Nanoparticles in a diblock copolymer background: The potential of mean force

We have investigated the potential of mean force between two nanoparticles that are surrounded by a symmetric diblock copolymer matrix. The hard nanoparticles are modeled as attractive to one kind of polymer. Using self-consistent-field theory (SCFT), we analyze the energy change of the system when the distance between the particles is changed and subsequently derive the potential of mean force between the particles. Above the order-disorder transition (ODT) the attractive potential of the particles for one kind of monomers leads to a lamellar structure around the particles. These density waves interfere with each other when the distance between the particles is changed, leading to separations with alternating attraction and repulsion between the particles. We further derive analytic results for the potential of mean force in the limit of a weak influence of the particles on the system using the random phase approximation for a diblock copolymer melt. These analytical results are compared with SCFT results. Below the ODT, we insert the particles in such a way that the axis connecting them is either perpendicular or parallel to the lamellar polymer structure. Using SCFT, we study the energy and structural change of the system when the particle distance is changed for these two cases.