受限高分子的熵力與側向漲落

Abstract

在受限高分子的系統裡，熵力雖是不可忽略的作用力。然而其重要性與強度卻很少有明確的評估。在這篇論文裡，我們成功利用了一個遞回公式計算出了某些受限高分子系統的熵與熵力。在聚合物穿越微小孔洞的過程中，為了量測純粹聚合物在穿越微小孔洞的過程中熵力的作用，我們設計了一項Langevin動力學模擬。透過量測光鑷子的作工與Jarzynski不等式，我們得到了在該過程中的熵力變化。我們發現其結果與我們利用遞回公式所得到的結果非常吻合。並且我們進一步推導出一條熵力的廣義公式，式中與可以透過比較通道的寬度與剛度而得。最後我們同樣利用了Langevin動力學的模擬，探討並分析了高分子聚合物在穿越狹縫時的側向漲落。我們發現，分子的側向漲落可分以為三個部分，各有其相對應的機制。

Despite entropic force is widely recognized as crucial for confined polymers, to what extent is its importance is rarely explicitly evaluated. We successfully used recursive formula obtained the entropic force of confined polymers. To extract the pure entropic contribution during polymer tug-of-war and recoiling, we carry out a dry experiment of Langevin dynamics simulation. Its entropic forces are easured by an optical tweezer via Jarzynski equality and determined theoretically by a recursion formula. These two approaches are more general than Freed-Edward’s diffusion equation and provide highly coincident force values beyond the precision estimated by Muthukumar’s formalism. We further derive a general formula for entropic force, where γ and a are summarized from the channel width, channel stiffness, polymer persistence length, and excluded volume strength of the desired force f and a reference force at temperature T. As applications, we use this formula to quantify the entropic contribution in several DNA force experiments. On the other hand, we also used simulations and theoretical approaches to discuss and analyze the entropic effects on the lateral fluctuations of a polymer in a nano-slit. We found that this fluctuation can be divided into three parts with specific underlying mechanisms.