This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels.

ESPResSo is an extensible simulation package for research on soft matter. This versatile molecular dynamics program was originally developed for coarse-grained simulations of charged systems [Limbach et al., Comput. Phys. Commun. 174, 704 (2006)]. The scope of the software has since broadened considerably: ESPResSo can now be used to simulate systems with length scales spanning from the molecular to the colloidal. Examples include, self-propelled particles in active matter, membranes in biological systems, and the aggregation of soot particles in process engineering. ESPResSo also includes solvers for hydrodynamic and electrokinetic problems, both on the continuum and on the explicit particle level. Since our last description of version 3.

We developed a new method for coarse-grained simulations of acid-base equilibria in a system coupled to a reservoir at a given pH and concentration of added salt, that we term the Grand-reaction method. More generally, it can be used for simulations of any reactive system coupled to a reservoir of a known composition. Conceptually, it can be regarded as an extension of the reaction ensemble, combining explicit simulations we showed that neglecting one or the other eect may lead to erroneous predictions or misinterpretations of results. In contrast, the Grand-reaction method accounts for both eects on the results and allows us to quantify them. Finally, we outline possible extensions and generalizations of the method and provide a set of guidelines for its safe application by a broad community of users.

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 pKa values.