Effects of electrostatic correlations and ion–solvent interactions of finite-sized ions on the electrophoresis of a soft particle

A numerical study supplemented with theoretical analysis is made, to analyse the electrophoresis of highly charged soft particles in electrolytes with trivalent counterions. The electrokinetic model is devised under the continuum hypothesis, which incorporates the ion–ion electrostatic correlations, hydrodynamic steric interactions of finite sized ions and ion–solvent interactions. The governing equations for ion transport and electric field are derived from the volumetric free energy of the system, which includes the first-order correction for the non-local electrostatic correlations of interacting ions, excess electrochemical potential due to finite ion size as well as the Born energy difference of ions due to dielectric permittivity variation. The electrolyte viscosity is considered to be a function of the local volume fraction of finite-sized ions, which causes the diffusivity of ions to vary locally. The occurrence of mobility reversal of a soft particle having the same polarity of its core and soft shell charge and formation of a coion-dominated zone in the soft layer is elaborated through this study. This can explain the mechanisms for the attraction between like-charged soft particles, as seen in the condensation of DNAs. The impact of ion–ion correlations and ion–solvent interactions of finite-sized ions are analysed by comparing them with the results based on the standard model. At a higher range of the core charge density, the ion–ion correlations induce a condensed layer of counterions on the outer surface of the core, which draws coions in the electric double layer, leading to an inversion in polarity of the charge density and mobility reversal. The dielectric decrement and ion steric interactions create a saturation in ion distribution and hence, modify the condensed layer of counterions. The enhanced fixed charge density of the polyelectrolyte layer diminishes the ion correlations due to the stronger screening effects and prevents the formation of a coion dominated zone in the Debye layer. The impact of the counterion size and the mixture of monovalent and trivalent counterions on mobility is analysed.