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Langmuir 2008, 24, 8174-8180
Controlling Smectic Focal Conic Domains by Substrate Patterning Wei Guo, Stephan Herminghaus, and Christian Bahr* Max Planck Institute for Dynamics and Self-Organization Bunsenstr. 10, D-37073 Go¨ttingen, Germany ReceiVed NoVember 28, 2007. ReVised Manuscript ReceiVed April 8, 2008 We describe a simple method to control the generation and the dimensions of focal conic domains in smectic liquid-crystal films. The surface of silicon substrates is structured in a way that areas with homeotropic anchoring conditions alternate with areas possessing random planar anchoring conditions. In smectic films on such substrates, the anchoring pattern translates into a presence-and-absence pattern of focal conic domains. The lateral dimensions of the planar anchoring areas determine an upper limit of the diameter of the focal conic domains. Thus, an almost arbitrary two-dimensional arrangement of focal conic domains can be achieved by controlling the size and position of individual domains.
Introduction Defect structures in liquid crystals are of interest from both fundamental and applied viewpoints. For instance, the distortion of the director field in a nematic phase by small water droplets or solid particles leads to novel colloidal interactions,1 which may be used for the design of new self-assembling microsystems.2–4 The nematic liquid-crystal phase is a liquid in which the rodlike molecules tend to align along a common direction, described by a unit vector n (director). The smectic-A liquid-crystal phase possesses, in addition, a density wave resulting in a layered structure, the layer thickness being comparable to one molecular length and the layer normal being parallel to n. The elastic constant controlling the compression and dilation of the smectic layers is several orders of magnitude larger than that controlling deformations of the nematic director field. Thus, in a smectic phase, only defect structures compatible with a constant layer thickness are possible resulting in the formation of so-called focal conic domains.5,6 In focal conic domains, the smectic layers are wrapped around two defect lines that have the shape of an ellipse and a parabola. The two lines are localized in two planes perpendicular to each other and pass through each others focal point. Focal conic domains often form spontaneously in bulk liquidcrystal samples when cooling from the isotropic or nematic phase to the smectic-A phase. They can also be generated on purpose in µm-thick films with antagonstic anchoring conditions of the liquid-crystal molecules. The focal conic domains then often self-organize in a regular two-dimensional lattice.7,8 The appearance of the focal conic domains in thin films is a result of a random planar anchoring condition (n parallel to the film plane, no preferred in-plane direction) at one interface of the film and a homeotropic anchoring condition (n perpendicular to the film * To whom corresponcence should be addressed. E-mail: christian.bahr@ ds.mpg.de (1) Poulin, P.; Stark, H.; Lubensky, T. C.; Weitz, D. A. Science 1997, 275, 1770. (2) Zapotocky, M.; Ramos, L.; Poulin, P.; Lubensky, T. C.; Weitz, D. A. Science 1999, 283, 209. (3) Meeker, S. P.; Poon, W. C. K.; Crain, J.; Terentjev, E. M. Phys. ReV. E 2000, 61, R6083. (4) Musˇevicˇ, I.; Sˇkarabot, M.; Tkalec, U.; Ravnik, M.; Zˇumer, S. Science 2006, 313, 954. (5) Friedel, G. Ann. Phys. (Paris) 1922, 18, 273. (6) Bouligand, Y. J. Phys. (Paris) 1972, 33, 525. (7) Fournier, J. B.; Dozov, I.; Durand, G. Phys. ReV. A 1990, 41, 2252. (8) Blanc, C.; Kleman, M. Phys. ReV. E 2000, 62, 6739.
Figure 1. Schematic of the smectic layer structure in two adjacent focal conic domains in a film on a solid substrate. The antagonistic anchoring conditions (homeotropic at the air interface and random planar at the substrate interface) result in the formation of focal conic domains in which the layers are wrapped around two defect lines (marked in red), a circle on the substrate plane and a straight line between substrate and air interface. Note that each focal conic domain causes a depression in the film/air interface.
plane) at the second interface. These antagonistic boundary conditions can be reconciled with each other only by bending the smectic layers resulting in the formation of focal conic domains. The two defect lines of each focal conic domain adopt in these films the shape of a straight line (instead of a hyperbola) and a circle (instead of an ellipse), i.e., the layers form a system of nested tori (cf. Figure 1). Controlling the dimensions and arrangement of focal conic domains may open the way to new applications based on regularly ordered micro- and nanosystems. For instance, a regular lattice of focal conic domains may be used in photonic applications.9 Recently, it was shown that a confinement of the smectic liquid crystal to microfluidic channels can result in the generation of regular arrays of focal conic domains.10–12 The details of the (9) Ruan, L. Z.; Sambles, J. R.; Stewart, I. W. Phys. ReV. Lett. 2003, 91, 033901. (10) Choi, M. C.; Pfohl, T.; Wen, Z.; Li, Y.; Kim, M. W.; Israelachvili, J. N.; Safinya, C. R. Proc. Natl. Acad. Sci., U.S.A. 2004, 101, 17340. (11) Shojaei-Zadeh, S.; Anna, S. L. Langmuir 2006, 22, 9986. (12) Yoon, D. K.; Choi, M. C.; Kim, Y. H.; Kim, M. W.; Lavrentovich, O. D.; Jung, H.-T. Nat. Mater. 2007, 6, 866.
10.1021/la703717k CCC: $40.75 2008 American Chemical Society Published on Web 06/21/2008
Controlling Smectic Focal Conic Domains
generated structures depend on the width and depth of the microchannels and the alignment conditions at the channel walls. Furthermore, a recent AFM study13 has shown that the temperature (more precisely, the temperature difference to the smecticA-nematic phase transition) provides another handle to influence the structure of focal conic domains. Thus, focal conic domains provide systems in which nanoscopic defect features, e.g., the central singular line running between the two film interfaces, are accurately positioned with respect to a microscale structure. In the present study, we describe a method to generate almost arbitrary two-dimensional arrangements of focal conic domains in smectic films possessing an otherwise homogeneous structure. The method is easily applicable for films possessing an air interface and a substrate interface. The substrate surface, which initially exhibits random planar anchoring conditions throughout its whole area, is modified in certain regions in a way that it induces a homeotropic anchoring. Since the air interface always induces a homeotropic anchoring, the regions with antagonistic and those with like-anchoring then coexist in a patterned fashion. This anchoring pattern will translate to a presence-and-absence pattern of focal conic domains.14 The substrate patterning is achieved by thermal evaporation of a thin gold layer, which is known to induce homeotropic anchoring,15 onto the substrate surface in the presence of an appropriate mask. When a smectic liquid-crystal film is prepared on such a substrate, the focal conic domains will be confined to the previously masked regions, while the unmasked regions are covered by a homogeneous film with a plane layer structure. The confined focal conic domains are studied by optical microscopy, fluorescence confocal microscopy, and scanning force microscopy. Our results show that the anchoring pattern on the substrate may be used to determine the position and the size of focal conic domains in smectic films on such substrates. For nematic liquid crystals, the behavior on substrates possessing an anchoring pattern has been studied for several years.16–20 In these works, the substrate patterning often results in multistable alignment configurations, tilted anchoring conditions, or microscale diffractive structures. While compiling the results described in the following, a beautiful study by Bramble et al. 21 on smectic liquid crystals on patterned substrates appeared. In ref 21, a similar concept to our study is employed: a gold surface is coated with different self-assembled monolayers, which promote random planar or homeotropic anchoring. The main difference from our study (besides the different method of generating the anchoring pattern) is that in ref 21, films with constant thickness between two solid substrates are studied, whereas in the present paper, we are studying samples in which the thickness varies in a wide range between
