本論文分別利用蒙地卡羅法與布朗運動法探討兩個主題。第一部份是研究DNA模型分子在稀薄高分子溶液中的電泳行為,在一般認知中,DNA分子通過稀薄高分子溶液時,會與高分子產生之纏繞,可藉此達到分離不同長度之DNA分子。經由蒙地卡羅法模擬發現,在保持高分子體積分率為0.2時,DNA分子在鏈長越短之高分子溶液情況下,泳動率越快;由模擬結果中,我們無法確認到底是否可以控制在相同之條件下,不同長短DNA分子的分離狀況。高分子體積分率為0.02時,不同鏈長DNA分子在相同的環境下,泳動率幾無差別。由於蒙地卡羅法在粒子越多的模擬條件下相當耗時,並為把溶劑效應一併考量,我們改用布朗運動法模擬。在高分子體積分率為0.2時,DNA分子遇較長鏈之高分子溶液,則會因與高分子接觸面積增大的情況下而容易被纏繞住,進而泳動率較小。但綜合以上之模擬結果,我們發現在無考量hydrodynamic interaction的情況下,對可否以稀薄高分子溶液分離不同長度之DNA分子,並無肯定的答覆。 第二部份則利用布朗運動法模擬DNA模型分子在微構造通道中電泳行為,利用不同長度與高度之微構造變化,來達到分離效果。模擬結果可證明,在大電場(E=0.7)下會使得在大部分的情況皆無法有效分離DNA分子,要改善這個缺點可從這兩方面著手:(1)增加entropic trapping的大小;(2)增加thin region的路徑長度,達到明顯的分離效果。當電場小(E=0.2),分離不同長度之DNA分子的效果更佳。在thick region與thin region長度比率為1時,路徑越長DNA分子泳動率越快。而在探討thick region效應的模擬中,電場小的情況,thick region的效應就會相當明顯,相同鏈長的DNA分子,在thick region越長的微構造泳動率越快。
There are two topics studied in this work on the basis of Monte Carlo (MC) and Brownian Dynamics (BD) simulation separately. Firstly, the DNA electrophoresis in dilute polymer solutions is investigated by MC and BD methods. We all know when the DNA goes through the dilute polymer solution; it will be entangled by the polymer dispersed in the solution. When the volume fraction of polymers is 0.2, the DNA’s mobility of electrophoresis is increased by shorter length of polymers in the solution. In the result of the simulation, we can’t be sure the exactly separation of different length of DNA, because of the uncertainty of the data. In the 0.02 of volume fraction, we found the mobility of different length of DNA is almost unvaried. As the result of the Monte Carlo method is too time-consuming in the situation of too many beads, we switched to the Brownian Dynamics and it will also provide the real solution effect. When the volume fraction of polymers is 0.2 in BD method, the mobility of DNA will be decreased by the longer length of polymers, which have larger contact aria with DNA, in solution. Totally speaking, we can’t be sure whether the different length of DNA could be separated in dilute polymer solution or not, when not considering the hydrodynamic effect. In the second part of this work, the Electrophoresis of a charged polymer (DNA) in a microfabricated channel is investigated by BD method. The results showed when the electric field is 0.7, we can’t separate the different length of DNA in most of the situations. In order to improve the result, we suggest that: (1) to increase the entopic trapping (height of channel); (2) to increase the length of the thin region. When 0.2 of electric field is used, the results of separating the different length of DNA are better. As the ratio of thick and thin region is one, longer the total length of thick and thin region, higher the mobility of DNA. In another way, the effect of the thick region is very obvious that longer the length of the thick region, higher the mobility of DNA in same length.