Ion partitioning effect on the electrophoresis of a soft particle with hydrophobic core

A theoretical study on the electrophoresis of a soft particle made up of a charged hydrophobic inner core surrounded by polyelectrolyte layer (PEL) is made. The dielectric permittivity of the PEL and aqueous solution are considered to be different, which creates the ion partitioning effect. The ion partitioning effect, which is accounted by the Born energy difference, modifies the distribution of mobile ions in the PEL and hence alters the particle electrophoresis. The combined effects of core hydrophobicity and the ion partitioning effect on the mobility are determined based on the Debye-Huckel approximation under a thin Debye layer assumption. An analytic expression for the electrophoretic mobility taking into account the core hydrophobicity and ion partitioning effect is obtained. The occurrence of zero mobility and reversal of mobility of the soft particle is illustrated.

Figure 1

Schematic illustrations depicting platelike soft particle covered by ion and fluid penetrable polyelectrolyte layer of thickness $d$.

Figure 2

Variation of the scaled mobility $\left({\overline{\mu }}_E\right)$, scaled by ${\epsilon }_f{\varphi }_0/\eta$, of a soft particle with uncharged inner core ($\sigma =0$) and charged PEL ($z=1,N=10$ mM, ${\rho }_{\mathrm{fix}}=9.65\times {10}^5{\mathrm{C}/\mathrm{m}}^3$) is shown in (a) with core slip length at different choice of the PEL-to-electrolyte permittivity ratio ${\epsilon }_r$ (= 0.1, 0.11, 0.13, 0.15, 0.2, 0.5, and 1) with fixed ${\lambda }^{-1}$ (=5 nm) and $d=10$ nm; (b) with core slip length at different values of ${\lambda }^{-1}$ (=1, 3, 5, and 10 nm) with fixed ${\epsilon }_r$ (=1) and $d=10$ nm. The red symbols correspond to the results due to Ohshima [7].

Figure 3

Variation of scaled mobility ${\overline{\mu }}_E$ with (a) slip length $\beta /d$ for different choice of ${\epsilon }_r(=0.1,0.11,0.13,0.15,0.2,0.5,1$) with fixed $N=10$ mM, ${\rho }_{\mathrm{fix}}=9.65\times {10}^5{\mathrm{C}/\mathrm{m}}^3$, $\sigma =-20$ mc/${\mathrm{m}}^2$, ${\lambda }^{-1}=5$ nm and $d=10$ nm; (b) PEL charge for different choice of ${\lambda }^{-1}(=1,3,5$, 10 nm) when $\sigma =-20$ mc/${\mathrm{m}}^2$, ${\epsilon }_r=1$, $d=10$ nm for a soft particle with superhydrophobic inner core.

Figure 4

Variation of the critical surface charge density and PEL charge to attain zero mobility are shown. The results are presented in (a) for different values of ${\epsilon }_r(=0.1,0.11,0.13,0.15,0.2,0.5,1)$ for fixed ${\lambda }^{-1}=5$ nm and $\beta /d=0$ (hydrophilic); (b) for different values of $\beta /d(=0,0.1,0.5,1,10,100)$ for fixed ${\epsilon }_r=0.1$ and ${\lambda }^{-1}=5$ nm; (c) for different values of ${\lambda }^{-1}(=1,3,5,10$ nm) when the inner rigid core in superhydrophobic in nature with fixed ${\epsilon }_r(=1)$.