奈米粒子被廣泛應用在各個領域，如藥物載體、基因治療、觸媒等等用途上。其中一個重要的應用是將其加入到高分子中形成具有特殊性質之高分子-奈米粒子複合材料，如在輪胎中加入奈米粒子使其表面之耐磨性增加。但是奈米粒子在高分子材料中的遷移和分佈會隨著溫度變化，影響到複合材料之性質，因此研究不同溫度下粒子在高分子中的動態行為，對於高分子-奈米粒子複合材料之設計非常重要。近年來的研究發現當溫度降低至接近高分子玻璃轉移溫度時，奈米粒子的擴散會從布朗運動漸轉變成超擴散，此種擴散的特別之處在於其擴散路徑較接近直線。關於此種擴散之起源仍未有一個定論，一般認為是由材料內部在温度降至接近玻璃轉移溫度時，產生局部應力不均引起彈性變形所致。本研究主要利用X光光子相關法(X-ray Photon Correlation Spectroscopy; XPCS)研究聚合聚苯乙烯的奈米金粒子在含有甲苯之聚苯乙烯中，由高溫冷卻至低溫的動態變化，並利用混和不同分子量之聚苯乙烯研究混合系統對奈米粒子動態之影響。所使用之金奈米粒子之直徑大約為6-12 nm，外接聚苯乙烯硫醇之分子量為11,000，聚苯乙烯基材之分子量分別為2000，6000，10000以及以1:1比例混合分子量2000和10000之聚苯乙烯，每個樣品中加入20 wt %甲苯。實驗溫度為從60 ℃降溫至20 ℃，每隔10 ℃作一次測量。
實驗利用國家同步輻射研究中心3 GeV TPS光源的25A同調X光源光束線進行，研究發現從60 ℃至20 ℃，粒子之運動大致都具有超擴散特性。但是分子量2000及混合的樣品，則可發現其擴散特性在50及60 ℃較高溫時，偏離超擴散而趨向布朗運動的明顯特性變化，此因分子量2000及混合的樣品具有較低的玻璃轉移溫度(較易融化)。而以1:1之比例混合分子量2000和分子量10000聚苯乙烯之樣品的實驗結果顯示，其擴散動態主要受分子量較小之聚苯乙烯所影響，動態相當近似於分子量2000的特性，但其鬆弛時間則介於分子量2000和分子量6000的鬆弛時間，在20 ℃時其鬆弛時間约等效於分子量4000的樣品，而在60 ℃時則約等效於分子量3500的樣品，雖然特性近似於分子量2000的聚苯乙烯樣品，但仍可看出其擴散運動仍會受到分子量10000聚苯乙烯影響。

Nanoparticles have wide applications, such as drug carrier, gene therapy, fuel cell catalyst, etc. One of the important applications is to mix nanoparticles with polymers to form polymer-nanoparticle composite that has better performance properties. For example, adding nanoparticles into tire could increase its surface durability. As the temperature changes, the dynamic of the polymer chains and the distribution of the nanoparticles would also change. This may indirectly affect the property of the polymer-nanoparticle composite. Therefore, studying the dynamics of nanoparticles at different temperatures is important for designing nanoparticle-polymer composite materials. It was found that the dynamics of nanoparticles in disordered materials could behave very differently from the typical Brownian diffusion under specific conditions. For examples, hyper diffusion occurs when the temperature is lowered to close to its glass transition temperature. The feature of such a diffusion mode is that the path of the nanoparticle is more close to a ballistic motion. The origin of such diffusion is still not very clear. In general, it has been regarded as a result of elastic deformation in response to local heterogeneity inside the material. In this study, we use X-ray photon correlation spectroscopy(XPCS) to study the dynamics of gold nanoparticles capped with polystyrene thiol in polystyrene with 20 wt% toluene. The radius of the synthesized gold nanoparticle is around 4 nm and the molecular weight of the capped polystyrene is 11,000. The molecular weight of the polystyrene matrix used in this study includes Mw 2000, 6000, 10000 and the mixed 2000 and 10000 in 1:1. The polymer is mixed with 20 wt% toluene. The samples are measured from 60 ℃ to 20 ℃ with a step of 10 ℃. The XPCS results show that the dynamics of Mw 6000 and 10000 samples behave more close to hyper diffusion from 60 ℃ to 20 ℃. As for the Mw 2000 and the mixed 2000/10000 samples, the dynamics is close to hyper diffusion at low temperatures and gradually change to close to Brownian diffusion at higher temperatures. This is due to the glass transition temperature is lower for the lower molecular weight polymers. Although the dynamics of the mixed sample is close to the feature of Mw 2000, the relaxation time of the mixed sample is still larger than that of Mw 2000 sample and it lies between that of Mw 2000 and 6000 samples. The q-averaged stretched exponent of the mixed sample is also found to be slightly larger than that of the Mw 2000 samples for 40, 50 and 60 ℃. This indicates that the presence of the Mw 10000 polymers in the mixed sample still could affect the motion of the nanoparticles even at higher temperatures.

1. Pal, K.; Pal, S. K.; Das, C. K.; Kim, J. K., Elastomeric Nanocomposites for Tyre Applications. In Recent Advances in Elastomeric Nanocomposites, Mittal, V.; Kim, J. K.; Pal, K., Eds. Springer Berlin Heidelberg: Berlin, Heidelberg, 2011, 201-231.
2. Hanemann, T.; Szabo, D. V., Polymer-Nanoparticle Composites: From Synthesis to Modern Applications. Materials 2010, 3 , 3468-3517.
3. Cipelletti, L.; Manley, S.; Ball, R. C.; Weitz, D. A., Universal Aging Features in the Restructuring of Fractal Colloidal Gels. Physical Review Letters 2000, 84 , 2275-2278.
4. Ramos, L.; Cipelletti, L., Ultraslow Dynamics and Stress Relaxation in the Aging of a Soft Glassy System. Physical Review Letters 2001, 87 , 245503.
5. Bellour, M.; Knaebel, A.; Harden, J. L.; Lequeux, F.; Munch, J. P., Aging processes and scale dependence in soft glassy colloidal suspensions. Phys Rev E 2003, 67 , 031405.
6. Bandyopadhyay, R.; Liang, D.; Yardimci, H.; Sessoms, D. A.; Borthwick, M. A.; Mochrie, S. G. J.; Harden, J. L.; Leheny, R. L., Evolution of Particle-Scale Dynamics in an Aging Clay Suspension. Physical Review Letters 2004, 93 , 228302.
7. Chung, B.; Ramakrishnan, S.; Bandyopadhyay, R.; Liang, D.; Zukoski, C. F.; Harden, J. L.; Leheny, R. L., Microscopic Dynamics of Recovery in Sheared Depletion Gels. Physical Review Letters 2006, 96 , 228301.
8. Brinker, K. L.; Mochrie, S. G. J.; Burghardt, W. R., Equilibrium Dynamics of a Polymer Bicontinuous Microemulsion. Macromolecules 2007, 40 , 5150-5160.
9. Guo, H.; Wilking, J. N.; Liang, D.; Mason, T. G.; Harden, J. L.; Leheny, R. L., Slow, nondiffusive dynamics in concentrated nanoemulsions. Phys Rev E 2007, 75 , 041401.
10. Brauer, S.; Stephenson, G. B.; Sutton, M.; Brüning, R.; Dufresne, E.; Mochrie, S. G. J.; Grübel, G.; Als-Nielsen, J.; Abernathy, D. L., X-Ray Intensity Fluctuation Spectroscopy Observations of Critical Dynamics in Fe3Al. Physical Review Letters 1995, 74 , 2010-2013.
11. Ruta, B.; Chushkin, Y.; Monaco, G.; Cipelletti, L.; Pineda, E.; Bruna, P.; Giordano, V. M.; Gonzalez-Silveira, M., Atomic-Scale Relaxation Dynamics and Aging in a Metallic Glass Probed by X-Ray Photon Correlation Spectroscopy. Physical Review Letters 2012, 109 , 165701.
12. Cipelletti, L.; Ramos, L.; Manley, S.; Pitard, E.; Weitz, D. A.; Pashkovski, E. E.; Johansson, M., Universal non-diffusive slow dynamics in aging soft matter. Faraday Discussions 2003, 123 , 237-251.
13. MacKintosh, F. C., Active diffusion: The erratic dance of chromosomal loci. Proceedings of the National Academy of Sciences 2012, 109 , 7138.
14. https://commons.wikimedia.org/wiki/File:Csm_Brownian-Motion_f99de6516a.png.
15. Dierker, S. B.; Pindak, R.; Fleming, R. M.; Robinson, I. K.; Berman, L., X-Ray Photon-Correlation Spectroscopy Study of Brownian-Motion of Gold Colloids in Glycerol. Physical Review Letters 1995, 75 , 449-452.
16. Thurn-Albrecht, T.; Steffen, W.; Patkowski, A.; Meier, G.; Fischer, E. W.; Grübel, G.; Abernathy, D. L., Photon Correlation Spectroscopy of Colloidal Palladium Using a Coherent X-Ray Beam. Physical Review Letters 1996, 77 , 5437-5440.
17. Grübel, G.; Zontone, F., Correlation spectroscopy with coherent X-rays. Journal of Alloys and Compounds 2004, 362 , 3-11.
18. Fluerasu, A.; Moussaïd, A.; Madsen, A.; Schofield, A., Slow dynamics and aging in colloidal gels studied by x-ray photon correlation spectroscopy. Phys Rev E 2007, 76 , 010401.
19. Czakkel, O.; Madsen, A., Evolution of dynamics and structure during formation of a cross-linked polymer gel. EPL (Europhysics Letters) 2011, 95 , 28001.
20. Bouchaud, J. P.; Pitard, E., Anomalous dynamical light scattering in soft glassy gels. The European Physical Journal E 2001, 6 , 231-236.
21. Duri, A.; Cipelletti, L., Length scale dependence of dynamical heterogeneity in a colloidal fractal gel. Europhysics Letters (EPL) 2006, 76 , 972-978.
22. Weeks, E. R.; Weitz, D. A., Subdiffusion and the cage effect studied near the colloidal glass transition. Chemical Physics 2002, 284 , 361-367.
23. Malik, A.; Sandy, A. R.; Lurio, L. B.; Stephenson, G. B.; Mochrie, S. G. J.; McNulty, I.; Sutton, M., Coherent X-Ray Study of Fluctuations during Domain Coarsening. Physical Review Letters 1998, 81 , 5832-5835.
24. Dierker, S. B.; Pindak, R.; Fleming, R. M.; Robinson, I. K.; Berman, L., X-Ray Photon Correlation Spectroscopy Study of Brownian Motion of Gold Colloids in Glycerol. Physical Review Letters 1995, 75 , 449-452.
25. Robert, A.; Wagner, J.; Härtl, W.; Autenrieth, T.; Grübel, G., Dynamics in dense suspensions of charge-stabilized colloidal particles. The European Physical Journal E 2008, 25 , 77-81.
26. Pontoni, D.; Narayanan, T.; Petit, J. M.; Grübel, G.; Beysens, D., Microstructure and Dynamics near an Attractive Colloidal Glass Transition. Physical Review Letters 2003, 90 , 188301.
27. Trappe, V.; Pitard, E.; Ramos, L.; Robert, A.; Bissig, H.; Cipelletti, L., Investigation of q-dependent dynamical heterogeneity in a colloidal gel by x-ray photon correlation spectroscopy. Phys Rev E 2007, 76 , 051404.
28. Mochrie, S. G. J.; Mayes, A. M.; Sandy, A. R.; Sutton, M.; Brauer, S.; Stephenson, G. B.; Abernathy, D. L.; Grübel, G., Dynamics of Block Copolymer Micelles Revealed by X-Ray Intensity Fluctuation Spectroscopy. Physical Review Letters 1997, 78 , 1275-1278.
29. Lumma, D.; Borthwick, M. A.; Falus, P.; Lurio, L. B.; Mochrie, S. G. J., Equilibrium Dynamics in the Nondiffusive Regime of an Entangled Polymer Blend. Physical Review Letters 2001, 86 , 2042-2045.
30. Caronna, C.; Chushkin, Y.; Madsen, A.; Cupane, A., Dynamics of Nanoparticles in a Supercooled Liquid. Physical Review Letters 2008, 100 , 055702.
31. Kim, H.; Rühm, A.; Lurio, L. B.; Basu, J. K.; Lal, J.; Lumma, D.; Mochrie, S. G. J.; Sinha, S. K., Surface Dynamics of Polymer Films. Physical Review Letters 2003, 90 , 068302.
32. Guo, H.; Bourret, G.; Corbierre, M. K.; Rucareanu, S.; Lennox, R. B.; Laaziri, K.; Piche, L.; Sutton, M.; Harden, J. L.; Leheny, R. L., Nanoparticle Motion within Glassy Polymer Melts. Physical Review Letters 2009, 102 , 075702.
33. Yee, C. K.; Jordan, R.; Ulman, A.; White, H.; King, A.; Rafailovich, M.; Sokolov, J., Novel One-Phase Synthesis of Thiol-Functionalized Gold, Palladium, and Iridium Nanoparticles Using Superhydride. Langmuir 1999, 15 , 3486-3491.
34. Hoshino, T.; Murakami, D.; Tanaka, Y.; Takata, M.; Jinnai, H.; Takahara, A., Dynamical crossover between hyperdiffusion and subdiffusion of polymer-grafted nanoparticles in a polymer matrix. Phys Rev E 2013, 88 , 032602.
35. Guo, H.; Bourret, G.; Lennox, R. B.; Sutton, M.; Harden, J. L.; Leheny, R. L., Entanglement-Controlled Subdiffusion of Nanoparticles within Concentrated Polymer Solutions. Physical Review Letters 2012, 109 , 055901.
36. Conrad, H.; Lehmkühler, F.; Fischer, B.; Westermeier, F.; Schroer, M. A.; Chushkin, Y.; Gutt, C.; Sprung, M.; Grübel, G., Correlated heterogeneous dynamics in glass-forming polymers. Phys Rev E 2015, 91 , 042309.
37. https://www.hitachi-hightech.com/file/global/pdf/products/science/
appli/ana/thermal/application_TA_068e.pdf.
38. http://zh.wikipedia.org/wiki/Polystyrene
39. www.esrf.eu/files/live/sites/www/files/events/conferences/HSC/HSC1
7/presentations/08.edf
40. https://www.nsrrc.org.tw/www/eng/endstation/BL23A/saxs
41. http://nscric.web.nthu.edu.tw/files/15-1006-122296,c11814-1.php?Lang=zh-tw
42. Kadam, A. A.; Karbowiak, T.; Voilley, A.; Gay, J.-P.; Debeaufort, F., Plasticization of amorphous polystyrene by volatile organic compounds. Polym Bull 2016, 73, 1841-1853.