Exact solution for a general FJC polyelectrolyte model with up to Next Nearest Neighbour Interactions

TL;DR

This paper derives exact solutions for a flexible, ionizable polyelectrolyte chain model considering up to next-nearest neighbor electrostatic interactions, revealing finite size effects and convergence to the infinite chain limit.

Contribution

It introduces an exact analytical framework for a FJC polyelectrolyte with complex electrostatic interactions, including end effects and chain length convergence.

Findings

Finite chains show significant end effects on protonation and conformation.

Increasing chain length rapidly approaches the infinite chain behavior.

Exact expressions enable detailed analysis of electrostatic and conformational properties.

Abstract

This work presents a polyelectrolyte (PE) model based on a freely jointed chain (FJC) in which the beads are ionizable and the bonds are rigid. Electrostatic interactions considered are of the short range type up to next-nearest neighbours using a Debye-H\"uckel (DH) potential. Exact expressions for the conformational and protonation properties are obtained as a function of the pH using the transfer matrix method and the integration of the angular variables. For the finite cases with low N values, relevant differences arise on both the protonation curve and the end to end distance due to the end effects. However, when increasing N a rather rapid convergence is observed to the infinite chain limiting case.