製備藻類衍生物碳點與 Mxene複合材料並應用高效超級電容
本研究運用綠藻、螺旋藻、卡拉膠(k,i,λ)進行製備碳點並應用高效超級電容。本實驗已完成綠藻、螺旋藻、卡拉膠( k,i,λ)在不同的pH值中的溶解度測試,並找出綠藻、螺旋藻、卡拉膠(k,i,λ)各自適合溶解的溫度及溶液。此外,中途也已透過文獻中的實驗證實我們實驗中所運用的電化學實驗設計及裝置可以成功製備出碳點。而在電化學製備碳點的部分目前完成單獨藻類、藻類加histidne的電擊實驗以及測其吸收光譜,也運用先前製備出較穩定的碳點加入MXene進行電化學分析,透過碳點擴大MXene分層,以達到增加MXene電化學效能的效果。最後,預計之後將進行更多的電化學分析,進一步地確認碳點結合MXene能在超級電容的應用。
一價銠金屬催化肉桂胺衍生物進行不對稱氫芳基化反應
Rhodium(I)-Catalyzed Asymmetric Hydroarylation of Cinnamylamine Derivatives
一價銠金屬催化反應已經被廣泛應用於有機化學合成領域中。而本研究以具保護基之肉桂胺衍生物1與四芳基硼鈉試劑2a作為起始物進行銠金屬不對稱氫芳基化催化反應,得到具有保護基的掌性2,3-雙芳基丙胺衍生物3,並探討此反應的掌性雙烯配基對於反應的影響。本研究已完成使用Ts(對甲苯磺醯基)保護基之肉桂胺衍生物1a作為起始物進行反應,並改變與銠金屬錯合的配基,發現當配基使用2,5號位為芳基取代之配基L(掌性雙環[2,2,1]雙烯配基)時,反應有較好的位置選擇性,其中最佳的是芳基取代為苯基之配基L1,其位置選擇性比例為1:0:0.09。目前將進行改變起始物1之氮上的保護基,以L1作為配基進行反應,並與1a比較,優化反應性及產率。
The Maximum Area of N-gons within the Intersection Region of Two Congruent Circles
At the 61st National High School Science Fair of Taiwan, the first-rank paper "The Study of the Largest Area of Inscribed Triangle within the Intersection of two circles" was presented. The authors discussed several properties of maximum area of inscribed triangles within intersection regions of two congruent circles. They only claim their results but without providing a rigorous proof. However, we give a proof by showing the convergence of the iteration of finding the largest height. Subsequently, we offer new methods to approach the problems such as the trigonometric identities, Jensen's Inequality to prove the maximum area of triangles and quadrangles within the intersection region of two congruent circles. Finally, we determined the maximum area for the case of n-gons. We conducted further research and discussion on this issue. In the future, we hope to prove why the maximum area of n-gons within the intersection region of two congruent circles occurs when there are two points on the intersection points of the two circles. We aim similar problems in the three-dimensional space, namely the maximum volume of tetrahedron within the intersection of two unit spheres.