Liquid crystals in contact with structured substrates

Harnau, L.¹, Kondrat, S.¹, Poniewierski, A.², Guenther, F.¹, and Dietrich, S.^1
1Max-Planck-Institut fuer Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, Germany,

and Institut fuer Theoretische und Angewandte Physik, Universitaet Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

²Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland

The contact of soft matter with solid surfaces offers the possibility to imprint external lateral structures deep into the bulk of the adjacent complex fluid and thus to manipulate it in a controlled way. For fluids consisting of non-spherical particles in the presence of confining substrates, the competition between fluid-substrate and fluid-fluid interactions leads to application-relevant surface-driven changes of both the mean local densities and the orientations of the particles [1]. Examples are the patterned alignment of bistable liquid-crystal display devices and liquid-crystal based detection of biomolecular and chemical events occurring at surfaces. Various technical developments allow the controlled fabrication of tailored solid surfaces at the nano- to micrometer range.

Here we use the Frank-Oseen theory and density functional theory to study the properties of liquid crystals in contact with patterned substrates. We discuss the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength is varied. By first evaluating an effective surface free energy function characterizing the patterned substrate we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimization of the free energy functional are performed in order to test the predictions of the effective free energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches [2]. In addition the effective free energy method allows one to determine the energy barriers between two states in a bistable nematic device. The calculations reveal that phase transitions between two states can be triggered by applying a voltage between the substrates. Both dielectric interaction and flexoelectric polarization are taken into account, and in the numerical calculations particular attention is paid to the fact that the electric field is not constant throughout the cell [3].

Moreover, we use a microscopic density functional theory to study rod fluids near a right-angled wedge or edge as well as near a geometrically patterned substrate. Density and orientational order profiles, excess adsorptions, as well as surface and line tensions are determined. Near a hard wall which is periodically patterned with rectangular barriers, complete wetting of the wall by a nematic film occurs as a two stage process in which first the nematic phase fills the space between the barriers. In addition, the calculations exhibit an enrichment [depletion] of rods lying parallel and close to the corner of an individual right-angled wedge [edge].

References

[1] L. Harnau and S. Dietrich, in Soft Matter, Vol.3, edited by G. Gompper and M. Schick., 159 (2007).

[2] L. Harnau, S. Kondrat and A. Poniewierski, Phys. Rev. E 76, 051701 (2007).

[3] L. Harnau and S. Dietrich, Europhys. Lett. 73, 28 (2006).