Dimension of mesogenic molecules as atomic clusters

The problem regarding the mass dimension D of mesogenic molecules as atomic clusters is formulated and solved using computer simulation and analytical calculations. For a large number of compounds belonging to different chemical classes, it is shown that the cores of discotic lacunar (rodlike, lathlike) molecules forming nematic or columnar discotic (calamitic) phases have a fractional dimension 1 < D _c < 2 (D _c ≈ 1). The dependences of the dimension D _c on the symmetry, the conformation, and the structural-chemical features of the molecular core are determined. It is demonstrated that, in the region of side flexible chains in molecules of both types, the dimension D _ch can be either smaller or larger than unity, depending on the chain conformation. An analytical expression accounting for the results of numerical experiments is obtained for the dimension D _ch .