Lin Cheng, Qiang Xiaowei, Dong Hai-Long, Huo Jie, Tan Zhi-Jie
Center for Theoretical Physics and Key Laboratory of Artificial Micro & Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China.
School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China.
ACS Omega. 2021 Apr 5;6(14):9876-9886. doi: 10.1021/acsomega.1c00613. eCollection 2021 Apr 13.
Ion-mediated effective interactions are important for the structure and stability of charged particles such as colloids and nucleic acids. It has been known that the intrinsic electrostatic repulsion between like-charged particles can be modulated into effective attraction by multivalent ions. In this work, we examined the dependence of multivalent ion-mediated attraction between like-charged colloidal particles on the particle charge in a wide range by extensive Monte Carlo simulations. Our calculations show that for both divalent and trivalent salts, the effective attraction between like-charged colloidal particles becomes stronger with the increase of the particle charge, whereas it gradually becomes weakened when the particle charge exceeds a "critical" value. Correspondingly, as the particle charge is increased, the driving force for such effective attraction transits from an attractive electrostatic force to an attractive depletion force, and the attraction weakening by high particle charges is attributed to the transition of electrostatic force from attraction to repulsion. Our analyses suggest that the attractive depletion force and the repulsive electrostatic force at high particle charges result from the Coulomb depletion which suppresses the counterion condensation in the limited region between two like-charged colloidal particles. Moreover, our extensive calculations indicate that the "critical" particle charge decreases apparently for larger ions and smaller colloidal particles due to stronger Coulomb depletion and decreases slightly at higher salt concentrations due to the slightly enhanced Coulomb depletion in the intervening space between colloidal particles. Encouragingly, we derived an analytical formula for the "critical" particle charge based on the Lindemann melting law.
离子介导的有效相互作用对于诸如胶体和核酸等带电粒子的结构和稳定性至关重要。众所周知，多价离子可将带相同电荷粒子之间固有的静电排斥调节为有效吸引。在这项工作中，我们通过广泛的蒙特卡罗模拟，在很宽的范围内研究了多价离子介导的带相同电荷胶体粒子之间的吸引力对粒子电荷的依赖性。我们的计算表明，对于二价盐和三价盐，带相同电荷的胶体粒子之间的有效吸引力都随着粒子电荷的增加而增强，而当粒子电荷超过一个“临界”值时，吸引力会逐渐减弱。相应地，随着粒子电荷的增加，这种有效吸引的驱动力从吸引性静电力转变为吸引性排空力，高粒子电荷导致的吸引力减弱归因于静电力从吸引到排斥的转变。我们的分析表明，高粒子电荷下的吸引性排空力和排斥性静电力是由库仑排空引起的，库仑排空抑制了两个带相同电荷胶体粒子之间有限区域内的反离子凝聚。此外，我们的大量计算表明，由于更强的库仑排空，对于更大的离子和更小的胶体粒子，“临界”粒子电荷明显降低；由于胶体粒子之间中间空间中库仑排空略有增强，在更高盐浓度下“临界”粒子电荷略有降低。令人鼓舞的是，我们基于林德曼熔化定律推导出了“临界”粒子电荷的解析公式。
