Developing Local Order Parameters for Order–Disorder Transitions From Particles to Block Copolymers: Methodological Framework
Block copolymers self-assemble to form a variety of phases with highly regular patterns, depending on the microscopic ordering of molecules. Paramount to understanding and controlling this “order” is to have good “order parameters”—variables that can be used to track the changes occurring in the system as it transitions from disorder to order. In this paper, molecular dynamics are used to simulate the growth of lamella, cylinder, and gyroid phases from an isotropic liquid using as testbed a binary nanoparticle mixture model. The chosen model produces minimalistic versions of the basic repeat units of the phases of interest so that the formation of numerous such units can be efficiently simulated. Because phase domains are typically one- or two-particle-thick, local order parameters are developed based on the correlation of symmetries between a particle and its neighbors and used to identify and track the formation and growth of specific geometric motifs along the transition pathway. The proposed order par...