Interpretation of small-angle scattering of block copolymer/nanoparticle blends using random phase approximation

The scattering characteristics of block copolymer (BCP)/nanoparticle (NP) blend systems are analyzed in the weak segregation limit using random phase approximation (RPA). The scattering function is established and shown to adequately capture reported data of small-angle neutron scattering in poly(norbornene- b -d-norbornene dicarboxylic acid)/ Fe 3 O 4 nanoparticle blend systems over the entire small-angle range for a variety of BCP and NP compositions. Besides predicting the relevant length scales of microstructure formation, the RPA analysis reveals the increase of segregation in the BCP system upon NP addition. The insight into the thermodynamics of microstructure formation in BCP/NP blend systems that is provided by the RPA analysis should be a valuable asset for the design of BCP-based microstructured hybrid materials with predetermined structure and properties. Graphical abstract