本論文利用蒙地卡羅法及尺度分析,研究高分子鏈所形成可逆環狀結構的靜態及動態性質。我們所模擬的高分子鏈長度由N=14到N=90,每個分子具有兩個反應基,其作用位能為 。此開啟-密合之間的轉換可由高分子位於開啟狀態之機率隨溫度變化之曲線 ( vs. T)來表現。由統計熱力學導證得知 ,其中 為由 曲線中所得之熔化溫度 (melting temperature),而我們的研究結果發現所形成之可逆環狀結構可以歸納成三種形態:(1) 尾端-尾端環狀結構 (end-to-end), 其 ;(2) 尾端-內部環狀結構 (end-to-interior), 其 ;(3) 內部-內部環狀結構 (interior-to-interior) , 其 ;而常數G的值會隨著反應基位置的不同而改變。雖然較長的高分子鏈比較偏好end-to-end loop的形成,而較短的高分子鏈則偏好interior-to-interior loop的形成;我們的研究發現可以利用反應基在高分子鏈中的不同位置及不同高分子鏈的長度來控制可逆環狀結構的形成機會。此研究成果,顯示生物高分子也可以利用不同形態的可逆環狀結構來調節生物體內的各項生理作用。
The diffusion-limited loop formation is investigated for a flexible polymer owing to the reversible intrachain reaction. The polymer is made of N hard-sphere confined by slightly extensible bonds, and the two reactive sites with binding energy - are randomly located. The open-to-closed crossover is characterized by the probability curve which depicts the variation of the open-state probability with temperature. It is found that and we can classify the loop formation into three types: (i) end-to-end, ; (ii) end-to-interior, ; (iii) interior-to-interior, . The constant G varies with locations of the reactive sites. Although the end-to-end loop is most easily formed for long polymers, the interior-to-interior loop is preferred for short chains, according to our study, we can control the probability of loop formation by utilizing loop types and contour distance between reactive sites.