This dependence leads to an error accumulation, resulting in a more pronounced error in the swelling results, particularly at high values of pH res . In Fig. of the SI, we plot the maximum of the electric potential, Φ max , the net charge Z net and the electrostatic pressure contribution, π elec , versus the microgel size a trial for three different pH res for the nonlinear case and the linear approximation. These quantities depend on the electrostatic potential in a different way: while Φ max is obtained from evaluating Φ(r) at a single point, Z net and π elec are nonlinear functionals of Φ(r). By looking at the figure, we observe that the linear approximation is more accurate for quantities with a simpler dependence on Φ(r), such as Φ max or Z net , which is related to the zeroth moment of the microion density profiles. We observe that for more complex dependence on the electrostatic potential Φ(r), such as the case of π elec that also depends on higher order moments of the microion density distributions, the linear approximation turns out to be less accurate, particularly at higher pH res .