Bottom-up construction of dynamic density functional theories for inhomogeneous polymer systems from microscopic simulations

TL;DR

This paper develops methods to construct dynamic density functional theories for inhomogeneous polymer systems using microscopic simulations, focusing on accurately determining the mobility coefficient to predict system dynamics.

Contribution

It introduces a novel approach to extract the mobility coefficient from relaxation times, improving the construction of DDFTs for polymer systems.

Findings

DDFT predictions agree well with fine-grained simulations.

Green-Kubo based approach is impractical due to plateau issues.

Effective relaxation time method successfully characterizes polymer dynamics.

Abstract

We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of the mobility coefficient, $\Lambda(r,r')$, which relates the thermodynamic driving force on monomers at position $r'$ to the motion of monomers at position $r$. A first approach based on the Green-Kubo formalism turns out to be impractical because of a severe plateau problem. Instead, we propose to extract the mobility coefficient from an effective characteristic relaxation time of the single chain dynamic structure factor. To test our approach, we study the kinetics of ordering and disordering in diblock copolymer melts. The DDFT results are in very good agreement with the data from corresponding fine-grained simulations.