臺灣博碩士論文加值系統

相變化的觀點來看，凝膠化行為無疑是複雜的。因為它不但包含了多種相變的耦合，同時也涉及了微觀結構的形成（指高分子鏈間微結晶的形成，高分子溶液的spinodal decomposition）與巨觀物理狀態的改變（包括percolation現象與凝膠彈性）。而在這兩種尺度之間，又牽涉到自組織結構（self-assembling processes）的形成與演化的複雜行為。因此，探討高分子物理凝膠結構的形成堪稱為一『複雜系統（complex system）』。
本論文嘗試將凝膠化與相變化做一連結，並指出高分子物理凝膠形成基本上涉及三種相變行為：
1. 高分子的結晶化（液－固相轉變）；
2. 高分子溶液的相分離（液－液相分離）；
3. Percolation現象（幾何相變化）。
有鑑於此，大多數的學者僅能將此複雜系統劃分成幾個側面來進行研究。諸如探討凝膠架橋點的結構與熱物性以建立相關的凝膠相圖，或是利用percolation model進行sol-gel transioion過程的理論研究。上述兩者並結合形態學（morphology）作為凝膠平衡結構研究的兩大軸心。相對於此，僅有少數學者，對凝膠結構形成之動態過程進行研究，尤其在介觀的長度尺度上(mesoscopic length scale)。小角光散射儀(Small-Angle Light Scattering, SALS)是研究膠體聚集、高分子摻合物、『複雜流體』化學物理以及臨界現象的利器。因此設計一台具有可real-time追蹤結構及涵蓋結構發展之特徵長度尺度範圍的光散射儀，是本論文的重點之一。透過Time-resolved 小角光散射儀器(TRSALS)，我們一窺前所未見高分子物理凝膠結構形成的世界。
利用TRSALS技術，本本論文首次對凝膠化的過程進行real-time之觀察。令人訝異的是，實驗數據呈現前所未見的結果，同時也指出現行小角光散射理論不足之處。基本上，高分子物理凝膠，大多呈現大尺度的不均一性（large-scale heterogeneous gels）。因此，對於凝膠構造的形成，普遍認為高分子溶液的相分離(在這主要指，所謂的spinodal decomposition）扮演主要的角色。原因在於，就凝膠而言，它是一個高分子在溶液中所形成的三次元網狀結構。而在熱力學失穩的條件下，spinodal decomposition所形成的空間雙連續相結構（percolation 結構）與凝膠形成的必要條件（三次元架橋的網目構造）相對應。同時在凝膠結構進行設計的觀點上，更吸引人的是，只要能控制spinodal decomposition的進程，就可以直接控制凝膠的網目構造。因此，對於一個具有大尺度不均一性的凝膠，spinodal decomposition的思考是基本上的不二條件。而對於成核－成長相分離則被揚棄在凝膠結構形成的思考之外。但是在本論文中，我們經由散射實驗證實，spinodal decomposition並不是形成大尺度不均一性凝膠結構的必要條件。相對於此，我們提出了nucleation gels這一個概念。Nucleation gels結構形成主要包含了以下幾個過程：首先是在亞穩態(meta stable)溶液當中所進行的成核－成長過程，在此一過程當中結晶性高分子透過液－液相分離(nucleation and growth)與高分子鏈間的結晶化價橋形成所謂的微凝膠粒子(microgels)，其次通過微凝膠粒子間的分形(fractal)聚集，形成一大尺寸的聚集集團(clusters)進而形成三次元的網目結構。最終凝膠為了進一步的降低其兩相間的表面能(指微凝膠粒子所形成的相疇與溶劑相間)以及穩定凝膠的網目結構，系統進一步的使凝膠結構進行後期的粗化行為(late-stage coarsening process )。對於此一嶄新的凝膠化行為，我們建立了一個基於現象學概念的結構模型，並且可以在散射理論當中完美的呈現此一模型與實際結構的對應。

Gelation is the phase transition from a collection of finite clusters to a state with the formation of an infinite network. The essential physical feature of a gel is its geometrical connections, and hence theoretical progress generally emphasizes percolation phenomena to gelation theory. In addition to this, an even more noteworthy subject is the nature and formation of network junctions in physical gels. Thermoreversible physical gel is a three-dimensional network of polymer chains cross-linked by physical junctions, and it can arise either as the result of a phase transition or through some specific molecular association or as a result of entanglements. In the present study, we confine our attention to the case of gels associated with phase transition. Physical gels passing through phase transition are especially complex systems; and it is generally accepted that the gelation is typically governed by the coupling of several phase transitions like the liquid-liquid phase separation, the crystallite formation of the polymer chain segments, and percolation phenomena. However, the complexity introduced by these coupling mechanisms has limited theoretical progress largely to purely phenomenological approaches, resulting in difficulties to explain fully in terms of gelation phenomena.
Most studies of gelation behaviors have focused on phase behavior, structural morphology, and rheological properties in physical gels. Experimentally, there is a lack of data on the dynamics of the gelation process, which may be attributed to both the complex nature of the gelation phenomena and practical difficulties in real-time observation of structural development of physical gels. By using the time-resolved small angle light scattering (TRSALS) technique, we present the first real-time measurement of the physical gelation process for a crystalline polymer. The finding is that the light scattering patterns show a unique feature in the Hv and the Vv scattering for PVDF gel electrolytes. To investigate the growth kinetics, a complete picture of the gel structural formation should be differentiated into, the nucleation and growth of the microgels, the diffusive aggregation of the microgels, the percolation in cluster-cluster aggregation process, and the late-stage coarsening by Ostwald ripening process. We propose some phenomenological functions to describe the hierarchical structure of the nucleation gels. The modeling of the late-stage gel structure could be built upon following three relevant categories, the structure of the primary particle, the nonfractal local structure of a random packing of the nearest neighbors, and the fractal correlations between the particles constituting the aggregates. The model is able to reproduce the overall behavior of Hv and Vv scattering intensity distributions over the experimental -range, and holds the truth of the gel structural development in the late-stage coarsening process. It is clear that the experimental results are entirely different from the general concept of “spinodal gels” and also imply that the spontaneous concentration fluctuation by spinodal decomposition is not a prerequisite for the formation of the large-scale heterogeneous gels. In contrast with spinodal gels, now we call it nucleation gels.

Chapter 1 Introduction 1
1.1 Gelation and Phase Transition 1
1.1.1 Percolation and Critical Phenomena on Gelation 2
1.1.2 First-Order Phase transition on Gelation 2
1.1.2.a Crystallization 2
1.1.2.b Phase Separation 3
1.2 Large-Scale Inhomogeneities of the Gel Structure 3
1.3 Fractal Nature of Gels 4
1.4 Probing Structure by Scattering Techniques 4
1.5 The Purpose of This Thesis 5
Chapter 2 Theoretical Background 7
2.1 Light Scattering Theories: Classical Approximations 8
2.2 Scattering Matrix Calculated for a Single Particle 9
2.3 Amplitude Function of a Single Particle 10
2.4 Light Scattering Applied to Aggregating Systems 11
Chapter 3 Experimental Section 13
3.1 Materials 13
3.2 Preparation of Polymer Gels 13
3.3 Light Microscopy 13
3.4 Time-Resolved Small-Angle Light Scattering Apparatus 13
3.4.1 Instrumental Setup 14
3.4.2 Calibration 15
Chapter 4 Results and Discussion 17
4.1 Scattering Patterns of the Nucleation Gels 17
4.2 Time Evolution of the Scattering Profiles 20
4.3 Fractal Nature of the Gel Structure 22
4.4 Growth Kinetics 22
4.5 Nucleation and Growth of Microgels 24
4.6 Modeling of Late-Stage Gel Structure 28
4.6.1 Structure Factor of Fractal Aggregates 29
4.6.2 Interference Function of Two Interpenetrated Spheres 30
4.7 Structural Development of Nucleation Gels 37
Chapter 5 Summary 39
Reference 41

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