双电层的电容和结构：布朗动力学与经典密度泛函理论的比较
Capacitance and Structure of Electric Double Layers: Comparing Brownian Dynamics and Classical Density Functional Theory
摘要：
本文研究了水电解质双电层的结构和微分电容。我们考虑由球形阳离子和阴离子组成的双电层电容器（EDLC），它们被限制在平面阴极和阳极之间的介电连续体中。该模型系统包括空间以及库仑离子-离子和离子-电极相互作用。我们比较计算昂贵，但“精确”，布朗动力学（BD）模拟与近似的，但便宜，基于经典的密度泛函理论（DFT）的计算结果。优秀的整体协议被发现为一个大的系统参数$-$，包括浓度，离子的大小和价不对称性，施加的电压，和电极间距$-$提供的正则系综的BD模拟和巨正则系综的DFT之间的差异被适当地考虑。特别地，在固定离子数下的差分电容$C_N$和固定离子化学势下的差分电容$C_μ$之间进行仔细区分。此外，我们推导和利用它们的热力学关系。将来这些关系也可用于比较和对比。
英文摘要：
We present a study of the structure and differential capacitance of electric double layers of aqueous electrolytes. We consider Electric Double Layer Capacitors (EDLC) composed of spherical cations and anions in a dielectric continuum confined between a planar cathode and anode. The model system includes steric as well as Coulombic ion-ion and ion-electrode interactions. We compare results of computationally expensive, but "exact", Brownian Dynamics (BD) simulations with approximate, but cheap, calculations based on classical Density Functional Theory (DFT). Excellent overall agreement is found for a large set of system parameters $-$ including variations in concentrations, ionic size- and valency-asymmetries, applied voltages, and electrode separation $-$ provided the differences between the canonical ensemble of the BD simulations and the grand-canonical ensemble of DFT are properly taken into account. In particular a careful distinction is made between the differential capacitance $C_N$ at fixed number of ions and $C_μ$ at fixed ionic chemical potential. Furthermore, we derive and exploit their thermodynamic relations. In the future these relations are also useful for comparing and contrasting.
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