Molecular dynamics simulations were conducted using the generalized replica exchange method (gREM) on the 4-cyano-4'-n-alkyl biphenyl (nCB) system with n = 5, 6, 7, and 8, which exhibits a nematic-isotropic (NI) phase transition. Sampling near the phase transition temperature in systems undergoing first-order phase transitions, such as the NI phase transition, is demanding due to the substantial energy gap between the two phases. To address this, gREM, specifically designed for first-order phase transitions, was utilized to enhance sampling near the NI phase transition temperature. Free-energy calculations based on the energy representation (ER) theory were employed to characterize the NI phase transition. ER evaluates the insertion free energy of the nCB molecule for both nematic and isotropic phases, revealing a change in the temperature dependence across the NI phase transition. Further decomposition into energetic and entropic terms quantitatively shows the balance between these contributions at the NI phase transition temperature.
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