荷电膜渗透传质过程的计算机模拟:多价离子的传递

Computer simulation on the transport of ions through a charged membrane by percolation theory:transport of multi-valent ions

荷电膜的传质研究不仅对以电膜为基础的分离研究具有重要借鉴作用,而且对以非分离为基础的材料的导电-绝缘特性的转换判定和相关材料的制备具有重要的指导意义。为此,本文在一价离子通过荷电膜传质问题的研究基础上,用渗透理论的有关原理和方法,研究了二价、三价离子通过荷电膜的渗透传质问题,采用计算机模拟,计算得出二价、三价离子形态的渗透临界值：在二维50×50中,二价和三价离子的渗透临界值分别为0．435和0．516；在三维30×30×30中,二价、三价离子的渗透临界值分别为0．159和0．199。这说明无论是二维还是三维,随着离子价态的升高,渗透临界值增加。模拟的阶数虽与实际膜相差甚远,但模拟结果中阶数增大突跃的趋势已经十分明显,因此研究结果可用于预测多价离子在荷电膜中的传导机理。

The transport of divalent ions and trivalent ions through a charged membrane was investigated by percolation approach. Based on percolation concept and theory, theoretical simulation was conducted for two-dimension（2D） and three-dimension （3D） and the percolation threshold was calculated by the simple scaling rules. The results showed that whatever for 2D lattices or 3D lattices, there exists an obvious skip or pereoltion threshold with charged components. When the percolation thresholds of ions with different valence are compared, it is shown that percolation threshold depends not only on the dimensions but also on the valence of ions ：percolation threshold decreases with an increase in lattices but increase with an increase in the valence of transported ions：in a 2-D 50 × 50 lattices,the percolation threshold for mono-, di-and tri-valent ions are 0. 401, 0. 435 and 0. 516, respectively ;while in a 3-D 30 × 30 × 30 lattices, these percolation threshold values are 0. 119,0. 159 and 0. 199, respectively.