Second-virial Onsager theory and Its limitations in the prediction of the ordering transitions of confined hard rods between two parallel hard walls

We studied the phase behavior of hard rectangular rods with edge lengths L, D, and D. All the calculations have been carried out through Onsager second virial theory within the three-state Zwanzig approximation. The uniaxial paranematic-biaxial paranematic (P_U-P_B) and the biaxial paranematic-biaxial nematic (P_B-N_B) phase transitions have been calculated for a wide range of wall-to-wall distances (10 ≤ H/D ≤ 100) while for each pore width, the aspect ratios (L/D) of the particles are changing. By increasing the aspect ratio, a fast decrement in both the transitions is observed for L < H/3. In this study, we could find the P_B-N_B transition neither for H/D ≤ 29.00 nor L/D ≤ 7.50. Moreover, despite all efforts, we could not find the P_U-P_B transition for L/D ≤ 6.69 in the entire studied range of H/D. (author)