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首页> 外文期刊>The European physical journal, E. Soft matter >Sharp diffusion front in diffusion problem with change of state
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Sharp diffusion front in diffusion problem with change of state

机译：状态变化时扩散问题的尖锐扩散前沿

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摘要

We propose an alternative model of diffusion in polymers, which may explain formation of propagating sharp diffusion fronts to be observed in some experiments. Differently from typical Case II or Stefan problem models, plasticisation of the polymer matrix is not necessarily required. Instead, diffusing small molecules are assumed to be captured by some specific sites of the polymer matrix for certain retention times. For example, they may become adsorbed at the surface of the holes and microvoids that are considered to be present in glassy polymer regions according to the well-known dual-sorption model and are attributed to excess free volume frozen into the glassy matrix. On the other hand, the small molecules may become bound to polymer chains. In this adsorbed/bound state they have much smaller movability and thus are effectively excluded from the diffusion. This adsorption/binding is considered to be a reversible process of state changing, but with asymmetric probabilities for direct and reverse events. With this assumption, taking into account that the amount of space available for such immobilised molecules is limited (limited free volume, limited number of anchoring sites) the model naturally results in the formation of sharp diffusion fronts or strong concentration gradients. Such a diffusion front is a region of effective immobilisation (adsorption/binding, though reversible) of the free diffusing molecules. For the simplest prescribed boundary conditions the diffusion front propagates linearly with the square root of time. By means of imposing generalised boundary conditions, it is possible to model other regimes of propagation of the diffusion front, including constant velocity. Graphical abstract: [Figure not available: see fulltext.]
机译：我们提出了一种在聚合物中扩散的替代模型，该模型可以解释在某些实验中观察到的传播性急剧扩散前沿的形成。与典型的Case II或Stefan问题模型不同，不一定需要对聚合物基体进行增塑。相反，假定扩散的小分子被聚合物基质的某些特定位置捕获了一定的保留时间。例如，根据众所周知的双重吸附模型，它们可能会吸附在被认为存在于玻璃状聚合物区域中的孔和微孔的表面，并归因于冻结在玻璃状基质中的过量自由体积。另一方面，小分子可能会与聚合物链结合。在这种吸附/结合状态下，它们的可移动性小得多，因此有效地从扩散中排除。这种吸附/结合被认为是状态改变的可逆过程，但是具有直接和反向事件的不对称概率。在此假设下，考虑到可用于此类固定分子的空间数量有限（有限的自由体积，有限的锚固位点数量），该模型自然会导致形成尖锐的扩散峰或强浓度梯度。这样的扩散前沿是自由扩散分子的有效固定（吸附/结合，尽管是可逆的）的区域。对于最简单的规定边界条件，扩散前沿与时间的平方根线性传播。通过施加广义边界条件，可以对扩散前沿的其他传播方式（包括恒定速度）进行建模。图形摘要：[该图不可用：请参见全文。]

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