DEVELOPING ORDER PARAMETERS FOR ORDER-DISORDER TRANSITIONS: FROM PARTICLES TO BLOCK COPOLYMERS

Abstract

Block copolymers self-assemble to form a variety of different 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. Some common phases that block copolymers form include the lamellar, cylinder and gyroid network. In this paper, we use molecular dynamics to simulate the growth of these phases from an isotropic liquid. A binary nanoparticle mixture model is used that allows the simulation of systems with large enough sizes for the desired phase to nucleate and grow. We develop local order parameters based on particle symmetries and geometrical constraints that can identify and track the nucleation and growth of ordered domains along the transition pathway. We put forth a framework that could be extended towards understanding the self-assembly of other bicontinuous phases such as the double diamond or plumber’s nightmare, as well as prove useful in estimating free energy barriers and nucleation rates using rare-event sampling techniques.