The interaction of hybrid nanoparticles inserted within surfactant bilayers

We determine by small-angle x-ray scattering the structure factor of hydrophobic particles inserted within lamellar surfactant phases for various particle concentrations. The data are then analyzed by numerically solving the Ornstein-Zernicke equation, taking into account both the intra- and interlayer interactions. We find that particles within the same layer repel each other and that the interaction potential (taken as independent of the concentration) has a contact value of 2.2 k$_{\text{B}}$T and a range of about 10 {\AA}. If the amplitude is allowed to decrease with increasing concentration, the contact value in the dilute limit is about 5 k$_{\text{B}}$T for a similar range.