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Publications 2020

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

Convergence of finite volume schemes for the Euler equations via dissipative measure--valued solutions
E. Feireisl, M. Lukáčová-Medvid’ová, H. Mizerová
Found Comput Math 20, 923-966 (2020);
doi:10.1007/s10208-019-09433-z

The Cauchy problem for the complete Euler system is in general ill-posed in the class of admissible (entropy producing) weak solutions. This suggests that there might be sequences of approximate solutions that develop fine-scale oscillations. Accordingly, the concept of measure-valued solution that captures possible oscillations is more suitable for analysis. We study the convergence of a class of entropy stable finite volume schemes for the barotropic and complete compressible Euler equations in the multidimensional case. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measure-valued solution of the Euler system. Here dissipative means that a suitable form of the second law of thermodynamics is incorporated in the definition of the measure-valued solutions. In particular, using the recently established weak-strong uniqueness principle, we show that the numerical solutions converge pointwise to the regular solution of the limit systems at least on the lifespan of the latter.

A finite volume scheme for the Euler system inspired by the two velocities approach
E. Feireisl, M. Lukacova-Medvidova, H. Mizerova
Num. Math. 144 (89-132), (2020);
doi:10.1007/s00211-019-01078-y

We propose a new finite volume scheme for the Euler system of gas dynamics motivated by the model proposed by H. Brenner. Numerical viscosity imposed through upwinding acts on the velocity field rather than on the convected quantities. The resulting numerical method enjoys the crucial properties of the Euler system, in particular positivity of the approximate density and pressure and the minimal entropy principle. In addition, the approximate solutions generate a dissipative measure-valued solutions of the limit system. In particular, the numerical solutions converge to the smooth solution of the system as long as the latter exists.

K-convergence as a new tool in numerical analysis
E.Feireisl, M. Lukacova-Medvidova, H. Mizerova
IMA J. Num. Anal. 40, 2227–2255 (2020);
doi:10.1093/imanum/drz045

We adapt the concept of K-convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions of the limit continuous problem possess minimal regularity. We apply the abstract theory to a finite volume method for the isentropic Euler system describing the motion of a compressible inviscid fluid. The result can be seen as a nonlinear version of the fundamental Lax equivalence theorem.

On the convergence of a finite volume method for the Navier–Stokes–Fourier system
E.Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She
IMA J. Num. Anal. , (2020);
C5 Project
doi:10.1093/imanum/draa060

We study convergence of a finite volume scheme for the Navier-Stokes-Fourier system describing the motion of compressible viscous and heat conducting fluids. The numerical flux uses upwinding with an additional numerical diffusion of order O(h^{ε+1}), 0<ε<1. The approximate solutions are piecewise constant functions with respect to the underlying mesh. We show that any uniformly bounded sequence of numerical solutions converges unconditionally to the solution of the Navier-Stokes-Fourier system. In particular, the existence of the solution to the Navier-Stokes-Fourier system is not a priori assumed.

Combination of Hybrid Particle-Field Molecular Dynamics and SlipSprings for the Efficient Simulation of Coarse-Grained Polymer Models: Static and Dynamic Properties of Polystyrene Melts
Zhenghao Wu, Giuseppe Milano, Florian Müller-Plathe
Journal of Chemical Theory and Computation, (2020);
doi:10.1021/acs.jctc.0c00954

A quantitative prediction of polymer entangled dynamics based on molecular simulation is a grand challenge in contemporary computational material science. The drastic increase of relaxation time and viscosity in high molecular-weight polymeric fluids essentially limits the usage of classic molecular dynamics simulation. Here, we demonstrate a systematic coarse-graining approach for modeling entangled polymers under the slip-spring particle-field scheme. Specifically, a frequency-controlled slip-spring model, a hybrid particle-field model and a coarse-grained model of polystyrene melts are combined into a hybrid simulation technique. Via a rigorous parameterization strategy to determine the parameters in slip-springs from existing experimental or simulation data, we show that the reptation behavior is clearly observed in multiple characteristics of polymer dynamics: mean-square displacements, diffusion coefficients, reorientational relaxation and Rouse mode analysis, consistent with the predictions of the tube theory. All dynamical properties of the slip-spring particle-field models are in good agreement with classic molecular dynamics models. Our work provides an efficient and practical approach to establish chemical-specific coarse-grained models for predicting polymer entangled dynamics.

How Alcoholic Disinfectants Affect Coronavirus Model Membranes: Membrane Fluidity, Permeability, and Disintegration
Hossein Eslami, Shubhadip Das, Tianhang Zhou, and Florian Müller-Plathe
J. Phys. Chem. B 124 (46), 10374–10385 (2020);
URL: https://pubs.acs.org/doi/abs/10.1021/acs.jpcb.0c08296
doi:10.1021/acs.jpcb.0c08296

Atomistic molecular dynamics simulations have been carried out with a view to investigating the stability of the SARS-CoV-2 exterior membrane with respect to two common disinfectants, namely, aqueous solutions of ethanol and n-propanol. We used dipalmitoylphosphatidylcholine (DPPC) as a model membrane material and did simulations on both gel and liquid crystalline phases of membrane surrounded by aqueous solutions of varying alcohol concentrations (up to 17.5 mol %). While a moderate effect of alcohol on the gel phase of membrane is observed, its liquid crystalline phase is shown to be influenced dramatically by either alcohol. Our results show that aqueous solutions of only 5 and 10 mol % alcohol already have significant weakening effects on the membrane. The effects of n-propanol are always stronger than those of ethanol. The membrane changes its structure, when exposed to disinfectant solutions; uptake of alcohol causes it to swell laterally but to shrink vertically. At the same time, the orientational order of lipid tails decreases significantly. Metadynamics and grand-canonical ensemble simulations were done to calculate the free-energy profiles for permeation of alcohol and alcohol/water solubility in the DPPC. We found that the free-energy barrier to permeation of the DPPC liquid crystalline phase by all permeants is significantly lowered by alcohol uptake. At a disinfectant concentration of 10 mol %, it becomes insignificant enough to allow almost free passage of the disinfectant to the inside of the virus to cause damage there. It should be noted that the disinfectant also causes the barrier for water permeation to drop. Furthermore, the shrinking of the membrane thickness shortens the gap needed to be crossed by penetrants from outside the virus into its core. The lateral swelling also increases the average distance between head groups, which is a secondary barrier to membrane penetration, and hence further increases the penetration by disinfectants. At alcohol concentrations in the disinfectant solution above 15 mol %, we reliably observe disintegration of the DPPC membrane in its liquid crystalline phase.

Supramolecular Packing Drives Morphological Transitions of Charged Surfactant Micelles
Ken Schäfer, Hima Bindu Kolli, Mikkel Killingmoe Christensen, Sigbjørn Løland Bore, Gregor Diezemann, Jürgen Gauss, Giuseppe Milano, Reidar Lund, Michele Cascella
Angewandte Chemie International Edition 59 (42), 18591-18598 (2020);
doi:10.1002/anie.202004522

The shape and size of self-assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long-range interactions. Combin- ing small-angle X-ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry breaking of the irreducible building blocks, with the formation of transient surfactant dimers mediated by the counterions that promote the stabili- zation of cylindrical instead of spherical micelles. The present model is of general applicability and can be extended to all systems controlled by the presence of mobile charges.

Force-dependent folding pathways in mechanically interlocked calixarene dimers via atomistic force quench simulations
Ken Schäfer, Gregor Diezemann
Molecular Physics 118 (19-20), e1743886 (2020);
doi:10.1080/00268976.2020.1743886

Single-molecule force spectroscopy and molecular simulations are well-established techniques to study the mechanical unfolding of supramolecular complexes in various fields of biomolecular physics. In the present study, we investigate the details of the force-dependent folding transition of a well-studied model system, a calix[4]arene catenane dimer, using atomistic force quench simu- lations. This protocol allows us to reach a range of much smaller forces than possible with the more common force ramp simulations where the force is changed with a constant velocity. We find that the folding pathway changes its character as a function of external force. For small forces (on the order of 50 pN), the folding transition occurs via the transition to a metastable intermediate structure in about 30% of the simulations. We characterise the structure of this intermediate and demonstrate its relevance by considering the averaged potential of mean force of the system as a function of a well-defined reaction coordinate. When the force increases, the importance of the intermediate diminishes and for high external forces (500 pN), our results can be interpreted in terms of a simple two-state model, that has also been used in earlier simulations on the same system.

Atomistic hybrid particle‐field molecular dynamics combined with slip‐springs: Restoring entangled dynamics to simulations of polymer melts
Zhenghao Wu, Andreas Kalogirou, Antonio De Nicola, Giuseppe Milano, Florian Müller‐Plathe
Journal of Computational Chemistry, (2020);
doi:https://doi.org/10.1002/jcc.26428

In hybrid particle‐field (hPF) simulations (J. Chem. Phys., 2009 130, 214106), the entangled dynamics of polymer melts is lost due to chain crossability. Chains cross, because the field‐treatment of the nonbonded interactions makes them effectively soft‐core. We introduce a multi‐chain slip‐spring model (J. Chem. Phys., 2013 138, 104907) into the hPF scheme to mimic the topological constraints of entanglements. The structure of the polymer chains is consistent with that of regular molecular dynamics simulations and is not affected by the introduction of slip‐springs. Although slight deviations are seen at short times, dynamical properties such as mean‐square displacements and reorientational relaxation times are in good agreement with traditional molecular dynamics simulations and theoretical predictions at long times.

Why Do Elastin-Like Polypeptides Possibly Have Different Solvation Behaviors in Water–Ethanol and Water–Urea Mixtures?
Yani Zhao, Manjesh K. Singh, Kurt Kremer, Robinson Cortes-Huerto, Debashish Mukherji
Macromolecules 53 (6), 2101-2110 (2020);
doi:10.1021/acs.macromol.9b02123

Investigating the Conformational Ensembles of Intrinsically Disordered Proteins with a Simple Physics-Based Model
Yani Zhao, Robinson Cortes-Huerto, Kurt Kremer, Joseph F. Rudzinski
The Journal of Physical Chemistry B 124 (20), 4097-4113 (2020);
doi:10.1021/acs.jpcb.0c01949

Open-boundary Hamiltonian adaptive resolution. From grand canonical to non-equilibrium molecular dynamics simulations
Maziar Heidari, Kurt Kremer, Ramin Golestanian, Raffaello Potestio, Robinson Cortes-Huerto
The Journal of Chemical Physics 152 (19), 194104 (2020);
doi:10.1063/1.5143268

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.

Supramolecular Packing Drives Morphological Transitions of Charged Surfactant Micelles
Ken Schäfer, Hima Bindu Kolli, Mikkel Killingmoe Christensen, Sigbjørn Løland Bore, Gregor Diezemann, Jürgen Gauss, Giuseppe Milano, Reidar Lund, Michele Cascella
Angewandte Chemie International Edition, (2020);
doi:10.1002/anie.202004522

The shape and size of self‐assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long‐range interactions. Combining small‐angle X‐ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry breaking of the irreducible building blocks, with the formation of transient surfactant dimers mediated by the counterions that promote the stabilization of cylindrical instead of spherical micelles. The present model is of general applicability and can be extended to all systems controlled by the presence of mobile charges.

Kernel-Based Machine Learning for Efficient Simulations of Molecular Liquids
Christoph Scherer, René Scheid, Denis Andrienko, Tristan Bereau
Journal of Chemical Theory and Computation 16 (5), 3194-3204 (2020);
doi:10.1021/acs.jctc.9b01256

The Grignard Reaction – Unraveling a Chemical Puzzle
Raphael Mathias Peltzer, Jürgen Gauss, Odile Eisenstein, Michele Cascella
Journal of the American Chemical Society 142 (6), 2984-2994 (2020);
doi:10.1021/jacs.9b11829

More than 100 years since its discovery, the mechanism of the Grignard reaction remains unresolved. Ambiguities arise from the concomitant presence of multiple organomagnesium species and the competing mechanisms involving either nucleophilic addition or the formation of radical intermediates. To shed light on this topic, quantum-chemical calculations and ab initio molecular dynamics simulations are used to study the reaction of CH3MgCl in tetrahydrofuran with acetaldehyde and fluorenone as prototypical reagents. All organomagnesium species coexisting in solution due to the Schlenk equilibrium are found to be competent reagents for the nucleophilic pathway. The range of activation energies displayed by all of these compounds is relatively small. The most reactive species are a dinuclear Mg complex in which the substrate and the nucleophile initially bind to different Mg centers and the mononuclear dimethyl magnesium. The radical reaction, which requires the homolytic cleavage of the Mg–CH3 bond, cannot occur unless a substrate with a low-lying π*(CO) orbital coordinates the Mg center. This rationalizes why a radical mechanism is detected only in the presence of substrates with a low reduction potential. This feature, in turn, does not necessarily favor the nucleophilic addition, as shown for the reaction with fluorenone. The solvent needs to be considered as a reactant for both the nucleophilic and the radical reactions, and its dynamics is essential for representing the energy profile. The similar reactivity of several species in fast equilibrium implies that the reaction does not occur via a single process but by an ensemble of parallel reactions.

A generalized Newton iteration for computing the solution of the inverse Henderson problem
Fabrice Delbary, Martin Hanke, Dmitry Ivanizki
Inverse Problems in Science and Engineering, 1-25 (2020);
doi:10.1080/17415977.2019.1710504

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