We present a statistical mechanics theory of rubber-like elasticity in swollen and unswollen polymer networks characterized by explicitly non-Gaussian distribution functions (Laplace’s, Cauchy’s, and continuous Poisson’s in the exponential limit). An important outcome is the derivation of new families of statistical and mechanical laws, including a discussion of energy functions of strain invariants, which are reasonably simple for a model comparison with available data on polymer networks. Accordingly, a theoretical–experimental approach based on LF-NMR was devised to identify the most likely end-to-end length distribution in an arbitrary network. When this strategy is applied to agar 1 %, alginate 1 %, and scleroglucan 2 % hydrogels, it turns out that the end-to-end distribution should be never regarded as Gaussian even if, as in agar and scleroglucan systems, the normal statistics is the best among those here regarded. Remarkably, Poisson’s distribution is proved instead to be the most realistic for the alginate hydrogel.

我们提出了一种膨胀和未膨胀聚合物网络中橡胶状弹性的统计力学理论，其特征是明确的非高斯分布函数（拉普拉斯、柯西和指数极限中的连续泊松）。一个重要的成果是推导了新的统计和力学定律家族，包括对应变不变量的能量函数的讨论，这对于与聚合物网络上的可用数据进行模型比较来说相当简单。因此，设计了一种基于 LF-NMR 的理论-实验方法来识别任意网络中最可能的端到端长度分布。当将该策略应用于 1% 的琼脂、1% 的藻酸盐和 2% 的硬葡聚糖水凝胶时，结果表明，端到端分布不应被视为高斯分布，即使，与琼脂和硬葡聚糖系统一样，正常统计数据是这里所认为的最好的。值得注意的是，泊松分布被证明是藻酸盐水凝胶最现实的分布。