環環相「扣」－奇偶性守恆與歸零的模式探究
本研究一開始在六邊形的六個頂點各填入一個數字後，作連續操作:擦去一個數，寫上其相鄰兩數之差的絕對值。從這些數字在環狀排列的設定條件下，探討其守恆的狀態或使之全數歸零的模式研究。在初步研究過程中我們建構了研究模型以及操作架構，找尋n邊形在「|x-y|型操作」下相對應的「理想k值」。在初始推廣階段，特別運用到了奇偶數的特性。 在延伸的變化形式探討上，則朝向同餘性守恆的方向發展，並給出了三種建構同餘守恆狀態的方法，對於「x-y型操作」與「x-2y型操作」的「同餘守恆數」與「同餘守恆模式」有深入的探究，並發現到跟盧卡斯數列與梅森數列有密切的相關。 我們目前已得到以下結果: 1.在|x-y|型操作下: (1)當3 ∤ n時，則n邊形的「理想k值」為任意正整數。 (2)當3│n時，則n邊形的「理想k值」為所有的奇數和小於 的偶數。 2.在x-y型操作下: (1)同餘守恆數: (2)同餘守恆模式: 若n和φn皆為質數，則將所有基態列出後，恰好數字1~φn-1各出現一次。 3.在x-2y型操作下: (1)同餘守恆數: (2)同餘守恆模式: a.若n和φn皆為質數，則將所有基態列出後，恰好數字1~φn-1各出現一次。 b.若n和φn皆為奇數，且n個數照逆時針方向依序記為a1,a2,…,an，則有: ak+1≡2ak(mod φn) 其中k=1,2,…,n且an+1=a1。
Graphene Nanoplatelet-Embedded Acrylic Paint for Low Cost Waterproof Paintable Capacitive Sensors and Free Standing Supercapacitors
Modern capacitive touch input and proximity sensing technologies are rigid and limited to flat substrates making it impossible to apply them onto objects with irregular geometries like textiles or car handles. Furthermore, the high cost restricts the applications to small surfaces and cannot be scaled up to be applied on large surfaces such as walls. Therefore, a paint-on scheme would broaden the applications of capacitive touch input and proximity sensing devices. Paintable capacitive sensors are an emerging technology hindered by the high cost and lackluster properties of conductive paints. Existing conductive paints utilize expensive filler materials such as silver and gold to achieve high conductivity but suffer from low surface area. High surface area is critical for capacitive proximity sensors to detect objects from far distances and for overall sensitivity. Carbonaceous alternatives using micronized graphite exhibit low conductivity, require high loadings and most disintegrate when in contact with water. Multilayer graphene nanoplatelets are investigated for their high conductivity, high surface area, low cost, flexibility and eco friendliness. A waterproof acrylic latex is combined with multilayer graphene and dispersed via bath sonication. The optimal time of sonication and optimal graphene loading is determined through systematic testing. An Arduino Uno is loaded with a CapSense library and the graphene based paint is utilized as the interface to sense both touch and proximity.
New approach to the synthesis of functionalized fluoroalkenes
Fluorine has a big influence on physical, chemical and biological properties of organic structures. Organofluorine compounds are widely used in modern medical chemistry to develop new drugs. Insertion of fluorine atom into organic molecules can improve their reactivity in biological systems, increase their metabolic stability, lipophilicity and permeability through membranes. As a consequence, in recent years, the percentage of drugs containing one or more fluorine atoms has increased rapidly up to 40%. The fluoroallylic fragment is also able to change properties of bioactive molecules. Its introduction into such structures as inhibitors of histonedeacetylase, inhibitors of matrix metalloproteinase, asparagine, glutamine, etc. increases their biological activity and electronic properties. We propose a new method for the synthesis of functionalized fluoroalkenes, based on the generation of fluoroallyl nucleophiles from silyl- and boronyl-substituted fluorocyclopropanes and their further usage in the allylation of carbonyl compounds or their derivatives. Due to the fact that the cyclopropanation of alkenyl boronates is not possible under conditions of alkaline dehydrohalogenation of dibromofluoromethane, we have developed a new method for the preparation of silyl- and boronyl-substituted cyclopropanes, which consist of carbene cyclopropanation of multiple C=C bonds by sodium dibromofluoroacetate catalyzed by (IPr)AgCl. The new method is effective for the cyclopropanation of not only boronyl- and silyl-substituted olefins, but also for low-reactivity alkenes, such as monoalkyl substituted alkenes, allyl alcohol ethers and α,β-unsaturated carbonyl compounds. The conditions for isomerization of silyl- and boronyl-substituted fluorohalocyclopropanes in the presence of catalytic amounts of copper (I) bromide in acetonitrile was selected. It was shown that the regioselectivity of the process is determined by the thermodynamic control. Thus, the formation of fluorovinylsilanes or fluorovinylboranes in the isomerization of α-silyl- or α-boronyl-gem-bromofluorophenylcyclopropanes and fluoroallylsilanes upon isomerization of β-silyl-gem-bromofluorophenylcyclopropanes was observed. Thus, new types of fluorinated reagents were obtained that are not previously described in the literature (...)
Light as energy source in chemical reaction. New synthesis of valuable dithienylacetylenes
Photochromism (from Greek φωζ photo “light” and χρωμα chroma “colour”) is determined as reversible transformation between two chemical species, induced by action of light [1]. Herewith, initial form and photoinduced isomer have different physical and chemical properties. The phenomenon is attractive for the design of hi-tech materials, including optical memory elements and molecular switches. Diarylethenes is the most promising class of organic photochromic compounds due to outstanding thermal stability of both isomers and high photostability [2]. The size of so-called ethene bridge significantly affects the photochromic reaction. The photochromic diarylethenes with 4-, 5-, and 6-membered cyclic ethene bridge are known, but there is no example with 3-membered bridge. In this study we report a new approach towards dithienylacetylenes 3 that include the synthesis of diarylcyclopropenones 2 via Friedel-Crafts alkylation of heterocyclic compounds 1 with tetrachlorocyclopropene and following UV-irradiation. It was found that the diarylethenes 2 do not display photochromic properties, but they undergo quantitative photoelimination of carbon monoxide upon UV-irradiation resulting in dithienylacetylene 3. Thus, we have proposed a new synthetic two-step approach to dithienylacetylenes 3 [3], which could be useful synthons in synthesis of photochromic diarylethenes with various ethene bridges.