No abstract

Supramolecular coordination self-assembly on the solid surface offers great possibilities for creating nanostructures and thin films with unique physicochemical properties. In this work, we present a simple lattice model based on competitive coordination motifs that enables predictions of the phase behavior and thermal stability of metal−organic networks consisting of 1,3,5-tris(pyridyl)benzene (TPyB) and transition metals on the Au(111) surface. The main parameter of the model is the ratio between the energies of the two-fold and three-fold metal−ligand coordination defined by the type of the metal center. The model reveals a homologous series of flower phases that differ in the metal/ligand composition. Existing ranges of the phases in terms of the chemical potential (or partial pressure) of the components are determined by the mentioned ratio. The closer the value of this parameter is to unity, the more diverse is the phase behavior of the metal−organic network. This ratio is always greater than unity and increases in the following series Ag ≤ Cu < Ni < Co < Fe. The results of the Monte Carlo and tensor renormalization group calculations well reproduce the published experimental data on the self-assembly of metal−organic networks based on the TPyB linker. As an example, we have calculated the phase diagram of the TPyB−Cu/Au(111) adsorption layer and have estimated thermal stability of the phases. The honeycomb, flowerlike, and triangular close-packed phases are ascertained to be stable at room temperature. The remaining nanostructures appearing on the scanning tunneling microscopy images of this layer are apparently metastable.

This study presents a method of external fields to determine thermodynamic characteristics of rigid crystalline phases in the framework of a kinetic Monte Carlo algorithm. The method is based on modeling of the gas−crystal system with explicit accounting for the interface and uses the condition of equal chemical potentials in coexisting phases. Two non-uniform fields are imposed on the gas phase. The first one is the usual external potential, while the other is a proposed-here damping field reducing intermolecular potentials up to zero. This makes the coexisting gas always ideal at any desired density under controlled crystal pressure. It opens an efficient way to reliably determine the chemical potential of very rigid solids. The effect of changing the damping field along the simulation cell is similar to that produced by the temperature gradient, but the condition of equilibrium is not violated. The approach was tested on the model of a self-assembled layer of trimesic acid at specified values of temperature and pressure. In all cases, thermodynamic consistency of the approach was convincingly confirmed. The proposed approach is a promising tool for modeling rigid crystalline structures such as self-assembled monolayers formed by relatively large functional organic molecules.

A general methodology for determining the thermodynamic characteristics of orientationally ordered rigid crystals is presented. The basic problem here is associated with a very small flux of primary molecules that are released from a narrow interface and carry main information on thermodynamic properties of the crystal. The proposed approach is based on the kinetic Monte Carlo simulation of the gas−crystal system with an external "damping field" that reduces the intermolecular potential at the crystal edges and switches it off in the gas phase. Such a technique increases the primary molecular flux by several orders of magnitude, which is crucial for accurate determination of thermodynamic functions. In this study, we applied the approach to the thermodynamic analysis of the trimesic acid monolayer, explicitly accounting for hydrogen bonds, the dispersion, and electrostatic potentials. We considered equations of state, heat capacities, Helmholtz free energies, and entropies of three polymorphous structures: honeycomb, flower-like, and hexagonally close-packed structures in a wide range of temperatures and pressures. The calculated free energy and entropy excellently obey the Gibbs−Duhem equation, which confirms the thermodynamic consistency of our approach. The role of hydrogen bonds in the stability of different phases, as well as the condition of phase transitions, was also considered.

A technique has been developed for calculating the thermodynamic characteristics of rigid self-assembled organic adsorption layers and the parameters of polymorphic transitions using two types of external fields and the kinetic Monte Carlo method.