In this work, we report original analytical expressions defining the electrophoretic mobility of composite soft particles comprising an inner core and a surrounding polymer shell with differentiated permeabilities to ions from aqueous background electrolyte and to fluid flow developed under applied DC field conditions. The existence of dielectric permittivity gradients operational at the core/shell and shell/solution interfaces is accounted for within the Debye–Hückel approximation and flat plate configuration valid in the thin double layer regime. The proposed electrophoretic mobility expressions, applicable to weakly to moderately charged particles with size well exceeding the Debye layer thickness, involve the relevant parameters describing the particle core/shell structure and the electrohydrodynamic features of the core and shell particle components. It is shown that the analytical expressions reported so far in literature for the mobility of hard (impermeable) or porous particles correspond to asymptotic limits of the more generic results detailed here. The impacts of dielectric‐mediated effects of ions partitioning between bulk solution and particle body on the electrophoretic response are further discussed. The obtained expressions pave the way for a refined quantitative, analytical interpretation of electrophoretic mobility data collected on soft (nano)particles (e.g., functionalized dendrimers and multilayered polyelectrolytic particles) or biological cells (e.g., viruses) for which the classical hard core‐soft shell representation is not appropriate.

中文翻译：

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介电梯度介导的离子分配对复合软颗粒电泳的影响：一种分析理论

在这项工作中，我们报告了原始的分析表达式，这些表达式定义了复合软颗粒的电泳迁移率，该复合软颗粒包括一个内芯和一个周围的聚合物壳，具有不同的渗透性，可渗透到来自水性背景电解质的离子和在施加的直流电场条件下形成的流体。在核/壳和壳/溶液界面处可操作的介电常数梯度的存在，可以解释为在薄双层体系中有效的Debye-Hückel近似和平板结构。拟议的电泳迁移率表达式适用于大小远超过Debye层厚度的弱至中度带电粒子，涉及描述颗粒核/壳结构以及核和壳颗粒组分的电流体动力学特征的相关参数。结果表明，到目前为止，文献中报道的关于硬质（不渗透性）或多孔质颗粒迁移率的分析表达式与此处详述的更为通用的结果的渐近极限相对应。进一步讨论了电介质介导的离子在本体溶液和颗粒体之间分配对电泳响应的影响。所获得的表达式为在柔软的（纳米）颗粒（例如，功能化的树枝状聚合物和多层聚电解颗粒）或生物细胞（例如，