本論文使用官能基化石墨烯和聚甲基丙烯酸甲酯製備成奈米複合材料，以此提升其基本機械性質與熱性質，並藉由材料分析去探討石墨烯使聚甲基丙烯酸甲酯性質改變的可能機制。
而聚甲基丙烯酸甲酯和溶劑的交互作用可以用Harmon model很好的解釋，所以我們嘗試使用Harmon model去分析溶劑在官能基石墨烯/聚甲基丙烯酸甲酯複合材料的質傳行為，得到特徵常數D和v`，這兩個常數都符合阿瑞尼士方程式，故可以分別得到D和v的活化能。而我們再進一步探討此複合材料的裂縫癒合行為，其癒合速度雖然隨著添加石墨烯而下降，但是機械強度卻會隨著添加石墨烯而增加。

We use functionalized graphene sheets to enhance the PMMA properties, and utilize solution mixing method to prepare the graphene/PMMA nanocomposites. We investigate the mechanical and thermal properties and try to explain the probable mechanism between graphene sheets and PMMA matrix.
The interaction between solvent and PMMA has been studied for several years. We use Harmon model to fit the mass transport of methanol in PMMA and graphene/PMMA nanocomposites. The characteristic parameters of diffusion coefficient (D) and velocity (v) are calculated from the data of curve fitting, and the results satisfy Arrhenius equation. Moreover, we study the crack healing behavior of PMMA and graphene/PMMA nanocomposites in methanol, because this phenomenon only occurs when the operating temperature is higher than the effective glass transition temperature, and we confirm that the activation energy of crack healing is also related to the diffusion coefficient (D) in mass transport.

1. P. R. Wallace. The band theory of graphite. Phys. Rev. 71, 622–634 (1947).
2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov. Electric field effect in atomically thin carbon films. Science. 306, 666–669 (2004).
3. C. Lee, X. Wei, J. W. Kysar, and J. Hone. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science. 321, 385–388 (2008).
4. A. A.Balandin. Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008).
5. M. D. Stoller, S. Park, Y. Zhu, J. An, and R. S. Ruoff. Graphene-based ultracapacitors. Nano Lett. 8, 3498–3502 (2008).
6. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer. Ultrahigh electron mobility in suspended graphene. Solid State Commun. 146, 351–355 (2008).
7. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, A. K. Geim. Fine structure constant defines visual transparency of graphene. Science. 320(5881), 1308-1308 (2008).
8. X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, H. Dai. Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors. Physical Review Letters. 100(20), 206803 (2008).
9. X. Wang, L. J. Zhi, K. Mullen. Transparent, conductive graphene electrodes for dye-sensitized solar cells. Nano Lett. 8(1), 323-327 (2008).
10. H. A. Becerril, J. Mao, Z. Liu, R. M. Stoltenberg, Z. Bao, Y. Chen. Evaluation of solution-processed reduced graphene oxide films as transparent conductors. ACS Nano. 2(3), 463-470 (2008).
11. S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff. Graphene-based composite materials. Nature. 442, 282-286 (2006).
12. B. Debelak, K. Lafdi. Use of exfoliated graphite filler to enhance polymer physical properties. Carbon. 45, 1727-1734 (2007).
13. R. Sengupta, M. Bhattacharya, S. Bandyopadhyay, A. K. Bhowmick. A review on the mechanical and electrical properties of graphite and modified graphite reinforced polymer composites. Progress in Polymer Science. 36, 638-670 (2011).
14. H. Kim, A. A. Abdala, and C. W. Macosko. Graphene/Polymer Nanocomposites. Macromolecules. 43, 6515–6530 (2010).
15. S. Pei and H. M. Cheng. The reduction of graphene oxide. Carbon. 50, 3210-3228 (2012).
16. M. Eizenberg, and J. M. Blakely. Carbon monolayer phase condensation on Ni(III). Surf. Sci. 82,228–236 (1978).
17. H. Hibino, S. Tanabe, S. Mizuno, and H. Kageshima. Growth and electronic transport properties of epitaxial graphene on SiC. J. Phys. D: Appl. Phys. 45, 154008 (2012).
18. W. S. Hummers and R. E. Offeman. Preparation of graphitic oxide. J. Am. Chem. Soc. 80, 1339 (1958).
19. Z. S. Wu, W. Ren, L. Gao, B. Liu, C. Jiang, and H. M. Cheng. Synthesis of high-quality graphene with a pre-determined number of layers. Carbon. 47,493-499 (2009).
20. H. C. Schniepp, J. L. Li, M. J. McAllister, H. Sai, H. A.Margarita, D. H. Adamson, R. K. Prud’homme, Roberto Car, D. A. Saville, and I. A. Aksay. Functionalized single graphene sheets derived from splitting graphite oxide. J. Phys. Chem. B. 110, 8535-8539 (2006).
21. R. Verdejo, M. M. Bernal, L. J. Romasanta and M. A. Lopez-Manchado. Graphene filled polymer nanocomposites. J. Mater. Chem. 21, 3301-3310 (2011).
22. M. Fang, K. G. Wang, H. B. Lu, Y. L. Yang and S. Nutt. Single-layer graphene nanosheets with controlled grafting of polymer chains. J. Mater. Chem. 20, 1982–1992 (2010).
23. S. H. Lee, D. R. Dreyer, J. H. An, A. Velamakanni, R. D. Piner, S. Park, Y. W. Zhu, S. O. Kim, C. W. Bielawski and R. S. Ruoff. Polymer Brushes via Controlled, Surface-Initiated Atom Transfer Radical Polymerization (ATRP) from Graphene Oxide. Macromol. Rapid Commun. 31, 281–288 (2010).
24. M. Fang, K. G. Wang, H. B. Lu, Y. L. Yang and S. Nutt. Covalent polymer functionalization of graphene nanosheets and mechanical properties of composites. J. Mater. Chem. 19, 7098–7105 (2009).
25. S. R. Wang, M. Tambraparni, J. J. Qiu, J. Tipton and D. Dean. Thermal Expansion of Graphene Composites. Macromolecules. 42, 5251–5255 (2009).
26. M. A. Rafiee, J. Rafiee, Z. Wang, H. Song, Z.-Z. Yu and N. Koratkar. Enhanced Mechanical Properties of Nanocomposites at Low Graphene Content. ACS Nano. 3, 3884–3890 (2009).
27. J. R. Potts, D. R. Dreyer, C. W. Bielawski, and R. S. Ruoff. Graphene-based polymer nanocomposites. Polymer. 52, 5-25 (2011).
28. S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen and R. S. Ruoff. Graphene-based composite materials. Nature. 442, 282–286 (2006).
29. T. Ramanathan and A. A. Abdala. Functionalized graphene sheets for polymer nanocomposites. Nature Nanotechnology. 3, 327-331 (2008).
30. Y. Shang, T. Li, X. Zhu, Y. Zhang, X. Chen, and T. Zhao. Effect of the graphene sheets derived from multistep oxidized carbon nanotubes on the performance of graphene sheets/poly(methyl methacrylate) composites. Journal of Analytical and Applied Pyrolysis. 114, 243-249 (2015).
31. H. Kim, Y. Miura and C. W. Macosko. Graphene/Polyurethane Nanocomposites for Improved Gas Barrier and Electrical Conductivity. Chem. Mater. 22, 3441–3450 (2010).
32. P. Steurer, R. Wissert, R. Thomann and R. Mulhaupt. Functionalized Graphenes and Thermoplastic Nanocomposites Based upon Expanded Graphite Oxide. Macromol Rapid Commun. 30, 316–327 (2009).
33. H. Kim and C. W. Macosko. Processing-property relationships of polycarbonate/graphene composites. Polymer. 50, 3797–3809 (2009).
34. J. Wang, H. Hu, X. Wang, C. Xu, M. Zhang and X. Shang. Preparation and Mechanical and Electrical Properties of Graphene Nanosheets–Poly(methyl methacrylate) Nanocomposites via In Situ Suspension Polymerization. J. Appl. Poly. Sci. 122, 1866-1871 (2011).
35. V. H. Pham, T. T. Dang, S. H. Hur, E. J. Kim, and J. S. Chung. Highly Conductive Poly(methyl methacrylate) (PMMA)-Reduced Graphene Oxide Composite Prepared by Self-Assembly of PMMA Latex and Graphene Oxide through Electrostatic Interaction. Appl. Mater. Interfaces. 4, 2630 – 2636 (2012).
36. J. R. Potts, S. H. Lee, T. M. Alam, J. An, M. D. Stoller, R. D. Piner, and R. S. Ruoff. Thermomechanical properties of chemically modified graphene/poly(methyl methacrylate) composites made by in situ polymerization. Carbon. 49, 2615-2623 (2011).
37. D. Li, M. B. Müller, S. Gilje, R. B. Kaner, and G. G. Wallace. Processable aqueous dispersions of graphene nanosheets. Nature Nanotechnology. 3, 101-105 (2008).
38. Y.-J. Wan, L.-C. Tang, D. Yan, L. Zhao, Y.-B. Li, L.-B. Wu, J.-X. Jiang, and G.-Q. Lai. Improved dispersion and interface in the graphene/epoxy composites via a facile surfactant-assisted process. Composites Science and Technology. 82, 60-68 (2013).
39. E. E. Tkalya, M. Ghislandi, G. de With, and C. E. Koning. The use of surfactants for dispersing carbon nanotubes and graphene to make conductive nanocomposites. Current Opinion in Colloid and Interface Science. 17, 225-232 (2012).
40. H. Bai, C. Li, and G. Shi. Functional Composite Materials Based on Chemically Converted Graphene. Adv. Mater. 23, 1089-1115 (2011).
41. N. Roy, R. Sengupta, and A. K. Bhowmick. Modifications of carbon for polymer composites and nanocomposites. Progress in Polymer Science. 37, 781-819 (2012).
42. M. J. McAllister, J.-L. Li, D. H. Adamson, H. C. Schniepp, A. A. Abdala, J. Liu, M. Herrera-Alonso, D. L. Milius, Roberto Car, Robert K. Prud’homme, and I. A. Aksay. Single Sheet Functionalized Graphene by Oxidation and Thermal Expansion of Graphite. Chem. Mater. 19, 4396–4404 (2007).
43. Y. Xu, H. Bai, G. Lu, C. Li, and G. Shi. Flexible Graphene Films via the Filtration of Water-Soluble Noncovalent Functionalized Graphene Sheets. J. AM. CHEM. SOC. 130, 5856–5857 (2008).
44. M. Fang, K. Wang, H. Lu, Y. Yang and S. Nutt. Covalent polymer functionalization of graphene nanosheets and mechanical properties of composites. J. Mater. Chem. 19, 7098-7105 (2009).
45. A. Silberberg. The Role of Matrix Mechanical Stress in Swelling Equilibrium and Transport through Networks. Macromolecules. 13, 742-748 (1980).
46. H. B. Hopfenberg and H. L. Frisch. Transport of organic micromolecules in amorphous polymers. J. Polym. Sci. (B), 405-409 (1969).
47. T. Alfrey, E. F. Gurnee, and W. G. Lloyd. Diffusion in glassy polymers. J. Polym. Sci. (C), 12, 249-261 (1966).
48. J. P. Harmon, S. Lee, and J. C. M. Li. Anisotropic methanol transport in PMMA after mechanical deformation. Polymer. 29, 1221-1226 (1988).
49. J. P. Harmon, S. Lee, and J. C. M. Li. Methanol transport in PMMA: The effect of mechanical deformation. J. Polym. Sci. (A), 27, 397 (1987).
50. C. B. Lin, S. Lee, and K. S. Liu. Methanol-induced crack healing in poly(methyl methacrylate). Polymer Engineering and Science. 21, 1399-1406 (1990).
51. K. Jud, H. H. Kausch, and J. G. Williams. Fracture mechanics studies of crack healing and welding of polymers. J. Mater. Sci. 16, 204-210 (1981).
52. R. P. Wool and K. M. O’Connor. A theory of crack healing in polymers. J. Appl. Phys. 52, 5953 (1981).
53. R. P. Wool and K. M. O’Connor. Time dependence of crack healing. J. Polym. Sci. 20, 7-16 (1982).
54. P. G. de Gennes. Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 55, 572 (1971).
55. H. H. Kausch and K. Jud. Molecular aspects of crack formation and healing in glassy polymers. Plast. Rubber Proc. Appl. 2, 265-268 (1982).
56. P. P. Wang, S. Lee, and J. P. Harmon. Ethanol-induced crack healing in poly(methyl methacrylate). J. Polym. Sci. (B), Polym. Phys. 327, 1217-1227 (1994).
57. G. D. Smith, D. Bedrov, L. Li, and O. Byutner. A molecular dynamics simulation study of the viscoelastic properties of polymer nanocomposites. J. Chem. Phys. 117, 9478-9489 (2002).
58. S. N. Tripathi, P. Saini, D. Gupta, V. Choudhary. Electrical and mechanical properties of PMMA/reduced graphene oxide nanocomposites prepared via in situ polymerization. J. Mater. Sci. 48, 6223–6232 (2013).
59. A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. iscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim. Raman Spectrum of Graphene and Graphene Layers. Phys. Rev. Lett. 97, 187401 (2006).
60. C. P. Ennis, and I. K. Ralf. Mechanistical studies on the electron-induced degradation of polymethylmethacrylate and Kapton. Phys. Chem. Chem. Phys. 12, 14902-14915 (2010).
61. M. Wall. The Raman Spectroscopy of Graphene and the Determination of Layer Thickness. Thermo Fisher Scientific. (2011).
62. M. Alexandre, and P. Dubois. Polymer-layered silicate nanocomposites: preparation, properties and uses of a new class of materials. Materials Science and Engineering, 28, 1–63 (2000).