2維組裝偶極轉子在有機薄膜中的介電函數

Abstract

近期由Fukushima團隊對於有機薄膜提出了一個新的方法。然而，在常見的的晶體中，是由許多單一的晶體域(domain)所組成，但是在他們的有機薄膜中，沒有域邊界(domain boundary)到達肉眼可見的範圍。這個特性指出了此有機薄膜在肉眼可見的尺度範圍內具有“完美”的晶體特性，此特性提供了多種高性能的有機物質或元件的可能性。最近，他們替代1,2-二氟苯(diflurobenzene)分子(運動模式類似轉子)被夾在上述石蠟三腳的三蝶烯(triptycene)薄膜中。他們也量測介電函數來找出轉子的角度變化。我們預期這類具有偶極轉子的大面積薄膜可以做為理想的有機光電材料。Garcia-Garibay團隊也研究了類似的系統，但是他們研究的是單晶或是粉末，為了解釋他們的實驗，採用了在過阻尼極限下所使用的理論：隨機共振(stochastic resonance)。 在此論文中，我們研究欠阻尼極限以及過阻尼極限裡的介電函數。我們使用兩個系統做討論，雙位能井、餘弦位能，而後者可被視為極性轉子的最簡單模型。我們計算自相關函數來得到其衰減速率以及介電函數，再利用欠阻尼以及過阻尼的實驗中得到衰減速率的簡單公式。我們的公式在低溫極限中與Kramers定律吻合，在高溫範圍裡，我們的公式會比Kramers定律更好。我們發現在欠阻尼以及過阻尼極限中顯現了相似的介電函數，即使兩者背後的動力學非常不同，再者，我們藉由公式擬合Fukushima團隊的實驗結果來獲得摩擦常數和活化能，但是其擬合結果並不令人滿意，這也指出了轉子之間的作用力或者量子效應的重要性。

Recently Fukushima et al. reported a space-filling design for the rational synthesis of organic thin films with exceptionally long-range structural integrity based on the geometric consideration on tessellation of Euclidean plane by regular hexagon. While usual crystal consists of many single crystal domains, their thin film has no domain boundary up to macroscopic (~cm^2) scale. This indicates that the thin film consist of perfect crystal with macroscopic size, giving rise to the possibilities of various ideal high performance organic materials/devices. Recently they substitute diflurobenzene molecules (acting as dipole rotors) sandwiched by the above mentioned paraffinic tripodal triptycene thin film. They also measured the dielectric response to find out the time scale of the angle change of the rotors. We expect that this large scale thin film with dipole rotors can be an ideal organic photonic material. Garcia-Garibay et al studied similar systems, but they are in s single crystal or powder state. In order to explain their experiment, stochastic resonance theory has been used, which is valid in the over damping limit. In this thesis we study the dielectric response in both the under and over damping limit. We take two systems, double well and cosine potentials, the latter of which can be regarded as the simplest model of dipole rotor. We calculated the autocorrelation function, with which we obtained the decay rate and the dielectric function. We obtained the simple empirical formulae for the decay rate both in the under and over damping limit. Our formulae agree with Kramers’ law in the low temperature limit, and works better in the high temperature region. We found out that both under and over damping limit show a similar dielectric response, even though the dynamics are quite different. Furthermore, these formulae are used as fitting functions to obtain the friction constant and the activation energy of the molecular rotor in thin film used in Fukushima’s experiment. Our fitting can reproduce the peak positions, but the fitting quality is not satisfactory. This may indicate the importance of the rotor-rotor interaction or quantum effect