The influence of dielectric decrement on electrokinetics

Abstract

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) equations 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 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, the dielectric decrement decreases Me with an increasing α. At large ζ, it is well 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.

Nonlinear electrophoresis in the presence of dielectric decrement

“…Similarly, setting the variational derivative δF/δφ to zero, we obtain the modified Poisson-Boltzmann equation in a similar form as those obtained by Hatlo et al [41] and Zhao et al [43]:…”

“…In the dielectric decrement model [41,43], it is assumed that the permittivity m of the solvent varies linearly with the concentration:…”

“…[43]. In our model, to simplify the analysis, we consider that the dielectric decrement parameters of both co-ions and counter-ions are equal.…”

“…This approach was originally introduced by O'Brien et al [14]. It was applied by Khair and Squires [32] to study electrophoresis of fixed surface charge particles in the presence of steric effects due to the finite size of ions and by Zhao and Zhang [43] to investigate the influence of dielectric decrement effects.…”

“…Recently, Nakayama and Andelman [42] incorporated both dielectric decrement and steric effects in a model aimed at predicting the differential capacitance of the EDL. The influence of dielectric decrement on electrophoresis of particles with fixed surface charges has been studied by Zhao and Zhai [43], who showed that dielectric decrement significantly reduces surface conduction, therefore yielding higher electrophoretic velocities.…”