上海交通大学自然科学研究院和数学系博士生刘沛和特别研究员徐振礼与合作者发表的题为 “Ionic size effects: generalized Boltzmann distributions, counterion stratification and modified Debye length”的研究论文被遴选为Nonlinearity杂志2013年的Highlights论文。该论文通过研究带电系统的变分模型，详细分析了非均匀离子尺寸大小对系统的影响，和离子浓度满足的推广玻尔兹曼分布的性质，利用渐近方法分析在高电势情况下解释了离子的分层现象，在低电势情况下提出修正德拜长度用以描述电解液的屏蔽效应。论文的合作者为加州大学圣地亚哥分校数学系李波教授和周圣高博士。Nonlinearity 是应用数学和非线性分析领域重要学术杂志之一。完整Nonlinearity2013Highlights论文可参看链接:
Near a charged surface, counterions of different valences and sizes cluster; and their concentration profiles stratify. At a distance from such a surface larger than the Debye length, the electric field is screened by counterions. Both recent studies using a variational mean-field approach that includes ionic size effects and Monte Carlo simulations suggest that counterion stratification is determined by the ionic valence-to-volume ratios. Central in the mean-field approach is a free-energy functional of ionic concentrations in which the ionic size effects are included through the entropic effect of solvent molecules. The corresponding equilibrium conditions define the generalized Boltzmann distributions relating the ionic concentrations to the electrostatic potential. This paper presents a detailed analysis and numerical calculations for such a free-energy functional to understand the dependence of the ionic charge density on the electrostatic potential through the generalized Boltzmann distributions, the role of ionic valence-to-volume ratios in the counterion stratification and the modification of Debye length due to the effect of ionic sizes.