How Implementation of Entropy in Driving Structural Ordering of Nanoparticles Relates to Assembly Kinetics: Insight...

The ability to understand and exploit entropic contributions to ordering transition is of essential importance in the design of self-assembling systems with well-controlled structures. However, much less is known about the role of assembly kinetics in entropy-driven phase behaviors. Here, by combining computer simulations and theoretical analysis, we report that the implementation of entropy in driving phase transition significantly depends on the kinetic process in the reaction-induced self-assembly of newly designed nanoparticle systems. In particular, such systems comprise binary Janus nanoparticles at the fluid-fluid interface and undergo phase transition driven by entropy and controlled by the polymerization reaction initiated from the surfaces of just one component of nanoparticles. Our simulations demonstrate that the competition between the reaction rate and the diffusive dynamics of nanoparticles governs the implementation of entropy in driving the phase transition from randomly mixed phase to intercalated phase in these interfacial nanoparticle mixtures, which thereby results in diverse kinetic pathways. At low reaction rates, the transition exhibits abrupt jump in the mixing parameter, in a similar way to first-order, equilibrium phase transition. Increasing the reaction rate diminishes the jumps until the transitions become continuous, behaving as a second-order-like phase transition, where a critical exponent, characterizing the transition, can be identified. We finally develop an analytical model of the blob theory of polymer chains to complement the simulation results and reveal essential scaling laws of the entropy-driven phase behaviors. In effect, our results allow for further opportunities to amplify the entropic contributions to the materials design via kinetic control.