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Polygonal tessellations as predictive models of molecular monolayers

Krisztina Regős1, Rémy Pawlak2, Xing Wang3, Ernst Meyer2, Silvio Decurtins3, Gábor Domokos1, Kostya S. Novoselov4, Shi-Xia Liu3, Ulrich Aschauer3*

1 Department of Morphology and Geometric Modeling, and ELKH-BME Morphodynamics Research Group, Budapest University of Technology and Economics H-1111 Budapest, Hungary

2 Department of Physics, University of Basel 4056 Basel, Switzerland

3 Department of Chemistry, Biochemistry and Pharmacy, University of Bern, 3012 Bern, Switzerland

4 Institute for Functional Intelligent Materials, National University of Singapore, 117544, Singapore

* Corresponding authors emails: ulrich.aschauer@unibe.ch
DOI10.24435/materialscloud:e4-h1 [version v1]

Publication date: Mar 22, 2023

How to cite this record

Krisztina Regős, Rémy Pawlak, Xing Wang, Ernst Meyer, Silvio Decurtins, Gábor Domokos, Kostya S. Novoselov, Shi-Xia Liu, Ulrich Aschauer, Polygonal tessellations as predictive models of molecular monolayers, Materials Cloud Archive 2023.48 (2023), doi: 10.24435/materialscloud:e4-h1.


Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large variety of complex patterns even in two dimensions (2D). Prediction of pattern formation for 2D molecular networks is extremely important, though very challenging, and so far, relied on computationally involved approaches such as density functional theory, classical molecular dynamics, Monte Carlo, or machine learning. Such methods, however, do not guarantee that all possible patterns will be considered and often rely on intuition. Here we introduce a much simpler, though rigorous, hierarchical geometric model founded on the mean-field theory of 2D polygonal tessellations to predict extended network patterns based on molecular-level information. Based on graph theory, this approach yields pattern classification and pattern prediction within well-defined ranges. When applied to existing experimental data, our model provides an entirely new view of self-assembled molecular patterns, leading to interesting predictions on admissible patterns and potential additional phases. While developed for hydrogen-bonded systems, an extension to covalently bonded graphene-derived materials or 3D structures such as fullerenes is possible, significantly opening the range of potential future applications.

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Molecular self assembly Tesselation 2D monolayer

Version history:

2023.48 (version v1) [This version] Mar 22, 2023 DOI10.24435/materialscloud:e4-h1