A new method for reactive constant pH simulations

Abstract: We present a simulation method that allows us to calculate the titration curves for systems undergoing protonation/deprotonation reactions -- such as charged colloidal suspensions with acidic/basic surface groups, polyelectrolytes, polyampholytes, proteins, etc. The new approach allows us to simultaneously obtain titration curves both for systems in contact with salt and acid reservoir (semi-grand canonical ensemble) and for isolated suspensions (canonical ensemble). To treat the electrostatic interactions, we present a new method based on Ewald summation -- which accounts for the existence of both Bethe and Donnan potentials within the simulation cell. We show that that the Donnan potential affects dramatically the pH of suspension. Counter intuitively, we find that for concentrated suspensions of low ionic strength, the number of deprotonated groups can be 100\% larger in an isolated system, compared to a system connected to a reservoir by a semi-permeable membrane -- with both systems being at exactly the same pH.