Computation of Free Energies of Cubic Bicontinuous Phases for Blends of Diblock Copolymer and Selective Homopolymer

Abstract

Cubic bicontinuous phases like the double gyroid (G), double diamond (D), and plumber’s nightmare (P) are of great practical interest for many emerging applications requiring highly regular nanoscale networks or porous materials. Such phases can be formed from A–B diblock copolymers by the addition of A-type homopolymer over a range of compositions and relative chain lengths. Particle-based molecular simulations were used to delineate the phase diagram in a region where self-consistent field theory predicts the presence of a G–D–P triple point. Since the simulation box size must be commensurate with the morphology-specific 3D unit cell size (which is not known a priori), accurate free energy estimates are required for a range of box sizes, particularly when multiple competing phases can occur at the conditions of interest. A variant of thermodynamic integration was implemented to obtain such free energies (and hence identify the stable phases and their optimal box sizes) by tracing a reversible path conne...