To perform rGCMCD simulations requires knowledge of the chemical potential of all ions present in the reservoir. This can be obtained using Widom's particle insertion method or by performing a separate grand canonical MC simulation just for the reservoir. There is also an additional complication that the Donnan potential must be calculated self-consistently during the simulation. Clearly, it is desirable to be able to obtain the titration curves directly for an isolated (canonical) system -without going through a semi-grand canonical algorithm. The difficulty is that in a canonical reactive MC simulation, one does not control the pH of the system, instead the total number of ions and protons present inside the simulation cell is specified. The simulation then determines how many of the protons will remain free and how many will be associated with the polyelectrolyte monomers. After the equilibrium is established, one can use Widom's particle insertion method to calculate the excess chemical potential of protons: