Effects of dielectric gradients‐mediated ions partitioning on the electrophoresis of composite soft particles: An analytical theory

Abstract

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.

Electrophoresis of soft particles with hydrophobic inner core grafted with pH‐regulated and highly charged polyelectrolyte layer

“…The Brinkmann screening length of various core-shell structured bioparticles ranges up to 30 nm [19,20]. In addition, several studies have shown that the dielectric permittivity of peripheral polymeric membrane of such a particle can be significantly lower than that of the aqueous medium [31][32][33][34][35][36]53,54].…”

Ion partitioning effect on the electrostatic interaction between two charged soft surfaces

“…Since polyelectrolyte layer and bulk electrolyte solution have distinct dielectric permittivity, the self-energies of an ion, W i , in the two regions differ from each other. The difference in self-energy of the ion causes ion partitioning, which can be quantified as ion partition coefficient [44,45,46,47,48,49,50]…”

“…Ion partitioning effect modifies the charge density in polyelectrolyte layer and consequently affects the electrophoresis of soft charged particles as well as electrokinetics in soft nanochannels. Very recently, ion partitioning effect attracted a great deal of interest of researchers studying the electrophoresis of charged soft particles immersed in electrolytes [44,45,46,47,48,49,50] and electrokinetic transport in soft nanochannels [51,52,53]. The analytical and numerical studies [44,49,50,45,46,47,48],…”

“…Very recently, ion partitioning effect attracted a great deal of interest of researchers studying the electrophoresis of charged soft particles immersed in electrolytes [44,45,46,47,48,49,50] and electrokinetic transport in soft nanochannels [51,52,53]. The analytical and numerical studies [44,49,50,45,46,47,48],…”

Steric Effects on Space Electroosmotic Thrusters in Soft Nanochannels

“…The effects of ion partitioning on the electrokinetics in soft nanochannels were analyzed in order to offset the existing work results with the consideration of equal permittivity inside and outside the ECL [22]. A large number of articles dealt with such effects in various research studies [23][24][25]. In this paper, however, we have not added the ion partitioning effect to present thruster systems since this consideration is repetitive.…”