Experiments, Modelling, and Simulations for a Gel Bonded to a Rigid Substrate
Experiments, Modelling, and Simulations for a Gel Bonded to a Rigid Substrate
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DOI：
10.1007/s10659-022-09911-6
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发表时间：
2022-07
影响因子：
2
通讯作者：
Si-Mon Song;Ronald A. Siegel;Manuel A. Sánchez;M. Calderer;Duvan Henao
中科院分区：
文献类型：
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作者：
Si-Mon Song;Ronald A. Siegel;Manuel A. Sánchez;M. Calderer;Duvan Henao
在准备一个更彻底的研究的基础上，我们自己的实验工作的剥离薄膜凝胶与刚性基板的界面上的应力集中，在这篇文章中，我们重新审视，从数学，实验和有限元模拟之间的协同作用的角度来看，一个薄的矩形聚丙烯酰胺凝胶的底部表面上共价键合到载玻片的溶胀问题。与变分法和微扰理论的方法，我们表明，相应的零位移边值问题的解决方案收敛，在薄膜的限制，到一个唯一定义的均匀单轴延伸的方向上垂直于基板。我们进行的实验和有限元模拟都证实了侧向膨胀的量非常小，两种方法之间具有非常好的定量一致性。所提出的模型的能量泛函，包括一个长期的弹性变形和Flory-Huggins表达式的混合熵的最小化，从而实验和数值验证，参数来自实验测量，包括在实验室中合成的水凝胶的初始聚合物体积分数（这是作为参考配置，而不是干聚合物）。
In preparation for a more thorough study based on our own experimental work of the debonding of a thin film gel by stress concentration on the interface with a rigid substrate, in this article we revisit, from the viewpoint of the synergy between mathematics, experiments, and finite element simulations, the problem of the swelling of a thin rectangular polyacrylamide gel covalently bonded on the bottom surface to a glass slide. With methods of the calculus of variations and perturbation theory we show that the solution to the corresponding zero-displacement boundary value problem converges, in the thin film limit, to a uniquely defined uniform uniaxial extension on the direction normal to the substrate. Both the experiments and the finite element simulations that we perform confirm that the amount of lateral swelling is very small, with a very good quantitative agreement between the two approaches. The proposed model of minimizing an energy functional comprising both a term for the elastic distortion and the Flory-Huggins expression for the entropy of mixing is thus experimentally and numerically validated, with parameters coming from experimental measurements, including the initial polymer volume fraction of the hydrogel synthesized in the laboratory (which is taken as the reference configuration instead of the dry polymer).