本論文藉由分析奈米薄膜與厚矽膠之間的交互作用，精確量測高分子薄膜內部的殘留應力，並據以探討高分子薄膜的楊氏係數、凍結形變和殘留應力之間的關係，以及溫度對其造成的影響。
利用旋轉塗佈法製備高分子薄膜時，由於溶劑快速揮發，使高分子鏈處在不穩定的狀態，含有凍結應變和殘留應力在其中，而這個殘留應力與高分子的光電性能有著密切的相關。
由於在橡膠態有較高的分子運動能力，當將奈米高分子薄膜置於玻璃轉換溫度(T_g)之上時，分子鏈會在殘留應力以及毛細力的作用下進行運動，而會引起薄膜的除潤現象。我們曾透過對高分子薄膜在矽基板(Si-wafer)的初期除潤之精細觀察，由除潤孔洞周圍的形變，藉由楊氏係數，測量出薄膜內部之殘留應力。但高分子在由橡膠態轉為玻璃態時，楊氏係數會上升數千倍，假如奈米薄膜內高分子的殘留應變不隨著溫度而做太大的變化，在室溫所對應之殘留應力將相當巨大，甚至超越高分子薄膜的機械強度，顯然不合理。此外，先前的實驗中我們所引用的是高分子塊材之楊氏係數，而高分子塊材和高分子薄膜的楊氏係數是否一致，仍是高分子科學的一大疑團。
為了解決上述之顧慮，我們引進了高分子薄膜在厚矽膠上面的除潤實驗，由除潤的高分子薄膜與此彈性基材的機械交互作用，量測高分子薄膜的殘留應力。此種方法可不受高分子薄膜楊氏係數實際數值的影響。藉著能量守恆，高分子薄膜在除潤時所釋放的能量，將等於除潤過程中產生的新表面能，加上厚矽膠基材的機械形變能。與以前的計算結果比對之後，驗證高分子處於橡膠態時，薄膜的楊氏係數和塊材相同。
我們接著分析殘留應力與溫度的關係。在分子鏈沒有進行分子鏈段的滑移前提下，並忽略熱膨脹效應，我們假設薄膜內高分子鏈的分子組態與溫度無關。由於殘留應力主要乃因分子鏈由非平衡態轉為平衡態的分子回彈作用，因此，在玻璃態時分子鏈段上的機械應力，應該乃等於橡膠態時的分子鏈應力。在玻璃態時，由於分子的運動能力凍結，此分子鏈應力無法釋放，但仍保留在分子鏈段中，一旦分子鏈取得足夠的運動能力，此分子鏈應力便會釋放出來，成為所謂的殘留應力。在線性彈性理論的架構下，玻態高分子的殘留應變並不等於實質應變，所以，殘留應力也就不等於其凍結形變乘以楊氏係數。若我們要使用線性彈性理論去解釋這時候的高分子鏈行為，就必須對其凍結形變做一些修正，也就是僅考慮極小部分可以自由運動的的高分子鏈。
解決楊氏係數的問題之後，我們進而發現薄膜內的殘留應力，其實會隨著在厚度方向上不同的位置，而有不同的大小。此現象乃與分子鏈因基板附著所帶來的拘束狀態有密切關聯。因為薄膜內不同位置的高分子鏈乃處於不同的拘束狀態，在熱退火處理過程中所釋放的應力，亦會有所不同。
最後，我們嘗試將此測量方式用於量測共軛高分子P3HT薄膜的殘留應力。我們發現P3HT薄膜在高溫熱退火處理後並未有除潤行為發生。原因是P3HT為硬桿型高分子，其薄膜強度較高足以承受分子鏈上的應力而不致破裂，因此沒有除潤現象的發生。我們將可以透過混摻PS，利用不同的混摻比例以及不同的PS分子量，並藉由除潤行為的分析來量測其殘留應力。此部分將由本實驗室新進同學接續進行。

This thesis aims to investigate the segmental stresses operative in polymer molecules confined in ultrathin films, by analyzing the dewetting instability of the polymer film on silicone substrate. From the mechanical interactions between the polymer film and the rubber, the residual stress as well as the segmental stresses were determined, from which the relationship between frozen molecular strains, Young’s modulus, and the residual stresses were analyzed and clarified.
Ultrathin polymer films were usually prepared by spin coating from solutions, the molecular chains in these films so prepared are not at the equilibrium state. Rather, large residual strains and stresses were created to the molecules in the thin films, mainly due to the rapid solvent elapse. The molecular state defined by the residual stress and strains is intimately related to the optoelectronic property of conjugated polymers within-in.
The residual stresses in ultrathin polymer films have been measured previously, by our group, from the elastic stress release at incipient dewetting holes on a hard substrate. In that work, the local strain released at the dewetting temperature, usually above Tg, around a dewetting hole not yet touching the substrate was determined, which was then multiplied with the Young’s modulus, acquired from literatures for the bulk polymer at the dewetting temperature, to yield the residual stress. However, the main problem with this method is that the magnitude of the Young’s modulus varies drastically with temperature around Tg. Hence, for molecular strains that are reasonably assumed not varying significantly with temperature below Tg, the residual stress as determined from dewetting above Tg would increase thousands times with the Young’s modulus as the molecules are brought from the rubbery state to glassy state, to the point of exceeding typical molecular strengths to cause prevalent film fracture. This scenario, however, is not correct. In addition, the Young’s modulus for the calculations was acquired from experiments using bulk polymers, and it is still unresolved if the Young’s modulus of ultrathin films is the same as that of the bulk.
To resolve these problems, we employ a thick PDMS underlayer and let the ultrathin polymer film dewet on the rubber. By analyzing the interactions between the film and the rubber substrate during the instability, the residual stresses in polymer films were determined, without the need of the knowledge of Young’s modulus of the polymer films, from energy conservation that the released energy from the dewetting film is equal to the sum of the new surface energy and the strained energy stored in the rubber. We further found that by comparing the results with that of the previous work the Young’s modulus of polymer thin films in the explored thickness range is in fact equal to that of the bulk.
We then analyze the dependence of the residual stress on temperature. With the premise that there is only negligible molecular slippery and by ignoring the effect of thermal expansion, we can reasonably assume that the conformations of polymer chains in the ultrathin film do not change with temperature. Since the origin of the residual stress is molecular recoiling from the unstable states to the equilibrium state, the mechanical stresses acting on polymer segments in the glassy state should be locked in to the same values as that at the rubbery state. In glass state, the molecular mobility is so low that the segmental stresses have no way to release but it is still conserved in molecular segments so that when enough mobility is imparted to the molecules, it will be released as the so-called residual stress. Under the framework of linear elasticity, the frozen strains of the glassy molecules polymer are not equal to the truthful strains, and hence the residual stresses do not equal the frozen strains multiplied by the Young’s modulus. The frozen strains have to be modified substantially, considering that only a very small part of them is effective in order to fit into the linear elasticity where the stress can be estimated from the strain with the Young’s modulus.
After sorting out the complexity surrounding the Young’s modulus, we further found that the residual stress in polymer thin film is not a constant, but in fact forms a distribution along the thickness direction. This behavior of the residual stress is related to the disparity of the molecular constraint states along the thickness arising principally from the adhesion to the substrate. The disparity gives rise to variance of the released elastic stresses during the thermal treatment.
Finally, we attempt to apply this methodology to thin films of conjugated polymer P3HT. However, P3HT thin films do not dewet under extended thermal annealed due to the mechanical robustness of the rigid-rod polymer that has prevented the nucleation of dewetting holes. This hurdle, however, may be overcome by blending in the film with PS of with various molecular weights and concentrations in the dewetting method. This work will be carried out, hopefully, by new members of our lab.

[1] K.-P. Tung, C.-C. Chen, P.-W. Lee, Y.-W. Liu, T.-M. Hong, K.-C.
Hwang, K.C. Hsu , J.H. White, D. Jonathan, A. C.− M. Yang, ACS
Nano. 5, 7296-7302 (2011)
[2] G. Reiter, M. Hamieh, P. Damman, S. Sclavons, S. Gabriele,T. Vilmin, A.E. Raphaël, Nature Mater. 4, 754-758 (2005)
[3] M. H. Yang, S. Y. Hou, Y. L Chang, A. C.-M.Yang, Phys. Rev. Lett. 96, 066105 (2006)
[4] G. Reiter, Phys. Rev. Lett. 68, 75-78 (1992)
[5] G. Reiter, Langmuir 9, 1344-1351 (1993)
[6]Vrij, A., & Overbeek, J. T. G., J.American Chem. Soc. 90, 3074-3078. (1968).
[7] J. W. Cahn, J. Chem. Phy. 42, 93 (1965)
[8] M. Sferrazza, C. Xiao, R.A.L. Jones, D.G. Bucknall, J. Webster, J. Penfold, Phys. Rev. Lett. 78, 3693 (1997)
[9] T. Vilmin and E. Raphael, Europhy. Lett. 72, 781 (2005)
[10] S. A. Akhrass, G. Reiter, S. Y. Hou, M. H. Yang, Y. L. Chang, F. C. , C. F. Wang, A. C.-M. Yang, Phys. Rev. Lett. 100, 178301 (2008)
[11] G. Reiter, P.G. de Gennes, The Euro. Phys. J. 6, 25-28 (2001)
[12] G. Reiter, Macromolecules 27, 3046-3052 (1994)
[13] M.H. Yang, S. Y. Hou, Y. L. Chang, A.C.-M. Yang, Phys. Rev. Lett. 96, 066105 (2006)
[14] R. Seemann, S. Herminghaus and K. Jacobs, Phys. Rev. Lett. 86, 5534–5537 (2001)
[15] A. Sharma, Langmuir 9, 861 (1993)
[16] A. Sharma, Langmuir 9, 3580 (1993).
[17] R. Seemann, , S. Herminghaus, and K. Jacobs, Phys. Rev. Lett. 86, 5534 (2001)
[18] L. Rayleigh, Proc. London Math. Soc. 10, 4 (1978)
[19] K. Jacobs, S. Herminghaus, and K.R. Mecke, Langmuir 14, 965 (1998)
[20] G. Reiter, Phy. Rev. Lett. 68, 75 (1922)
[21] R. Xie, A. Karim, J.F. Douglas, C.C. Han, R.A. Weiss, Phys. Rev. Lett. 81, 1251-1254 (1998)
[22] T. G. Stange and D. F. Evans, Langmuir 13, 4459 (1997)
[23] G. Reiter, Adv. Poly. Sci. 252, 29-64 (2013)
[24] K.Y. Suh and H.H. Lee, Phys. Rev. Lett. 87, 135502 (2001).
[25] A. Sharma and J. Mittal, Phys. Rev. Lett. 89, 186101 (2002)
[26] M. Sferrazza et al., Phys. Rev. Lett. 81, 5173 (1998)
[27] T.G. Stange, D.F. Evans, W.A. Hendrickson, Langmuir 13, 4459-4465 (1997)
[28] 簡毅,高分子超薄膜分子拘束造成機械不穩態、發光行為變異、和楊氏係數下降之研究. 清華大學材料系碩士論文(2011)
[29] P. F. Barbara, A. J. Gesquire, S.-J. Park, Y. J. Lee, Acc. Chem. Res. 38, 602 (2005)
[30] J. Yu, D. Hu, P. F. Barbara, Sci. 289, 1327 (2000)
[31] J. C. Bolinger, M. C. Traub, T. Adachi, P. F. Barbara, Sci. 331, 4 (2011)
[32] J. Shinar and J. Partee, Syn. Met. 84, 525-528 (1997)
[33] L. J. Rothberg, M. Yan, S. Son, M. E. Galvin, E.W. Kwock, T. M.
Miller, H. E. Katz, R. C. Haddon, F. Papadimitrakopoulos, Syn.
Met. 78, 213-216 (1996)
[34] T. W. Lee and O. O. Park, Adv. Mater. 12, 11 (2000)
[35] T. Q. Nguyen, I. B. Martini, J. Liu, and B. J. Schwartz, J. Phys.
Chem. B 104, 237-255 (2000)
[36] H. J. Chen, L. Y. Wang, W. Y. Chiu, Eur. Poly. J. 43, 4750–4761 (2007)
[37] J. Liu, T. F. Guo, and Y. Yang, Appl. Phys. Lett. 91, 3 (2002)
[38]楊志偉,利用除潤與薄膜拉伸測試研究分子鏈運動對共軛高分子發光之影響. 清華大學材料系碩士論文(2006)
[39]張昱崙,拘束於旋塗奈米超薄脅內的高分子團之分子力、堆積、和形變量測與分析研究. 清華材料系碩士論文(2006)
[40]陳炳志,表面除潤摩擦形變引起之共軛高分子巨大之光電增益. 清華大學材料系碩士論文(2010)
[41]李培煒,共軛高分子薄膜之分子堆積、除潤運動與拉伸的發光增益研究. 清華大學材料系碩士論文(2011)
[42] X. Yang and J. Loos, Macromolecules 40, 1353 (2007).
[43] D. E. Markov, E. Amsterdam, P. W. M. Blom, A. B. Sieval, and J. C.
Hummelen, J. Phys. Chem. 109, 5266 (2005).
[44] J. J. M. Halls, K. Pichler, R. H. Friend, S.C. Moratti, and A. B.
Holmes, Appl. Phys. Lett. 68, 3120 (1996).
[45] D. E. Markov, C. Tanase, P. W. M. Blom, and J. Wildeman, Phys.
Rev. B 72, 045217 (2005)
[46] T. Q. Nguyen, V.Doan, B. J. Schwartz, J. Chem. Phys. 110, 4068 (1999)
[47] E. Collini, G. D. Scholes , Sci. 323, 369-373 (2009)
[48] T. Q. Nguyen, J. Wu, V. Doan, B. J. Schwartz, S. H.Tolbert, Sci. 288, 652-656 (2000)
[49] J. Vogelsang, T.Adachi, J .Brazard, D. A. Vanden Bout, P. F. Barbara, Nature Mater. 10, 942-946 (2011)
[50] J. Vogelsang, J. Brazard, T. Adachi, J. C.Bolinger, , P. F. Barbara, , Angewandte Chemie International Editon 50, 2257-2261 (2011)
[51] J. L. Brédas, R. Silbey, Sci. 323, 348-349 (2009)
[52] B. J. Schwartz, Annual Rev. Phys. Chem. 54, 141-172 (2003)
[53] B. J. Schwartz, Nature Mater. 7, 427-428 (2008)
[54] M. Rubinstein and R.H. Colby, Poly. Phys. (2003)
[55] A. R. Khokhlov , A.Y. Grosberg, V. S. Pande, Statistical Physics of Macromolecules (Polymers and Complex Materials) (1994)
[56] A. Brûlet, F. Boué, and J. P. Cotton, Journal de Physique II 6.6 (1996)
[57] Su, C. H., et al. Macromolecules 42, 6656-6664 (2009)
[58] C. L. Gettinger, A. J. Heeger, J. M. Drake & D. J. Pine, Molecular Crystals and Liquid Crystals 256, 507-512 (1994)
[59] V.-D Tuan, Nanotechnology in Biology and Medicine, Met. (2007)
[60] Inigo, A. R., et al., J. Chinese Chem. Soc. 57, 459-468 (2010)
[61] de Gennes, J. Chem. Phys. 55, 572 (1971)
[62] wikipedia.org
[63] 楊雅薇,共軛高分子薄膜之分子應力與分子堆積研究. 清華大學材料系碩士論文(2015)
[64] product information (SYLGARD® 182 Silicone Elastomer), DOW CORNING
[65] C. J. Ellison, John M. Torkelson, Nature Mater. 2, 695–700 (2003)
[66] Chang C P, Chao C Y, Huang J H, et al. Fluorescent Conjugated Polymer Films as TNT Chemosensors J. 144, 297-301 (2004)