將掛軸或手卷攤平舒展後，其邊緣會呈兩個半月形向上翻捲，稱之為「起瓦（Qi-Wa）」。它除了有礙美觀外，還會造成卷軸畫產生不可逆的變形，進而成為裂痕，讓顏料脫落等狀況，自從中國發展裝裱工藝一千六百多年以來一直困擾著藝術家們。但在過去裝裱師父及研究人員探討此問題時，總是將其歸因於氣候問題、保存條件、裝裱工序及制糊的方法等，而在本研究我們強調是由紙張塑性所產生的「內在曲率（spontaneous extrinsic curvature）」才是造成起瓦的主因。在實驗上我們發現起瓦高度會和紙張的長度、寬度、厚度以及曲率呈簡單的冪次關係，這亦可從分子動力學模擬（Molecular Dynamics (MD) simulation）和理論推導得到同樣的現象。由理論的暗示，我們歸納出幾種可以改善起瓦的方法，在真實的裝裱紙和分子動力學模擬皆證明其可行。而此類的捲曲問題不只存在於中國的卷軸畫中，在工業上也會遇到類似的問題，例如近年來熱門的可撓式面板、電子紙以及印刷太陽能板，同樣會因為捲曲而起瓦變形。

"Qi-Wa" is the phenomenon that occurs in handscrolls and hanging scrolls; once we spread the roll paper, it is easy to notice the up curl on the sides of paper. In addition to aesthetic aspect, it results in irreversible effects such as tears and pigment loss, which has troubled Chinese artisans for more than 1600 years. Previous works suggest that Qi-Wa comes from the climate effect, conservation conditions, and/or mounting procedures. However, we find that the main cause of Qi-Wa is the spontaneous extrinsic curvature incurred from the storage. According to experiments, we find that the height of Qi-Wa obeys simple power laws with the scroll's length, width, thickness and curvature. This result is supported by Molecular Dynamics (MD) simulation and theoretic derivations. Based on the theory, we propose several methods to reduce Qi-Wa. These methods have been tested by use of real mounted paper and simulations, and are proved workable. Our study can be applied to modern technologies, since similar warps occurs not only in Chinese scrolls but also in industry productions of flexible display, electronic paper, and paper solar cell circuit.

摘要 . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . iii

致謝 . . . . . . . . . . . . . . . . . . . . . . v

1 緒論 Introduction . . . . . . . . . . . . . . 1
1.1 裝裱卷軸簡史 . . . . . . . . . . . . . . 3

2 現象學理論 Phenomenological Theory . . . . . . 7
2.1 起瓦的成因 . . . . . . . . . . . . . . . 7
2.1.1 兩種可能的起瓦機制 . . . . . . . . 10
2.2 兩種類型的起瓦 . . . . . . . . . . . . . 19
2.2.1 U型起瓦 . . . . . . . . . . . . . 21
2.2.2 V型起瓦 . . . . . . . . . . . . . 26
2.2.3 卷軸腹部凹陷 . . . . . . . . . . . 29
2.3 U-V相圖 . . . . . . . . . . . . . . . . 33

3 實驗分析 Experimental Analysis . . . . . . . . 39
3.1 實驗設置 . . . . . . . . . . . . . . . . 39
3.1.1 高度測量設置 . . . . . . . . . . . 41
3.1.2 輪廓曲線儀設置 . . . . . . . . . . 41
3.2 不同材質的卷軸是否起瓦 . . . . . . . . . . 43
3.2.1 實驗設計 . . . . . . . . . . . . . 43
3.2.2 實驗結果 . . . . . . . . . . . . . 43
3.3 測量垂直捲動方向的曲率 . . . . . . . . . . 44
3.3.1 實驗設計 . . . . . . . . . . . . . 44
3.3.2 實驗結果 . . . . . . . . . . . . . 45
3.4 起瓦與材料幾何參數關係 . . . . . . . . . . 46
3.4.1 實驗設計 . . . . . . . . . . . . 46
3.4.2 實驗結果 . . . . . . . . . . . . 46
3.5 改善起瓦實驗 . . . . . . . . . . . . . . 52
3.5.1 實驗設計 . . . . . . . . . . . . 52
3.5.2 實驗結果 . . . . . . . . . . . . 54

4 改善方法 Improvement . . . . . . . . . . . . 61
4.1 纖維方向 . . . . . . . . . . . . . . . 63
4.2 邊緣區域加厚 . . . . . . . . . . . . . . 66
4.3 中央區域裏打 . . . . . . . . . . . . . . 68

5 結論與討論 Conclusion and Discussion . . . . . 71

Appendix . . . . . . . . . . . . . . . . . . . 75
分子動力學模擬於起瓦 . . . . . . . . . . . . . 77

參考資料 . . . . . . . . . . . . . . . . . . . . 77

[1] 香港藝術館, 立軸. 香港藝術館, 1997.

[2] 香港藝術館, 手卷. 香港藝術館, 1999.

[3] 張彥遠, 歷代名畫記. 人民美術出版社, 2005.

[4] 登石健三, 表具的科學, ch. 4. 東京國立文化財研究所, 1977.

[5] 登石健三, “論卷軸裱褙法,” 故宮季刊, vol. 15, p. 117, 1981.

[6] 康建國, 中國書畫裝裱技法. 四川科學技術出版社, 2006.

[7] 楊正旗, 中國書畫裝裱大全. 山東美術出版社, 1997.

[8] V. D. Daniels and L. E. Fleming, “The cockling and curling of paper in museum,” in Proc. of the Symposium in Conservation of Historic and Artistic Works on Paper (H. D. Burgress, ed.), p. 155, 1988.

[9] T. Leppanen, Effect of fiber orientation on cockling of paper. PhD thesis, University of Kuo-pio, 2007.

[10] 徐文娟，陳元生, “書畫裝裱材料-宣紙形穩定性的研究,” 文物保護與考古科學, vol. 17, p. 27, 2005.

[11] 岑德麟, “宣紙-為何成為中國書畫裝裱的主要用紙,” 故宮文物月刊, vol. 20.6, p. 14, 2002.

[12] V. Lee, X. Gu, and Y.-L. Hou, “The treatment of chinese ancestor portraits: An intro-duction to chinese painting conservation techniques,” Journal of American Institute for Conservation, vol. 42, p. 463, 2003.

[13] I. Nielsen and D. Priest, “Dimensional stability of paper in relation to lining and drying procedures,” Paper Conservator, vol. 21, p. 26, 1997.

[14] 岑德麟, “漿糊-書畫裝裱的粘貼劑,” 故宮文物月刊, vol. 20.10, p. 106, 2003.

[15] A. C. Jain and R. A. Cairncross, “Effect of moisture sorption on microstructure and properties of paper,” in 12th International Coating Science and Technology Sympo-sium, (Rochester), p. 190, 2004.

[16] C. D. M. M. Warner and D. Corbett, “Curvature in nematic elastica responding to light and heat,” Proc. R. Soc. A, vol. 466, p. 2975, 2010.

[17] C. D. M. M. Warner and D. Corbett, “Suppression of curvature in nematic elastica,” Proc. R. Soc. A, vol. 466, p. 3561, 2010.

[18] L. Giomi and L. Mahadevan, “Multi-stability of free spontaneously curved anisotropic strips,” Proc. R. Soc. A, vol. 468, p. 511, 2011.

[19] 王以坤, 書畫裝潢源革考. 紫禁城出版社, 1991.

[20] 林政宜, “中國掛軸形式演變試析,” 故宮文物月刊, vol. 51, p. 22, 1987.

[21] 馮鵬生, 中國書畫裝裱概說. 上海人民美術出版社, 1982.

[22] T. Yokoyama and K. Nakai, “Evaluation of in-plane orthotropic elastic constants of paper and paperboard,” in Proc. of Annual Conference and Exposition on Experi-mental and Applied Mechanics, 2007.

[23] K. Binmore and J. Davies, Calculus: Concepts and Methods. Cambridge University Press, 2001.

[24] K. Kincade, “Flexible displays open new windows of opportunity,” Laser Focus World, vol. 40, p. 65, 2004.

[25] M.-C. Choi, Y. Kim, and C.-S. Ha, “Polymers for flexible displays: From material selection to device applications,” Progress in Polymer Science, vol. 33, p. 581, 2008.

[26] L. Zhou, A. Wanga, S.-C. Wu, J. Sun, S. Park, and T. N. Jackson, “All-organic active matrix flexible display,” Appl. Phys. Lett.,vol.88,083502,2006.

[27] D. L. Blair and A. Kudrolli, “Geometry of crumpled paper ,” Phys. Rev. Lett., vol. 94, 166107, 2005.

[28] D.-Y. Khang, H. Jiang, Y. Huang, and J. A. Rogers, “A stretchable form of single-crystal silicon for high-performance electronics on rubber substrates,” Science, vol. 311, p. 208, 2005.

[29] H.-J. Kwon, H. Shim, S. Kim, W. Choi, Y. Chun, I. Kee, and S. Lee, “Mechani-cally and optically reliable folding structure with a hyperelastic material for seam-less foldable displays,” Appl. Phys. Lett.,vol.98,151904, 2011.

[30] S. De, P. E. Lyons, S. Sorel, E. M. Doherty, P. J. King, W. J. Blau, P. N. Nirmalraj, J. J. Boland, V. Scardaci, J. Joimel, and J. N. Coleman, “Transparent, flexible, and highly conductive thin films based on polymernanotube composites,” ACS Nano, vol. 3, p. 714, 2009.

[31] M. C. Barr, J. A. Rowehl, R. R. Lunt, J. Xu, A. Wang, C. M. Boyce, S. G. Im, V. Bulovi’c, and K. K. Gleason, “Direct monolithic integration of organic photo-voltaic circuits on unmodified paper,” Adv. Mater., vol. 23, p. 3500, 2011.

[32] B. A. van der Pluijm and S. Marshak, Earth Structure - An Introduction to Structural Geology and Tectonics. W. W. Norton, 2004.