Shell formation in short like-charged polyelectrolytes in a harmonic trap

TL;DR

This paper develops a theoretical model using RISM integral equations to study how short, like-charged polyelectrolytes arrange themselves in a harmonic trap, revealing shell formation influenced by polymer length and correlations.

Contribution

It introduces a RISM-based approach to predict equilibrium density profiles of polyelectrolytes in external potentials, highlighting the role of correlations in shell formation.

Findings

Longer polymers form boundary shells at moderate coupling.

Point charges do not form shells at any coupling in mean field limit.

Including correlations results in sharp shells even at weak coupling.

Abstract

Inspired by recent experiments and simulations on pattern formation in biomolecules by optical tweezers, a theoretical description based on reference interaction site model (RISM) integral equation method is developed to calculate the equilibrium density profiles of small polyelectrolytes in an external potential. The formalism is applied to the specific case of a finite number of polyelectrolytes trapped in a harmonic potential. The density profiles of flexible Gaussian and rigid rod-like polyelectrolytes are studied over a range of lengths and numbers of polyelectrolytes in the trap and the Coulomb coupling parameter. For smaller polymers we recover the results for point charges. In the mean field limit the point particles do not form shells for any values of the coupling parameter whereas the longer polymers form a shell at the boundary at moderate coupling. When the inter-polymer cor- relations are included the density profile of the polymers shows sharp shells even at weak coupling. The implications of these results are also discussed.