Effect of ion partitioning on the electrostatics of soft particles with a volumetrically charged core

In most studies of the electrostatics of soft particles, the permittivities of the shell and the electrolyte are assumed to be equal so the ion partitioning effect, arising from the permittivity difference between these two media, can be neglected. On the other hand, recent investigations have revealed that considering the volumetric charge and finite permittivity of the rigid core results in more realistic descriptions of the electrostatics of biological particles. Here, the simultaneous impact of ion partitioning and core volumetric charge on the electrostatics of spherical soft particles is studied using theoretical methods. The equations governing the general case are solved numerically, and analytical expressions are also derived using the Debye-Huckel linearization, which are found to be accurate even in the presence of large core charges. It is observed that, whenever there is a difference between the permittivities of two neighboring media, there is a noticeable change in the slope of the electrostatic potential profile at the interface, with the result that the electrostatic potential distribution of the system deviates from literature predictions. Based on these findings, it is strongly recommended to take the effect of ion partitioning into account when studying the electrostatics of soft particles, especially in the case of low-shell permittivity and concentrated electrolytes.