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標題: | 使用自洽場理論預測高分子奈米材料之平衡結構 Predicting Equilibrium Structure of Polymer Nanocomposites using Self-Consistent Field Theory |
作者: | Guan-Ting Pan 潘冠廷 |
指導教授: | 游琇?(Hsiu-Yu Yu) |
關鍵字: | 高分子自洽場理論,自組裝結構,高分子嫁接之奈米粒子, self-consistent field theory for polymers,equilibrium structure,polymer-based nanomaterials, |
出版年 : | 2018 |
學位: | 碩士 |
摘要: | 本研究中,我們結合高分子自洽場理論與粒子密度泛函理論,以探討含有高分子的奈米材料的微觀自組裝結構。在過去的研究中,已發現高分子嫁接之奈米粒子在無溶劑狀態下仍能具有流動性,且其平衡結構依據不同的高分子嫁接密度與分子量等條件,可由系統的熵值來調控。因此,本篇論文著重在無溶劑條件下單聚高分子或共聚高分子分別與奈米粒子的作用,以近一步了解分子與粒子間的作用力如何影響材料之微結構與相變化。
數值方法的使用與編譯上,本研究以Fortran語言編寫理論模擬程式,重現前人的研究以檢驗此程式的正確性,同時減少來自數值方法上的誤差。最後,我們選擇使用pseudo-spectral method 並用picard iteration進行數值計算。由較簡單的一維系統開始,我們進行了三種不同系統的數值模擬,分別為僅有高分子、高分子中加入奈米顆粒以及嫁接高分子的平行平板。在僅有高分子的系統中,我們調整高分子中兩種單體的比例,以及之間的交互作用力,可以看到不規則分布(液體狀態)以及層狀結構的兩種相。而在高分子加入奈米顆粒的系統中,也看到了在適當的顆粒大小,會形成高分子層狀結構包覆奈米顆粒的結果。嫁接高分子平行平板系統,則是看到了因為無溶劑狀態,高分子會在平板距離增加時被強迫拉伸,最後自由能大幅提升。 三維的系統我們也進行了僅有高分子以及高分子加入奈米顆粒的模擬。僅有高分子的系統可以表現出更多種結構,我們將收斂的結果標記於相圖中,雖然可以成功重現相圖上的結構,但因為數值方法的關係,我們使用的方法難以區分面心立方及多孔螺旋曲面相。高分子加入奈米顆粒的模擬,則是最後會收斂在體心立方的結構,而這裡使用的高分子參數,在去除奈米顆粒之後,形成的應該是均勻液相,也就是加入奈米顆粒顯著地改變了系統的自由能在液相與體心立方相的差異,而影響了最終形成的結構。 最後,本研究未來期望使用目前的理論架構進行高分子嫁接之奈米顆粒(一種特殊有機無機混成材料)的相行為探討,並與僅使用密度泛函理論所預測的結果相比較。由目前我們的結果推測,系統應該會隨著高分子和顆粒間的排斥力提升或顆粒體積分率的增加,,形成體心立方、面心立方等等讓奈米顆粒形成可以達成最密堆積的結果。同時,給定作用力參數下,在調整高分子鏈長與嫁接密度後,亦可能形成非對稱性規則結構(如片狀或鏈狀)以降低整體的自由能。 Employing self-consistent field theory (SCFT) for polymers and density-functinal theory (DFT) for nanoparticles, we investigate the equilibrium structure and phase behavior of polymer-based nanomaterials. In literature, it has been shown that homopolymer-functionalized nanoparticles can exhibit fluid-like behavior in the absence of intervening solvent. Depending on the grafting density and molecular weight of polymers, the configurational entropic change drives the system towards equilibrium. In order to understand the effects of both entropic and enthalpic interactions on the microstructure and phase behavior of nanomaterials, in this study we consider several systems including one-dimensional homopolymer-grafted brushes, one-dimensional diblock copolymers with and without nanoparticles, and three-dimensional diblock copolymers with and without nanoparticles. We use Fortran as the computing language to write numerical codes that reproduce the expected results in previous studies to verify the correctness of the program. After comprehensive testing of various partial differential equation (PDE) solvers, we choose pseudo-spectral method combined with the Picard iteration to obtain satisfactory results with affordable computational costs. In one-dimensional studies, we choose three different systems, namely diblock-only system, diblock-nanoparticle mixtures, and two parallel homopolymer brushes. In the diblock-only system, we adjust the polymerization ratio of the two monomers in the polymer as well as the interaction parameters between them. Both the disorder liquid and the lamellar phases are observed. In diblock- nanoparticle mixtures, we discover the formation of center-filled lamella structure where nanoparticles collect in the center of one block. In the brush system, it is seen that in the solvent-free condition the polymers are forced to stretch as the separation distance increases, thus leading to a substantial increase in the system free energy. Advancing to three-dimensional systems, we perform calculations on diblock-only systems and diblock-nanoparticle mixtures. For the diblock-only system, the converged results are consistent with previous findings, and may be mapped on the phase diagram known for AB-diblock copolymers. For diblock-nanoparticle mixtures, we predict disorder-order (body-centered cubic, BCC) transition. Interestingly, the same parameter space for the diblock copolymers leads to disordered liquid phase in the absence of nanoparticles. This suggests that the addition of nanofillers significantly alters the free energy changes in disordered liquid and ordered BCC phases. Ultimately, our goal is apply the current theoretical framework to predict the phase diagram of solvent-free polymer-grafted nanoparticles (a type of inorganic-organic hybrid materials), and further make a close comparison with literature results. We expect that as the repulsion between polymers and particles increases or as the nanoparticle volume fraction increases, a transition from BCC to face-centered cubic (FCC) structure may occur to achieve a closer packing of nanoparticles. Moreover, given the same interaction parameters, changing the grafting density and/or chain length of polymers may lead to isotropic to anisotropic (chain-like or sheet-like) order transition as a result of the competition of polymer configurational entropy. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70688 |
DOI: | 10.6342/NTU201802795 |
全文授權: | 有償授權 |
顯示於系所單位: | 化學工程學系 |
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