Example of the system setup, with GayBerne (GB) uid particles conned between two surfaces: the impenetrable solid surface consisted of a single layer of Lennard-Jones (LJ) particles, centered at z = 0 (black dash-dot line), while a repulsive harmonic potential acted on the centre of each uid particle at the penetrable vapour-like interface (dashed black line) to prevent evaporation. The plot at the top right is representative of the form of this potential. The bulk region was dened as being within ±3σ S of the z coordinate of the centre of the box (z mid , black solid line). z max is the maximum z coordinate of any particle during the simulation, σ sub the diameter of a substrate particle, and dotted black lines indicate the bounds of the bulk region. This region was suciently far from both interfaces that, except for a couple of the systems that formed anisotropic phases, the uid had uniform density here. The position of the vapour interface, z v (green line), was dened as the z-coordinate where the average density was equal to half the average bulk value. The average molecular orientation at the vapour interface, s vap , was calculated as the average of s(z) from eqn (2) over particles whose centres were at z coordinates within z v ± σ S /2 (region indicated in gure). The average molecular orientation at the solid interface, s sub , was calculated by averaging s(z) over uid particles whose centres were within σ S of the surface of the substrate (i.e. at z < σ sub /2 + σ S , cyan line). These denitions selected, to a good approximation, the particles within the rst uid layer at either interface. Particles are coloured by the orientational order parameter s(z) (which is -0.5 and +1, respectively, for fully side-on and face-on orientations), averaged over the entire simulation of this system (κ = 0.4, κ = 0.2, T * ≡ k B T /ε = 0.73, substrate = graphene). The particles in the two interfacial regions are coloured by the average order parameter calculated over all particles within this region, while all other particles are coloured according to the value of s(z) corresponding to their z coordinate shown in (c). (b) Fluid density ρ(z) and (c) orientational order parameter s(z) proles calculated over the entire simulation of this system. The shaded areas correspond to the interfacial uid regions at the solid or vapour interface. Dashed and dotted horizontal lines in (c) correspond to the values of s sub and s vap respectively. Additional ρ(z) and φ (z) proles can be found in the ESI, section S5.