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  • 學位論文

分子動力學在起瓦的應用

Application of Molecular Dynamics Simulation in Qi-Wa

指導教授 : 洪在明

摘要


一幅捲軸在打開的狀態下,長邊中央常會出現翹起的現象,因為很像中國傳統屋簷邊緣翹起的形狀,中國裝裱師傅稱之為「起瓦」。起瓦的成因有很多種,諸如溫度、濕度、裝裱用的複合紙張甚至裝裱的技術都會影響,我們的研究則不考慮這些外在不可調控的因素,單就紙張的特性來解釋起瓦的成因,並嘗試用物理的方法來降低起瓦程度。 分子動力學是由微觀出發來探討巨觀物體的一種方法,常被用來模擬蛋白質的結構或聚合物的動力學表現,也有用來模擬二維薄膜的性質[],我的研究內容就是 承繼羅鈞肇學長所做的揉皺二維薄膜模擬所用的程式碼,將之應用在「起瓦」的現象上,另外由沈維昭學長與周明翰同學負責實驗與理論。 在模擬方面,一開始我們用以往的習慣,採取單層的薄膜--三角晶格上的節點擺上粒子,並直接在面跟面加上內在曲率(intrinsic curvature),薄膜確實可以成功捲起,但是這個模型要求在施加彎曲回復力時,三角晶格的面跟面必須要合力為零,因此看到的起瓦並不是真實的,甚至會看到相反的結果,於是我們把模型改成兩層,用上下兩層的長度差來造成薄膜彎曲,也就是說有等效的彎曲回復力,在這個雙層薄膜的模型,我們發現與實驗結果在力學表現上大致相符,然而還是有不盡相同的地方,這在之後會加以說明。 起瓦的高度會隨著越往紙張寬邊中心而越小,最後降到零的所走的寬度,我們稱之為「區域1」。對於大部分的捲軸書畫,受到起瓦影響的區域1侷限在長邊邊緣,中間仍然存在平坦的區域2,我們把這種情形叫做U-shape。只當捲軸異常的狹窄(類似春聯),才會導致兩邊的區域1相連在一起,它和U-shape有截然不同的現象,改善起瓦的方法也不同,我們稱其為V-shape。另外,我們也發現如果沒有桌子支撐(例如當掛軸離牆壁有一段間縫時),也會造成起瓦高度與其他物理量的冪次有不一樣的關係,因此可分成「U vs. V-shape」和「有vs.無」四種情形,我們最終發現實驗與模擬的冪次大致是吻合的。 改進方法中,我們只討論最常見的U-shape,先從傳統日本師傅的裏打開始探討,發現裏打確實可以降低起瓦,但最好避開起瓦邊緣拉伸的部分,才能得到最佳效果;接著嘗試把邊緣區域1加厚,此舉也可以降低起瓦;最明顯的改善來自調整紙張纖維和卷軸相對角度,發現當纖維方向若是與捲軸捲的的方向平行時,起瓦高度最小。 下列網址為模擬的實際動畫,為一張薄膜攤開的過程: http://www.youtube.com/watch?v=3dikfPc1wc0

關鍵字

分子動力學 捲軸

並列摘要


A spool in the opened state, the long side of the central often occur tilt phenomenon, called "Qi-Wa," because much like the roof of traditional Chinese. Since there are many causes of "Qi-Wa," such as temperature, humidity, and even mounted paper framed with composite skills will affect the result.Our study exclude these external factors can not be regulated, one on the characteristics of paper to explain the causes of "Qi-Wa" and try to use physical methods to reduce the extent of s"Qi-Wa". Molecular dynamics simulation is a method from starting to explore micro macroscopic object often used to simulate the structure of the protein or polymer dynamics performance, but also has application in two-dimensional film .My research is inherited the code of Jun-Chao Luo ,studied crumpling paper used the same method ,to explore "Qi-Wa".The theory and experiment are done by Wei-zhao Shen and ming-Han Zhou. At the beginning we used in the past habits, take monolayer film,put particle on each triangular lattice, and directly plus the intrinsic curvature in face to face.The film can indeed successfully rolled , but this model requires the summation of restoring force applied on the triangular lattice plane together must be zero.So that "Qi-Wa" in this model is not true.And we even have seen the opposite result.So we changed the model to two layers structure, with the upper and lower layers of the film caused by the bond length difference, that there is an equivalent bending restoring force, in this bilayer model, we found that with the experimental results broadly in line with the mechanical performance, but still have difference, which will be described in this thesis later. In improved methods, we only discussed the most common case.We havethree remedies to mitigate Qi-Wa: align the fiber along the rolling direction, extra layer to side borders, and introducing point defects. Among these, fiber alignment is most effective. The following URL is a movie demonstrates a process of spread finished by simulation: http://www.youtube.com/watch?v=3dikfPc1wc0

並列關鍵字

無資料

參考文獻


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