Wen Jiayi, Zhou Shenggao, Xu Zhenli, Li Bo
Department of Mathematics,University of California, San Diego, 9500 Gilman Drive, Mail Code 0112, La Jolla, California 92093-0112, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Apr;85(4 Pt 1):041406. doi: 10.1103/PhysRevE.85.041406. Epub 2012 Apr 26.
Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling.
采用包含尺寸效应的平均场理论和蒙特卡罗（MC）模拟研究了多种反离子对带电表面的竞争吸附。受泊松方程约束的离子浓度平均场静电自由能泛函，通过增广拉格朗日乘数法进行数值最小化。使用无限制原胞模型和具有 metropolis 准则的正则系综 MC 模拟来预测带电表面周围的离子分布。结果发现，对于低表面电荷密度，高价离子的吸附更占优势，这与现有研究一致。对于高电荷表面，平均场理论和 MC 模拟均表明反离子紧密结合在带电表面周围，导致不同种类的反离子分层。混合熵与静电能之间的竞争导致一种折衷，即价体积比更高的离子物种更有可能形成分层的第一层。特别是，MC 模拟证实了离子价体积比在对带电表面的竞争吸附中的关键作用，这一点此前已由平均场理论预测。MC 模拟预测了含盐水溶液离子体系的电荷反转，而平均场理论未预测到这一点。这项工作有助于更好地理解反离子对带电表面的竞争吸附，并呼吁进一步研究离子尺寸效应及其在大规模生物分子建模中的应用。
