The evaluation of the thermodynamic properties of an ideal discotic mesophase needs the determination of a partition function, that depends upon two basic types of energy storage, translational and rotational. Here, we suppose we can substitute for the complex effective intermolecular potential, different mean potentials acting on each individual molecule. The defining assumptions for a discotic mesophase include the stipulations, first—that each simple disk-like molecule is, during most of the time, confined to a cell, secondly—that each molecule has an external rotation which is more or less hindered by a periodic potential. The cells are stacked in columns and the columns form a regular hexagonal array, each molecule moves in a cell as in an infinite potential well due to the neighbouring molecules.

This model has allowed the general formulation of the mesophase-free energy. From this, we obtain the form of the coefficient of isothermal compressibility when the external rotations of the molecules are hindered and the vibrational energy is weak.