Finite-size scaling analysis of isotropic-nematic phase transitions in an anisometric Lennard-Jones fluid

By means of Monte Carlo simulations in the isothermal-isobaric ensemble, we perform a finite-size scaling analysis of the isotropic-nematic (IN) phase transition. Our model consists of egg-shaped anisometric Lennard-Jones molecules. We employ the cumulant intersection method to locate the pressure P* at which the IN phase transition occurs at a given temperature T. In particular, we focus on second-order cumulants of the largest and middle eigenvalues of the alignment tensor. At fixed T, cumulants for various system sizes intersect at a unique pressure P*. Various known scaling relations for these cumulants are verified numerically. At P*, the isobaric heat capacity passes through a maximum value c(P)(m), which depends on the number of molecules N. This dependency can accurately be described by a power law such that lim(N ->infinity) c(P)(m)(N) -> infinity. For sufficiently large N, the pressure at which c(P)(m) is located shifts only very slightly in agreement with the apparent insensitivity of the cumulant intersection to N. In addition, we analyze our data in terms of Landau's theory of phase transitions. Our results are consistent with a weakly discontinuous entropy-driven phase transition.