Electrophoresis of composite soft particles with differentiated core and shell permeabilities to ions and fluid flow

Abstract

Within the framework of analytical theories for soft surface electrophoresis, soft particles are classically defined by a hard impermeable core of given surface charge density surrounded by a polyelectrolyte shell layer permeable to both electroosmotic flow and ions from background electrolyte. This definition excludes practical core-shell particles, e.g. dendrimers, viruses or multi-layered polymeric particles, defined by a polyelectrolytic core where structural charges are distributed and where counter-ions concentration and electroosmotic flow velocity can be significant. Whereas a number of important approximate expressions has been derived for the electrophoretic mobility of hard and soft particles, none of them is applicable to such generic composite core-shell particles with differentiated ions-and fluid flow-permeabilities of their core and shell components. In this work, we elaborate an original closed-form electrophoretic mobility expression for this generic composite particle type within the Debye-Hückel electrostatic framework and thin double layer approximation. The expression explicitly involves the screening Debye layer thickness and the Brinkman core and shell hydrodynamic length scales, which favors so-far missing analysis of the respective core and shell contributions to overall particle mobility. Limits of this expression successfully reproduce results from Ohshima's electrophoresis theory solely applicable to soft particles with or without hard core.

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

“…In addition, in the electrolyte medium the volumetric electric body force density is written as . The reader is referred to [41] for a detailed discussion on the governing hydrodynamic equations and associated relevant boundaries. Then, following the strategy adopted in [41], the velocity field for Sc‐Ssl particles with account of ions partitioning effects can be explicitly derived.…”

“…In addition, the internal particle core has been exclusively tackled with assuming insignificant permeation to ions and flow within it. However, as recently argued by Maurya et al [41], there are many soft particle types of practical relevance, like functionalized nanodendrimers [19], where the core may also be permeable to ions and/or fluid flow depending on its chemical composition. Accordingly, Maurya et al [41] introduced the generic term “composite soft particles” to denote core–shell systems for which not only the shell (hereafter denoted as “sl”) but also the particle core (hereafter denoted as “c”) may host ions from the background electrolyte and/or be permeable to flow under applied field conditions.…”

“…However, as recently argued by Maurya et al [41], there are many soft particle types of practical relevance, like functionalized nanodendrimers [19], where the core may also be permeable to ions and/or fluid flow depending on its chemical composition. Accordingly, Maurya et al [41] introduced the generic term “composite soft particles” to denote core–shell systems for which not only the shell (hereafter denoted as “sl”) but also the particle core (hereafter denoted as “c”) may host ions from the background electrolyte and/or be permeable to flow under applied field conditions. This led Maurya et al [41] to distinguish between different composite soft particles along the lines detailed in Table 1, with the qualification “soft” (“S” in short) and “semi‐soft” (“SS” in short) applying to a particle compartment (core or shell) that is permeable to both ions and flow, and to a particle compartment that is permeable to ions but not to flow, respectively.…”

“…Accordingly, Maurya et al [41] introduced the generic term “composite soft particles” to denote core–shell systems for which not only the shell (hereafter denoted as “sl”) but also the particle core (hereafter denoted as “c”) may host ions from the background electrolyte and/or be permeable to flow under applied field conditions. This led Maurya et al [41] to distinguish between different composite soft particles along the lines detailed in Table 1, with the qualification “soft” (“S” in short) and “semi‐soft” (“SS” in short) applying to a particle compartment (core or shell) that is permeable to both ions and flow, and to a particle compartment that is permeable to ions but not to flow, respectively. Particles denominated by the abbreviations “Sc‐Ssl,” “SSc‐Ssl,” and “SSc‐SSsl” thus refer to various combinations of flow‐ and ions‐permeability properties in the core and shell regions ( Table 1 ).…”

Transient electrophoresis of a charged porous particle

“…Electrophoresis is one of the most widely used experimental methods and practical operations for the transport, manipulation, separation, assembly, and characterization of colloidal particles. In the past, some formulas for the steady electrophoretic mobility of a charged particle were derived analytically for the cases of hard sphere (impermeable to both the solvent and small ions) , porous sphere (permeable) , soft sphere (hard in the core but porous in the surface layer) , and porous spherical shell (e.g. microcapsule or vesicle) .…”