SIMULATION OF STRUCTURE AND DYNAMICS NEAR THE ISOTROPIC-NEMATIC TRANSITION

We present a computer simulation study of orientational correlations in a molecular liquid approaching the isotropic-nematic transition, including the first calculation of the direct correlation function c(1,2) in this regime. While the second-rank orientational correlation length diverges, the associated component of c(1,2) remains short-ranged, and its spatial integral approaches the mechanical instability limit for the isotropic phase as predicted by density-functional theory. Orientational correlation lengths and times are quite well described by Landau-de Gennes theory. The nematic liquid crystal phase is characterized by long-ranged correlations of molecular orientation, while the positional degrees of freedom remain disordered. The appropriate orientational order parameter is a second-rank quantity [1]; it is conveniently expressed as S = 〈P2(u · n)〉 , (1) where P2 is the second Legendre polynomial, u is a typical molecular orientation vector, n is the bulk preferred orientation or director, and 〈. . .〉 represents an ensemble average. The transition between the isotropic liquid and the nematic phase is known, experimentally, to be weakly first order. This means that, for example, if one approaches the transition by lowering the temperature T from the isotropic side, the second-rank orientational correlation length ξ2 becomes large, and it is possible to extrapolate ξ 2 → 0 at a divergence temperature T . This limit, however, is pre-empted by the occurrence of the transition at a slightly higher temperature TNI, where (TNI − T )/TNI ≈ 10 −3. Both the statics and the dynamics of orientational correlations are of interest in the vicinity of this transition. Computer simulations to fully characterize the I-N transition present great challenges. Studies of simplified lattice spin models [2, 3] using finite-size scaling approaches [4–6] required system sizes of the order of N = 303 spins, and run-lengths of order 106 Monte Carlo moves per spin, to convincingly demonstrate weak first-order character. However, such lattice models relate to real liquid crystals only in the most coarsegrained sense: no connection to molecular properties is possible. Molecular simulations are more expensive than those using spins, and a study analogous to the ones described above is out of reach at present. Nonetheless, there is great interest in locating the I-N transition, and in studying pretransitional phenomena, using molecular models. An early study on systems of a few hundred molecules [7] presented some evidence of the slowing down of collective reorientation, and the growth of static orientational correlations, for the hard ellipsoid fluid. However, these results were limited to ranges of a few molecular diameters. One aim of the present paper is to study the growth of rather longer ranged structure in the appropriate components of the pair correlation function h(1,2) on approaching the transition. It is of particular interest to show whether or not the corresponding components of the direct correlation function c(1,2) (defined below) remain short-ranged in this limit. A second aim of this work is to examine the way in which correlation times for collective reorientation scale with the range of the relevant correlations, on the approach to the transition: in other words, how orientational domain size affects collective reorientation.