Solis Francisco J, Olvera de la Cruz Monica
School of Mathematical and Natural Sciences, Arizona State University, Glendale, Arizona 85306, USA.
Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.
J Chem Phys. 2021 Sep 14;155(10):104703. doi: 10.1063/5.0058810.
In solid-liquid, or liquid-liquid, interfaces with dielectric contrast, charged particles interact with the induced polarization charge of the interface. These interactions contribute to an effective self-energy of the bulk ions and mediate ion-ion interactions. For flat interfaces, the self-energy and the mediated interactions are neatly constructed by the image charge method. For other geometries, explicit results are scarce and the problem must be treated via approximations or direct computation. The case of interfaces with roughness is of great practical importance. This article provides analytical results, valid to first-order in perturbation theory, for the self-energy of particles near rough substrates. Explicit formulas are provided for the case of a sinusoidal deformation of a flat surface. Generic deformations can be treated by superposition. In addition to results for the self-energy, the surface polarization charge is presented as a quadrature. The interaction between an ion and the deformed surface is modified by the change in relative distance as well as by the local curvature of the surface. Solid walls, with a lower dielectric constant than the liquid, repel all ions. We show that the repulsion is reduced by local convexity and enhanced by concavity; dimples are more repulsive than pimples.
在具有介电对比度的固 - 液或液 - 液界面中，带电粒子与界面的感应极化电荷相互作用。这些相互作用对体离子的有效自能有贡献，并介导离子 - 离子相互作用。对于平面界面，自能和介导的相互作用可通过镜像电荷法精确构建。对于其他几何形状，明确的结果很少，必须通过近似或直接计算来处理该问题。具有粗糙度的界面情况具有重要的实际意义。本文给出了微扰理论一阶有效下粗糙基底附近粒子自能的解析结果。给出了平面正弦形变情况下的显式公式。一般形变可通过叠加处理。除了自能结果外，表面极化电荷以积分形式给出。离子与形变表面之间的相互作用因相对距离的变化以及表面的局部曲率而改变。介电常数低于液体的固体壁排斥所有离子。我们表明，排斥力因局部凸性而减小，因凹性而增强；凹坑比凸起更具排斥性。
