Project C1: Using molecular fields to bridge between particle and continuum representations of macromolecular systems

In this project, we explore the potential of so-called “molecular field” theories to bridge between particle-based and continuum representations of macromolecular materials. Regarding static equilibrium properties, they canbe linked to particle models via the well-established self-consistent field theory, a sophisticated density functional theory for polymers, and extensions thereof. Our goal is to design systematic mapping procedures for dynamic properties, i.e., devising dynamic density functionals (DDFs) of comparable quality.

The work in the second funding period was motivated by a finding at the end of the first funding period, where we had identified severe shortcomings of the previously available DDF models. The central quantities in these DDF models are nonlocal mobility functions describing the response of the monomer current to a spatially varying field. We have devised a bottom-up method to construct these mobility functions from known microscopic trajectories or from a known expression for the single chain structure factor. We have applied this approach to ordering/disordering kinetics in inhomogeneous copolymer melts and shown that the resulting DDF models can reproduce the results of particle-based simulations at a quantitative level. Currently, we are investigating weakly and strongly entangled melts, using microscopic input data from other TRR groups (e.g., data from project A8). As a side project, we have also developed a dynamic mapping scheme from microscopic to extremely coarse-grained particle-based polymer models which is based on our mobility functions.

In the coming funding period, we plan to extend these studies in three directions. First (i), we will apply our approach to a variety of other problems, e.g., mixtures of components with different mobilities, composition-dependent mobilities, and partially crosslinked polymers. Second (ii), we will explore different ways to introduce inertia in the DDF model in order to incorporate stress and model hydrodynamic effects. Third (iii), we will investigate systems far from equilibrium where polymers cannot relax to equilibrium, and where hence a description in terms of a free energy density functional is no longer justified. Combining (ii) and (iii), we will then evaluate the connection between the dynamic density functional approaches and viscoelastic models for polymer flow such as those studied in project C3.

Understanding and Modeling Polymers: The Challenge of Multiple Scales
F. Schmid
ACS Polymers Au (2022)
see publication

Dynamic coarse-graining of polymer systems using mobility functions
Bing Li, Kostas Daoulas, Friederike Schmid
Journal of Physics: Condensed Matter 33 (19), 194004 (2021)
see publication

Adsorption Active Diblock Copolymers as Universal Agents for Unusual Barrier-Free Transitions in Stimuli-Responsive Brushes
Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Friederike Schmid
Macromolecules 54 (6), 2592-2603 (2021)
see publication

Defects and defect engineering in Soft Matter
Amir Jangizehi, Friederike Schmid, Pol Besenius, Kurt Kremer, Sebastian Seiffert
Soft Matter 16 (48), 10809-10859 (2020)
see publication

Dynamic Self-Consistent Field Approach for Studying Kinetic Processes in Multiblock Copolymer Melts
Friederike Schmid, Bing Li
Polymers 12 (10), 2205 (2020)
see publication

Bottom-up Construction of Dynamic Density Functional Theories for Inhomogeneous Polymer Systems from Microscopic Simulations
Sriteja Mantha, Shuanhu Qi, Friederike Schmid
Macromolecules 53 (9), 3409-3423 (2020)
see publication

Using Copolymers to Design Tunable Stimuli-Reponsive Brushes
Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Friederike Schmid
Macromolecules 53 (13), 5326-5336 (2020)
see publication

Shear Modulus of an Irreversible Diblock Copolymer Network from Self-Consistent Field Theory
Shuanhu Qi, Jiajia Zhou, Friederike Schmid
Macromolecules 52 (24), 9569-9577 (2019)
see publication

Polydispersity Effects on Interpenetration in Compressed Brushes
Leonid I. Klushin, Alexander M. Skvortsov, Shuanhu Qi, Torsten Kreer, Friederike Schmid
Macromolecules 52 (4), 1810-1820 (2019)
see publication

How ill-defined constituents produce well-defined nanoparticles: Effect of polymer dispersity on the uniformity of copolymeric micelles
Sriteja Mantha, Shuanhu Qi, Matthias Barz, Friederike Schmid
Physical Review Materials 3 (2), (2019)
see publication

Phase transitions in single macromolecules: Loop-stretch transition versus loop adsorption transition in end-grafted polymer chains
Shuangshuang Zhang, Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Dadong Yan, Friederike Schmid
The Journal of Chemical Physics 148 (4), 044903 (2018)
see publication

Tuning Transition Properties of Stimuli-Responsive Brushes by Polydispersity
Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Mingjie Liu, Jiajia Zhou, Friederike Schmid
Advanced Functional Materials 28 (49), 1800745 (2018)
see publication

Dynamic Density Functional Theories for Inhomogeneous Polymer Systems Compared to Brownian Dynamics Simulations
Shuanhu Qi, Friederike Schmid
Macromolecules 50 (24), 9831-9845 (2017)
see publication

Hybrid particle-continuum simulations coupling Brownian dynamics and local dynamic density functional theory
Shuanhu Qi, Friederike Schmid
Soft Matter 13 (43), 7938-7947 (2017)
see publication

Simulating copolymeric nanoparticle assembly in the co-solvent method: How mixing rates control final particle sizes and morphologies
Simon Keßler, Klaus Drese, Friederike Schmid
Polymer 126, 9-18 (2017)
see publication

Self-Assembly of Polymeric Particles in Poiseuille Flow: A Hybrid Lattice Boltzmann/External Potential Dynamics Simulation Study
Johannes Heuser, G. J. Agur Sevink, Friederike Schmid
Macromolecules 50 (11), 4474-4490 (2017)
see publication

Combining cell-based hydrodynamics with hybrid particle-field simulations: efficient and realistic simulation of structuring dynamics
G. J. A. Sevink, F. Schmid, T. Kawakatsu, G. Milano
Soft Matter 13 (8), 1594-1623 (2017)
see publication

Numerical reduction of self-consistent field models of macromolecular systems
A. Disterhoft, T. Raasch, F. Schmid
Proceedings in Applied Mathematics and Mechanics 16, 915-916 (2016)
see publication

A hybrid particle-continuum resolution method and its application to a homopolymer solution
S. Qi, H. Behringer, T. Raasch, F. Schmid
The European Physical Journal Special Topics 225 (8-9), 1527-1549 (2016)
see publication

Stimuli-Responsive Brushes with Active Minority Components: Monte Carlo Study and Analytical Theory
Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Alexey A. Polotsky, Friederike Schmid
Macromolecules 48 (11), 3775-3787 (2015)
see publication

Using field theory to construct hybrid particle–continuum simulation schemes with adaptive resolution for soft matter systems
Shuanhu Qi, Hans Behringer, Friederike Schmid
New Journal of Physics 15 (12), 125009 (2013)
see publication