Incompatible interactions between different constituents of inhomogeneous polymer systems causes them to assemble into ordered morphologies. These assembled morphologies have found applications as thermoplastic elastomers, materials for drug delivery and release, gas capture, water purification, energy conversion, and also in soft lithography. Consequently, comprehending the relation between the molecular features of polymers and the ordered morphologies formed by them has been a subject of active investigation for a long time. So far, various scattering and reflectometry techniques have been employed to study the kinetic pathways leading to order − order and order−disorder transitions in block copolymer systems. However, the dynamics in inhomogeneous polymer systems involves relaxation processes occurring over multiple length and time scales. As a result, finding an experimental technique that can capture the dynamics over the entire spectrum of length and time scales is an extremely daunting task. Currently, Dynamic density functional theory (DDFT) or the dynamic self-consistent field theory have been promoted as a theoretical alternative to study the polymer dynamics on the relevant mesoscopic length and time scales. DDFT has significantly advanced current knowledge regarding polymer dynamics; however, it suffers from the problem that DDFT models are typically constructed in an ad hoc manner.
Recent publications have also revealed that the particular choice of DDFT model has a crucial influence on the results. Where so-called “local” models tend to overestimate the speed of structure formation, other “non-local” models tend to underestimate it, also the pathways of structure formation are affected. Therefore, it is pivotal that the shortfalls of DDFT be addressed. On this account, researchers at the Johannes Gutenberg University of Mainz in Germany: Dr. Sriteja Mantha and Professor Friederike Schmid, in collaboration with Dr. Shuanhu Qi at Beihang University in China explored two physically motivated bottom up construction schemes for determining DDFT mobility functions Λ (r, r′) from microscopic simulations. Their work is currently published in the research journal, Macromolecules.
In their approach, the research team proposed and compared different strategies to construct DDFTs for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. In particular, they focused on the systematic construction of the mobility coefficient, Λ(r,r′), which relates the thermodynamic driving force on monomers at position r′ to the motion of monomers at position r.
Surprisingly, a first approach that was based on the Green−Kubo formalism turned out to be impractical because of a severe plateau problem. As a result, the team proposed to extract the mobility coefficient from an effective characteristic relaxation time of the single chain dynamic structure factor. To test their approach, they studied the kinetics of ordering and disordering in diblock copolymer melts, and obtained excellent agreement between DDFT calculations and microscopic simulations.
In summary, the study presented the development of a systematic bottom-up coarse-graining strategies for constructing nonlocal mobility functions Λ̂(q) in DDFT models for polymeric systems. Their goal was to extract the mobility functions from trajectories of fine-grained, microscopic simulations. As such, they explored two physically motivated approaches. Remarkably, the DDFT results were in very good agreement with the data from corresponding fine-grained simulations. In a statement to Advances in Engineering, Professor Friederike Schmid, the corresponding author, said their work showed a way how to systematically construct dynamic field-based models for polymeric systems, which capture both the global dynamics and the relaxation due to local rearrangements of the chain at the relevant length scales.
Sriteja Mantha, Shuanhu Qi, Friederike Schmid. Bottom-up Construction of Dynamic Density Functional Theories for Inhomogeneous Polymer Systems from Microscopic Simulations. Macromolecules 2020, volume 53, page 3409−3423.