本研究利用蒙地卡羅模擬法，探討有限濃度的膠體溶液中反離子凝聚現象。反離子於溶液中受到靜電作用力以及亂度的相互競爭，為了達到自由能最低的平衡狀態，部份反離子會凝聚在膠體粒周遭，此稱為反離子凝聚現象。對於無限稀釋以及無限長的圓柱聚離子系統中，反離子凝聚轉移現象(counterion condensation transition,CCT)被廣泛的討論著，例如Manning提出了在堅硬的聚電解質溶液中，存有一臨界聚電解質電荷密度，用來區分反離子的凝聚與解離。但在真實的膠體溶液中，濃度都是有限的。 針對單一顆反離子系統，利用理論推導可得到一代表系統溫度、靜電作用力強弱、系統濃度影響的無因次值 ，並證實在有限溶液濃度下，反離子會由完全凝聚狀態，經由一連續的轉變成為完全解離狀態，由系統比熱變化可知反離子凝聚轉移現象非相變行為，而為一隨著 改變的連續，並針對系統不同狀態進行熱力學性質的研究。 對於多顆反離子系統或是多顆膠體粒子系統，理論計算過於龐大且複雜，無法得到反離子狀態的變化，利用模擬方法可得到不同狀態的熱力學性質以及解離度變化，並探討不同帶電量膠體粒子、鹽離子對於反離子轉移現象的影響。 A colloidal dispersion, consisting of many charged particles and small ions, is a very complicated system owing to the long-range nature of the electrostatic interactions. Counterions are not distributed evenly in the solution but prefer to stay in the vicinity of the oppositely charged colloid. The extent of counterions residing near the particles is generally depicted by the concept of counterion condensation, which mediates how colloids interact among themselves and thus influence the physical properties of colloidal dispersion. The concept of counterion condensation basically characterizes a battle fought between energy and entropy in minimizing the free energy of a solution of mobile charges in the neighborhood of charged particles. The counterion-condensation transition (CCT) at infinitely long charged cylinders in the infinite-dilution limit and infinitely low added salt concentration has been extensively studied. For example, Manning's theory of counterion condensation predicts a certain quantity of counterions condenses onto a stiff polymer whose charge density exceeds a critical value. In reality, the colloidal dispersion is at finite concentration. In this work the CCT at charged spheres is investigated using Monte Carlo simulations for an ideal model (neglecting effects of inhomogeneous surface charges) based on Wigner-Seitz cell. The crossover temperature T* is identified by the behavior of energy and heat capacity. In addition to establish the relation between effective charge and CCT, the effects of particle charge, particle concentration and salt addition on the crossover temperature are explored as well.
