On-surface self-assembly of tetratopic molecular building blocks

Equilibrium structure of a dense trimesic acid monolayer on a homogeneous solid surface: from atomistic simulation to thermodynamics

A general methodology for determining the thermodynamic characteristics of rigid organic crystals on the atomistic level is presented. The proposed approach is based on a combination of grid interpolation of the precalculated intermolecular potential and kinetic Monte Carlo simulation of the gas-crystal system with an explicit interphase. The two-phase system is stabilized in a wide range of external parameters with an imposed external potential and damping field. The damping field reduces the intermolecular potential at the edges of the crystals and turns it off in the gas phase. To determine the thermodynamic characteristics of a crystal the conditions of equality of chemical potentials in coexisting phases are used. The intermolecular pairwise potential can be calculated on the atomistic or quantum level. In the kinetic Monte Carlo simulations, a grid interpolation of the precalculated potential is performed on each iteration of the algorithm. We have applied the approach to the thermodynamic analysis of a dense monolayer of trimesic acid on a homogeneous surface. The calculated free energy and entropy for the dense "superflower" and filled chicken-wire phases obey the Gibbs-Duhem equation, which confirms the thermodynamic consistency of our approach. Using the proposed approach, we have revealed that the dense "superflower" phase becomes metastable at zero pressure and 470-500 K. Under these conditions, the filled chicken-wire structure with partially released hexagonal cages is thermodynamically favourable. The proposed approach is a potentially universal tool for the thermodynamic analysis of crystals formed by "rigid" organic molecules of any complexity on the atomistic level.

Order-Disorder Transition of Two-Dimensional Molecular Networks through a Stoichiometric Design

Materials with disordered structures may exhibit interesting properties. Metal-organic frameworks (MOFs) are a class of hybrid materials composed of metal nodes and coordinating organic linkers. Recently, there has been growing interest in MOFs with structural disorder and the investigations of amorphous structures on surfaces. Herein, we demonstrate a bottom-up method to construct disordered molecular networks on metal surfaces by selecting two organic molecule linkers with the same symmetry but different sizes for preparing two-component samples with different stoichiometric ratios. The amorphous networks are directly imaged by scanning tunneling microscopy under ultrahigh vacuum with a submolecular resolution, allowing us to quantify its degree of disorder and other structural properties. Furthermore, we resort to molecular dynamics simulations to understand the formation of the amorphous metal-organic networks. The results may advance our understanding of the mechanism of formation of monolayer molecular networks with structural disorders, facilitating the design and exploration of amorphous MOF materials with intriguing properties.

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.

Structural Quantification of the Surface-Confined Metal-Organic Precursors Simulated with the Lattice Monte Carlo Method

The diversity of surface-confined metal-organic precursor structures, which recently have been observed experimentally, poses a question of how the individual properties of a molecular building block determine those of the resulting superstructure. To answer this question, we use the Monte Carlo simulation technique to model the self-assembly of metal-organic precursors that precede the covalent polymerization of halogenated PAH isomers. For this purpose, a few representative examples of low-dimensional constructs were studied, and their basic structural features were quantified using such descriptors as the orientational order parameter, radial distribution function, and one- and two-dimensional structure factors. The obtained results demonstrated that the morphology of the precursor (and thus the subsequent polymer) could be effectively tuned by a suitable choice of molecular parameters, including size, shape, and intramolecular distribution of halogen substituents. Moreover, our theoretical investigations showed the effect of the main structural features of the precursors on the related indirect characteristics of these constructs. The results reported herein can be helpful in the custom designing and characterization of low-dimensional polymers with adjustable properties.

Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction

Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.

Monte Carlo Simulations of the Metal-Directed Self-Assembly of Y-Shaped Positional Isomers

The rational fabrication of low-dimensional materials with a well-defined topology and functions is an incredibly important aspect of nanotechnology. In particular, the on-surface synthesis (OSS) methods based on the bottom-up approach enable a facile construction of sophisticated molecular architectures unattainable by traditional methods of wet chemistry. Among such supramolecular constructs, especially interesting are the surface-supported metal–organic networks (SMONs), composed of low-coordinated metal atoms and π-aromatic bridging linkers. In this work, the lattice Monte Carlo (MC) simulation technique was used to extract the chemical information encoded in a family of Y-shaped positional isomers co-adsorbed with trivalent metal atoms on a flat metallic surface with (111) geometry. Depending on the intramolecular distribution of active centers (within the simulated molecular bricks, we observed a metal-directed self-assembly of two-dimensional (2D) openwork patterns, aperiodic mosaics, and metal–organic ladders. The obtained theoretical findings could be especially relevant for the scanning tunneling microscopy (STM) experimentalists interested in a surface-assisted construction of complex nanomaterials stabilized by directional coordination bonds.

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.

SuSMoST: Surface Science Modeling and Simulation Toolkit

We present to the scientific community the Surface Science Modeling and Simulation Toolkit (SuSMoST), which includes a number of utilities and implementations of statistical physics algorithms and models. With SuSMoST it is possible to predict or explain the structure and thermodynamic properties of adsorption layers. SuSMoST automatically builds formal graph and tensor-network models based on atomic description of adsorption complexes and helps to do ab initio calculations of interactions between adsorbed species. Using methods of various nature SuSMoST generates representative samples of adsorption layers and computes its thermodynamic quantities such as mean energy, coverage, density, and heat capacity. From these data one can plot phase diagrams of adsorption systems, assess thermal stability of self-assembled structures, simulate thermal desorption spectra, and so forth.

Theoretical Modeling of the Surface-Guided Self-Assembly of Functional Molecules

Directing the self-assembly of organic building blocks with 2D templates has been a promising method to create molecular superstructures having unique physicochemical properties. In this work the on-surface self-assembly of simple ditopic functional molecules confined inside periodic nanotemplates was modeled by means of the lattice Monte Carlo simulation method. Two types of confinement, that is honeycomb porous networks and parallel grooves of controlled diameter and width were used in the calculations. Additionally, the effect of (pro)chirality of the adsorbing molecules on the outcome of the templated self-assembly was examined. To that end, enantiopure and racemic assemblies were studied and the resulting structures were identified and classified. The obtained findings demonstrated that suitable tuning of the structural parameters of the templates enables directing the self-assembly towards linear and cyclic aggregates with controlled size. Moreover, chiral resolution of the molecular conformers using honeycomb networks with adjusted pore size was found possible. Our theoretical predictions can be helpful in designing structured surfaces to direct self-assembly and polymerization of organic functional building blocks.

Probing the supramolecular features via π–π interaction of a di-iminopyrene-di-benzo-18-crown-6-ether compound: experimental and theoretical study

Herein, we report the formation of a potential supramolecular arrangement mediated by inter- and intra-molecular interactions between di-iminopyrene-dibenzo-18-crown-6-ether molecules.

Surface-Confined Self-Assembly of Asymmetric Tetratopic Molecular Building Blocks

Surface-confined self-assembly of functional molecular building blocks has recently been widely used to create low-dimensional, also covalent, superstructures with tailorable geometry and physicochemical properties. In this contribution, using the lattice Monte Carlo simulation method, we demonstrate how the structure-property relation can be established for the 2D self-assembly of a model tetrapod molecule with reduced symmetry. To that end, a rigid functional unit comprising a few interconnected segments arranged in different tetrapod shapes was used and its self-assembly on a triangular lattice representing a (111) crystal surface was simulated. The results of our calculations show strong dependence of the structure formation on the molecular symmetry, in particular on the (pro)chiral nature of the building block. The simulations predicted the formation of unusual ordered racemic networks with unique aperiodic spatial distribution of the surface enantiomers. Molecular symmetry was also found to have significant influence on the enantiopure self-assembly which resulted in the Kagome and brickwall networks and other less ordered extended superstructures with parallelogram pores. The theoretical findings of this contribution can be relevant to designing and on-surface synthesis of molecular superstructures with predefined geometries and functions. In particular, the predicted molecular architectures can stimulate experimental efforts to fabricate and explore new nanostructures, for example graphitic, having the composition and geometry proposed in our study.