Finding free energy barriers for complex mesophases

Block copolymers are known to self-assemble into a multitude of phases with vastly different geometries. Amongst these, the double gyroid holds a special place due to its highly symmetric, complex and ordered network that imparts it with many useful properties. In order to tap into the unique properties of the double gyroid phase, we need to be able to design and control its formation. This requires a deeper understanding of the nucleation and growth mechanisms through which it self-assembles. In this paper we attempt to evaluate the nucleation pathway for the disorder to gyroid phase transition, simulated using molecular / dissipative particle dynamics, that to the best of our knowledge still remains largely unknown. We make use of a local order parameter framework developed in an earlier study and put forth multiple approaches to evaluate the free energy barriers for the transition, such as the mean first passage time, hybrid monte carlo, and other novel variants of the umbrella sampling technique.