在本研究中，我們嘗試以分子動力學來模擬數種水泥質相關的材料性質，像是矽酸鈣水化物、矽酸三鈣、矽酸二鈣、鋁酸三鈣、11和14埃的雪矽鈣石，以及以鎂取代雪矽鈣石的中鈣的模擬且可以穩定存在。本研究之分子模型以LAMMPS，配合經驗勢能使其達到到平衡，並計算其應力-應變關係。而量子分子動力學(SIESTA)來分析它們的結構，另用埃爾德法(Ewald)來計算庫倫電場勢能，計算其熱膨脹係數及體容積模數。利用徑向分布函數、結構因子、X光繞射分析對其原子結構進行分析，並討論其力學性質。研究結果中14埃雪矽鈣石的剪力模數約為15.8 GPa到37.5 GPa間、體膨脹係數為70.20 (10^6K^-1)、常壓下體容積模數為46.0 GPa，其中14埃雪矽鈣石在8 GPa的環境下可能發生相變化。

In this study, we perform molecular dynamics (MD) simulation on several cementitious-related materials, such as CSH, C3S, C3A, as well as 11 and 14 °A tobermorite. A magnesium-substituted tobermorite model is studied, and can be stabilized. Our molecular models are equilibrated and stabilized with empirical interatomic potentials through LAMMPS for stress-strain relationships. In addition, quantum molecular dynamics (QMD) simulation, with SIESTA, was performed on the minerals to verify their structures, as well as thermal expansion coefficients and bulk modulus. The Ewald method was adopted to calculate Coulomb electric potentials. Atomic structural analysis, such as radial distribution function (RDF), structure factor (SF), X-ray diffraction (XRD), of the materials are conducted. Vibration spectra are calculated from velocity autocorrelation functions. Mechanical properties of the materials are discussed from calculated quantities. In the result of 14 °A tobermorite, the shear modulus is around 15.8 GPa ~ 37.5 GPa, thermal expansion coefficient is (10^6K^-1) and bulk modulus is 46.0 GPa in atmospheric. In addition, 14 °A tobermorite may undergo a phase change around 8 GPa at room temperature, according to a change in bulk modulus and atomic configuration.

[1] K. V. Vliet, R. Pellenq, M. J. Buehler, J. C. Grossman, H. Jennings, F. J. Ulm, and S. Yip. Set in stone? a perspective on the concrete sustainability challenge. Materials Research Society, 37(395-402), 2012.
[2] R. Shahsavari. Hierarchical Modeling of Structure and Mechanics of Cement Hydrate. PhD thesis, Massachusetts Institute of Technology, February 2011.
[3] V. S. Ramachandran. Concrete Admixtures Handbook: Properties, Science, and Technology. Noyes Publications, USA, 1989.
[4] R. J. M. Pellenq, A. Kushima, R. Shahsavari, K. J. Van Vliet, M. J. Buehler, S. Yip, and F. J. Ulm. A realistic molecular model of cement hydrates. Proceedings of the National Academy of Sciences, 106(38):16102–16107, 2009.
[5] D. Hou and Z. Li. Molecular dynamics study of water and ions transport in nano-pore of layered structure: A case study of tobermorite. Microporous and Mesoporous Materials, 195:9–20, 2014.
[6] G. C. Bye. Portland Cement: Composition, Production and Properties. Pergamon Press, UK, 1983.
[7] P. Mondal and J. W. Jeffery. Crystal structure of c3a. Acta Crystallographica, 31B:686, 1975.
[8] Wikipedia. http://en.wikipedia.org.
[9] http://webmineral.com/data/Jennite.shtml#.U6Va3LFyRnZ.
[10] http://www.cementlab.com/cement-art.htm.
[11] http://content.edu.tw/junior/earth/tdjb/content.
[12] http://www.hpcbridgeviews.com/i67/Article3.asp.
[13] A. J. Allen, J. J. Thomas, and H. M. Jennings. Composition and density of nanoscale calcium-silicate-hydrate in cement. Nature Materials, 6:311–316, 2007.
[14] D. Frenkel and B. Smit. Understanding Molecular Dynamics from Algorithms to Applications. Academic Press, New York, 2002.
[15] R. Shahsavari, R. J.-M. Pellenq, and F.J. Ulm. Empirical force fields for complex hydrated calcio-silicate layered materials. Physical Chemistry Chemical Physics, 13:1002–1011, 2011.
[16] M. Youssef, R. J.-M. Pellenq, and B. Yildiz. Glassy nature of water in an ultra confining disordered material: the case of calcium-silicate-hydrate. Journal of the American Chemical Society, 133(2499-2510), 2011.
[17] P. A. Bonnaud, Q. Ji, B. Coasne, R. J. M. Pellenq, and K. J. Van Vliet. Thermodynamics of water confined in porous calcium-silicate-hydrates. American Chemical Society, 28:11422–11432, 2012.
[18] Q. Ji, R. J.-M. Pellenq, and K. J. Van Vliet. Comparison of computational water models for simulation of calcium-silicate-hydrate. Computational Materials Science, 53:234–240, 2012.
[19] D. Ebrahimi, R. J.-M. Pellenq, and A. J. Whittle. Nanoscale elastic properties of montmorillonite upon water adsorption. Langmuir, 28:16855–16863, 2012.
[20] P. A. Bonnaud, Q. Ji, and K. J. Van Vliet. Effects of elevated temperature on the structure and properties of calcium-silicate-hydrate gels: the role of confined water. Soft Matter, 9:6418–6429, 2013.
[21] H. Heinz, R. A. Vaia, and B. L. Farmer. Interaction energy and surface reconstruction between sheets of layered silicates. The Journal of Chemical Physics, 124:224713, 2006.
[22] R. K. Mishra, R. J. Flatt, and H. Heinz. Force field for tricalcium silicate and insight into nanoscale properties: Cleavage, initial hydration, and adsorption of organic molecules. The Journal of Physical Chemistry, 117:10417–10432, 2013.
[23] R. K. Mishra, L. Fernandez-Carrasco, R. J. Flatt, and H. Heinz. A force field for tricalcium aluminate to characterize surface properties, initial hydration, and organically modified interfaces in atomic resolution. Dalton Transactions, 43:10602–10616, 2014.
[24] D. Hou, Y. Zhu, Y. Lu, and Z. Li. Mechanical properties of calcium silicate hydrate (c-s-h) at nano-scale: A molecular dynamics study. Materials Chemistry and Physics, 146:503–511, 2014.
[25] D. Hou, H. Ma, Y. Zhu, and Z. Li. Calcium silicate hydrate from dry to saturated state: Structure, dynamics and mechanical properties. Acta Materialia, 67:81–94, 2014.
[26] G. Hantal, L. Brochard, H. Laubie, D. Ebrahimi, R. J.-M. Pellenq, F.-J. Ulm, and B. Coasne. Atomic-scale modeling of elastic and failure properties of clays. Molecular Physics, 112:1294–1305, 2014.
[27] L. Liu, A. Jaramillo-Botero, W. A. Goddard, III, and H. Sun. Development of a reaxff reactive force field for ettringite and study of its mechanical failure modes from reactive dynamics simulations. The Journal of Physical Chemistry, 116:3918–3925, 2012.
[28] H. Sato, K. Ono, C. T. Johnston, and A. Yamagishi. First-principles studies on the elastic constants of a 1:1 layered kaolinite mineral. American Mineralogist, 90:1824–1826, 2005.
[29] O. V. Pupysheva, A. A. Farajian, and B. I. Yakobson. Fullerene nanocage capacity for hydrogen storage. American Chemical Society, 8(3):767–774, 2008.
[30] V. Labet, P. Gonzalez-Morelos, R. Hoffmann, and N. W. Ashcroft. A fresh look at dense hydrogen under pressure. i. an introduction to the problem, and an index probing equalization of h-h distances. The Journal of Chemical Physics, 136:074501, 2012.
[31] G. C. Maitland, M. Rigby, E. B. Smith, and W. A. Wakeham. Intermolecular forces: their origin and determination. Clarendon Press, UK, 1981.
[32] D. C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge University Press, New York, 2004.
[33] M.T. Dove. Introduction to Lattice Dynamics. Cambridge University Press, New York, 1993.
[34] G.L. Squires. Introduction to the Theory of Thermal Neutron Scattering. Cambridge University Press, New York, 1978.
[35] M. E. Tuckerman. Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press, UK, 2010.
[36] B. D. Cullity. Elements of X-Ray Diffraction. Addison-Wesley, California, 1978.
[37] Siesta 3.1 user’sguide. http://www.uam.es/siesta.
[38] Lammps documentation. http://lammps.sandia.gov.
[39] Crystalmaker. http://www.crystalmaker.com/.
[40] H. Heinz and U. W. Suter. Atomic charges for classical simulations of polar systems. Journal of Physical Chemistry B, 108(47):18341–18352, 2004.
[41] H. Heinz, H. Koerner, K. L. Anderson, R. A. Vaia, and B. L. Farmer. Force field for phyllosilicates and dynamics of octadecylammonium chains grafted to montmorillonite. Chemistry of Materials, 17:5658–5669, 2005.
[42] J. Moon, S. Yoon, R. M. Wentzcovitch, S. M. Clark, and P. J. M. Monteiro. Elastic properties of tricalcium aluminate from high-pressure experiments and first-principles calculations. Journal of the American Ceramic Society, 95(9):2972–2978, 2012.