We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter dfacet → 0 we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit LDebye dfacet, an ensemble of non-interacting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces.

中文翻译：

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多晶电极-电解质界面建模：微分电容

我们提出并分析了基于改进的连续模型的多晶电极表面模型，该模型考虑了有限离子大小和溶剂化。有限尺寸小平面图案的数值模拟允许研究两种极限情况：当小平面尺寸直径 dfacet → 0 时，我们得到空间均匀但可能是非晶或液体表面的典型电容，在极限 LDebye dfacet 中，非-接近相互作用的单晶表面。对于中等尺寸的小平面直径，通过添加由其各自表面分数加权的贡献小平面的单晶电容的经典方法，电容非常好地近似。因此，在电容的局部最小值处不一定能达到零电荷的电位，但可能位于局部电容最大值处。此外，结果表明，通过将理想平坦的多晶表面电容乘以一个因子，可以准确地考虑表面粗糙度。特别是，我们发现刻面图案的实际几何形状的影响可以忽略不计，我们的理论为复杂的真实多晶表面的随机描述开辟了道路。