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.

The statistical three-state model is proposed to describe the ordering of triangular TMA molecules into flower phases. The model is solved on a rescaled triangular lattice, assuming following intermolecular interactions: exclusion of any molecules on nearest neighbor sites, triangular trio H-bonding interactions for molecules of the same orientation on next-nearest neighbor sites, and dimeric H-bonding interactions for molecules of different ("tip-to-tip") orientations on third-nearest neighbor sites. The model allows us to obtain the analytical solution for the ground state phase diagram with all homologous series of flower phases included, starting with the honeycomb phase (n=1) and ending with the superflower structure (n=∞). Monte Carlo simulations are used to obtain the thermodynamical properties of this model. It is found that phase transitions from disordered to any of the flower phases (except n=1) undergo via intermediate correlated triangular domains structure. The transition from the disordered phase to the intermediate phase is, most likely, of the first order, while the transition from the intermediate to the flower phase is definitely first order phase transition. The phase diagrams including low-temperature flower phases are obtained. The origin of the intermediate phase, phase separation, and metastable structures are discussed.

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The high power conversion efficiency of the hybrid CHNHPbX (where X = I, Br, Cl) solar cells is believed to be tightly related to the dynamics and arrangement of the methylammonium cations. In this Letter, we propose a statistical phase transition model which accurately describes the ordering of the CHNH cations and the whole phase transition sequence of the CHNHPbI perovskite. The model is based on the available structural information and involves the short-range strain-mediated and long-range dipolar interactions between the cations. It is solved using Monte Carlo simulations on a three-dimensional lattice allowing us to study the heat capacity and electric polarization of the CHNH cations. The temperature dependence of the polarization indicates the antiferroelectric nature of these perovskites. We support this result by performing pyrocurrent measurements of CHNHPbX (X = I, Br, Cl) single crystals. We also address the possible occurrence of the multidomain phase and the ordering entropy of our model.

Self-assembly of a two-component mixture of trimesic acid (TMA) and 1,3,5-benzene-tribenzoic acid (BTB) was studied by a Monte Carlo calculation. To describe the ordering, the three-state lattice model with homo- and heteromolecular dimeric and trimeric interactions was proposed. We also took advantage of the same symmetry and size effect of TMA and BTB molecules. The molecular interactions between TMA and BTB molecules were calculated by the density functional theory. Our simulations reproduced the self-assembly of all pure and bicomponent phases of TMA and BTB previously found in the experiments. Several new mixed structures were predicted at TMA:BTB ratios of 2:1, 1:1, and 1:2. The conditions of TMA and BTB phase intermixing and coexistence were also clarified by the ground state analysis. The simplest hypothetical structures which might occur due to the mixed trimeric interactions were studied, and their formation conditions were determined.

We propose a combined experimental and numerical study to describe an order-disorder structural phase transition in perovskite-based [(CH3)2NH2][M(HCOO)3] (M = Zn(2+), Mn(2+), Fe(2+), Co(2+) and Ni(2+)) dense metal-organic frameworks (MOFs). The three-fold degenerate orientation of the molecular (CH3)2NH2(+) (DMA(+)) cation implies a selection of the statistical three-state model of the Potts type. It is constructed on a simple cubic lattice where each lattice point can be occupied by a DMA(+) cation in one of the available states. In our model the main interaction is the nearest-neighbor Potts-type interaction, which effectively accounts for the H-bonding between DMA(+) cations and M(HCOO)3(-) cages. The model is modified by accounting for the dipolar interactions which are evaluated for the real monoclinic lattice using density functional theory. We employ the Monte Carlo method to numerically study the model. The calculations are supplemented with the experimental measurements of electric polarization. The obtained results indicate that the three-state Potts model correctly describes the phase transition order in these MOFs, while dipolar interactions are necessary to obtain better agreement with the experimental polarization. We show that in our model with substantial dipolar interactions the ground state changes from uniform to the layers with alternating polarization directions.

The ability of catecholamines to undergo oxidative self-polymerization provides an attractive route for preparation of coatings for biotechnology and biomedicine applications. However, efforts toward developing a complete understanding of the mechanism that underpins polymerization have been hindered by the multiple catechol crosslinking reaction pathways that occur during the reaction. Scanning tunneling microscopy allows the investigation of small molecules in a reduced-complexity environment, providing important insight into how the intermolecular forces drive the formation of supramolecular assemblies in a controlled setting. Capitalizing on this approach, we studied the self-assembly of 5,6-dihydroxy-indole (DHI) on Au(111) and Ag(111) to investigate the interactions that affect the two-dimensional growth mechanism and to elucidate the behavior of the catechol group on these two surfaces. X-ray photoelectron spectroscopy, together with density functional theory and Monte Carlo modeling, helps unravel the differences between the two systems. The molecules form large ordered domains, yet with completely different architectures. Our data reveal that some of the DHI molecules deposited on Ag are in a modified redox state, with their catechol group oxidized into quinone. On Ag(111), the molecules are deposited in long-range lamellar patterns stabilized by metal-organic coordination, while covalent dimer pairs are observed on Au(111). We also show that the oxidation susceptibility is affected by the substrate, with the DHI/Au remaining inert even after being exposed to O2 gas.

The crystal structure of β-quinol clathrate was investigated by empirical force-field calculations using two sets of potential functions—AMBER and CVFF. The crystal was approximated by the fragments containing 3402 and 15 750 quinol atoms. It was shown that the AMBER potentials are more precise when describing the experimental data on structure of β-quinol clathrate. The bond stretching, valence angle and out-of-plane bendings, dihedral torsion, van der Waals and electrostatic interactions, and hydrogen bonding were taken into account in the potential energy U. The contribution of each of these energies to the formation of structure was estimated. The energy U was minimized with respect to the independent coordinates of the lattice, unit-cell parameters, and both translation and orientation parameters of included molecules. The equilibrium states of encaged guest molecules, β-quinol lattice structure, and energy of clathrate formation were determined for 27 encaged guest molecules. It was shown that the β-quinol lattice can contract as well as expand depending on the type of an encaged molecule. The distribution of charges around the cage favors the positively charged atoms of the molecule to be located in the center of a cage, in contrast with those negatively charged which occupy the sites in the vicinity of peripheral hydroxyl hexagons. The electrostatic component of guest–guest interaction strongly affects the equilibrium position of guest molecules with large dipole moment. Quantitative estimates of various structural and energetic characteristics for β-quinol clathrate prove to be in good agreement with experimental data.