Two packing pathways of Janus-like homopolymer-grafted nanoparticles at fluid-fluid interfaces

Polymer-grafted nanoparticles (PGNPs) assembled at fluid-fluid interfaces significantly reduce interfacial tension and effectively stabilize multiphase liquid systems. Understanding and actively controlling the packing of these PGNPs is of significant fundamental interest for the interfacial behavior of nanoparticles and of interest in soft matter physics. Here, we investigate the packing of Janus-like homopolymer-grafted nanoparticles at fluid-fluid interfaces using molecular dynamics simulations and umbrella sampling methods. For bare nanoparticles at interfaces, where enthalpic interactions dominate, interface-mediated attractions drive nanoparticle aggregation. This results in locally ordered hexagonal clusters with high average order parameters. As the packing fraction increases, the system evolves from small, locally hexagonal aggregates to a globally ordered hexagonal phase (path I). This pathway contrasts sharply with the behavior of purely repulsive particles in two dimensions, which undergo an entropy-driven, sharp disorder-to-order transition (path II). For Janus-like PGNPs at interfaces, the packing behavior is governed by the competition between two factors: (i) interface-mediated attractive interactions (enthalpic contribution) and (ii) steric repulsion between grafted polymer chains (entropic contribution). Increasing either grafting density or grafted chain lengths enhances the entropic contribution and repulsive interactions, causing a shift in the dominant packing mechanism from enthalpy-driven (path I) to entropy-driven (path II). This competition induces a transition between ordering pathways. Notably, at a chain length of N = 15 and grafting number Z = 8, the entropic effects completely suppress hexagonal ordering. We attribute this suppression to the significant interface deformation by the PGNPs, which maximizes the system's entropy by disrupting the close-packing structure. Our study provides novel insights into the interfacial packing of PGNPs and reveals how competition between enthalpy and entropy drives transitions between distinct ordering pathways.