Notice that for 0 ≤ r ≤ a, we have kept only the term that fulfills Φ ′ (0) = 0. The integration constants A, B and C are determined by the boundary condition Φ ′ (R) = 0 and by demanding continuity of the electrostatic potential and electric field at the microgel surface, i.e. Φ(r → a + ) = Φ(r → a -) and Φ ′ (r → a + ) = Φ ′ (r → a -).