Computer simulation of the behaviour of a solute in a model liquid crystalline solvent

Abstract

A method is described for modelling the behaviour of solute molecules dissolved in a model liquid crystalline solvent. The method is illustrated for benzene as the solute, and the solvent is a collection of particles interacting with each other via the Gay Berne potential. The interaction between the benzene and each solvent particle is modelled as a Lennard-Jones site-site potential between six united carbon and hydrogen atoms on the benzene with four interaction centres on the solvent particle. The results of the simulations are used to calculate the second-rank orientational order, the translational diffusion coefficients and second-rank rotational correlation functions of the benzene molecule in the isotropic, nematic and smectic B phases. The second-rank, orientational order parameters of the benzene [Pbar] ₂ ^b and the solvent particles [Pbar] ₂ ^GB are similar in magnitude, and show the same increase with decreasing temperature in the nematic phase as benzene dissolved in real nematic solvents. On entering the smectic B phase, [Pbar] ₂ ^GB increases, but [Pbar] ₂ ^b decreases, which has also been observed experimentally for some small solutes in smectic solvents. The calculated diffusion coefficients parallel (D _║) and perpendicular (D _┴) to the sample director are also found to have similar magnitudes to those found experimentally. Thus, D _xV>D _┴ in the nematic phase, whereas in the smectic B the reverse order holds with D _║ being essentially zero, that is, the benzene is confined to one smectic layer for the duration of the simulation. The rotational correlation functions have the correct initial values, and all decay to their correct infinite time values within the course of the simulation. They are not single exponential decays, which conflicts with the simple models often used to describe such functions, but is in accord with more realistic theories, such as small step rotational diffusion. The confinement of the benzene within a smectic layer does not have a large effect on the rotational correlation functions.