Here, a is the microgel radius and U acid and U base are the self-energies of the acidic and basic sites in the microgel, respectively. U aµ and U bµ are the potential energies due to the interaction between the acidic and basic backbone charge distributions of the microgel and the different microionic species, which are determined by the interaction potential between the microions and the anionic and cationic microgel charge distributions u aµ and u bµ , respectively. N µ corresponds to the number of positively and negatively charged microions, µ = +, -, respectively. Finally, U µµ is the energy resulting from the microion-microion interactions, obtained from the microion-microion pair interaction u µµ (r). Note that the numbers of positively and negatively charged microions in the system are chosen such that the system is electroneutral when accounting for the charges of the central microgel.