Simulation of the surface tension
of a nematic liquid crystal in contact with a planar solid

P. E.
Brumby¹, H. H. Wensink², A. J. Haslam³, and George
Jackson³

¹Department of Mechanical
Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

²Laboratoire de Physique des Solides, Université Paris Sud & CNRS, 91405 Orsay Cedex, France

³Department of Chemical
Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ,
United Kingdom

Corresponding
author e-mail: g.jackson@imperial.ac.uk

Knowledge of the surface
tension between a liquid crystalline phase and solid substrate is of prime
importance in broad areas of the physical and biological sciences ranging from
gaining an understanding of the organisation of molecules in optoelectronic
devices to the microstructures formed in living organisms. The direct molecular
simulation of the interfacial tension of high-density liquid crystals in
contact with solids is particularly challenging. The usual methodology involves
the use of a thermodynamic route based on integrating the Gibbs adsorption
equation where the change in the interfacial tension is related to the change
in the chemical potential for a given value of the adsorption. This type of thermodynamic
approach requires knowledge of the chemical potential with simulations in the
grand canonical ensemble or from free-energy integration which is
computationally prohibitive for high-density ordered states. In our current
work we employ an efficient and versatile free-energy perturbation method based
on the calculation of the components of the pressure tensor that it is
applicable to non-spherical and non-convex molecules from a series of ‘ghost’
anisotropic test-volume deformations [1]. For inhomogeneous systems this method
provides a particularly convenient route to the calculation of the interfacial
tension (surface free energy) from molecular simulations [2]. We study the
structural properties and interfacial tension of a fluid of hard-spherocylinder rod-like particles in contact with hard structureless at walls by means of Monte Carlo simulation.
The calculated surface tension between the rod fluid and the substrate is
characterized by a non-monotonic trend as a function of bulk concentration
(density) over the range of isotropic bulk concentrations. A surface-ordering
scenario is confirmed from our simulations: the local orientational
order close to the wall changes from uniaxial to biaxial nematic
when the bulk concentration reaches about 85% of the value at the onset of the
isotropic-nematic phase transition. The surface ordering
coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension,the adsorption, and the
average particle-wall contact distance are reported (over a broad range of
densities into the dense nematic region for the first
time), which may serve as a useful benchmark for future theoretical and
experimental studies on confined rod fluids. The simulation data are
supplemented with predictions from

[1] P. E. Brumby, A. J. Haslam, E.
de Miguel, and G Jackson, “Subtleties in the calculation of the pressure and
pressure tensor of anisotropic particles from volume-perturbation methods and
the apparent asymmetry of the compressive and expansive contributions,” Molecular Physics, 109, 169-189 (2014)

[2] P. E. Brumby, H. H. Wensink,
A. J. Haslam, and G. Jackson, “Structure and interfacial tension of a hard-rod
fluid in planar confinement,” Langmuir,
33, 11754-11770 (2017).