵引或某种形式的负压，空穴可能是空的，也可能是被溶剂淹没的。处理所有这类奇点的直接和统一的数学方法是基于构造适当的检验函数，其灵感来自于均匀膨胀或压缩的特殊状态。这篇文章的最后一个主题解决了一个在研究界引起争议的统计力学问题，提供了一个实验和分析研究，以支持体模弹性能与仿射弹性能的对比。
This article studies equilibrium singular configurations of gels and addresses open questions concerning gel energetics. We model a gel as an incompressible, immiscible and saturated mixture of a solid polymer and a solvent that sustain chemical interactions at the molecular level. We assume that the energy of the gel consists of the elastic energy of its polymer network plus the Flory-Huggins energy of mixing. The latter involves the entropic energies of the individual components plus that of interaction between polymer and solvent, with the temperature dependent Flory parameter,, encoding properties of the solvent. In particular, agood solventpromoting the mixing regime, is found below the threshold value, whereas the phase separating regime develops above that critical value. We show that cavities and singularities develop in the latter regime. We find two main classes of singularities: (i) drying out of the solvent, with water possibly exiting the gel domain through the boundary, leaving behind a core of exposed polymer at the centre of the gel; (ii) cavitation, in response to traction on the boundary or some form of negative pressure, with a cavity that can be either void or flooded by the solvent. The straightforward and unified mathematical approach to treat all such singularities is based on the construction of appropriate test functions, inspired by the particular states of uniform swelling or compression. The last topic of the article addresses a statistical mechanics rooted controversy in the research community, providing an experimental and analytic study in support of the phantom elastic energy versus the affine one.