Ordered Assemblies of Triangular-Shaped Molecules with Strongly Interacting Vertices: Phase Diagrams for Honeycomb and Zigzag Structures on Triangular Lattice

Abstract

The model for ordering of triangular-shaped molecules with strongly interacting vertices is proposed and solved by the Monte Carlo method. The model accounts for three main intermolecular interactions and three states (two main orientations and a vacancy state) of a molecule on triangular lattice, the situation which is encountered in self-assembly of TMA molecules characterized by strongly directional H-bonding. Distinguishing the main "tip-to-tip" interaction, we calculate the phase diagrams for the honeycomb and frustrated honeycomb structures and demonstrate how these structures shrink and vanish with gradual increase of two other ("side-to-side" and "tip-to-side") interactions. We study the effect of frustration on the phase diagram, since the frustrated phase is obtained at the Ising limit of the model. We also demonstrate how the inclusion of longer-range interactions leads to substitution of the frustrated phase by the zigzag structure. Finally, we obtain the phase diagram with two experimentally found TMA structures (honeycomb and zigzag) and discuss the conditions of their existence by comparison with the experimental results.

Phase behaviour of self-assembled monolayers controlled by tuning physisorbed and chemisorbed states: A lattice-model view

“…Lattice models have been shown in numerous instances to express a rich phase behaviour, qualitatively reproducing the experimental observations for systems such as dicarboxylic acids [8] or trimesic acid [9,10] on Au(111), anthraquinone on Cu(111) [11], tripod molecules at the liquid/HOPG interface [12] or porphyrin on Au(111) [13]. Studies of multiple adsorption states include lattice gas models that simulated different adsorption orientations, such as a monolayer of vertically standing diatomic heteronuclear molecules with two distinct adsorption states [14], or homodimers allowed to assume either perpendicular or parallel orientations with respect to the supporting surface [15].…”

Two-Dimensional Self-Assembly of a Symmetry-Reduced Tricarboxylic Acid

“…27,36 Monte Carlo simulations predicted the stability of this zigzag phase for a model system composed of triangular molecules with strongly interacting vertices. 58 By dissolving TMA in 1-phenyloctane, Ha et al demonstrated that solovophobic effects drive the higher-symmetry molecule to assemble into a dense dimerically associated zigzag structure, where O−H···O cyclic dimerization occupies only two of the carboxylic groups on each molecule and the third is involved in a single O−H···O bond, maximizing the surface molecular density. 25 Although the experimental and calculated geometries for the strong bonding along the zigzag chain agree, the DFT-predicted geometry deviates from our observed geometry along the direction governed by the weak bonds.…”

Phase transition properties of the Bell-Lavis model

“…To obtain densitytemperature phase diagrams or predict new ordering motifs, the statistical models of phase transitions might also be used 13,[19][20][21][22] as an alternative or a supporting simulation. Since the triangular molecules are symmetric and their layout is planar, they possess a three-fold symmetry with respect to 120 • rotation.…”