Simulation and theory of hybrid aligned liquid crystal films

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager’s second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

Figure 1

I-N phase diagram of the HGO fluid: ${\rho }^{*}=\rho {\sigma }_0^3$ and $\kappa$ are the reduced density and the elongation, respectively. Solid lines: Onsager theory with Parsons-Lee density rescaling. Dashed lines: Onsager theory [13]. Solid squares: MC simulation results [22].

Figure 2

Reduced density ${\rho }^{*}\left(z\right)$ (top), order parameter $Q_{zz}\left(z\right)$ (middle), and order parameter $⟨P_2⟩\left(z\right)$ (bottom) profiles for a hybrid film of HGO particles of elongation $\kappa =3$ and needle length ${\kappa }_S^{\prime }=0.2$ on the small-$z$ (or bottom) substrate and ${\kappa }_S^{\prime }=0.0$ on the large-$z$ (or top) substrate, for ${\rho }_{\mathit{\text{bulk}}}^{*}=0.28$ (solid line and open circles) and ${\rho }_{\mathit{\text{bulk}}}^{*}=0.34$ (dashed line and solid squares). Lines are from theory; symbols are from simulation. The lower density lies in the I phase, the higher density in the N phase. See the text for details.

Figure 3

Same as Fig. 2, but for ${\kappa }_S^{\prime }=0.5$ at the small-$z$ substrate.

Figure 4

Same as Figs. 2, 3, but for ${\kappa }_S^{\prime }=0.8$ at the small-$z$ substrate.

Figure 5

(Color online) Configuration snapshots for hybrid films with strong homeotropic anchoring at the top substrate $({\kappa }_S^{\prime }=0.0)$. Bottom substrate: (a) and (b) weakly homeotropic $({\kappa }_S^{\prime }=0.2)$, (c) and (d) bistable $({\kappa }_S^{\prime }=0.5)$, and (e) and (f) planar $({\kappa }_S^{\prime }=0.5)$. Snapshots (a), (c), and (e), on the left, correspond to the bulk isotropic phase $({\rho }^{*}=0.28)$; (b), (d), and (f), on the right, to the bulk nematic phase $({\rho }^{*}=0.34)$.

Figure 6

Reduced density ${\rho }^{*}\left(z\right)$ (top), order parameter $Q_{zz}\left(z\right)$ (middle), and order parameter $⟨P_2⟩\left(z\right)$ (bottom) profiles for a hybrid film of HGO particles of elongation $\kappa =3$ and needle length ${\kappa }_S^{\prime }=1.0$ on the small-$z$ (bottom) substrate and ${\kappa }_S^{\prime }=0.0$ on the large-$z$ (top) substrate, for ${\rho }_{\mathit{\text{bulk}}}^{*}=0.35$. Solid line and open circles: $L_z=4\kappa {\sigma }_0$. Dashed line and solid squares: $L_z=6\kappa {\sigma }_0$. Dotted line and crosses: $L_z=8\kappa {\sigma }_0$. Lines are from theory; symbols are from simulation.

Figure 7

(Color online) Typical configuration snapshots of hybrid films of HGO particles of elongation $\kappa =3$, using the HNW surface potential with ${\kappa }_S^{\prime }=1.0$ (bottom) and ${\kappa }_S^{\prime }=0.0$ (top). (a) $L_z=4\kappa {\sigma }_0$ and $N=1000$ particles, (b) $L_z=6\kappa {\sigma }_0$ and $N=1250$ particles, and (c) $L_z=8\kappa {\sigma }_0$ and $N=2000$ particles. In all cases, ${\rho }_{\mathit{\text{bulk}}}^{*}=0.35$.