standard dodecahedral structures and two-layer high-genus fullerenes.
He has intentionally pushed the vertices inward so one can see the possibility
of hole opening at that position.
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| From Dec 25, 2008 |
Saturday, December 27, 2008
Precursor of a high-geneus fullerene
Chuang made this beaded model in order to illustrate the connection between
standard dodecahedral structures and two-layer high-genus fullerenes.
He has intentionally pushed the vertices inward so one can see the possibility
of hole opening at that position.
standard dodecahedral structures and two-layer high-genus fullerenes.
He has intentionally pushed the vertices inward so one can see the possibility
of hole opening at that position.
Thursday, December 25, 2008
A new type of helically coiled carbon nanotube
This HCNT consists an octagon and two pentagons in each unit cell.
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| From Dec 25, 2008 |
Yet another beaded buckyball (YABB)
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| From Dec 25, 2008 |
Chuang made his model with 20mm (2cm) beads. These are largest beads we can find in the local store at Taipei.
High-genus structures
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
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| From Dec 25, 2008 |
C168
C168 is quite uniqe because it correponds to C60 in the hyperbolic space.
We can view standard fullerenes as a tiling of graphene sheet on a sphere, which is a two-dimensional manifold with postive curvature everywhere. C60 corresponds to the smallest fullerene with all pentagons separated by only one CC bond. Similarly, C168 is the smallest fullerene in a hyperbolic space with all heptagons separated by only one CC bond.
In the bead model I created, purple beads stand for the edges of heptagons, and white beads are the CC bonds separating different heptagons.
(I gave this model to Dirk Huylebrouck, a professor in the department of architecture at Sint Lucas (Brussels, Belgium) at the Bridges Pecs, Hungary 2010)
We can view standard fullerenes as a tiling of graphene sheet on a sphere, which is a two-dimensional manifold with postive curvature everywhere. C60 corresponds to the smallest fullerene with all pentagons separated by only one CC bond. Similarly, C168 is the smallest fullerene in a hyperbolic space with all heptagons separated by only one CC bond.
In the bead model I created, purple beads stand for the edges of heptagons, and white beads are the CC bonds separating different heptagons.
 |
| From Dec 25, 2008 |
(I gave this model to Dirk Huylebrouck, a professor in the department of architecture at Sint Lucas (Brussels, Belgium) at the Bridges Pecs, Hungary 2010)
Monday, December 22, 2008
Torus with tetravalent vertices
This amazing beaded structure is connected by a tetravalent network, which is different our previous trivalent beaded fullerenes. The construction rule for this type of toroidal systems, however, is exactly similar to that we used for carbon tori. But, instead of pentagons and heptagons, here we use triangle and pentagons to simulate the positive and negative Gaussian curvatures located in the outer- and inner-rim of the torus. Generalization to other topologically nontrivial 2-D structures seems to be straightforward.
(work by Chuang)
(work by Chuang)
Thursday, December 18, 2008
Tetrahedron
I try to experiment with the idea that using three beads to stand for an edge of polyhedron. In this case, I made a tetrahedron. Previously, I have posted some of this kind of models. The original idea came from Chuang again.
Precursor of a high-geneus fullerene
Here is an icosahedral fullerene in which the sharp vertices are forced innerward such that we can view this structure as the precursor for forming the outer part of a hight-genus fullerene. (created by Chuang)
Wednesday, September 10, 2008
Another Way of Displaying Graphenoid on Computers
I tried to make comparison between computer graphs and capsule-shaped beaded molecules...
Monday, September 8, 2008
Content: Introduction
純sp2碳分子體系材料在近十年來受到科學界非與倫比的重視，雖然個別碳原子間的鍵結只有一種，但經由巧妙的幾何安排，使得各種維度的穩定碳分子體系得以存在：零維的富勒烯、一維的奈米碳管與奈米碳緞帶、二維的石墨烯以及三維的石墨與具有特別的拓樸性質的週期最小曲面。由於這樣豐富的幾何變異性，各種與一般物質大不相同的物理性質也被廣泛討論。本實驗室也進行了以共軛碳分子體系為主的理論探討，從中我們發現縱使有電腦輔助繪圖，分子的各種幾何性質仍然難以一眼看清；更尤其在純碳體系中，如上所述，其幾何、拓樸的變異性之廣大，可謂化學家的樂高(Lego)遊樂場一般，對一般社會大眾、有志從事科學的中學生甚至是具相當經驗的科學工作者都不容易有清楚的圖像。
上述的困難可歸結到一個解決的辦法，即是在化學課中常見的分子模型。我們嘗試了利用坊間常見的分子模型套件來製作這些純碳分子，然而並不順利，其中最大的困難便在於純碳分子體系動輒數百甚至數千的原子數，若分子模型的材料有數公分的大小，則完成之分子模型便有巨大至數公尺之譜！如此的模型固然可能可以在大型博物館中展示，但也已失去建構分子實體模型以幫助學生學習化學分子形狀的原意。
然而這個情形在一次偶然的發現中有了轉機：我們發現一般手工藝界常用於裝飾的材料：串珠，恰可用於製作一大類純碳體系的分子模型。在本實驗室於96學年度進行之化學、幾何、藝術：串珠分子模型的製作┘計畫中，我們提出一種新式分子模型的製作方法：分子的串珠表象，此方法特別適合用於富勒烯(fullerene)與其他具有更複雜之拓樸及幾何變異的sp2純碳分子，如碳奈米環、碳奈米螺旋管、高虧格富勒烯以及週期最小曲面等例子。
在串珠分子模型中，分子中的化學鍵兩端恰可對應到珠子孔洞的兩端，亦即我們可以用串珠的方式沿著分子中化學鍵的分布一步步將該分子實現出來，珠子相鄰處即是原子所在。珠子間的硬殼球排斥相當程度模擬了化學鍵理論的價層電子對排斥理論(VSEPR)，使得串珠模型的型狀甚至於力學性質與計算機模擬的分子十分相似。且在一般手工藝店可買到的珠子均約在毫米大小，以之製作出來的串珠分子模型大小在數公分至數十公分的範圍，恰可在手上旋轉把玩，極利學生學習其中的化學與幾何。另外，其材料的易取得性、經濟性也是串珠分子模型的一大優點。更甚者，已完成的模型本身就是相當美觀且耐久。
然而經一年的實作經驗，我們發現具有一定高斯曲率變化的幾何形狀之分子的串珠表象具有較高的力學穩定度。這是由於珠子間的硬殼球排斥與穿線的張力之間的互相競爭，在有一定曲率變化的子空間的限制下的回饋力常數較高，所以較能抵抗外力的影響；我們認為這在某種程度上反映了實際化學分子在受到應力時的情況。於是我們鎖定在文獻中少被探討的較複雜之純碳分子體系：週期最小曲面、碳奈米螺旋管以及高虧格富勒烯，前者為均勻分布的負高斯曲率的連續曲面，後二者則為高斯曲率的符號呈特定分布的曲面。在這些例子的初步計算機模擬中，具有某些特定特徵形狀的分子有較穩定的化學構型，是故我們將製作這些分子的串珠模型以進一步驗證以上的推測。
另外，在我們已開設的短期教學班與一些較零碎的與中學教師、學生們的接觸中，我們發現串珠分子模型中的球型珠子常被誤認為分子中的原子，然而如前所述，珠子的孔洞實際上代表了連接原子間的化學鍵，而非原子本身。在此我們亦提出了以較長型的珠子為材料，如此完成的模型應較不易令人有此誤解。
有鑑於串珠分子模型的各種優點以及在推廣過程中的良好經驗，我們希望持續推動各種教學推廣計畫，使得更多人，包括化學從業人員、大專學生、中小學生，甚至藝術工作者，都能透過串珠分子模型的建構，認識到這種在二十一世紀，最具潛能的物質與材料之結構，以及這種化學分子結構，所能激發的藝術想像。本計畫計畫在四個方面，進行串珠分子模型的研究與推廣：這包括（一）開發新型串珠富勒烯的模型，其中尤專注於週期最小曲面、奈米螺旋管及高虧格富勒烯；（二）使用長型珠子為材料，製作更貼近一般球與棒子模型的串珠分子模型；（三）開授串珠分子模型課程與進行適當之分子串珠活動；（四）改良、擴充串珠分子模型網頁。
上述的困難可歸結到一個解決的辦法，即是在化學課中常見的分子模型。我們嘗試了利用坊間常見的分子模型套件來製作這些純碳分子，然而並不順利，其中最大的困難便在於純碳分子體系動輒數百甚至數千的原子數，若分子模型的材料有數公分的大小，則完成之分子模型便有巨大至數公尺之譜！如此的模型固然可能可以在大型博物館中展示，但也已失去建構分子實體模型以幫助學生學習化學分子形狀的原意。
然而這個情形在一次偶然的發現中有了轉機：我們發現一般手工藝界常用於裝飾的材料：串珠，恰可用於製作一大類純碳體系的分子模型。在本實驗室於96學年度進行之化學、幾何、藝術：串珠分子模型的製作┘計畫中，我們提出一種新式分子模型的製作方法：分子的串珠表象，此方法特別適合用於富勒烯(fullerene)與其他具有更複雜之拓樸及幾何變異的sp2純碳分子，如碳奈米環、碳奈米螺旋管、高虧格富勒烯以及週期最小曲面等例子。
在串珠分子模型中，分子中的化學鍵兩端恰可對應到珠子孔洞的兩端，亦即我們可以用串珠的方式沿著分子中化學鍵的分布一步步將該分子實現出來，珠子相鄰處即是原子所在。珠子間的硬殼球排斥相當程度模擬了化學鍵理論的價層電子對排斥理論(VSEPR)，使得串珠模型的型狀甚至於力學性質與計算機模擬的分子十分相似。且在一般手工藝店可買到的珠子均約在毫米大小，以之製作出來的串珠分子模型大小在數公分至數十公分的範圍，恰可在手上旋轉把玩，極利學生學習其中的化學與幾何。另外，其材料的易取得性、經濟性也是串珠分子模型的一大優點。更甚者，已完成的模型本身就是相當美觀且耐久。
然而經一年的實作經驗，我們發現具有一定高斯曲率變化的幾何形狀之分子的串珠表象具有較高的力學穩定度。這是由於珠子間的硬殼球排斥與穿線的張力之間的互相競爭，在有一定曲率變化的子空間的限制下的回饋力常數較高，所以較能抵抗外力的影響；我們認為這在某種程度上反映了實際化學分子在受到應力時的情況。於是我們鎖定在文獻中少被探討的較複雜之純碳分子體系：週期最小曲面、碳奈米螺旋管以及高虧格富勒烯，前者為均勻分布的負高斯曲率的連續曲面，後二者則為高斯曲率的符號呈特定分布的曲面。在這些例子的初步計算機模擬中，具有某些特定特徵形狀的分子有較穩定的化學構型，是故我們將製作這些分子的串珠模型以進一步驗證以上的推測。
另外，在我們已開設的短期教學班與一些較零碎的與中學教師、學生們的接觸中，我們發現串珠分子模型中的球型珠子常被誤認為分子中的原子，然而如前所述，珠子的孔洞實際上代表了連接原子間的化學鍵，而非原子本身。在此我們亦提出了以較長型的珠子為材料，如此完成的模型應較不易令人有此誤解。
有鑑於串珠分子模型的各種優點以及在推廣過程中的良好經驗，我們希望持續推動各種教學推廣計畫，使得更多人，包括化學從業人員、大專學生、中小學生，甚至藝術工作者，都能透過串珠分子模型的建構，認識到這種在二十一世紀，最具潛能的物質與材料之結構，以及這種化學分子結構，所能激發的藝術想像。本計畫計畫在四個方面，進行串珠分子模型的研究與推廣：這包括（一）開發新型串珠富勒烯的模型，其中尤專注於週期最小曲面、奈米螺旋管及高虧格富勒烯；（二）使用長型珠子為材料，製作更貼近一般球與棒子模型的串珠分子模型；（三）開授串珠分子模型課程與進行適當之分子串珠活動；（四）改良、擴充串珠分子模型網頁。
Abstract for the Proposal 2008
延續96學年度進行之┌化學、幾何、藝術：串珠分子模型的製作┘計畫，本實驗室將繼續以一般手工藝界中的串珠技巧製作化學中的富勒烯結構之分子模型，並將目標著重於新式沸石結構/週期性最小曲面以及文獻中較少討論之具有負高斯曲率高虧格(genus)拓樸性質的純碳分子體系。由已有的經驗，我們了解到串珠分子模型特別適合模擬具有一定限度曲率變化之分子幾何，這是由於珠子間的硬殼球排斥與穿線的張力之間的互相競爭，在有一定曲率變化的子空間的限制下的回饋力常數較高，是故具有較穩定的力學性質；通過以上所列目標的串珠模型製作，我們相信能更加理解分子模型與實際分子內力場的異同，從而幫助學生在製作過程中對於實際化學分子之幾何的認識。
本計畫將分為四個部份：
第一：我們將有系統地探討沸石結構、週期最小曲面以及高虧格拓樸之純碳體系，並且用串珠建構出這些實體模型。
第二：藉由選擇膠囊形的珠子，製作更為貼近一般球與棒子分子模型的串珠分子。
第三：開設短期訓練課程，讓高中生、大學生參與串珠富勒烯分子之編織，從而介紹同學各類碳烯分子之結構。
第四：持續擴充串珠分子的討論網頁與部落格之內容。
In this proposal, we continue the project in academic year 2007 named ┌Chemistry, Geometry, and Art: The Beaded Molecules┘, in which we discussed the viability of handicraft beading to represent general fullerene molecules with all sorts of topologies and geometries. We will further focus on newly discovered zeolite/triply periodic minimal surfaces and, in particular, high genus structures, which scarcely appear in the literature. As we have learned in previous experience, the beaded molecules nicely simulate fullerenes with finite variations on their embedded geometrical object such as icosahedrons in the usual Ih-symmetric fullerenes. This is originated from the fact that the interplay between the hard-sphere interaction between adjacent beads and the tensile force exerted by the thread inevitably results in a relatively high recovery force constant, in other words, the beaded model has high mechanical stability. We believe that in the mean while students making beaded molecules will be acquainted with molecular geometry besides having a great deal of pleasure about the beauty of beaded molecules. Short-term workshop teaching the basic theory and techniques of beading beaded fullerene will be presented. Refinement and augmentation of currently established homepage and other internet resources will be made.
本計畫將分為四個部份：
第一：我們將有系統地探討沸石結構、週期最小曲面以及高虧格拓樸之純碳體系，並且用串珠建構出這些實體模型。
第二：藉由選擇膠囊形的珠子，製作更為貼近一般球與棒子分子模型的串珠分子。
第三：開設短期訓練課程，讓高中生、大學生參與串珠富勒烯分子之編織，從而介紹同學各類碳烯分子之結構。
第四：持續擴充串珠分子的討論網頁與部落格之內容。
In this proposal, we continue the project in academic year 2007 named ┌Chemistry, Geometry, and Art: The Beaded Molecules┘, in which we discussed the viability of handicraft beading to represent general fullerene molecules with all sorts of topologies and geometries. We will further focus on newly discovered zeolite/triply periodic minimal surfaces and, in particular, high genus structures, which scarcely appear in the literature. As we have learned in previous experience, the beaded molecules nicely simulate fullerenes with finite variations on their embedded geometrical object such as icosahedrons in the usual Ih-symmetric fullerenes. This is originated from the fact that the interplay between the hard-sphere interaction between adjacent beads and the tensile force exerted by the thread inevitably results in a relatively high recovery force constant, in other words, the beaded model has high mechanical stability. We believe that in the mean while students making beaded molecules will be acquainted with molecular geometry besides having a great deal of pleasure about the beauty of beaded molecules. Short-term workshop teaching the basic theory and techniques of beading beaded fullerene will be presented. Refinement and augmentation of currently established homepage and other internet resources will be made.
Thursday, September 4, 2008
How to Take Good Pics of Beaded Molecules?
Yesterday I went to IKEA searching for an adequate book shelf, and I was happened to find a nice light stand (I don't know the word... 燈座 in Chinese anyway). Together with a 23W light bulb that Jin gave me last time I was able to take some better pictures of our beaded molecules. I have picked out some of them that looks pretty well...
I found that, in particular, some of the color combinations of beads don't look so well while others, like the ones shown above, seem much more aesthetically pleasing when taken into pictures. And, interestingly, even if all the settings remain, the color of the photoed object actually affects the color of background in the pics, for example the last photo has some kind of bluish background. I guess using background cloth with opposite (or conjugated?) color against the object may produce better photo. Think I'll get some other cloths with different colors for further experiments...
I found that, in particular, some of the color combinations of beads don't look so well while others, like the ones shown above, seem much more aesthetically pleasing when taken into pictures. And, interestingly, even if all the settings remain, the color of the photoed object actually affects the color of background in the pics, for example the last photo has some kind of bluish background. I guess using background cloth with opposite (or conjugated?) color against the object may produce better photo. Think I'll get some other cloths with different colors for further experiments...
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