Confinement free energy of flexible polyelectrolytes in spherical cavities

TL;DR

This study uses self-consistent field theory to analyze the free energy of weakly charged flexible polyelectrolytes confined in spherical cavities, highlighting the roles of solvent entropy, electrostatics, and chain length.

Contribution

It introduces a detailed SCFT analysis of confined polyelectrolytes, emphasizing the impact of solvent entropy and fluctuations on free energy and osmotic properties.

Findings

Charge density wave formation under confinement

Solvent entropy dominates for short chains

Fluctuations lower free energy and affect osmotic pressure

Abstract

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed using self-consistent field theory (SCFT) within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.