Analytical solutions to mathematical models of the surface and bulk erosion of solid polymers
Analytical solutions to mathematical models of the surface and bulk erosion of solid polymers
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DOI：
10.1002/polb.20340
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发表时间：
2005-02-15
影响因子：
--
通讯作者：
Untereker, D
中科院分区：
文献类型：
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作者：
Lyu, S;Sparer, R;Untereker, D
聚合物材料水解并消失在其环境中的过程通常称为侵蚀。根据水解发生的方式，定义了两种类型的侵蚀。如果整个试样同时发生水解，则称为整体侵蚀。如果水解主要局限于样品表面附近的区域，并且表面通过向内移动而不断降解，则称为表面侵蚀。本文提出了一个体冲蚀的动力学关系式。这种关系提供了一种方法来估计水解动力学常数为本体侵蚀聚合物。同样的关系也适用于微观层面的表面侵蚀。通过与扩散反应方程相结合，并提供移动边界条件，获得了稳态表面侵蚀问题的解析解。侵蚀速率、侵蚀前沿宽度和诱导时间都可以表示为聚合物键水解速率、水扩散率和溶解度以及可以通过实验确定的其他参数的简单函数。腐蚀前沿宽度是诱导时间和腐蚀速率的乘积。侵蚀前沿宽度与聚合物试样厚度的比率是确定试样是否经历表面或本体侵蚀的参数。将理论结果与文献中的实验观测结果进行了比较，并发现了一致性。
The process by which polymeric materials hydrolyze and disappear into their environments is often called erosion. Two types of erosion have been defined according to how the hydrolysis takes place. If hydrolysis occurs throughout the entire specimen at the same time, it is called bulk erosion. If the hydrolysis is mainly confined to a region near the surface of the specimen and the surface continuously degrades by moving inward, it is termed surface erosion. In this article, a kinetic relationship for bulk erosion is developed. This relationship provides a method for estimating the hydrolysis kinetic constants for bulk-eroding polymers. This same relationship is also applicable to surface erosion at a microscopic level. Through its combination with a diffusion-reaction equation and the provision of moving boundary conditions, an analytical solution to the steady-state surface-erosion problem is obtained. The erosion rate, erosion front width, and induction time can all be expressed as simple functions of the rate of polymer bond hydrolysis, water diffusivity, and solubility, plus other parameters that can be experimentally determined. The erosion front width is the product of the induction time and the erosion rate. The ratio of the erosion front width to the polymer specimen thickness is a parameter that determines whether the specimen undergoes surface or bulk erosion. Theoretical results are compared with experimental observations from the literature, and agreement is found. (C) 2005 Wiley Periodicals, Inc.