Caetano Daniel L Z, de Carvalho Sidney J, Bossa Guilherme V, May Sylvio
Institute of Chemistry, State University of Campinas (UNICAMP), Campinas, São Paulo 13083-970, Brazil and Center for Computational Engineering and Sciences, State University of Campinas (UNICAMP), Campinas, São Paulo 13083-970, Brazil.
Department of Physics, São Paulo State University (UNESP), Institute of Biosciences, Humanities and Exact Sciences, São José do Rio Preto, São Paulo 15054-000, Brazil.
Phys Rev E. 2021 Sep;104(3-1):034609. doi: 10.1103/PhysRevE.104.034609.
Monte Carlo simulations are employed to determine the differential capacitance of an electric double layer formed by small size-symmetric anions and cations in the vicinity of weakly to moderately charged macroions. The influence of interfacial curvature is deduced by investigating spherical macroions, ranging from flat to moderately curved. We also calculate the differential capacitance using a previously developed mean-field model where, in addition to electrostatic interactions, the excluded volumes of the ions are taken into account using either the lattice-gas or the Carnahan-Starling equation of state. For both equations of state, we compare the mean-field model for arbitrary curvature with a recently developed second-order curvature expansion. Our Monte Carlo simulations predict an increase in the differential capacitance with growing macroion curvature if the surface charge density is small, whereas for moderately charged macroions the differential capacitance passes through a local minimum. Both mean-field models tend to somewhat overestimate the differential capacitance as compared with Monte Carlo simulations. At the same time, they do reproduce the curvature dependence of the differential capacitance, especially for small surface charge density. Our study suggests that the quality of mean-field modeling does not worsen when weakly or moderately charged macroions exhibit spherical curvature.
采用蒙特卡罗模拟法来确定由小尺寸对称阴离子和阳离子在弱电荷至中等电荷大离子附近形成的双电层的微分电容。通过研究从扁平到中等曲率的球形大离子来推断界面曲率的影响。我们还使用先前开发的平均场模型计算微分电容，在该模型中，除了静电相互作用外，还使用晶格气体或卡纳汉 - 斯塔林状态方程来考虑离子的排除体积。对于这两种状态方程，我们将任意曲率的平均场模型与最近开发的二阶曲率展开式进行比较。我们的蒙特卡罗模拟预测，如果表面电荷密度较小，微分电容会随着大离子曲率的增加而增加，而对于中等电荷的大离子，微分电容会经过一个局部最小值。与蒙特卡罗模拟相比，两种平均场模型都倾向于略微高估微分电容。同时，它们确实再现了微分电容的曲率依赖性，特别是对于小表面电荷密度。我们的研究表明，当弱电荷或中等电荷的大离子呈现球形曲率时，平均场建模的质量不会变差。
