Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

Abstract

The equilibrium electric double layer (EDL) that surrounds the colloidal particles is determinant for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed by the charged colloidal particles and the ionic countercharge released by the charging mechanism. The existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterions concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the large importance of such corrections for moderate to high particle charges at every particle volume fraction, specially, when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study nonequilibrium properties in concentrated colloidal suspensions, particularly the salt-free ones with small and highly charged particles.

Superviscosity and electroviscous effects at an electrode/aqueous electrolyte interface: An atomic force microscope study

“…On the other hand, the trend of increasing effective viscosity with increasing electrolyte concentration (experiment (B) vs. (A)) might also be a hint toward a strong structuring of counterions close to the electrodes. As pointed out recently in a modeling paper by Roa et al [32], in close proximity to a highly charged surface, the concentration of counterions can be much higher than in bulk. This strong condensation of counterions causes a partial or complete loss of their hydration shells and a ''saturated'' ionic surface layer.…”

Recent developments in electrokinetics of salt-free concentrated suspensions

“…Some of the new approaches concern microscopic descriptions of the previous considerations although restricted mainly to equilibrium conditions. The classical approach of the standard electrokinetic model is a macroscopic description that considers average interactions by mean field approximations [21, [63][64][65][66][67][68][69][70][71][72][73]. Important phenomena like overcharging [74] have no convincing explanation when ion-ion correlations including steric effects are neglected, as the classical approach does, while it has been satisfactorily explained with…”

“…r dr (24) where the equilibrium counterion concentration is expressed as: The unknown coefficient b c is evaluated as before via an iterative procedure. A robust mathematical method has also been reported to avoid the latter iterative procedure reducing considerably numerical instabilities and computational times [69].…”

Predictions of the maximum energy extracted from salinity exchange inside porous electrodes

“…For our purposes, existing models on the description of the EDL potential profile at interfaces with different geometries [38,34,39,40,41,42,43,44,45] cannot be applied to porous electrodes because such models are usually restricted to dilute suspensions, so that the likely overlap between EDLs from opposite walls of the pores is not considered. Theoretical models including EDL overlap and ionic size effects have been applied to salt free suspensions [42], and are based on cell models, which are appropriate in the case of homogeneous distributions of non-contacting spherical particles [41].…”

“…Theoretical models including EDL overlap and ionic size effects have been applied to salt free suspensions [42], and are based on cell models, which are appropriate in the case of homogeneous distributions of non-contacting spherical particles [41].…”