在水中加入陽離子型、陰離子型、兩性離子型等界面活性劑(surfactant)，會解離出反離子(counterion)。當界劑達到CMC時，會聚集形成微胞(micelles)，其散佈在水中的反離子會靠近帶Z價電荷的微胞表面，這就是反離子凝聚(condensation)現象。從遠處感受微胞的電荷也就不再是Z價電荷了，我們以Debye-Hückel進似理論來得到有效電荷Z*，例如計算DLVO位能時就必須考慮到有效電荷Z*。而一個帶電膠體系統擁有效電荷的現象就稱為電荷的重正化(charge renormalization)。 對一個未加鹽類(salt-free)的膠體(colloidal)懸浮溶液，我們採用球型系統(spherical Wigner-Seitz cell) ，在系統的正中心放入帶電粒子，周圍散佈著因帶電粒子解離出的反離子，整個系統視為電中性，改變球型系統的大小，相當於改變真實情況的濃度。以蒙地卡羅模擬法(MC)得到各式各樣的熱力學性質 At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charges Z* is therefore invoked in the models based on Debye-Hückel approximation, such as the DLVO potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties ω in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged spheres with Z may display the same value of ω as those around a weakly charged sphere with Z*, i.e., ω(Z) = ω(Z*). There exists a maximally attainable value of ω at which Z = Z*. Defining Z* as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Hückel expression ωDH. Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.
