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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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.

Using Monte Carlo calculations we analyze the order and the universality class of phase transitions into a low density (honeycomb) phase of a triangular antiferromagnetic three-state Bell-Lavis model. The results are obtained in a whole interval of chemical potential µ corresponding to the honeycomb phase. Our results demonstrate that the phase transitions might be attributed to the three-state Potts universality class for all µ values except for the edges of the honeycomb phase existence. At the honeycomb phase and the low density gas phase boundary the transitions become of the first order. At another, honeycomb-to-frustrated phase boundary, we observe the approach to the crossover from the three-state Potts to the Ising model universality class. We also obtain the Schottky anomaly in the specific heat close to this edge. We show that the intermediate planar phase, found in a very similar antiferromagnetic triangular Blume-Capel model, does not occur in the Bell-Lavis model.

We present a study of the q-orientational statistical model for the self-assembly of symmetric triangular molecules of trimesic acid in two dimensions. Density functional theory is used to estimate the pair interactions of two such molecules located at the ground state (dimeric H-bond) distance for q 2 different mutual orientations of these molecules. The interaction energies for models with q up to 120 are determined. The Monte Carlo simulation employing these interactions reveals the ordering of the molecules into the honeycomb (HON) phase for the entire range of models (q = 2–120) which is manifested by the peak in temperature dependence of the specific heat C V(T). The increase of q from 2 to 120 causes the ordering temperature T c to decrease and become much closer to the experimental value. Our results imply that in terms of computational efficiency and the magnitude of T c, the q = 12 model is the optimal choice for calculations. The C V(T) dependence has a second peak at a low temperature point T 1 < T c. We find that between T c and T 1, the HON network even at a stoichiometric molecular density still possesses a large portion of filled hexagonal pores and the expulsion of molecules from the pores coincides with the C V peak at T 1. In more refined models (q ≥ 12), the HON phase also displays a slightly distorted bonding geometry from T c down to very low temperature. Finally, our finite size scaling analysis implies that the phase transition in all studied q > 2 models belongs to the three-state Potts universality class.

Self-assembly of trimesic acid (TMA) molecules into the honeycomb structure with filled pores and the resulting host–guest chemistry are studied by the density functional theory (DFT) and Monte Carlo (MC) simulations. The DFT calculations demonstrate that a guest TMA molecule prefers a noncentral position in a relaxed hexagonal pore formed of six TMA molecules, and it is binded by two intermolecular interactions. The symmetric central position of the guest molecule is energetically favorable only in the honeycomb structure, which is compressed by more than 3%. Based on the estimated host–guest dimeric interactions, a model is proposed to identify the conditions for central and noncentral positioning of TMA molecules within the pore during their ordering into the honeycomb structure with partly filled pores. The MC simulations reveal that increase of the molecule–substrate interaction in the center of the pore or interactions of the central molecule with the cage molecules have a significant effect in preserving the central position of the guest molecule. However, if these interactions are not too strong, the noncentral position is favored due to multiplicity of noncentral arrangements in a hexagonal cage.

The nearest neighbor model is proposed to explain the occurrence of the metalassisted pinwheel structures of deprotonated trimesic acid molecules on Ag(111). The main bonding interactions of molecules in these structures are estimated by the density functional theory calculations. The determined interaction energies are further used as a starting point for Monte Carlo simulations performed for a broad range of interaction parameters and different deprotonation levels of molecules. In this paper, we use the molecular engineering approach by selecting the sets of molecules with different deprotonation levels to obtain the structures similar to those observed experimentally. For a large number of once-deprotonated molecules, we obtain a discrete pinwheel phase, PW1, which can also coexist with the knitted pinwheel structure, PW2, if completely deprotonated molecules participate in the self-assembly. The PW1 phase could also be formed of twice-deprotonated molecules, and coexistence of this phase with the PW2 structure is possible for strong binding intermolecular interactions. We demonstrate domains of different enantiomers occurring in the PW1 and PW2 structures.

We propose two models describing the self-assembly of intact and deprotonated benzene-1,3,5-triyl-tribenzoic acid (BTB) molecules into the oblique (O) and ribbon (R) phases. The models are also extended to describe the formation of the honeycomb (HON) structure. To determine the intermolecular interaction potentials for the R and O phases, we performed the DFT calculations for the clusters of neutral and charged BTB molecules. The obtained values were used as an input in the Monte Carlo (MC) simulations. The model and MC simulations for the R phase demonstrate how ionic interactions between singly deprotonated BTB molecules lead to the formation of ribbons separated by the interribbon gap, and how these ribbons pack into the ordered two-dimensional structure. The O phase is treated in our model as the structure that might be composed of both intact and singly deprotonated molecules, owing to the occurrence of this phase in polarization switching experiments for positive surface bias. The ground-state analysis and MC modeling for the O and HON structures with the DFT-calculated interaction parameters demonstrate that for intact molecules (deprotonation level (DPL) = 0) the energy of the HON structure is always lower than that of the O phase. With an increase of DPL, the difference between the energies of these two structures decreases: while for DPL = 0.5, the possibilities to obtain the HON or O phase are very similar, for DPL = 1 the O phase has a higher probability to exist in comparison to the HON phase.