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 α and when α = 0 the standard PNP model is recovered. Our model shows that ions saturate at large zeta potentials (ζ ) . 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 (lc ) . For the electro-osmotic mobility, the dielectric decrement weakens the electro-osmotic flow owing to the decrease of the dielectric permittivity. At large ζ , when α = 0 , the electro-osmotic mobility is found to be proportional to ζ / 2 , in contrast to ζ as predicted by the standard PNP model. This is attributed to ion saturation at large ζ . In terms of the electrophoretic mobility Mₑ , we carry out both an asymptotic analysis in the thin-double-layer limit and solve the full modified PNP model to compute Mₑ . Our analysis reveals that the impact of the dielectric decrement is intriguing. At small and moderate ζ ~(< 6kT/ e) , the dielectric decrement decreases Mₑ with increasing α . At large ζ , it is known that the surface conduction becomes significant and plays an important role in determining Mₑ . It is observed that the dielectric decrement effectively reduces the surface conduction. Hence in stark contrast, Mₑ increases as α increases. Our predictions of the contrast dependence of the mobility on α 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 ζ the validity of the thin-double-layer approximation is determined by lc rather than the traditional Debye length.