Stoichiometry of electrostatic complexes determined by light scattering

We report on the electrostatic complexation between oppositely charged polymers and inorganic nanoparticles investigated by static and dynamical light scattering. The nanoparticles put under scrutiny were citrate-coated nanocrystals of cerium oxide (CeO2, nanoceria), of iron oxide (gamma-Fe2O3, maghemite), and of europium-doped yttrium vanadate (Eu:YVO4) with sizes in the 10 nm range. For the polymers, we have used cationic-neutral diblock copolymers (poly(trimethylammonium ethyl acryl ate)-b-po ly(acryl amide), hereafter referred to as PTEA-b-PAM) with different molecular weights. For the three colloidal dispersions, we show that the electrostatic complexation gives rise to the formation of stable nanoparticle clusters in the 100 nm range. The complexation was monitored by systematic measurements of the scattering intensity vs X, the mixing ratio between nanoparticles and polymers. For five nanoparticle/polymer pairs, namely CeO2/PTEA(5K)-b-PAM(30K), gamma-Fe2O3/PTEA(5K)-b-PAM(30K), gamma-Fe2O3/PTEA(11K) -b-PAM(30K), Eu:YVO4/PTEA(2K)-b-PAM(60K), and Eu:YVO4/PTEA(5K)-b-PAM(30K), we found a unique behavior: the scattering intensity exhibits a sharp and prominent peak in the intermediate X range. To account for this behavior, we have developed a model which assumes that, regardless of X, the mixed aggregates are formed at a fixed polymer-to-nanoparticle ratio. The agreement between the results and the model is excellent on the five systems. Results at different molecular weights suggest that the stoichiometry of the mixed aggregates is controlled by the electrostatic interactions between the opposite charges. The model allows to derive the molecular weight and the stoichiometry of the mixed aggregates.