The influence of dielectric decrement on electrokinetics

We treat the dielectric decrement induced by excess ion polarization as a source of ion specificity and explore its impact on electrokinetics. We employ a modified Poisson–Nernst–Planck (PNP) model accounting for the dielectric decrement. The dielectric decrement is determined by the excess-ion-polarization parameter $\alpha $ and when $\alpha = 0$ the standard PNP model is recovered. Our model shows that ions saturate at large zeta potentials $(\zeta )$. Because of ion saturation, a condensed counterion layer forms adjacent to the charged surface, introducing a new length scale, the thickness of the condensed layer $({l}_{c} )$. For the electro-osmotic mobility, the dielectric decrement weakens the electro-osmotic flow owing to the decrease of the dielectric permittivity. At large $\zeta $, when $\alpha \not = 0$, the electro-osmotic mobility is found to be proportional to $\zeta / 2$, in contrast to $\zeta $ as predicted by the standard PNP model. This is attributed to ion saturation at large $\zeta $. In terms of the electrophoretic mobility ${M}_{e} $, we carry out both an asymptotic analysis in the thin-double-layer limit and solve the full modified PNP model to compute ${M}_{e} $. Our analysis reveals that the impact of the dielectric decrement is intriguing. At small and moderate $\zeta ~({\lt }6kT/ e)$, the dielectric decrement decreases ${M}_{e} $ with increasing $\alpha $. At large $\zeta $, it is known that the surface conduction becomes significant and plays an important role in determining ${M}_{e} $. It is observed that the dielectric decrement effectively reduces the surface conduction. Hence in stark contrast, ${M}_{e} $ increases as $\alpha $ increases. Our predictions of the contrast dependence of the mobility on $\alpha $ at different zeta potentials qualitatively agree with experimental results on the dependence of the mobility among ions and provide a possible explanation for such ion specificity. Finally, the comparisons between the thin-double-layer asymptotic analysis and the full simulations of the modified PNP model suggest that at large $\zeta $ the validity of the thin-double-layer approximation is determined by ${l}_{c} $ rather than the traditional Debye length.