Project B6: Topological validation of coarse-grained polymer models
Computational studies of polymer-based materials on large length and time scales require mesoscopic models: drastically coarse-grained descriptions where non-bonded potentials between interacting particles are on the order of the thermal energy. Such “soft” models are either used as “stand alone” descriptions or as elements of strategies, where the microscopic description of the material is recovered through sequential backmapping in a hierarchy of mesoscopic models. In the previous funding period, we focused on using single-chain topology ─ polymer knots ─ to validate mesoscopic models and hierarchical backmapping schemes for bulk high-molecular-weight polymer melts.
We made three important findings: A) We demonstrated that polymer knots are, in general, multiscale objects, i.e. they simultaneously depend on microscopic and medium-scale features. As such, they cannot be always accurately described by mesoscopic models. B) Nevertheless, we identified conditions when mesoscopic models can quantitatively reproduce knotting properties of underlying microscopically-resolved melts. This happens when the Kuhn length substantially exceeds characteristic scales of excluded volume interactions. C) We demonstrated that two different state-of-the-art algorithms — configurational assembly and a hierarchical backmapping strategy — used for equilibrating high-molecular-weight bulk polymer melts deliver samples with consistent knotting behaviour.
Building upon these results we will expand our research to polymer films. Combining extensive microscopic and mesoscopic simulations of melts confined by solid or vapour interfaces, we will understand the behaviour of knots in these systems and corroborate theoretical concepts of films. Conformational, topological, and structural properties in our “brute-force” microscopic simulations will be extensively compared with their counterparts in films generated with a novel hierarchical backmapping strategy.
Apart from studying films, we will modify the configuration assembly and backmapping algorithms to prepare bulk melts with different amounts of knotted chains. Analysing these samples will provide insights whether (and if yes how) knots affect material properties.
The response of polymer knots to symmetry-breaking phenomena is a largely unexplored theoretical question. In the new funding period, we will use special mesoscopic models with anisotropic potentials to explore the behaviour of knotting properties during two basic symmetry-breaking events: the isotropic-nematic transition in main-chain polymer liquid crystals and emergence of chirality in helical polymers.
Publications
Polymer knots in thin films: Thickness dependence, local effects, and stiffness
M.P. Schmitt, H. Meyer, Peter Virnau
Arxiv preprint
Link: https://doi.org/10.48550/arXiv.2605.02644
Influence of topology on rheological properties of polymer ring melts
Ranajay Datta, Peter Virnau
The Journal of Chemical Physics 162, 094902 (2025)
Link: https://doi.org/10.1063/5.0250414
Knots in polymer molecules under Poiseuille flow
M.P. Schmitt, A. Milchev
Foundations 5, 28 (2025)
Link: https://doi.org/10.3390/foundations5030028
Can Dynamic Helical Polymers be Reduced to Linear Chains of Spins? Non-Local Effects from Polymer Self-Avoidance
Keerti Chauhan, Marcus Müller, Kostas Ch. Daoulas
Macromolecules 58, 5408-5420 (2025)
Link: https://doi.org/10.1021/acs.macromol.4c03197
Effect of simple shear on knotted polymer coils and globules
Andrey Milchev, Maurice P. Schmitt, Peter Virnau
The Journal of Chemical Physics 161, 224905 (2024)
Link: https://doi.org/10.1063/5.0236904
Topological comparison of flexible and semiflexible chains in polymer
melts with θ-chains
Maurice P. Schmitt, Sarah Wettermann, Dostas Ch. Daoulas, Hendrik Meyer, Peter Virnau
The Journal of Chemical Physics 161, 144904 (2024)
Link: https://doi.org/10.1063/5.0228826
Can polymer helicity affect topological chirality of polymer knots?
Yani Zhao, Jan Rothörl, Pol Besenius, Peter Virnau, Kostas Ch. Daoulas
ACS Macro Letters 12, 234-240 (2023)
Link: https://doi.org/10.1021/acsmacrolett.2c00600
Viscosity of flexible and semiflexible ring melts: Molecular origins and flow-induced segregation
Ranajay Datta, Fabian Berressem, Friederike Schmid, Arash Nikoubashman, Peter Virnau
Macromolecules 56, 7247-7255 (2023)
Link: https://doi.org/10.1021/acs.macromol.3c01046
Influence of ionic conditions on knotting in a coarse-grained model
Sarah Wettermann, Ranajay Datta, Peter Virnau
Frontiers in Chemistry 10, 1096014 (2023)
Link: https://doi.org/10.3389/fchem.2022.1096014
Knot formation of dsDNA pushed inside a nannochannel
Jan Rothörl, Sarah Wettermann, Peter Virnau, Ankiet Bhattacharya
Scientific Reports 12, 5342 (2022)
Link: https://doi.org/10.1038/s41598-022-09242-5
AlphaFold predicts the most complex protein knot and composite protein knots
Brems, Maarten A. and Runkel, Robert and Yeates, Todd O. and Virnau, Peter
Protein Science 31, e4380 (2022)
Link: https://doi.org/10.1002/pro.4380
Dynamic coarse-graining of polymer systems using mobility functions
Bing Li, Kostas Daoulas, Friederike Schmid
Journal of Physics: Condensed Matter 33 (19), 194004 (2021)
Link: https://doi.org/10.1088/1361-648X/abed1b
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)
Link: https://doi.org/10.1088/1361-648x/abf20c
A minimal Gō-model for rebuilding whole genome structures from haploid single-cell Hi-C data
S. Wettermann, M. Brems, J.T. Siebert, G.T. Vu, T.J. Stevens, P. Virnau
Computational Materials Science 173, 109178 (2020)
Link: https://doi.org/10.1016/j.commatsci.2019.109178
Can Soft Models Describe Polymer Knots?
Jianrui Zhang, Hendrik Meyer, Peter Virnau, Kostas Ch. Daoulas
Macromolecules 53 (23), 10475-10486 (2020)
Link: https://doi.org/10.1021/acs.macromol.0c02079
Generic Model for Lamellar Self-Assembly in Conjugated Polymers: Linking Mesoscopic Morphology and Charge Transport in P3HT
Cristina Greco, Anton Melnyk, Kurt Kremer, Denis Andrienko, Kostas Ch. Daoulas
Macromolecules 52 (3), 968-981 (2019)
Link: https://doi.org/10.1021/acs.macromol.8b01863
Mapping onto Ideal Chains Overestimates Self-Entanglements in Polymer Melts
Hendrik Meyer, Eric Horwath, Peter Virnau
ACS Macro Letters 7 (6), 757-761 (2018)
Link: https://doi.org/10.1021/acsmacrolett.8b00210