A sheet of glassy polymers placed in a solvent shows swelling behaviors quite different from that of soft polymers (rubbers and gels). (1) Non-Fickian diffusion (called case II diffusion): As solvent permeates into the sample, a sharp front is created between the swollen part and the glassy part, and it moves toward the center at constant speed. (2) Nonmonotonous swelling: The thickness of the sample first increases and then decreases toward the equilibrium value. Here we propose a theory to explain such anomalous behavior by extending the previous theory for swelling of soft gels. We regard the material as a continuum mixture of a glassy polymer network and solvent. We assume that the polymer network is a viscoelastic gel of glassy polymers, and its relaxation time depends strongly on solvent concentration. We show that this theory explains the above two characteristics of glassy polymers in a simple and unified framework. The theory predicts how the permeation speed of the solvent and the characteristic times of the swelling process depend on material parameters and experimental conditions, which can be checked experimentally.

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玻璃态聚合物凝胶非菲克扩散和反常膨胀的统一模型

置于溶剂中的玻璃状聚合物片材表现出与软聚合物（橡胶和凝胶）截然不同的溶胀行为。 （1）非菲克扩散（称为情况II扩散）：当溶剂渗透到样品中时，在膨胀部分和玻璃状部分之间产生尖锐的前沿，并以恒定的速度向中心移动。 (2)非单调膨胀：样品厚度先增大后减小，趋于平衡值。在这里，我们提出了一种理论，通过扩展先前的软凝胶膨胀理论来解释这种异常行为。我们将该材料视为玻璃状聚合物网络和溶剂的连续混合物。我们假设聚合物网络是玻璃状聚合物的粘弹性凝胶，其弛豫时间很大程度上取决于溶剂浓度。我们证明该理论在一个简单而统一的框架中解释了玻璃态聚合物的上述两个特征。该理论预测了溶剂的渗透速度和溶胀过程的特征时间如何取决于材料参数和实验条件，这些可以通过实验进行检查。