Tensor renormalization group study of orientational ordering in simple models of adsorption monolayers

A simple lattice model of the orientational ordering in organic adsorption layers that considers the directionality of intermolecular interactions is proposed. The symmetry and the number of rotational states of the adsorbed molecule are the main parameters of the model. The model takes into account both the isotropic and directional contributions to the molecule-molecule interaction potential. Using several special cases of this model, we have shown that the tensor renormalization group (TRG) approach can be successfully used for the analysis of orientational ordering in organic adsorption layers with directed intermolecular interactions. Adsorption isotherms, potential energy, and entropy have been calculated for the model adsorption layers differing in the molecule symmetry and the number of rotational states. The calculated thermodynamic characteristics show that entropy effects play a significant role in the self-assembly of dense phases of the molecular layers. All the results obtained with the TRG have been verified by the standard Monte Carlo method. The proposed model reproduces the main features of the phase behavior of the real adsorption layers of benzoic, terephthalic, and trimesic acids on a homogeneous surface of metal single crystals and graphite.

Designing 2D covalent networks with lattice Monte Carlo simulations: precursor self-assembly

Organic synthesis reactions in the adsorbed phase have been recently an intensively studied topic in heterogeneous catalysis and material engineering. One of such processes is the Ullmann coupling in which halogenated organic monomers are transformed into covalently bonded polymeric structures. In this work, we use the lattice Monte Carlo simulation method to study the on-surface self-assembly of organometallic precursor architectures comprising tetrasubstituted naphthalene building blocks with differently distributed halogen atoms. In the coarse grained approach adopted herein the molecules and metal atoms were modeled by discrete segments, two connected and one, respectively, placed on a triangular lattice representing a (111) metallic surface. Our simulations focused on the influence of the intramolecular distribution of the substituents on the morphology of the resulting superstructures. Special attention was paid to the molecules that create porous networks characterized by long-range order. Moreover, the structural analysis of the assemblies comprising prochiral building blocks was made by running simulations for the corresponding enantiopure and racemic adsorbed systems. The obtained results demonstrated the possibility of directing the on-surface self-assembly towards networks with controllable pore shape and size. These findings can be helpful in designing covalently bonded 2D superstructures with predefined architecture and functions.

Ring structure of selected two-dimensional procrystalline lattices

Recent work has introduced the term "procrystalline" to define systems which lack translational symmetry but have an underlying high-symmetry lattice. The properties of five such two-dimensional (2D) lattices are considered in terms of the topologies of rings which may be formed from three-coordinate sites only. Parent lattices with full coordination numbers of four, five, and six are considered, with configurations generated using a Monte Carlo algorithm. The different lattices are shown to generate configurations with varied ring distributions. The different constraints imposed by the underlying lattices are discussed. Ring size distributions are obtained analytically for two of the simpler lattices considered (the square and trihexagonal nets). In all cases, the ring size distributions are compared to those obtained via a maximum entropy method. The configurations are analyzed with respect to the near-universal Lemaître curve (which connects the fraction of six-membered rings with the width of the ring size distribution) and three lattices are highlighted as rare examples of systems which generate configurations which do not map onto this curve. The assortativities are considered, which contain information on the degree of ordering of different sized rings within a given distribution. All of the systems studied show systematically greater assortativities when compared to those generated using a standard bond-switching method. Comparison is also made to two series of crystalline motifs which shown distinctive behavior in terms of both the ring size distributions and the assortativities. Procrystalline lattices are therefore shown to have fundamentally different behavior to traditional disordered and crystalline systems, indicative of the partial ordering of the underlying lattices.

Thermodynamics, EOS, and heat capacity in molecular modeling of self-assembled molecular layers

Self-assembled monolayers (SAMs) on solid surfaces represent a rapidly developed class of non-autonomous phases widely used in organic electronics, sensors, catalysis, and other applications. In many cases, the same organic molecules form various stable and metastable polymorphous structures that can transform to each other at certain parameters. A high rigidity of SAMs extremely complicates the evaluation of the chemical potential using standard methods based on thermodynamic integration. This study presents results of molecular modeling of two-dimensional structures of tripod-shaped molecules associated with the trimesic acid (TMA) molecules. A technique used here is based on a recently developed method of external fields imposed on an elongated simulation cell in the framework of a kinetic Monte Carlo algorithm. These fields are the external potential and a damping field that reduces the intermolecular potential and affects the system similar to the increase in temperature. Equations of state (EOS) for several TMA polymorphs have been obtained with the conventional Monte Carlo simulation. It was shown that, in each case, only one constant links the chemical potential obtained with the external field method and the EOS at any temperature and pressure. The heat capacities of SAMs at constant volume and pressure were also determined as functions of temperature and compressibility of the structure at given degrees of freedom. The approach can be used as a general tool for modeling and evaluation of thermodynamic properties of various rigid structures, including SAMs of functional organic molecules.

Tensor renormalization group study of hard-disk models on a triangular lattice

High accuracy and performance of the tensor renormalization group (TRG) method have been demonstrated for the model of hard disks on a triangular lattice. We considered a sequence of models with disk diameter ranging from a to 2sqrt[3]a, where a is the lattice constant. Practically, these models are good for approximate description of thermodynamics properties of molecular layers on crystal surfaces. Theoretically, it is interesting to analyze if and how this sequence converges to the continuous model of hard disks. The dependencies of the density and heat capacity on the chemical potential were calculated with TRG and transfer-matrix (TM) methods. We benchmarked accuracy and performance of the TRG method comparing it with TM method and with exact result for the model with nearest-neighbor exclusions (1NN). The TRG method demonstrates good convergence and turns out to be superior over TM with regard to considered models. Critical values of chemical potential (μ_{c}) have been computed for all models. For the model with next-nearest-neighbor exclusions (2NN) the TRG and TM produce consistent results (μ_{c}=1.75587 and μ_{c}=1.75398 correspondingly) that are also close to earlier Monte Carlo estimation by Zhang and Deng. We found that 3NN and 5NN models shows the first-order phase transition, with close values of μ_{c} (μ_{c}=4.4488 for 3NN and 4.4<μ_{c}<4.5 for 5NN). The 4NN model demonstrates continuous yet rapid phase transition with 2.65<μ_{c}<2.7.

Pressure-varying Langmuir parameters and stepped nitrogen adsorption on alumina and silica

Insights into surface structures and thermodynamics are provided for nitrogen adsorption on two nonporous alumina adsorbents and two macroporous silica adsorbents by modelling high-resolution data using the simple Langmuir isotherm equation combined with pressure-varying flexible least squares. The fitted parameters, maximum adsorption capacity and standard Gibbs energy change for each adsorbent show multiple steps that are assumed to be indicative of transitions to different complete monolayer and multilayer structures. Pressure-varying N2 cross-sectional areas for three of the adsorbents are calculated by assuming that one of the steps is the Brunauer-Emmett-Teller monolayer with molecular area 16.2 Å2. The silica with added octyldimethylsilyl groups has pressure-varying parameter profiles that differ from the other adsorbents and here the N2 cross-sectional area is assumed to be 21.3 Å2 to ensure consistency with the literature surface area. Seven monolayers and multilayers are identified across the four adsorbents, and corresponding molecular areas compare favourably with reported values. At low pressures, adsorption occurs at the strongest sites, and is localised and dependent on surface heterogeneity and topography. Up to five complete, two-dimensional lattice structures are apparent in the mid-pressure ranges. At high pressures, multilayers and liquefaction points are observed and are independent of surface composition and heterogeneity.

On-surface self-assembly of tetratopic molecular building blocks

Self-assembly of functional molecules on solid substrates has recently attracted special attention as a versatile method for the fabrication of low dimensional nanostructures with tailorable properties. In this contribution, using theoretical modeling, we demonstrate how the architecture of 2D molecular assemblies can be predicted based on the individual properties of elementary building blocks at play. To that end a model star-shaped tetratopic molecule is used and its self-assembly on a (111) surface is simulated using the lattice Monte Carlo method. Several test cases are studied in which the molecule bears terminal arm centers providing interactions with differently encoded directionality. Our theoretical results show that manipulation of the interaction directions can be an effective way to direct the self-assembly towards extended periodic superstructures (2D crystals) as well as to create assemblies characterized by a lower degree of order, including glassy overlayers and quasi one-dimensional molecular connections. The obtained structures are described and classified with respect to their main geometric parameters. A small library of the tetratopic molecules and the corresponding superstructures is provided to categorize the structure-property relationship in the modeled systems. The results of our simulations can be helpful to 2D crystal engineering and surface-confined polymerization techniques as they give hints on how to functionalize tetrapod organic building blocks which would be able to create superstructures with predefined spatial organization and range of order.

X3 synthon geometries in two-dimensional halogen-bonded 1,3,5-tris(3,5-dibromophenyl)benzene self-assembled nanoarchitectures on Au(111)-()

The self-assembly of star-shaped 1,3,5-tris(3,5-dibromophenyl)benzene molecules on Au(111)-() in a vacuum is investigated using scanning tunneling microscopy and core-level spectroscopy. Scanning tunneling microscopy shows that the molecules self-assemble into a hexagonal porous halogen-bonded nanoarchitecture. This structure is stabilized by X_3-A synthons composed of three type-II halogen-interactions (halogen-bonds). The molecules are oriented along the same direction in this arrangement. Domain boundaries are observed in the hcp region of the herringbone gold surface reconstruction. Molecules of the neighboring domains are rotated by 180°. The domain boundaries are stabilized by the formation of X_3-B synthons composed of two type-II and one type-I halogen-interactions between molecules of the neighboring domains. Core-level spectroscopy confirms the existence of two types of halogen-interactions in the organic layer. These observations show that the gold surface reconstructions can be exploited to modify the long-range supramolecular halogen-bonded self-assemblies.

Enhancing intramolecular features and identifying defects in organic and hybrid nanoarchitectures on a metal surface at room temperature using a NaCl-functionalized scanning tunneling microscopy tip

Scanning tunneling microscopy using an NaCl-functionalised tip is a powerful method to assess the morphology of two-dimensional nanoarchitectures and their local variations of electronic properties.