本論文針對高分子電解質在鹽溶液中形成複合物以及利用電場操控此複合物的行為進行了一連串的朗日凡動力學模擬，主要研究結果如下所述：
首先，溶液中加入的多價鹽可依序引發兩個高分子電解質的構形變化：一個高分子鏈濃縮反應和一個反濃縮反應。鏈硬度會影響這兩的構形變化變化形式，也決定了高分子鏈是否會呈現有序的結構。與此同時，溶液中離子的分佈通常會反應出局部或全域的高分子電解質構形，所以鏈硬度也是影響溶液中離子分佈的一個重要因素。
其次，高分子鏈和吸附於其上的離子會形成的高分子電解質複合物，此複合物在直流電場作用下，當電場強度超越臨界值E*時會被拉開。此臨界值E*與多價鹽濃度Cs具有非單調的關連性，這是由於不同鹽濃度下，極化複合物的難易度不同所致。此時，極化難易度由單一離子的吸附作用強度與全部離子吸附數量所共同決定。臨界電場E*也與鏈長N有關，且具指數關係E*~N-θ。其中的指數θ隨多價鹽價數Zs提高而減小。利用E*與Cs， Zs，及N的關係，可為在自由溶液中進行的電泳分離技術提供穩固的基礎。
最後，濃縮之高分子電解質可利用交流電場將其拉伸，只需此電場強度強於直流臨界電場E*且電場頻率小於某臨界值。此臨界頻率可對應到高分子鏈上介面處多價離子的電荷鬆弛/脫離時間之倒數。此一鬆弛時間正好與直流電場下高分子鏈構形的震盪時間一致。這意味著在交流電場中，吸附的多價反離子從在介面上鬆弛及從界面上脫離的行為控制了高分子電解質上電偶極的形成和拉伸行為的動力學現象。

In this thesis, a series of Langevin dynamics simulations are performed to investigate the complexation
of polyelectrolytes (PE) in multivalent salt solutions and the manipulation of those PE complexes by electric fields. Our study provides the following results.
Firstly, the addition of multivalent salt can induce two consequent conformational (or phase) transitions of PE: a condensation of PE, followed by a decondensation. The chain stiffness affects the transition-order of both condensation and decondensation. It also determines whether or not the PE structure can be ordered. It modifies the ion distribution around the chain at the same time because the distribution profiles usually reflect either local or global structure of the PE chain.
Secondly, a PE chain, which forms PE complex with condensed ions, can be unfolded in a direct-current (DC) electric field once the field strength exceeds a critical value E*. The value of E* dependence on Cs and the dependence is non-monotonic. This is because the difficulties for polarized a PE complex at different Cs are different. The difficulty is attributed to both the binding strength of condensed ions and the amount of them. E* also depends on the chain length N and shows a power-law-like relation E* ∼ N-θ. The exponent θ decreases with increasing salt valence Zs. The dependences of E_ on Cs, Zs and N provide a solid foundation to separate PE chains by length in free solutions.
Finally, a collapsed PE chain can be unfolded by an alternating-current (AC) electric field when the field strength exceeds the DC threshold E* and the frequency is below a critical value. The critical frequency corresponds to the inverse charge relaxation/dissociation time of condensed multivalent counterions at the interface of the collapsed PE. The relaxation time is coincident with the DC chain fluctuation time. This suggests that, in an AC electric field, the dissociation of condensed polyvalent counterion on the collapsed PE interface controls the PE dipole formation and unfolding dynamics.

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