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Grand-reaction method for simulations of ionization equilibria coupled to ion partitioning

revised on 18.03.2020, 22:00 and posted on 19.03.2020, 10:20 by Jonas Landsgesell, Oleg Rud, Pascal Hebbeker, Raju Lunkad, Peter Košovan, Christian Holm
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 of reactions within the system and Grand-canonical exchange of particles with the reservoir. To demonstrate its strength, we applied our method to a solution of weak polyelectrolytes in equilibrium with a reservoir. Our results show that the ionization and swelling of a weak polyelectrolyte are affected by the Donnan effect due to the partitioning of ions and by the polyelectrolyte effect due to electrostatic repulsion along the chain. Both effects lead to a similar shift in ionization and swelling as a function of pH; albeit for different physical reasons. By comparison with published results, we showed that neglecting one or the other effect may lead to erroneous predictions or misinterpretations of results. In contrast, the Grand-reaction method accounts for both effects 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.


Czech Science foundation, grant 17-02411Y

Grant agency of the Charles University, GAUK 978218

German Research Foundation (DFG) - 423435431 as part of FOR2811 and from DFG through Grants HO 1108/26-1 and AR 593/7-1


Email Address of Submitting Author


Charles University


Czech Republic

ORCID For Submitting Author


Declaration of Conflict of Interest

The authors declare no conflict of interest.

Version Notes

This is a second version of this manuscript, after a major revision. The original version, submitted in August 2019, contained a major flaw which we now removed, re-computed all affected results, and corrected the interpretation.