Cao Zheng, Kruczek Boguslaw, Thibault Jules
Department of Chemical and Biological Engineering, University of Ottawa, Ottawa, ON K1N 6N5, Canada.
Membranes (Basel). 2022 Oct 27;12(11):1053. doi: 10.3390/membranes12111053.
Recent years have seen the explosive development of mixed-matrix membranes (MMMs) for a myriad of applications. In gas separation, it is desired to concurrently enhance the permeability, selectivity and physicochemical properties of the membrane. To help achieving these objectives, experimental characterization and predictive models can be used synergistically. In this investigation, a Monte Carlo (MC) algorithm is proposed to rapidly and accurately estimate the relative permeability of ideal MMMs over a wide range of conditions. The difference in diffusivity coefficients between the polymer matrix and the filler particle is used to adjust the random progression of the migrating species inside each phase. The solubility coefficients of both phases at the polymer−filler interface are used to control the migration of molecules from one phase to the other in a way to achieve progressively phase equilibrium at the interface. Results for various MMMs were compared with the results obtained with the finite difference method under identical conditions, where the results from the finite difference method are used in this investigation as the benchmark method to test the accuracy of the Monte Carlo algorithm. Results were found to be very accurate (in general, <1% error) over a wide range of polymer and filler characteristics. The MC algorithm is simple and swift to implement and provides an accurate estimation of the relative permeability of ideal MMMs. The MC method can easily be extended to investigate more readily non-ideal MMMs with particle agglomeration, interfacial void, polymer-chain rigidification and/or pore blockage, and MMMs with any filler geometry.
近年来，混合基质膜（MMMs）在众多应用中得到了迅猛发展。在气体分离领域，人们期望同时提高膜的渗透性、选择性和物理化学性质。为了有助于实现这些目标，可以协同使用实验表征和预测模型。在本研究中，提出了一种蒙特卡罗（MC）算法，用于在广泛的条件下快速准确地估计理想MMMs的相对渗透率。利用聚合物基质和填料颗粒之间扩散系数的差异来调整各相中迁移物种的随机进程。聚合物-填料界面处两相的溶解度系数用于控制分子从一相迁移到另一相的方式，从而在界面处逐步实现相平衡。将各种MMMs的结果与在相同条件下用有限差分法获得的结果进行了比较，在本研究中，有限差分法的结果被用作基准方法来测试蒙特卡罗算法的准确性。发现在广泛的聚合物和填料特性范围内，结果非常准确（一般误差<1%）。MC算法简单易行，能准确估计理想MMMs的相对渗透率。MC方法可以很容易地扩展到研究更容易出现颗粒团聚、界面空隙、聚合物链刚性化和/或孔堵塞的非理想MMMs，以及具有任何填料几何形状的MMMs。
