Polygonal tessellations as predictive models of molecular monolayers

TL;DR

This paper introduces a hierarchical geometric model based on polygonal tessellations to predict 2D molecular self-assembly patterns, offering a simpler alternative to complex computational methods.

Contribution

The authors develop a graph theory-based tessellation model that predicts molecular network patterns from molecular data, expanding the predictive toolkit for self-assembled structures.

Findings

Provides a new geometric perspective on molecular pattern formation.

Successfully applied to experimental data, predicting possible new patterns.

Extensible to other molecular systems like graphene and fullerenes.

Abstract

Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the 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.