Multiorientation Model for Planar Ordering of Trimesic Acid Molecules

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 q² 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 T₁ < T_c. We find that between T_c and T₁, 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 T₁. 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.