Titration in Canonical and Grand-Canonical Ensembles

TL;DR

This paper examines the challenges of defining pH in heterogeneous systems and demonstrates how titration isotherms differ between semi-grand canonical and canonical Monte Carlo simulations, highlighting implications for simulation accuracy.

Contribution

It introduces a comparison of titration isotherms from semi-grand canonical and canonical simulations, addressing issues in pH definition for heterogeneous systems.

Findings

Titration isotherms vary significantly between simulation methods.

pH definition in heterogeneous systems is thermodynamically inconsistent.

Simulation method choice impacts the accuracy of titration predictions.

Abstract

We discuss problems associated with the notion of pH in heterogeneous systems. For homogeneous systems, standardization protocols lead to a well defined quantity, which although different from S\o rensen's original idea of pH, is well reproducible and has become accepted as the measure of the ``hydrogen potential". On the other hand, for heterogeneous systems, pH defined in terms of the chemical part of the electrochemical activity is thermodynamically inconsistent and runs afoul of the Gibbs-Guggenheim principle that forbids splitting of the electrochemical potential into separate chemical and electrostatic parts -- since only the sum of two has any thermodynamic meaning. The problem is particularly relevant for modern simulation methods which involve charge regulation of proteins, polyelectrolytes, nanoparticles, colloidal suspensions etc. In this paper we show that titration isotherms calculated using semi-grand canonical simulations can be very different from the ones obtained using canonical reactive Monte Carlo simulations.