Monte Carlo simulations and mean-field modeling of electric double layers at weakly and moderately charged spherical macroions,Physical Review E

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Monte Carlo simulations and mean-field modeling of electric double layers at weakly and moderately charged spherical macroions
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-23 , DOI: 10.1103/physreve.104.034609
Daniel L Z Caetano ₁ , Sidney J de Carvalho ₂ , Guilherme V Bossa ₂ , Sylvio May ₃

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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.

中文翻译：

微弱和中等带电球形宏观电子双电层的蒙特卡罗模拟和平均场建模

蒙特卡罗模拟被用来确定由小尺寸对称阴离子和阳离子在弱到中等带电的宏离子附近形成的双电层的微分电容。界面曲率的影响是通过研究从平坦到适度弯曲的球形宏观来推导出来的。我们还使用先前开发的平均场模型计算微分电容，其中除了静电相互作用外，还使用晶格气体或 Carnahan-Starling 状态方程考虑了排除的离子体积。对于这两个状态方程，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，则差分电容会随着宏观曲率的增加而增加，而对于中等电荷的宏观，差分电容会通过局部最小值。与 Monte Carlo 模拟相比，两种平均场模型都倾向于高估差分电容。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，当弱或中等带电的宏观粒子呈现球面曲率时，平均场建模的质量不会恶化。与 Monte Carlo 模拟相比，两种平均场模型都倾向于高估差分电容。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，当弱或中等带电的宏观粒子呈现球面曲率时，平均场建模的质量不会恶化。与 Monte Carlo 模拟相比，两种平均场模型都倾向于高估差分电容。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，当弱或中等带电的宏观粒子表现出球面曲率时，平均场建模的质量不会恶化。

更新日期：2021-09-23

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