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Publikationen 2021

Active droploids
Jens Grauer, Falko Schmidt, Jesús Pineda, Benjamin Midtvedt, Hartmut Löwen, Giovanni Volpe, Benno Liebchen
Nature Communications 12 (1), (2021);
doi:10.1038/s41467-021-26319-3

Existence, regularity and weak-strong uniqueness for the three-dimensional Peterlin viscoelastic model
Brunk, A., Lu, Y. & Lukáčová-Medviďová, M.
Commun. Math. Sci. , (2021 );
https://www.intlpress.com/site/pub/pages/journals/items/cms/_home/acceptedpapers/index.php

In this paper we analyze three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach we prove the existence of weak solutions. Further, combining parabolic regularity with the relative energy method we derive a conditional weak-strong uniqueness result.

A multi-scale method for complex flows of non-Newtonian fluids
F. Tedeschi, G.G. Giusteri, L. Yelash, M. Lukáčová-Medvid’ova
Mathematics in Engineering, (2021);

We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modeling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids.

Shear thinning in oligomer melts - molecular origins and applications
R. Datta, L. Yelash, F. Schmid, F. Kummer, M. Oberlack, M. Lukáčová-Medvid'ová, P. Virnau
Polymers 13 (16), 2806 (2021);
doi:https://doi.org/10.3390/polym13162806

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving–Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows.

Systematic derivation of hydrodynamic equations for viscoelastic phase separation
Dominic Spiller, Aaron Brunk, Oliver Habrich, Herbert Egger, Mária Lukáčová-Medvid'ová and Burkhard Dünweg
Journal of Physics: Condensed Matter 33 (36), 364001 (2021);
URL: https://iopscience.iop.org/article/10.1088/1361-648X/ac0d17
doi:https://doi.org/10.1088/1361-648X/ac0d17

We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the second law of thermodynamics. The model is therefore fully consistent with both equilibrium and non-equilibrium thermodynamics. The derivation proceeds in two steps: firstly, we derive an extended model comprising two scalar and four vector fields, such that inertial dynamics of the macromolecules and of the relative motion of the two fluids is taken into account. In the second step, we eliminate these inertial contributions and, as a replacement, introduce phenomenological dissipative terms, which can be modeled easily by taking into account the principles of non-equilibrium thermodynamics. The final simplified model comprises the momentum conservation equation, which includes both interfacial and elastic stresses, a convection–diffusion equation where interfacial and elastic contributions occur as well, and a suitably convected relaxation equation for the end-to-end vector field. In contrast to the traditional two-scale description that is used to derive rheological equations of motion, we here treat the hydrodynamic and the macromolecular degrees of freedom on the same basis. Nevertheless, the resulting model is fairly similar, though not fully identical, to models that have been discussed previously. Notably, we find a rheological constitutive equation that differs from the standard Oldroyd-B model. Within the framework of kinetic theory, this difference may be traced back to a different underlying statistical-mechanical ensemble that is used for averaging the stress. To what extent the model is able to reproduce the full phenomenology of viscoelastic phase separation is presently an open question, which shall be investigated in the future.

Simulation of Elastomers by Slip-Spring Dissipative Particle Dynamics
J. Schneider, F. Fleck, H. A. Karimi-Varzaneh, F. Müller-Plathe
Macromolecules 54, 5155 (2021);
doi:10.1021/acs.macromol.1c00567

We study elastomeric networks using dissipativeparticle-dynamics simulations. This soft-core method gives access to mesoscopic time and length scales and is potentially capable to study complex systems such as network defects and gels, but the unmodified method underestimates topological interactions and can only model phantom networks. In this work, we study the capability of slip springs to recover topological effects of network strands. We show that slip springs with a restricted mobility restore the topological contributions of trapped entanglements. Uniaxial strain experiments give access to the cross-link and entanglement contribution to the shear modulus of a slip-spring model network. We find these contributions to coincide with those reported for comparable hard-core Kremer−Grest networks (Gula et al. Macromolecules 2020, 53, 6907−6927). For network strands longer than the chains’ entanglement length, the contribution of slip springs to the shear modulus equals the plateau modulus of the un-crosslinked precursor melt. However, a constant number of slip springs overestimates the shear modulus for high cross-link densities. To probe their applicability, we successfully compare our simulations with experimental polyisoprene rubbers: a network obtained by parameter-free cross-linking of a simulated polyisoprene melt reproduces the viscoelastic moduli of experimental rubbers.

The Role of the Envelope Protein in the Stability of a Coronavirus Model Membrane against an Ethanolic Disinfectant
S. Das, M.K. Meinel, Z. Wu, F. Müller-Plathe
J. Chem. Phys., 245101 (2021);
doi:10.1063/5.0055331

Ethanol is highly effective against various enveloped viruses and can disable the virus by disintegrating the protective envelope surrounding it. The interactions between coronavirus envelope(E) protein and their membrane environment play key roles in the stability and function of the viral envelope. By using molecular dynamics simulation, we explore the underlying mechanism of ethanol-induced disruption of a model coronavirus membrane and, in detail, interactions of the E-protein and lipids. We model the membrane bilayer as PSM (N-palmitoyl-sphingomyelin) and POPC (1-palmitoyl 2-oleoylphosphatidylcholine) lipids and the coronavirus E-protein. The study reveals that ethanol causes an increase in the lateral area of the bilayer along with the thinning of the bilayer membrane and orientational disordering of lipid tails. Ethanol resides at the head-tail region of the membrane and enhances bilayer permeability. We found an envelope-protein-mediated increase in the ordering of lipid tails. Our simulations also provide important insights into the orientation of envelope protein in a model membrane environment. At ∼ 25 mol % of ethanol in the surrounding ethanol-water phase, we observe disintegration of the lipid bilayer and the dislocation of the E-protein from the membrane environment.

Computing oscillatory solutions of the Euler system via K-convergence
Eduard Feireisl, Mária Lukáčová–Medvid’ová, Bangwei She, Yue Wang
Mathematical Models and Methods in Applied Sciences 31 (03), 537-576 (2021);
doi:10.1142/s0218202521500123

We develop a method to compute effectively the Young measures associated to sequences of numerical solutions of the compressible Euler system. Our approach is based on the concept of K-convergence adapted to sequences of parameterized measures. The convergence is strong in space and time (a.e. pointwise or in certain L^q spaces) whereas the measures converge narrowly or in the Wasserstein distance to the corresponding limit.

Density-functional-theory approach to the Hamiltonian adaptive resolution simulation method
L A Baptista, R C Dutta, M Sevilla, M Heidari, R Potestio, K Kremer, R Cortes-Huerto
Journal of Physics: Condensed Matter 33 (18), 184003 (2021);
doi:10.1088/1361-648x/abed1d

Dynamic coarse-graining of polymer systems using mobility functions
Bing Li, Kostas Daoulas, Friederike Schmid
Journal of Physics: Condensed Matter 33 (19), 194004 (2021);
doi:10.1088/1361-648x/abed1b

Analysis of a viscoelastic phase separation model
Aaron Brunk, Burkhard Dünweg, Herbert Egger, Oliver Habrich, Mária Lukáčová-Medvid'ová, Dominic Spiller
Journal of Physics: Condensed Matter 33 (23), 234002 (2021);
doi:10.1088/1361-648x/abeb13

Dynamical properties across different coarse-grained models for ionic liquids
Joseph F Rudzinski, Sebastian Kloth, Svenja Wörner, Tamisra Pal, Kurt Kremer, Tristan Bereau, Michael Vogel
Journal of Physics: Condensed Matter 33 (22), 224001 (2021);
doi:10.1088/1361-648x/abe6e1

Coarse-grained model of a nanoscale-segregated ionic liquid for simulations of low-temperature structure and dynamics
Sebastian Kloth, Marvin P Bernhardt, Nico F A van der Vegt, Michael Vogel
Journal of Physics: Condensed Matter 33 (20), 204002 (2021);
doi:10.1088/1361-648x/abe606

Cross-correlation corrected friction in (generalized) Langevin models
Viktor Klippenstein, Nico F. A. van der Vegt
The Journal of Chemical Physics 154 (19), 191102 (2021);
doi:10.1063/5.0049324

An interplay of excluded-volume and polymer–(co)solvent attractive interactions regulates polymer collapse in mixed solvents
Swaminath Bharadwaj, Divya Nayar, Cahit Dalgicdir, Nico F. A. van der Vegt
The Journal of Chemical Physics 154 (13), 134903 (2021);
doi:10.1063/5.0046746

Commensurability between Element Symmetry and the Number of Skyrmions Governing Skyrmion Diffusion in Confined Geometries
Chengkun Song, Nico Kerber, Jan Rothörl, Yuqing Ge, Klaus Raab, Boris Seng, Maarten A. Brems, Florian Dittrich, Robert M. Reeve, Jianbo Wang, Qingfang Liu, Peter Virnau, Mathias Kläui
Advanced Functional Materials 31 (19), 2010739 (2021);
doi:10.1002/adfm.202010739

A Second-Order Finite Element Method with Mass Lumping for Maxwell's Equations on Tetrahedra
Herbert Egger, Bogdan Radu
SIAM Journal on Numerical Analysis 59 (2), 864-885 (2021);
doi:10.1137/20m1318912

Role of pH in the synthesis and growth of gold nanoparticles using L-Asparagine: A combined experimental and simulation study
Ricardo Baez, Luis A. Baptista, Samuel Ntim, Paulraj Manidurai, Shirly Espinoza, Charusheela Ramanan, Robinson Cortes-Huerto, Marialore Sulpizi
Journal of Physics: Condensed Matter, (2021);
doi:10.1088/1361-648x/abf6e3

Ultra-coarse-graining of homopolymers in inhomogeneous systems
Fabian Berressem, Christoph Scherer, Denis Andrienko, Arash Nikoubashman
Journal of Physics: Condensed Matter 33 (25), 254002 (2021);
doi:10.1088/1361-648x/abf6e2

Adversarial reverse mapping of condensed-phase molecular structures: Chemical transferability
Marc Stieffenhofer, Tristan Bereau, Michael Wand
APL Materials 9 (3), 031107 (2021);
doi:10.1063/5.0039102

Fluctuation–dissipation relations far from equilibrium: a case study
Gerhard Jung, Friederike Schmid
Soft Matter 17 (26), 6413-6425 (2021);
doi:10.1039/d1sm00521a

Computing inelastic neutron scattering spectra from molecular dynamics trajectories
Thomas F. Harrelson, Makena Dettmann, Christoph Scherer, Denis Andrienko, Adam J. Moulé, Roland Faller
Scientific Reports 11 (1), (2021);
doi:10.1038/s41598-021-86771-5

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);
doi:10.1021/acs.macromol.0c02095

Introducing Memory in Coarse-Grained Molecular Simulations
Viktor Klippenstein, Madhusmita Tripathy, Gerhard Jung, Friederike Schmid, Nico F. A. van der Vegt
The Journal of Physical Chemistry B 125 (19), 4931-4954 (2021);
doi:10.1021/acs.jpcb.1c01120

Sequence-Engineering Polyethylene–Polypropylene Copolymers with High Thermal Conductivity Using a Molecular-Dynamics-Based Genetic Algorithm
Tianhang Zhou, Zhenghao Wu, Hari Krishna Chilukoti, Florian Müller-Plathe
Journal of Chemical Theory and Computation 17 (6), 3772-3782 (2021);
doi:10.1021/acs.jctc.1c00134

Multistep and Runge–Kutta convolution quadrature methods for coupled dynamical systems
H. Egger, K. Schmidt, V. Shashkov
Journal of Computational and Applied Mathematics 387, 112618 (2021);
doi:10.1016/j.cam.2019.112618

Mathematical analysis of some iterative methods for the reconstruction of memory kernels
Martin Hanke
ETNA - Electronic Transactions on Numerical Analysis 54, 483-498 (2021);
doi:10.1553/etna_vol54s483

Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations
N Bockius, J Shea, G Jung, F Schmid, M Hanke
Journal of Physics: Condensed Matter 33 (21), 214003 (2021);
doi:10.1088/1361-648x/abe6df

Probability theory of active suspensions
B. Deußen, M. Oberlack, Y. Wang
Physics of Fluids 33 (6), 061902 (2021);
doi:10.1063/5.0047227

Vorticity Determines the Force on Bodies Immersed in Active Fluids
Thomas Speck, Ashreya Jayaram
Physical Review Letters 126 (13), (2021);
doi:10.1103/physrevlett.126.138002

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by—but far away from—the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a nonvanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We demonstrate that vorticity is localized close to the body and to points at which the local curvature changes, enabling the rational design of particle shapes with desired propulsion properties.

High-order simulation scheme for active particles driven by stress boundary conditions
B Deußen, A Jayaram, F Kummer, Y Wang, T Speck, M Oberlack
Journal of Physics: Condensed Matter 33 (24), 244004 (2021);
doi:10.1088/1361-648x/abf8cf

We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.

Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators
Luca Tubiana, Hideki Kobayashi, Raffaello Potestio, Burkhard Duenweg, Kurt Kremer, Peter Virnau, Kostas Daoulas
Journal of Physics: Condensed Matter, (2021);
doi:10.1088/1361-648x/abf20c

BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks
F. Berressem and A. Nikoubashman
J. Chem. Phys. 154, 124123 (2021);
URL: https://aip.scitation.org/doi/10.1063/5.0045441
doi:10.1063/5.0045441

Numerical methods for compressible fluid flows
E. Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She
Springer, Modeling, Simulation and Applications , Vol. 20 (2021);

This is book is devoted to the numerical analysis of compressible fluids in the spirit of the celebrated Lax equivalence theorem. The text is aimed at graduate students in mathematics and fluid dynamics, researchers in applied mathematics, numerical analysis and scientific computing, and engineers and physicists. The book contains original theoretical material based on a new approach to generalized solutions (dissipative or measure-valued solutions). The concept of a weak-strong uniqueness principle in the class of generalized solutions is used to prove the convergence of various numerical methods. The problem of oscillatory solutions is solved by an original adaptation of the method of K-convergence. An effective method of computing the Young measures is presented. Theoretical results are illustrated by a series of numerical experiments. Applications of these concepts are to be expected in other problems of fluid mechanics and related fields.

Force probe simulations using an adaptive resolution scheme
Marco Oestereich, J Gauss, Gregor Diezemann
Journal of Physics: Condensed Matter, (2021);
doi:10.1088/1361-648x/abed18

Iterative integral equation methods for structural coarse-graining
Marvin P. Bernhardt, Martin Hanke, Nico F. A. van der Vegt
The Journal of Chemical Physics 154 (8), 084118 (2021);
doi:10.1063/5.0038633

Combination of Hybrid Particle-Field Molecular Dynamics and Slip-Springs for the Efficient Simulation of Coarse-Grained Polymer Models: Static and Dynamic Properties of Polystyrene Melts
Zhenghao Wu, Giuseppe Milano, and Florian Müller-Plathe
J. Chem. Theor. Comput. 17, 474–487 (2021);
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.

Atomistic hybrid particle-field molecular dynamics combined with slip-springs: Restoring entangled dynamics to simulations of polymer melts
Z. Wu, A. Kalogirou, A. De Nicola, G. Milano, F. Müller-Plathe
J. Comput. Chem. 42, 6-18 (2021);
doi: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.

Knotting Behaviour of Polymer Chains in the Melt State for Soft-core Models with and without Slip-springs
Zhenghao Wu, Simon N. A. Alberti, Jurek Schneider, Florian Müller-Plathe
, J. Phys.: Condens. Matter , (2021);
doi:10.1088/1361-648X/abef25

We analyse the knotting behaviour of linear polymer melts in two types of soft-core models, namely dissipative-particle dynamics and hybrid-particle-field models, as well as their variants with slip-springs which are added to recover entangled polymer dynamics. The probability to form knots is found drastically higher in the hybrid-particle-field model compared to its parent hard-core molecular dynamics model. By comparing the knottedness in dissipative-particle dynamics and hybrid-particle-field models with and without slip-springs, we find the impact of slip-springs on the knotting properties to be negligible. As a dynamic property, we measure the characteristic time of knot formation and destruction, and find it to be (i) of the same order as single-monomer motion and (ii) independent of the chain length in all soft-core models. Knots are therefore formed and destroyed predominantly by the unphysical chain crossing. This work demonstrates that the addition of slip-springs does not alter the knotting behaviour, and it provides a general understanding of knotted structures in these two soft-core models of polymer melts.

Mechanisms of Nucleation and Solid−Solid-Phase Transitions in Triblock Janus Assemblies
Hossein Eslami, Ali Gharibi and Florian Müller-Plathe
Journal of Chemical Theory and Computation 17 (3), 1742−1754 (2021);
URL: https://dx.doi.org/10.1021/acs.jctc.0c01080
doi:10.1021/acs.jctc.0c01080

A model, including the chemical details of core nanoparticles as well as explicit surface charges and hydrophobic patches, of triblock Janus particles is employed to simulate nucleation and solid−solid phase transitions in two-dimensional layers. An explicit solvent and a substrate are included in the model, and hydrodynamic and many-body interactions were taken into account within many-body dissipative particle dynamics simulation. In order not to impose a mechanism a priori, we performed free (unbiased) simulations, leaving the system the freedom to choose its own pathways. In agreement with the experiment and previous biased simulations, a two-step mechanism for the nucleation of a kagome lattice from solution was detected. However, a distinct feature of the present unbiased versus biased simulations is that multiple nuclei emerge from the solution; upon their growth, the aligned and misaligned facets at the grain boundaries are introduced into the system. The liquid-like particles trapped between the neighboring nuclei connect them together. A mismatch in the symmetry planes of neighboring nuclei hinders the growth of less stable (smaller) nuclei. Unification of such nuclei at the grain boundaries of misaligned facets obeys a two-step mechanism: melting of the smaller nuclei, followed by subsequent nucleation of liquid-like particles at the interface of bigger neighboring nuclei. Besides, multiple postcritical nuclei are formed in the simulation box; the growth of some of which stops due to introduction of a strain in the system. Such an incomplete nucleation/growth mechanism is in complete agreement with the recent experiments. The solid−solid (hexagonal-to-kagome) phase transition, at weak superheatings, obeys a two-step mechanism: a slower step (formation of a liquid droplet), followed by a faster step (nucleation of kagome from the liquid droplet).

Wall slip and bulk yielding in soft particle suspensions
Gerhard Jung, Suzanne M. Fielding
Journal of Rheology 65 (2), 199-212 (2021);
Publication resulting from a PhD secondment of Gerhard Jung (TRR student) in Durham in 2018
doi:10.1122/8.0000171

We simulate a dense athermal suspension of soft particles sheared between hard walls of a prescribed roughness profile, fully accounting for the fluid mechanics of the solvent between the particles and for the solid mechanics of changes in the particle shapes. We, thus, capture the widely observed rheological phenomenon of wall slip. For imposed stresses below the material’s bulk yield stress, we show the slip to be dominated by a thin solvent layer of high shear at the wall. At higher stresses, it is augmented by an additional contribution from the fluidization of the first few layers of particles near the wall. By systematically varying the wall roughness, we quantify a suppression of slip with increasing roughness. We also elucidate the effects of slip on the dynamics of yielding following the imposition of constant shear stress, characterizing the timescales at which bulk yielding arises and at which slip first sets in

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