The phase transition of heptylcyanobiphenyl 7CB and pentylcyanobiphenyl 5CB liquid crystals was investigated using the differential scanning calorimetry DSC technique. Then, the phase transition of different compositions of 7CB/5CB binary mixture was studied to determine the eutectic point. The phase diagram of mentioned binary system in 7CB mole fraction of 0.45 at T = 273.45 K is in good agreement with that of predicted from Schroder-van Laar equation. The thermodynamic excess functions and interaction parameters were calculated to describe the phase transition physically using the non-random mixing for the first time. The P* randomicity parameter was used to describe the phase transitions of C-N and N-I in which a small amount of P* shows a non-random identity of C-N phase transition. Contrarily, the P* is greater in N-I phase transition showing a random mixing process. (C) 2014 Elsevier Ltd. All rights reserved.