Comment on ``Adsorption of Polyelectrolyte onto a Colloid of Opposite Charge''

TL;DR

This paper critiques a study on polyelectrolyte adsorption onto colloids, arguing that the reported overcharging effect is an artifact of the variational approximation and depends on the trial wave function choice.

Contribution

It challenges previous findings by analyzing the variational method's limitations and showing overcharging is not a definitive physical phenomenon.

Findings

Overcharging is likely an artifact of the approximation.

The existence of overcharging depends on the trial wave function.

The original study's overcharging factor is not physically robust.

Abstract

In a recent Letter, Gurovitch and Sens studied the adsorption of a weakly charged polyelectrolyte chain onto an oppositely charged colloidal particle. By using a variational technique they found that the colloidal particle can adsorb a polymer of higher charge than its own, and thus be ``overcharged.'' I argue that the observed overcharging by a factor of 16/5 is indeed an artifact of the approximations involved in the study. Moreover, I show that the existence of overcharging depends crucially on the choice of the trial wave function, contrary to their claim.