高分子奈米複合材料是以奈米粒子為添加物，加入高分子材料中，使材料同時具備高分子的原始性質與奈米粒子所增進的性質，例如機械強度上的提升等。增進的性質與材料內部奈米粒子的分散性有很大的關連，奈米粒子分散性越佳增進效果越佳，因此近期有許多研究探討奈米粒子在高分子基質中的分散機制。其中Mackay et al.認為當高分子迴旋半徑(radius of gyration, Rg)大於奈米粒子半徑時，奈米粒子會分散於高分子基質中，反之則聚集呈現相分離狀態。因此我們使用電腦模擬的方式來探討奈米粒子在高分子基質中聚集行為，並驗證Mackay et al.所提出的理論。
本研究利用耗散粒子動力學的模擬方法探討疏高分子與親高分子的奈米粒子在高分子基質中聚集程度的影響，以及造成聚集的原因。疏高分子的奈米粒子在高分子基質中最終會形成聚集，驅使奈米粒子聚集的原因是由系統內能降低為主導。實驗上所觀察到奈米粒子在較長的高分子基質中有較佳的分散性，是由於系統黏度的影響，造成分散型態上的差異。奈米粒子在長度較長的高分子基質中因系統黏度高，擴散係數較低，聚集速度較慢，所觀察到的分散程度較佳。較短的高分子中系統黏度低，擴散係數較高，聚集速度較快，所觀察到的分散程度較差。親高分子的奈米粒子在長度較長的高分子基質中也會形成聚集，驅使奈米粒子聚集的原因是由系統亂度上升為主導。奈米粒子間的作用力會隨著奈米粒子間的接觸面積與斥力參數的變化而有所不同，其形成原因類似於空乏力，系統傾向於最小空乏區與最大系統亂度的趨勢。

Dispersing nanoparticles in polymer matrix allows for the formulation of novel polymer nanocomposite materials that combine the properties and functionality of the nanoparticle and the polymer. It’s important to understand dispersion of nanoparticles in polymer matrix. In experiment, dispersion of nanoparticles into a polymer matrix is enhanced for systems where the radius of gyration of the linear polymer is greater than the radius of the nanoparticle.
We perform the Dissipative Particle Dynamics (DPD) simulation to study the dispersion mechanism of nanoparticles in the polymer matrix. For solvophobic nanoparticles, nanoparticles inevitably aggregate in polymer matrix, and aggregation is driven by the reduction of enthalpy. Experimental results show that nanoparticles tend to disperse in polymer matrix with large radius of gyration, this phenomenon is attributed to the high viscosity of system, reducing the diffusion coefficient cause nanoparticles slowly aggregate. For solvophilic nanoparticles, nanoparticles similarly aggregate in polymer matrix, and aggregation is driven by the increase of entropy. The effective interparticle force is similar to depletion attraction. The whole system tends to minimum depletion zone and maximum entropy. The effective intperparticle force depends on contact area of nanoparticles and repulsive parameter.

1. D.R. Paul, L.M. Robeson, Polymer nanotechnology : Nanocomposites, Polymer, 49, 3187, 2008.
2. Shiren Wang, Richard Liang, Ben Wang, Chuck Zhang, Dispersion and thermal conductivity of carbon nanotube composites, Carbon, 47, 53, 2009.
3. J. Jancar, J.F. Douglas, F.W. Starr, S.K. Kumar, P. Cassagnau, A.J. Lesser, S.S. Sternstein, M.J. Buehler, Current issues in research on structure-property relationships in polymer nanocomposites, Polymer, 51, 3321, 2010.
4. Mayu Si, Tohru Araki, Harald Ade, A. L. D. Kilcoyne, Robert Fisher, Jonathan C. Sokolov, Miriam H. Rafailovich, Compatibilizing Bulk Polymer Blends by Using Organoclays, Macromolecules, 39, 4793, 2006.
5. Alaitz Ruiz de Luzuriaga, Hans J. Grande, Jose A. Pomposo, Phase diagrams in compressible weakly interacting all-polymer nanocomposites, J. Chem. Phys., 130, 2009.
6. Michael E. Mackay, Anish Tuteja, Philip M. Duxbury, Craig J. Hawker, Brooke Van Horn, Zhibin Guan, Guanghui Chen, R. S. Krishnan, General Strategies for Nanoparticle Dispersion, Science, 311, 1740, 2006.
7. Joseph H. Koo., Polymer nanocomposites : processing, characterization, and applications, McGraw-Hill, New York, 2006.
8. Srinivasan, K., Composite Materials : production, properties, testing and applications, Alpha Science Intl. Ltd., Oxford, 2009.
9. Chung, Deborah D. L., Composites materials : functional materials for modern technologies, Springer, New York, 2003.
10. Ajayan, P. M., Schadler, L.S., Braun, P.V., Nanocomposite science and technology, Wiley-VCH, Weinheim, 2003.
11. Huaizhi Geng, Rachel Rosen, Bo Zheng, Hideo Shimoda, Leslie Fleming, Jie Liu, Otto Zhou, Fabrication and Properties of Composites of Poly(ethylene oxide) and Functionalized Carbon Nanotubes, Adv. Mater., 14, 19, 1387, 2002.
12. Raquel Verdejo, Fabienne Barroso-Bujans, Miguel Angel Rodriguez- Perez, Jose Antonio de Saja, Miguel Angel Lopez-Manchado, Functionalized graphene sheet filled silicone foam nanocomposites, J. Mater. Chem., 18, 2221, 2008.
13. Sung Heum Park, Anshuman Poy, Serge Beaupre, Shinuk Cho, Nelson Coates, Ji Sun Moon, Daniel Moses, Mario Leclerc, Kwanghee Lee, Alan J. Heeger, Bulk heterojunction solar cells with internal quantum efficiency approaching 100%, Nature Photonic, 3, 297, 2009.
14. Shifeng Yan, Jingbo Yin, Yan Yang, Zhengzhan Dai, Jia Ma, Xuesi Chen, Surface-grafted silica linked with L-lactic acid oligomer: A novel nanofiller to improve the performance of biodegradeable poly(L-lactide), Polymer, 48, 1688, 2007.
15. Qi-Fang Li, Yihui Xu, Jin-San Yoon, Guang-Xin Chen, Dispersions of carbon nanotubes/polyhedral oligomeric silsesquioxanes hybrids in polymer: the mechanical, electrical and EMI shielding properties, J. Matter Sci., 46, 2324, 2011.
16. Anish Tuteja, Philip M. Duxbury, Michael E. Mackay, Multifunctional Nanocomposites with Reduced Viscosity, Macromolecules, 40, 9427, 2007.
17. Jose A. Pomposo, Alaitz Ruiz de Luzuriaga, Agustin Etxeberria, Javier Rodriguez, Key role of entropy in nanoparticle dispersion : polystyrene-nanoparticle/linear-polystyrene nanocomposites as a model system, Phys. Chem. Chem. Phys., 10, 650, 2008.
18. Tai-His Fan, Remco Tuinier, Hydronamic interaction of two colloids in nonadsorbing polymer solution, Soft Matter, 6, 647, 2010.
19. Poon, W. C. K., The physics of a model colloid-polymer mixture, J. Phys.: Condens. Matter, Vol. 14, 859, 2002.
20. R. Tuinier, J. Rieger, C.G. de Kruif, Depletion-induced phase separation in colloid-polymer mixtures, Adv. Colloid Interface Sci., 103, 1, 2003.
21. J. C. Crocker, J. A. Matteo, A. D. Dinsmore, A. G. Yodh, Entropy Attraction and Repulsion in Binary Colloids Probed with a Line Optical Tweezer, Phys. Rev. Lett., 82, 21, 4352, 1999.
22. J. B. Hooper, K. S. Schweizer, T. G. Desai, R. Koshy, P. Keblinski, Structure, surface excess and effective interactions in polymer nanocomposites melts and concentrated solutions, J. Chem. Phys., 121, 14, 6986, 2004.
23. P. J. Hoogerbrugge, J. M. V. A. Koelman, Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics, Europhys. Lett., 19, 155, 1992.
24. R. D. Groot, P. B. Warren, Dissipative particle dynamics : Bridging the gap between atomistic and mesoscopic simulation, J. Chem. Phys. 107, 4423, 1997.
25. P. Español and P. Warren, Statistical Mechanics of Dissipative Particle Dynamics, Europhys. Lett. 30, 191, 1995.
26. J. B. Gibson, K. Chen and S. Chynoweth, Simulation of Particle Adsorption onto a Polymer-Coated Surface Using the Dissipative Particle Dynamics Method, J. Colloid Interface Sci. 206, 464, 1998
27. M. P. Allan & D. J. Tildesley, Computer Simulation of Liquids, Clarendon, Oxford, 1987.
28. R. D. Groot, T. J. Madden, Dynamic simulation of diblock copolymer microphase separation, J. Chem. Phys. 108, 8713, 1998.
29. D. C. Rapaport, The art of molecular dynamics simulation, Cambridge Univ. Press, Cambridge, 2001.