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研究生： 林宗翰
Lin, Zong-Han
論文名稱： 水化矽酸鈣力學性質之模擬研究
MOLECULAR DYNAMICS SIMULATION OF CSH UNDER VARIOUS LOADING AND THERMAL CONDITIONS
指導教授： 王雲哲
Wang, Yun-Che
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 102
中文關鍵詞： 分子動力學模擬 、水化矽酸鈣 、張力 、彎曲 、扭轉 、壓痕 、熱傳導係數
外文關鍵詞： molecular dynamics simulation, C-S-H, tension, bending, torsion, indentation, coefficient of thermal conductivity
相關次數： 點閱：100  下載：9 
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    • 本論文以分子動力學模擬技術，研究選定之水化矽酸鈣(C-S-H)的機械與熱性質，所選定之C-S-H原子模型，其化學式為(CaO)1.60(SiO2)(H2O)1.63，密度約為2.32 g/cm3。分子動力學模擬所使用之原子間勢能函數為CSHFF，是一種新版本的ClayFF，採用庫倫靜電勢能函數為長程的交互作用力，蘭納-瓊斯勢函數為短程的交互作用力。我們將對C-S-H原子模型進行拉伸、壓縮、剪切、扭轉、彎曲、壓痕等模擬，以了解材料性質與微觀結構的關聯性。C-S-H在室溫下表現出明顯的層狀結構，但層狀結構在高溫下變得均勻不明顯，此現象表示熱能會對原子位置引起大幅的波動。在室溫下，我們計算出的Q1：Q2：Q3比例約為15：50：35，與文獻資料類似，在高溫時，Q1比例幾乎是固定的且最多數，Q2減少，Q0增加，這種Qn比例的變化將會顯著地影響C-S-H的機械性能。在拉伸，壓縮和剪切試驗中，我們發現層狀結構和氧化矽鏈會影響斷裂機制，另外在高溫下明顯損失其強度和韌性。根據我們的計算，扭轉試驗的最大剪切模數約為18.30 GPa，彎曲試驗的最大楊氏模數約為75.00 GPa。C-S-H在各個加載方向下具有1.5到2.5 GPa的極限拉伸應力。通過壓痕試驗，硬度約為7.33 GPa，壓痕模數約為64.19 GPa，透過Green-Kubo平衡法計算出的熱導率係數為10.852 W/mK。

    In this research, we adopt the molecular dynamics simulation techniques to study the mechanical and thermal properties of the chosen C-S-H atomistic model. The chemical composition of the C-S-H model is (CaO)1.60(SiO2)(H2O)1.63, and its density is about 2.32 g/cm3. The interatomic potential is the CSHFF which is a new version of ClayFF, applying Coulombic electrostatic potential function as long-range interactions, and take Lennard-Jones potential function as shortrange interactions. Tension, compression, shear, torsion, bending, and indentation simulations were conducted to correlate properties with microstructures. The C-S-H model exhibits clear layered structure at room temperature, but the layered structure becomes more homogeneous at high temperature, indicating thermal energy causing large fluctuation in atom positions. At room temperature, our calculated Q1:Q2:Q3 ratio is about 15 : 50 : 35, consistent with literature data. At high temperature, Q1 is almost constant and dominant, Q2 decreases, and Q0 increases. This change in Q’s affects the mechanical properties of C-S-H significantly. In tensile, compressive, and shear tests, the layer structure and silicate chains affect fracture mechanisms. At high temperatures, the C-S-H loses its strength and toughness significantly. Based on our calculations, the largest shear modulus is about 18.30 GPa from the torsion test, and largest Young’s modulus is about 75.00 GPa from the bending test. The C-S-H exhibits ultimate tensile stresses between 1.5~2.5 GPa in responses to various loading directions. From indentation tests, the hardness is about 7.33 GPa and the indentation modulus is about 64.19 GPa. The calculated coefficient of thermal conductivity is 10.852 W/mK by the Green-Kubo equilibrium method.

    CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Goals and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Relevant materials in cement science . . . . . . . . . . . . . . . . . . 2 1.2.2 MD research on C-S-H . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Theoretical backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1 Hooke’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Torsion deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Bending deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Contact between a rigid indenter and an elastic half-space . . . . . . . . . . . . 10 2.4.1 Conical indenter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.2 Cylindrical indenter . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.3 Nanoindentation experiment analysis . . . . . . . . . . . . . . . . . . 12 2.5 Voigt-Reuss-Hill average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.6 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Molecular dynamics simulation backgrounds . . . . . . . . . . . . . . . . . . . . 16 3.1 Interaction potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 The C-S-H model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Statistical ensembles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.5 Nuclear magnetic resonance spectroscopy . . . . . . . . . . . . . . . . . . . . 22 4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.1 Verification of our methodology . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.1.1 Uniaxial deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.1.2 Shear deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.1.3 Torsion deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.1.4 Bending deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.1.5 Indentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.1.6 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2 Structural analysis of the C-S-H model . . . . . . . . . . . . . . . . . . . . . . 36 4.2.1 Radial distribution function (RDF) . . . . . . . . . . . . . . . . . . . . 36 4.2.2 Density profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2.3 NMR Qn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Loading tests of the C-S-H model . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.1 Tension deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.2 Compression deformation . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.3 Shear deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3.4 Torsion deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.3.5 Bending deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3.6 Indentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.7 Interactions between C-S-H and aggregate . . . . . . . . . . . . . . . . 78 4.3.8 Elastic constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.3.9 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3.10 Carbon nanotubes and graphene . . . . . . . . . . . . . . . . . . . . . 83 5 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 APPENDICES Appendix A: Matlab code for chemical bonds . . . . . . . . . . . . . . . . . . . . 91 Appendix B: Matlab code for NMR Qn . . . . . . . . . . . . . . . . . . . . . . . 95 Appendix C: Page number for all simulation cases . . . . . . . . . . . . . . . . . 99 VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

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