Framework to track Order-Disorder Transitions - From Particles to Block Copolymers

Block copolymers self-assemble into a variety of phases with highly regular patterns, depending on the ordering of molecules. Paramount to understanding and controlling this “order” is to have good “order parameters”, variables used to track changes in the system as it transitions from disorder to order. Molecular dynamics is used to simulate the growth of minimalistic versions of the lamella, cylinder and gyroid phases from an isotropic liquid using a binary nanoparticle mixture model. Based on the correlation of bonding symmetries between a particle and its neighbors, local order parameters are developed and used to track the formation and growth of specific geometric motifs along the transition pathway. They are then modified to study similar transitions in coarse-grained models of polymers and oligomers, namely the assembly of a linear symmetric diblock copolymer into the lamellar, and a branched bolaamphiphile into the single diamond phase. The framework also finds use in the estimation of free-energy barriers for such ordering transitions. These calculations are yet to be reported in literature for such systems and require the use of novel variants of nucleus-size pinning and umbrella sampling techniques.