量測物質之介電特性一直以來都是一門相當重要的技術，舉凡各種工業 製造行業或是學術研究皆無法離開這門領域。藉由精細量測介電性質可用於優化各式產線、協助設計元件亦或是幫助了解微觀物理特性。本研究提出一種操作於微波頻段 (100MHz-18GHz) 之寬頻流體介電量測方法，相較於其他種介電量測方式，本研究所提出方法具有非破獲性量測、所需樣品少以及易於量測之優點。並且我們利用此系統測量了四種低元單 羥基醇（甲醇、乙醇、1-丙醇和 1-丁醇）、四種低元羧酸（甲酸、乙酸、丙酸和油酸）以及其二元混合物之介電弛豫譜。透過適當選擇介電弛豫模型 (包含 Debye、Cole-Davidson、Cole-Cole 及 Havriliak–Negami) 來進行介電係 數擬合，且從中確定四種梭酸-乙醇混合物於九種不同莫爾濃度之弛豫參 數。藉由弛豫參數可加以計算得到各混和物之 Excess static permittivity、Excess Gibbs free energy、Kirkwood correlation factor 和 Bruggeman factor。這些數據可以在不同的微觀熱力學過程解釋之下得到一致之物理詮釋，其中牽涉現象包含氫鍵網路在分子間交互作用力下之旋轉、分解以及重構，同質及異質間偶極矩平行或反向排列趨勢，以及長鏈碳所引起之立體障礙等。這些結果不僅對極性流體間混和有更深入且清晰的了解，並且對工業製造 過程中所需之酯化反應設計以及藥物合成提供更具參考價值之數據。

Measuring the dielectric properties of matter has always been a very important technology, and all industrial manufacturing industries or academic research cannot leave this field. By finely measuring dielectric properties, it can be used to optimize various production lines, assist in the design of components, or provide clear insight in microphysical properties. This work proposes a method for broadband liquid dielectric characterization from 100 MHz to 18 GHz. We characterized the broadband dielectric properties of four primary alcohols (methanol, ethanol, 1-propanol and 1-butanol), four monocarboxylic acids (formic, acetic, propionic and oleic acids) and their dihydric dielectric spectrum of the mixture. The fitting process was performed by appropriate selection of dielectric relaxation models (including DB, CD, CC, and HN model), and four carboxylic acid-ethanol mixtures’ relaxation parameters were determined under nine different molar concentrations. Excess static permittivity, Excess Gibbs free energy, Kirkwood correlation factor and Bruggeman factor for each mixture can be calculated from the relaxation parameters. Various microscopic dynamics processes, including the orientational rearrangement of hydrogen bond networks under intermolecular interactions, the parallel or anti-parallel alignment trend of dipole moments, and dielectric screening effect and steric hindrance due to long carbon chain, were proposed to explain those experimental results consistently. This work not only provides insight into the relaxation processes in binary polar-polar mixtures, but also gives out important data for the esterification process designs in industrial manufacture.

Acknowledgements
摘要 i
Abstract ii
1 緒論 1
1.1 研究動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 介電係數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 介電量測方式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 共振與非共振系統 . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.2 寬頻同軸測量系統 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 理論推導 7
2.1 波導管分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 波導管本徵模式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 圓柱波導管 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 同軸波導管 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 同軸-圓波導管不連續介面 . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 對稱性、邊界條件與正交性 . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 S 矩陣建構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 HFSS 模擬 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 同軸-同軸波導不連續介面 . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 波模分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 HFSS 模擬 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 開底式同軸探針 (open ended coaxial probe) . . . . . . . . . . . . . . . . . . 24
2.4.1 波模分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 實驗架設與數據處理 27
3.1 實驗器具與架設 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 校正方式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 標準 OSL 校正 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 常見液體校正 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 光學量測 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 數據處理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 液體介電性質 35
4.1 等效介電與弛豫模型 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 靜場介電 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.2 弛豫過程 (Relaxation process) . . . . . . . . . . . . . . . . . . . . . . 36
4.2 純物質 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.1 低元醇類 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.2 低元有機酸類 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 二元混合 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.1 乙醇-有機酸混合介電譜與弛豫參數 . . . . . . . . . . . . . . . . . . 44
4.3.2 二元混合介電參數介紹 . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.3 實驗二元混合介電參數 . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 分子動力學模擬概述 (Gromacs 軟體) 53
5.1 計算原理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.1 近似條件 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.2 動力學方程 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2 模擬步驟 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.1 力場選擇 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.2 預平衡 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.3 模擬 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3 參數分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.1 密度 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.2 氫鍵數量 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.3 介電常數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.4 極化衰減函數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.5 徑向分布函數 (Radial distribution function) . . . . . . . . . . . . . . 61
6 結論 63
A 散射矩陣 (Scattering matrix) 65
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