One-dimensional colloidal model with dielectric inhomogeneity

TL;DR

This paper presents an exactly solvable one-dimensional colloidal model with dielectric inhomogeneity, revealing conditions for like-charge attraction and bridging the gap between microscopic interactions and mean-field predictions.

Contribution

It introduces an analytical model accounting for dielectric jumps, providing new insights into colloidal interactions and charge attraction phenomena.

Findings

Like-charge attraction occurs regardless of counterion confinement.

Dielectric inhomogeneity enables attraction even with even counterion numbers.

Results recover mean-field predictions as the number of counterions grows large.

Abstract

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counter-ions ($N$) being even. The results are shown to recover the mean-field prediction in the limit $N\to \infty$.