Poly(diallyldimethylammonium chloride) (PDADMAC, M w = 100,000, 35 wt.% in H2O), poly(ethyleneimine) (PEI, M w = 2,000, 50 wt.% in H2O), and poly(allylamine hychloride) (PAH, M w = 15,000) were obtained from Sigma-Aldrich, St. Louis, MO, USA, and used as received. The molecular formulas are given in Figure 2. Figure 2 Molecular structures of PTEA 11K – b -PAM 30K , PDADMAC, PEI, and PAH. Sample preparation NPs/PEs aggregates were prepared according to three different methods. The first method, called direct

mixing, utilized stock polymer and NPs solutions prepared without added salt. The two other protocols, dilution and dialysis, were based on a principle of desalting processes, AMN-107 ic50 starting all runs at the initial ionic strength I S  = 3 M of ammonium chloride (NH4Cl). The ionic strength was defined as [64] (1) 4SC-202 solubility dmso where c i and z i denote the concentration and valency of the ionic atomic species in solution, respectively. Direct mixing NPs/PEs complexes were obtained by mixing stock solutions prepared at the same weight concentration (c ∼ 0.1 wt.%) and same pH (pH 8). The mixing of the two initial solutions was characterized by the particles-polymers charges ratio Z. Z is defined as the structural charges ratio between the anionic NPs and the

cationic PEs. Here, the acido-basic titration was used to evaluate the number of available electrostatic charges per particle (see Additional file 1: SI-2). For the 8.3-nm γ-Fe2O3 NPs coated by PAA2K, we got the number of carboxylate groups available per particle . We can then

calculate the total number of the negative Cyclic nucleotide phosphodiesterase charges in the stock solution by: (2) Where V NP and c NP are the volume and mass concentration, respectively, of the stock solution containing NPs; is the molecular weight of the 8.3-nm γ-Fe2O3 NPs; N A is the Avogadro constant. For the cationic polymers, we calculated the number of positive charges from their molecular structures. (3) Where V poly and c poly are the volume and mass concentration, respectively, of the polymer stock solution; and are the molecular weight of the monomer and of the polymer, respectively; n is the number of the positive charges per each monomer. In this work, the two stock solutions were always prepared at the same concentration: c NP = c poly. We took the average molecular weight of particle = = 5.82 × 106 g mol−1 which was measured as a function of the concentration by using static light scattering (see Additional file 1: SI-2). Thus particles-polymer charges ratio Z can be expressed as: (4) By using Equation 4, we can then easily control the charges ratio Z by tuning the particle to polymer volume ratio X = V NP /V poly. For the four different polymers mentioned above, the relations between Z and X were shown in Table 2. Table 2 Particles-polymer charges ratio Z ( X ) of the mixing solution containing these PEs and magnetic NPs Polymer M w(g mol−1) n Z ( X ) Lenvatinib supplier PTEA11K-b-PAM30K 44,400 1 1.9 X PDADMAC 100,000 1 0.