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

The goal of this project is to use so-called “molecular field” models – which operate with continuous fields, but still retain explicit information on the molecular structure of materials - as bridges between particle-based and field-based views on macromolecular materials. In the first funding period, we have systematically compared the properties of particle models and established molecular field models, and derived different adaptive resolution schemes that combine the two representations. Building on this, we plan to (i) develop systematic methods for deriving dynamical molecular field models from particle simulations, (ii) further optimize the dynamical adaptive resolution schemes, and (iii) apply them to interesting materials such as transient networks.

Using Copolymers to Design Tunable Stimuli-Reponsive Brushes
Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Friederike Schmid
Macromolecules 53 (13), 5326-5336 (2020);
doi:10.1021/acs.macromol.0c00674

Recently, a new design for switch sensors has been proposedthat exploits a conformational transition of end-grafted minority adsorption-active homopolymers in a monodisperse polymer brush [Klushin et al.Phys.Rev. Lett.2014,113, 068303]. The transition is sharp andfirst-order type ifthe minority chain is longer than the brush chains. However, the intrinsicnature of the system imposes a constraint on the relation between thesharpness of the transition and the height of the free energy barriercontrolling the transition kinetics: The sharper the transition, the slower thetransition time. Here we demonstrate that adopting diblock copolymerswith the adsorption-active block anchored at the substrate as the minoritychains allows a much moreflexible control of the three main characteristicsof the transition, i.e., the transition point, its sharpness, and the barrier height. In particular, the barrier height can be greatly reducedwithout compromising the sharpness. We develop an analytical theory that predicts the relevant characteristics of the transition andverify it with SCF calculations and Monte Carlo simulations. We also demonstrate that from a thermodynamic point of view thetransition characteristics of a diblock copolymer are equivalent to those of the active block alone in a modified brush with the samegrafting density and reduced length.

Dynamic Self-Consistent Field Approach for Studying Kinetic Processes in Multiblock Copolymer Melts
Friederike Schmid, Bing Li
Polymers 12 (10), 2205 (2020);
URL: https://www.mdpi.com/2073-4360/12/10/2205
doi:10.3390/polym12102205

The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in these approaches is the mobility function, which describes the effect of chain connectivity on the nonlocal response of monomers to thermodynamic driving fields. In a recent study, one of us and coworkers have developed a method to systematically construct mobility functions from reference fine-grained simulations. Here we focus on melts of linear chains in the Rouse regime and show how the mobility functions can be calculated semi-analytically for multiblock copolymers with arbitrary sequences without resorting to simulations. In this context, an accurate approximate expression for the single-chain dynamic structure factor is derived. Several limiting regimes are discussed. Then we apply the resulting density functional theory to study ordering processes in a two-length scale block copolymer system after instantaneous quenches into the ordered phase. Different dynamical regimes in the ordering process are identified: at early times, the ordering on short scales dominates; at late times, the ordering on larger scales takes over. For large quench depths, the system does not necessarily relax into the true equilibrium state. Our density functional approach could be used for the computer-assisted design of quenching protocols in order to create novel nonequilibrium materials

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);
doi:10.1021/acs.macromol.0c00130

We propose and compare different strategies to constructdynamic density functional theories (DDFTs) for inhomogeneouspolymer systems close to equilibrium from microscopic simulationtrajectories. We focus on the systematic construction of the mobilitycoefficient,Λ(r,r′), which relates the thermodynamic driving force onmonomers at positionr′to the motion of monomers at positionr.Afirstapproach based on the Green−Kubo formalism turns out to beimpractical because of a severe plateau problem. Instead, we propose toextract the mobility coefficient from an effective characteristic relaxationtime of the single chain dynamic structure factor. To test our approach, we study the kinetics of ordering and disordering in diblockcopolymer melts. The DDFT results are in very good agreement with the data from correspondingfine-grained simulations

Using Copolymers to Design Tunable Stimuli-Reponsive Brushes
Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Friederike Schmid
Macromolecules 53 (13), 5326-5336 (2020);
doi:10.1021/acs.macromol.0c00674

Recently, a new design for switch sensors has been proposed that exploits a conformational transition of end-grafted minority adsorption-active homopolymers in a monodisperse polymer brush [Klushin et al. Phys. Rev. Lett.2014, 113, 068303]. The transition is sharp and first-order type if the minority chain is longer than the brush chains. However, the intrinsic nature of the system imposes a constraint on the relation between the sharpness of the transition and the height of the free energy barrier controlling the transition kinetics: The sharper the transition, the slower the transition time. Here we demonstrate that adopting diblock copolymers with the adsorption-active block anchored at the substrate as the minority chains allows a much more flexible control of the three main characteristics of the transition, i.e., the transition point, its sharpness, and the barrier height. In particular, the barrier height can be greatly reduced without compromising the sharpness. We develop an analytical theory that predicts the relevant characteristics of the transition and verify it with SCF calculations and Monte Carlo simulations. We also demonstrate that from a thermodynamic point of view the transition characteristics of a diblock copolymer are equivalent to those of the active block alone in a modified brush with the same grafting density and reduced length.

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);
doi:10.1021/acs.macromol.9b01985

Using self-consistentfield theory, we investigate thestretching-induced microphase separation in an irreversibly cross-linkedpolymer network composed of diblock copolymer chains and estimate itsshear modulus. The topology of the network isfixed to a planar square lattice.The monomer density, the distribution of cross-links, and the free energy ofthe system are calculated. Wefind that the system develops circular domainsat equilibrium, which may merge to lamellae upon compression or stretching.The lamellae are oriented perpendicular to the stretching direction. Cross-links are localized, but their distribution may be anisotropic. For asymmetricstrands, the distributions of different type of cross-links differ from eachother, indicating that the cross-linkfluctuations are inhomogeneous. Thestress is evaluated from the derivative of the free energy of stretched systemswith respect to the deformation in the stretching direction. Using theelasticity theory of isotropic solids allows us to estimate the shear modulus.Wefind that the shear modulus increases if the networkfluctuations are inhomogeneous. Ourfindings may provide guidance forthe design of stiffer soft matter materials.

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);
doi:10.1021/acs.macromol.8b02361

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);
doi:10.1103/physrevmaterials.3.026002

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);
doi:10.1063/1.5013346

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);
doi:10.1002/adfm.201800745

Dynamic Density Functional Theories for Inhomogeneous Polymer Systems Compared to Brownian Dynamics Simulations
Shuanhu Qi, Friederike Schmid
Macromolecules 50 (24), 9831-9845 (2017);
doi:10.1021/acs.macromol.7b02017

Hybrid particle-continuum simulations coupling Brownian dynamics and local dynamic density functional theory
Shuanhu Qi, Friederike Schmid
Soft Matter 13 (43), 7938-7947 (2017);
doi:10.1039/c7sm01749a

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);
doi:10.1016/j.polymer.2017.07.057

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);
doi:10.1021/acs.macromol.6b02684

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);
doi:10.1039/c6sm02252a

Numerical reduction of self-consistent field models of macromolecular systems
A. Disterhoft, T. Raasch, F. Schmid
Proc. Appl. Math. Mech. 16, 915-916 (2016);
doi:10.1002/pamm.201610446

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);
doi:10.1140/epjst/e2016-60096-8

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);
doi:10.1021/acs.macromol.5b00563

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);
doi:10.1088/1367-2630/15/12/125009

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