Connecting structure evolution and chain diffusion in dense polymeric systems using dynamical self-consistent field theory
We explore the role of chain diffusion in the structure formation of dense, inhomogeneous polymeric systems, in the first application to polymers of our recently-developed dynamical self-consistent field theory [1, 2]. Our approach enables us to study large length and time scales in these dense systems, while remaining connected, in a self-consistent manner, to the dynamics of our microscopic model for the many-body interacting problem. Our theory is highly flexible, can be modified to describe different polymeric systems, and can even be extended to applications beyond polymers, in the broader field of classical soft matter. We describe the numerical implementation of our technique, and characterize the sources of numerical error and the presence of finite chain-length effects. We apply the theory to the problem of spinodal decomposition in the binary homopolymer blend, and show that the theory captures the physics of spinodal decomposition, through our analysis of the early-time growth of composition fluctuations and the late-time coarsening of domains. The late-time scaling regime, characteristic of spinodal decomposition, sets in and a single growing length-scale L(t) emerges, describing the domain sizes, which satisfies the Lifshitz- Slyozov-Wagner power law L(t) ~ t^1/3. We then construct a theoretical framework in which the chain self-diffusion in ordered phases of the unentangled diblock copolymer melt can be explored systematically. The chain dynamics in the lamellar (LAM), cylindrical (HEX), spherical (BCC) and gyroid (GYR) phases exhibit distinct diffusive behaviours corresponding to diffusion parallel to the domain interfaces (free diffusion, independent of segregation strength) and suppressed diffusion perpendicular to the interfaces (hopping diffusion, with a segregation strength dependence), leading to an anisotropy in diffusivity for the lamellar and cylindrical phases that is in agreement with the literature. In the gyroid phase, our diffusion measurements are consistent with a network tortuosity value of 1.72, close to the literature value of 1.5. Finally, we measure the chain centre-of-mass diffusion coefficients during a phase transformation from metastable LAM to stable HEX over long times. This demonstrates the ability of our theory to simultaneously track the dynamics of individual chains (short time-scales) and simulate large-scale structure evolution (long time-scales).