含非球狀填充物的複合薄膜之有效擴散係數預測

複合薄膜兼具有傳統高分子薄膜之低製備成本的優點,其中添加之填充物具有高選擇性或高透過率的特色,為一有大規模運用之發展潛力的分離薄膜。就填充物之外型分類,可概括分類為球狀、管狀(一維)或層狀(二維)。管狀填充物如碳奈米管及金屬氧化物奈米管,其細長且管壁無法允許分子通透之特性,具有發展為分子篩填充物之潛力。層狀填充物如層狀沸石或粘土礦物,其厚度薄而大面積之特性, 一般認為可以改變分子透過時之質量傳遞長度,藉此提昇分離時之選擇性。一般用以計算複合薄膜之有效擴散係數及有效透過率之方程式為 Maxwell 模型,此為一做廣泛應用於計算有效擴散係數之解析方程式,此模型將球形填充物分散於基材中之行為類比做電阻串聯或並聯所推導而出。透過相同之推導邏輯,而後發展出針對管狀填充物之 KJN 模型以及層狀填充物之 Cussler 模型。然而,無論是 Maxwell 模型、KJN 模型或是 Cussler 模型,解析方程式無法徹底考慮真實管狀或層狀填充物分散於基材中之行為,因此在模型的預測中往往造成偏差。本研究使用有限元素分析法進行數值計算,首先建立仿真之三維模型,並於其中添加管狀或層狀填充物,並調控其佔基材之不同體積分率,透過 COMSOL MultiphysicsR 軟體進行質傳計算求得濃度分佈, 透過 Fick’s 擴散方程式的推導,進而得到包含更多資訊之數值方程式。對於管狀填充物而言,本研究進行了長寬比值、擴散係數比值、空間分布及填充物旋轉方向的探討。研究結果指出,提昇擴散係數比值可以有效的提升有效擴散係數,且其效應遠大於提昇長寬比值的提升幅度;而改變空間分布之效應非常顯著,倘若所有填充物延著垂直於擴散之方向增加比重,其提昇可以遠大於平行於擴散方向之增加比重的結果。旋轉方向效應亦指出,管壁垂直於擴散方向將不利於有效擴散係數,且會大幅降低有效擴散係數。本研究亦進行了具有隨機分佈旋轉方向填充物的效應,其結果指出,填充物的長寬比值效應並部顯著, 但擴散係數比值效應將會大幅改變有效擴散係數。對於層狀填充物而言,本研究進行了擴散係數比值以及非等向性擴散的效應。研究結果指出,具有非等向性擴散的填充物對整體有效擴散係數有顯著的影響。為了驗證本研究中預測模型的正確性,吾人與文獻中若干透過實驗所量測得之薄膜有效擴散係數,與本研究之模型及 Maxwell、KJN、 Cussler 模型做比較,其結果指出,本研究所預測之模型與其他解析方程式有較好的準確性。

關鍵字

複合薄膜；奈米管；層狀材料；有效擴散係數；膜分離

並列摘要

This article presents a series of calculation of the effective diffusivity from the detailed mass transfer modeling of mixed matrix membranes with non-spherical (tubular and layered) fillers. We construct the filler-and-matrix models mimicking the realistic mixed matrix membranes, and perform the mass transfer simulations. A number of mixed matrix membranes' parameters, including filler to matrix volume ratio, aspect ratio of fillers, filler to membrane's relative diffusivity, and filler's orientation are considered in our simulations. Our results show that tubular fillers' alignment is critical to the effective diffusivity. The aspect ratio of tubular fillers only shows marginal effect on the effective diffusivity. Our results also suggest that the increase of aspect ratio and the intrinsic diffusivity of tubular filler will cause the increase of the overall effective diffusivity. For layered fillers, the effective diffusivity is influenced by the isotropy of the layered fillers caused by the differences in the out-of-plane and in-plane diffusivity. Also, the binary species selectivity in separation of the mixed matrix membranes can be adjust by the difference of the anisotropic diffusivity of the species-filler construction. Finally, we compare our results with selected experimental results in the literature for validation the prediction of the effective diffusivity of mixed matrix membranes.

並列關鍵字

nanotube ； membrane separation ； mixed matrix membranes (MMMs) ； modeling ； effective diffusivity

參考文獻

[1] NadineSchmeling,RomanKonietzny,DanielSieffert,PatrickRolling,andClaudia Staudt. Functionalized copolyimide membranes for the separation of gaseous and liquid mixtures. Beilstein Journal of Organic Chemistry, 6(1):789–800, 2010.

[5] Lloyd M Robeson. Correlation of separation factor versus permeability for poly-

[6] Lloyd M Robeson. The upper bound revisited. Journal of Membrane Science,

[7] Lan Ying Jiang, Tai-Shung Chung, Chun Cao, Zhen Huang, and Santi Kul- prathipanja. Fundamental understanding of nano-sized zeolite distribution in the formation of the mixed matrix single- and dual-layer asymmetric hollow fiber mem- branes. Journal of Membrane Science, 252(1-2):89–100, 2005.

[8] M A Aroon, A F Ismail, T Matsuura, and M M Montazer-Rahmati. Performance studies of mixed matrix membranes for gas separation: A review. Separation and Purification Technology, 75(3):229–242, 2010.

國際替代計量

含非球狀填充物的複合薄膜之有效擴散係數預測

全文下載

主題瀏覽