Solvent determines nature of effective interactions between nanoparticles in polymer brushes

We study the effective interaction between two parallel rod-like nanoparticles in swollen and collapsed polymer brushes as a function of penetration depth by 2D self-consistent field calculations. In vertical direction, the interaction is always attractive. In lateral direction, the behavior under good and poor solvent conditions is qualitatively different. In swollen brushes (good solvent), nanoparticles always repel each other. In collapsed brushes (poor solvent), we identify two different regimes: an immersed regime, where the nanoparticles are fully surrounded by the brush, and an interfacial regime, where they are located in the interface between brush and solvent. In the immersed regime, the lateral interactions are repulsive, in agreement with previous theoretical predictions. In the interfacial regime, they are governed by the deformations of the interface and tend to be attractive. This implies that the nature of nanoparticle interactions can be manipulated by changing the solvent condition. The influence of particle size and grafting density are also briefly discussed.