Describing nonequilibrium soft matter with mean field game theory

Abstract

We demonstrate that combining an emerging approach to game theory with self-consistent mean field theory provides realistic treatments of diblock copolymer phase evolution. We especially examine order-order phase transformations upon quenched temperature change involving hexagonal cylinders, lamellae, and the gyroid. Our findings demonstrate that (i) the game theoretical dynamics produce realistic trajectories for the evolution of the local compositions, (ii) the predicted small-angle scattering follows experimentally observed trends, (iii) nucleation and growth is active when the system is quenched far from the critical point, and (iv) epitaxial growth is manifest. To our knowledge, the methodology presented provides the first merger of mean field game theory and statistical mechanics for soft matter systems, giving a new inroad to studying polymer dynamics.