We begin by analyzing the solution of the linearized Poisson-Boltzmann equation for a chargeregulating microgel with acidic and basic sites. First, we evaluate the approximation accuracy of Eqs. ( )-( ) by looking at the relative error of the different approximations with respect to the expected nonlinear form for different values of the electric potential Φ. These results are shown in Fig. of the SI, where we can see that Eq. ( ) for the acid-site contribution is the most accurate approximation, with an increasing relative error up to 0.006 for Φ ≈ 0.5.