标题： 电介质溶液中带电球体周期性阵列的低频介电响应：简单立方晶格 显示英文标题

标题： Low-frequency dielectric response of a periodic array of charged spheres in an electrolyte solution: The simple cubic lattice

摘要： 我们研究了在电解质溶液中排列成立方晶格的高电荷球体的低频介电响应。 我们关注在离子电荷中和的区域中，相位差电流的影响。 我们考虑带电球体没有表面电导率和频率依赖的表面电容的情况。 因此，介电常数的频率色散主要由双电层外中性电流的影响所主导。 在双电层较薄的极限下，我们在双电层的外表面使用Fixman的边界条件来捕捉电场与离子流动之间的相互作用。 对于周期性条件，我们将Lord Rayleigh为理解矩形排列障碍物之间的电导而开发的方法，以及Korringa、Kohn和Rostoker用于电子能带结构计算的方法结合起来。 当带电球体占据的体积分数非常小，小于1%时，我们的解与Maxwell Garnett混合公式以及单粒子极化响应一致，这是预期的结果，因为在稀释极限下粒子间相互作用变得不那么显著。 相比之下，即使带电球体只占据2%的体积，粒子间相互作用也会显著改变介电响应。 我们发现，特征频率相比于从单粒子极化响应得出的频率向更高值移动。 同时，带电球体浸入电解质中的介电增强现象，在周期性排列的带电球体中变得不那么明显。 我们的结果表明，由密集排列的带电球体组成的系统在电解质中的介电响应特征可能与稀释悬浮液有显著不同。 显示英文摘要

摘要： We study the low-frequency dielectric response of highly charged spheres arranged in a cubic lattice and immersed in an electrolyte solution. We focus on the influence of the out-of-phase current in the regime where the ionic charge is neutral. We consider the case where the charged spheres have no surface conductance and no frequency-dependent surface capacitance. Hence, the frequency dispersion of the dielectric constant is dominated by the effect of neutral currents outside the electric double layer. In the thin double-layer limit, we use Fixman's boundary condition at the outer surface of the double layer to capture interaction between the electric field and the flow of the ions. For periodic conditions, we combine the methods developed by Lord Rayleigh for understanding the electric conduction across rectangularly arranged obstacles and by Korringa, Kohn and Rostoker for the electronic band structure computation. When the charged spheres occupy a very small volume fraction, smaller than one percent, our solution becomes consistent with the Maxwell Garnett mixing formula together with the single-particle polarization response, as expected, because inter-particle interactions become less prominent in the dilute limit. By contrast, the inter-particle interaction greatly alters the dielectric response even when charged spheres occupy only two percent of the volume. We found that the characteristic frequency shifts to a higher value compared to that derived from the single-particle polarization response. At the same time, the low-frequency dielectric enhancement, a signature of charged spheres immersed in an electrolyte, becomes less prominent for the periodic array of charged spheres. Our results imply that the signature of the dielectric response of a system consisting of densely packed charged spheres immersed in an electrolyte can differ drastically from a dilute suspension.