# Simulation of weak polyelectrolytes: A comparison between the constant pH and the reaction ensemble method

## TL;DR

This study compares the reaction ensemble and constant pH methods for simulating protonation in weak polyelectrolytes, highlighting their similarities and differences, especially in systems with strong acids or confined geometries.

## Contribution

It demonstrates the conditions under which both methods agree and identifies the advantages of the reaction ensemble approach for complex systems with diverse pKa values.

## Key findings

- Good agreement between methods when reaction constant is swept
- Pronounced differences for strong acids/bases due to explicit protons
- Reaction ensemble better for confined geometries and diverse pKa values

## Abstract

The reaction ensemble and the constant pH method are well-known chemical equilibrium approaches to simulate protonation and deprotonation reactions in classical molecular dynamics and Monte Carlo simulations. In this article, we show similarity between both methods {under certain conditions}. We perform molecular dynamics simulations of a weak polyelectrolyte in order to compare the titration curves obtained by both approaches. Our findings reveal a good agreement between the methods when the reaction ensemble is used to sweep the reaction constant. Pronounced differences between the reaction ensemble and the constant pH method can be observed for stronger acids and bases in terms of adaptive pH values. These deviations are due to the presence of explicit protons in the reaction ensemble method which induce a screening of electrostatic interactions between the charged titrable groups of the polyelectrolyte. The outcomes of our simulation hint to a better applicability of the reaction ensemble method for systems in confined geometries and titrable groups in polyelectrolytes with different pK$_\text{a}$ values.