針對由N 個單體所組成的直線狀聚電解質而言，發生在其鏈上的反離子凝聚現象，可以藉由蒙地卡羅模擬其離子化程度（ α）來進行研究。而離子化程度可由為觀測到的反離子濃度與其本質上應有的反離子濃度的比值（ i o c c = α ）來定義之。而聚電解質系統中的觀測到的反離子濃度o c ，相當於擁有相同反離子的化學勢能的電解質溶液濃度，而此濃度可藉由實驗中直接測得，例如使用離子選擇性電極。如果將聚電解質固定在球形的Wigner-Seitz cell 中，則我們可以計算出單體與反離子沿著半徑方向的濃度分佈，而且可以利用Widom’s 提出的方法來計算出反離子沿著半徑方向的化學勢能分佈。而反離子的凝聚現象的主要驅動機制為靜電內能，而此靜電內能明顯的是由介電常數所造成的，就如同反離子的亂度會影響到離子化的程度。而我們模擬呈現出的結果為：在固定的線電荷密度情況下，離子化的程度會隨著聚電解質的鏈長、聚電解質鍵結的柔軟度、聚電解質的濃度與添加的單價鹽類離子濃度減少而增加。而上述結果都在性質上與 Muthukumar 在近期利用自我一致性原理所發表的文獻結果相符。 The phenomenon of counterion condensation around a linear polyelectrolyte chain with N monomers is investigated by Monte Carlo simulation in terms of the degree of ionization α. It is define as the ratio of observed to intrinsic counterion concentration, α=co/ci. The observed counterion concentration co in the polyelectrolyte system corresponds to an electrolyte solution with the same counterion chemical potential and can be determined directly by experiments such as ion-selective electrode. With the polyelectrolyte fixed at the center of the spherical Wigner-Seitz cell, the radial distributions of monomers and counterions are calculated and the chemical potential of counterion is obtained by the Widom’s method as well. The driven mechanism of counterion condensation is primarily the electrostatic internal energy, manifested by the effect of dielectric constant, while the counterion entropy influences the degree of ionization as well. Our simulation shows that for a specified line charge density, the degree of ionization increase with a decrease in the chain length, the chain flexibility, the polymer concentration and the monovalent salt concentration. These result agree qualitatively with the self-consistent theory proposed by Muthukumar recently (J. Chem. Phys. 120, 9343 (2004)).
