Ordering of triangular molecules into the honeycomb phase: Estimation of critical temperature for different lattice models of self-assembly

摘要

Ordering of triangular molecules into the honeycomb structure is taken as an example to demonstrate how the substrate lattice, the number of states, and the exclusions due to size of the molecule affect the ordering temperature T c of lattice models. We studied all range of rescalings of triangular lattice for diffusion of molecules, from very roughly rescaled lattice (characterized by shortage of lattice sites for hopping) to very finely rescaled. We found that very rough models are quite inaccurate in determining of T c. We demonstrated how the optimal model for calculations of transition thermodynamics might be determined satisfying both the requirements of T c accuracy and computational efficiency. Increase of number of states q leads to very strong decrease of T c for small q and exponential tail at higher q values. The exclusions were found to increase the T c for rough rescaling models, but has only marginal effect on T c for models with sufficiently large number of sites for hopping.