Population N_d(Z) and N_d0(Z) (measured in particle concentration), respectively, vs. charge excess Z evaluated at disc midplane at R = 10   AU. The Gaussian distribution of N_d(Z)/n_g with a peak around Z =  −8 refers to agglomerates made of N = 10⁶ monomers of size a₀ = 10^-5   cm while the profile with a peak at Z =  −70 is obtained for compact spheres with a_∗ = 10^-3  cm. The dotted and the dashes lines mark  ⟨ Z ⟩  and , respectively. The solid lines correspond to the values obtained by numerical integration while the values marked by (blue) filled circles are obtained using the semi-analytical solution.