When a polymer network is stretched, some polymer strands do not bear loads. Examples include looped strands, dangling strands, and extremely long strands. When the polymer network is submerged in a solvent, however, all strands mix with solvent molecules. This distinction between strands that bear loads and strands that do not leads us to modify the Flory-Rehner model. The modified model has three parameters: the density of load-bearing strands, N, the density of all strands, M, and the interaction parameter, χ. For a polymer network submerged in a reservoir of solvent and bearing triaxial stresses, the modified model provides equations of state, relating the stresses to stretches, as well as the chemical potential of solvent molecules and temperature in the reservoir. We synthesize polyacrylamide hydrogels using precursors of various concentrations of monomer, crosslinker, and transfer agent. We determine the three parameters N, M, and χ by fitting the modified model to several experiments, including free swelling, fast tension, and stress relaxation. In all samples tested, M is several times N, whereas χ is nearly constant. This work demonstrates the consequences of the notion that some polymer strands in a polymer network bear loads, but all strands contribute to swelling.

当聚合物网络被拉伸时，一些聚合物股线不承受载荷。示例包括环状股线、悬垂股线和极长股线。然而，当聚合物网络浸没在溶剂中时，所有链都与溶剂分子混合。承受载荷的股线和不承受载荷的股线之间的这种区别导致我们修改 Flory-Rehner 模型。修改后的模型具有三个参数：承载钢绞线的密度N、所有钢绞线的密度M和相互作用参数χ. 对于浸没在溶剂储层中并承受三轴应力的聚合物网络，修改后的模型提供了状态方程，将应力与拉伸以及溶剂分子的化学势和储层中的温度相关联。我们使用各种浓度的单体、交联剂和转移剂的前体合成聚丙烯酰胺水凝胶。我们通过将修改后的模型拟合到几个实验（包括自由膨胀、快速拉伸和应力松弛）来确定三个参数N、M和χ 。在所有测试的样本中，M是N的几倍，而χ几乎是恒定的。这项工作证明了聚合物网络中的一些聚合物股线承受载荷但所有股线都有助于溶胀这一概念的后果。