Abstract

In scope of the Poisson–Boltzmann theory, the electrostatic potential profiles in the vicinity of spherical particles immersed in 1 : 1 electrolyte solutions have been precisely calculated. Using the data on the behavior of the profiles at large distances from the particle surface, effective surface potential \({{\psi }_{{{\text{eff}}}}},\) and its limiting value \(\psi _{{{\text{eff}}}}^{{{\text{sat}}}},\) to which it tends upon an infinite growth of the surface charge, have been determined for a wide range of model parameters (surface charge density, particle radius, and electrolyte concentration). A universal curve has been plotted to represent the dependence of \(\psi _{{{\text{eff}}}}^{{{\text{sat}}}}\) on reduced particle radius κa (a is the radius and κ is the reciprocal Debye screening radius) and to evidently illustrate the existence of two known limiting laws of variations in the effective potential that corresponds to the saturation conditions. The energy criterion and the analysis of its sensitivity to the cutoff threshold have been employed to evaluate the thicknesses of the shells formed by immobilized counterions around the spherical particles. Dependences of the shell thickness on the surface charge density, particle radius, and 1 : 1 electrolyte concentration have been analyzed. It has been revealed that there is limiting thickness \(l_{{{\text{eff}}}}^{{{\text{sat}}}},\) which is reached upon the infinite growth of the surface charge density. A universal κ\(l_{{{\text{eff}}}}^{{{\text{sat}}}}\)(κa) curve is presented and compared with the \(\psi _{{{\text{eff}}}}^{{{\text{sat}}}}\)(κa) curve.

中文翻译：

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1：1电解质溶液中带电球形颗粒的有效参数

摘要

在Poisson–Boltzmann理论的范围内，已精确计算了浸入1：1电解质溶液中的球形颗粒附近的静电势分布。使用与粒子表面相距很远的轮廓行为的数据，有效表面电势\（{{\ psi} _ {{{\ text {eff}}}}} \\及其极限值\（\已针对各种模型确定了psi _ {{{\ text {eff}}}} ^ {{{{\ text {sat}}}}} \\，由于表面电荷无限增长而趋向于参数（表面电荷密度，粒子半径和电解质浓度）。一个普遍的曲线已被绘制来表示的依赖性\（\ PSI _ {{{\文本{EFF}}}} ^ {{{\文本{坐在}}}} \）上减小的颗粒半径κ一个（a是半径，k是倒数德拜屏蔽半径），显然可以说明存在两个与饱和条件相对应的有效电位变化的已知极限定律。能量标准及其对截止阈值的敏感性分析已用于评估由固定在球形颗粒周围的抗衡离子形成的壳的厚度。已经分析了壳厚度对表面电荷密度，颗粒半径和1：1电解质浓度的依赖性。已经发现，表面电荷密度的无限增长会达到极限厚度\（l _ {{{{text {eff}}}} ^ {{{text {sat}}}}，\）。通用κ\（升_ {{{\文本{EFF}}}} ^ {{{\文本{坐在}}}} \）（κ一个）曲线中，并用比较\（\ PSI _ {{{\文本{ EFF}}}} ^ {{{\文本{坐在}}}} \）（κ一个）曲线。