Planar degenerate substrate for micro- and nanopatterned. nematic liquid crystal cells

Transcription

1 Planar degenerate substrate for micro- and nanopatterned nematic liquid crystal cells Ishtiaque M. Syed, Giovanni Carbone, and Charles Rosenblatt Department of Physics, Case Western Reserve University, Cleveland, Ohio USA Bing Wen Rockwell Science Center, Thousand Oaks, California (March 15, 2005) Abstract A micro- or nanopatterned planar aligned cell ordinarily requires a pair of mirror-image patterned substrates that must be aligned in register to 1 µm. As an alternative we examine the director orientation profile of a nematic liquid crystal in a cell composed of one substrate whose easy axis is patterned on micrometer length scales λ and a second substrate treated for planar degenerate alignment using polymethyl methacrylate. For cell thickness < λ, the experimentally measured director profile in the bulk corresponds approximately to that imposed at the micropatterned substrate. The results are compared with theoretical calculations. This method provides an excellent alternative to the use of a pair of substrates aligned in close register. 1 Typeset using REVTEX

2 In recent years several techniques have been developed that facilitate a patterned orientation of the nematic liquid crystal (LC) director on length scales of a few micrometers down to 100 nm. Among these are polarized ultraviolet light modification of a polymer-coated substrate [1,2]; atomic beam nanolithography [3]; nanoprint lithography [4]; dip pen nanotlithography using an atomic force microscope (AFM); and perhaps most versatile, AFM nanoscribing of a polymer-coated substrate [5 7]. The AFM nanoscribing technique was introduced by Rüetschi, et al. [5], wherein they used the stylus of an AFM to scribe patterns into a polyimide substrate, causing the local alignment of the liquid crystal to be approximately parallel the rubbing direction. Several years later Pidduck, et al. [6] examined the interaction strength between the liquid crystal and AFM-scribed substrate. More recently Kim et al. demonstrated that a bistable or tristable director orientation may be achieved with tiny pixel sizes [8,9], and our group has examined a number of scientific phenomena these include elasticity, surface interactions, and phase transitions associated with liquid crystals that may be controlled and explored on nanoscopic length scales [10 12]. Additionally, AFM nanoscribing as applied to liquid crystals offers many technological possibilities [13], including devices for optical beam steering and wavelength demultiplexing in the broad field of optical communications [14], as well as nanopatterned chemical and biological sensors. Unless the intended alignment at one substrate is homeotropic, there are two routes to achieving good micro- and nanopatterned azimuthal LC alignment in a closed cell: i) both substrates need to be scribed with mirror-image patterns and aligned in close register, with a tolerance much smaller than the characteristic length scale λ of the pattern, or ii) the substrates must have a master-slave relationship. The first approach can be quite difficult, especially if the pattern s length scale λ < 10 µm; this would require registration to better than 1 µm. The alternative approach involves treating one of the substrates for planar degenerate alignment (PDA), in which the director lies parallel to the substrate but can adopt any azimuthal orientation with equal probability. In consequence the azimuthal orientation at the PDA (slave) substrate is controlled in part by the orientation at the patterned (mas- 2

3 ter) substrate. Nematic elasticity, of course, tends to homogenize the orientation profile along the z-axis, i.e., perpendicular to the patterned substrate. (The orientation also is homogenized parallel to the substrate plane when the anchoring strength coefficient W ϕ is finite). As a result of the homogenization along the z-axis, the master-slave approach in principle works best when the thickness of the cell d is somewhat less than λ. In this paper we report on the measured director orientation profile for a splay pattern having pixels of width 10 µm scribed at the master substrate, and polymethyl methacrylate (PMMA) as the PDA agent applied to the slave substrate. We find that the PMMA provides excellent planar degenerate alignment on initially filling the cell, and that the splay pattern at the slave substrate follows the scribed pattern at the master substrate reasonably well for d 5 µm. The system was modeled numerically, where we found reasonable agreement with the experimental results. The slave substrate was spin coated with PMMA (M w = ; M n = 39500) dissolved in a mixture of propylglycolmethyl ether acetate and γ-butyerolactone. The use of PMMA as a PDA agent was hinted at by Yang, et al [15], and independently recognized by Yokoyama [16]. Dozov, et al found that a few other materials produce reasonable PDA [17], although adsorption of liquid crystal molecules over time tends to induce a surface memory effect [18,19,10], a result of which is the development of a preferred axis for alignment, a so-called easy axis, at the originally PDA substrate. This is appropriate for our purposes, as we are interested primarily in a slave substrate at which the initial alignment of the director is controlled by the master substrate. In fact, for applications such as switchable optical gratings, which can be switched more rapidly when the boundary conditions become rigidified, the development of surface memory actually is quite useful. This is in contrast to another observation by Dozov, et al [17], which showed that a monolayer coating of glycidoxypropyl trimethoxysilane (glymo) maintains an approximately degenerate orientation, with only a very weak easy axis developing over time; such a surface would be useful in applications that require a non-stick boundary. 3

4 Our initial goal was to show that PMMA provides both azimuthally degenerate and true planar alignment. To that end we first examined a cell constructed of two PMMA coated substrates. The substrates were separated by mylar spacers of nominal thickness 5 µm and cemented. The cell was filled in the isotropic phase with the liquid crystal pentylcyanobiphenyl (5CB), and cooled into the nematic phase. Rather than breaking into small domains, we observed that the director forms a Schlieren texture that varies on length scales µm (Fig. 1), a good indication of degenerate alignment. We then created a master/slave cell, where the master substrate was coated with the planar aligning polyimide PI-2555 (DuPont). After baking this substrate, the polyimide coating was rubbed unidirectionally with a velvet cloth. The slave substrate was coated with PMMA, and the resulting cell was filled with 5CB in the nematic phase, flowing in a direction perpendicular to the rubbing direction. We found that the director was oriented parallel to the rubbing direction at the master surface, but that it was oriented parallel to the flow direction at the slave surface; this is equivalent to a 90 twisted nematic alignment through the cell. On heating the liquid crystal into the isotropic phase and cooling back into the nematic phase, the director was found to orient uniformly along the rubbing direction through the entire cell. These results again indicate azimuthally degenerate alignment on cooling from the isotropic phase. In order to determine whether the director is indeed planar at the PMMA substrate, we examined a cell in which the slave substrate was coated with electrically-conducting indium-tin-oxide, over which we deposited PMMA. The master substrate also was coated with indium-tin-oxide, followed by polyimide PI The master substrate then was baked and rubbed unidirectionally. The two substrates were separated by spacers and the cell thickness was measured by an interferometric scheme and found to be 31 ± 2 µm. The cell was filled with octylcyanobiphenyl (8CB) in the isotropic phase, and cooled below the nematic isotropic transition temperature T NI to T = T NI 3 C; this resulted in a uniform azimuthal orientation throughout the cell. On ramping an applied voltage from 0 to 10 V, the director underwent a Freedericksz transition [20], resulting in an optical retardation 4

5 change saturating at 38.6 ± 0.6 rad at the highest voltage for wavelength nm(from a He-Ne laser). Using published data for the birefringence n of 8CB [21], we determined that the director s polar orientation at the PMMA substrate had a polar pretilt θ < 5. Coupled with the earlier observation of a Schlieren texture with two PMMA surfaces and the flow-induced orientation in the nematic phase, we conclude that: i) the liquid crystal is approximately planar at the PMMA surface; ii) for short times its azimuthal alignment tendency is nearly degenerate at the PMMA surface, being random in the absence of an opposing master surface but ordering parallel to the master surface s rubbing direction in the presence of a master surface; iii) flow alignment in the nematic phase at the PMMA surface biases the azimuthal orientation of the director; and iv) over even short periods of time a surface memory effect develops at the PMMA surface so that upon cessation of flow the azimuthal alignment remains, even in the presence of an elastic torque. Next we examined the director orientation profile when the master surface was scribed with a splay pattern (Fig. 2). Using a force of 2.3 µn and a spacing between rub lines of 200 nm, the polyimide PI-2555 at the master surface was scribed with parallel pixels of width 10 µmandlength100 µm, such that the azimuthal scribing directions corresponded to +ϕ s,0, ϕ s,0,+ϕ s,0, ϕ s... in successive pixels. Patterns for which ϕ s =20, 30,and40 were examined. Because the azimuthal anchoring strength coefficient W ϕ is finite at the AFM-scribed surface, splay elasticity partially homogenizes the LC director in the plane of the substrate and results in an amplitude ϕ LC (z =0)< ϕ s for the LC s splay distortion. Similarly, the extrapolation length L K 11 /W ϕ,wherek 11 is the splay elastic constant, turns out to be a few micrometers, and thus the azimuthal director profile tends to vary moderately smoothly in the plane of the substrate at z = 0. The slave substrate was coated with PMMA. Cells were constructed with thicknesses d =5.4±0.2 and11.3±0.4 µm, where the thicknesses were determined interferometrically. Owing both to twist elasticity and to extremely weak azimuthal anchoring, the director tends to homogenize further at the PMMA surface (at z = d), where ϕ LC (z = d)isevensmallerthanϕ LC (z = 0). Each cell was housed in a temperature controlled oven. Light from a partially collimated but incoherent 5

6 white source passed through a polarizer mounted on a rotation stage, the cell, a lens to create an enlarged real image (by a factor of 50) downstream at the detector, an analyzer mounted on a rotation stage, a 200 µm diameter pinhole, a broadband filter centered at 538 nm and having a bandwidth at half transmission of 95 nm, and into a photodiode detector. By enlarging the image, the detector was able to select a narrow region (corresponding to 4 µm in real space) at the center of a given pixel that was scribed at orientation ϕ s. All measurements were performed at temperature T =38 C, which is 2.5 C below the nematic isotropic transition temperature T NI of 8CB. For a LC director rotation ϕ LC [= ϕ LC (z =0) ϕ LC (z = d)] through the cell it can be shown that there is a unique polarizer orientation angle γ P for which the outgoing light is linearly polarized and can be extinguished by an analyzer at angle γ A [22]. ϕ LC is given by the implicit expression [10,22] tan ( ϕ LC γ P + γ A π/2) = tan ³ ϕ LC 1+u 2 / 1+u2, (1) where u = πd n/λ ϕ LC and λ = 538 nm is the wavelength of light. For u the system is in the optical adiabatic limit and γ P γ A = ϕ LC ; otherwise γ P and γ A in general do not correspond exactly to ϕ LC (z = 0) and ϕ LC (z = d). γ P γ A + π/2 (andthereby ϕ LC )asfunctionsofϕ s and d. Our goal was to determine To that end, for a given ϕ s and d, the intensity I j was measured for polarizer orientation γ j P as a function of analyzer orientation γ j A, and the analyzer orientation γ j A,min and intensity I j min that correspond to the minimum intensity was obtained by a parabolic fit ofi j vs. γ j A. This procedure was performed for several polarizer orientations j. Thesefitted intensity minima I j min vs. γ j P in turn were fitted to a parabola, and the polarizer γ global P,min and analyzer γ global A,min orientations at which a global intensity minimum was achieved were recorded. ϕ LC was extracted using Eq. 1, with temperature T =38 Cand n =0.13 at λ = 538 nm, as determined using an Abbe reractometer. Results are presented in Table I for two cell thicknesses. We note that the spread in optical wavelength has little effect on the calculated values of ϕ LC. We have attempted to model our results numerically by assuming periodic boundary 6

7 conditions along the x-axis, dividing the 10 µm period into 20 slabs along x, and dividing the cell thickness into 4 slices per µm alongz [13]. WeusedtheelasticconstantsK 11 = for splay, K 22 = for twist, and K 33 = dyn for bend at T =38 C [21]. Additionally, a typical azimuthal anchoring strength coefficient W ϕ =0.005 dyn cm 2 was used for the master surface [10] and W 2 = 0 for the slave surface, where the surface free energy is given by F surf = 1W 2 ϕ(ϕ LC ϕ s ) 2 δ(z) in the Rapini-Papoular approximation [23]. The integral of the total free energy was approximated by a discrete summation and minimized by adjusting the azimuthal tilt angle profile ϕ LC (x, z) [13]. Table I also shows the calculated values of ϕ LC at z =0andatz = d. From Table I we see that the experimentally determined azimuthal rotation ϕ LC through the thicker cell is almost equal to the actual scribed orientation ϕ s for all three values of ϕ s. In fact, ϕ LC must be smaller than ϕ s because even at the master surface the splay (and to a lesser extent bend) elasticity will tend to force the director orientation slightly closer to zero. For W ϕ =0.005 erg cm 2 our numerical simulations indicate that the director s deviation from ϕ s at the master surface is approximately 5 10% of ϕ s,which would mean that the director at the slave surface is nearly uniform along the ϕ = 0 direction. Numerical simulations for this value of W ϕ areabitsmallerthantheexperimental values; a larger value of the anchoring strength coefficient (by about a factor of 2) brings the experimental and theoretical values into nearly complete agreement. For the thinner cell, for which d is about half the pixel width, we see that the experimental values of ϕ LC are considerably smaller, only about 30% of the scribed angle ϕ s. In this case the orientation at the PMMA slave substrate is similar to that at the master substrate. The numerical calculations show similar trends, although for the thinner cell the theoretical predictions for ϕ LC are all larger than the measured values. To bring theory and experiment into line it would be necessary to reduce W ϕ by a factor of about 2. Although we used a single value of W ϕ for the two cells, we suspect that the anchoring strengths in the two cells may differ even substantially. It is well known that the anchoring properties are very sensitive to the surface treatment [24], and because of the apparent yield stress of the polyimide very small 7

8 differences in rubbing can result in large differences in the anchoring strength [25]. The overall results show that for cells patterned with small pixels of characteristic length scale λ, the use of a PMMA-coated opposing substrate obviates the need to prepare and align a mirror-image pattern as long as the cell spacing d is considerably smaller than λ. The behavior of the cell may be predicted theoretically, although it clearly is important to have an accurate knowledge of the anchoring strength for accurate simulations. Acknowledgments: The authors are indebted to Drs. Ronald Pindak, Hiroshi Yokoyama, and Deng-ke Yang for useful discussions. This work was supported by the U.S. Department of Energy s Nanoscale Science, Engineering, and Technology program at Brookhaven National Laboratory under contract DE-AC02-98CH10886 and by the Donors of the Petroleum Research Fund, administered by the American Chemical Society under Grant AC7. 8

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11 Table I Thickness (µm) Angle ( ) ϕ s =40ϕ s =30 ϕ s = ± 0.4 Exp. 32 ± 2 26 ± 2 20 ± 2 Th ± 0.2 Exp. 12 ± 2 10 ± 2 6 ± 1 Th Table I. Experimental (Exp) and Theoretical (Th) values of director rotation angle ϕ LC (in degrees) through the cell for two different thickness cells, each with a splay pattern scribed at angles ϕ s = 20, 30, and

12 FIGURES FIG. 1. Photomicrograph of Schlieren texture of 5CB in a cell having both substrates coated with PMMA. FIG. 2. Schematic representation of cell. Each 10 µm wide pixel is scribed at the master substrate (z=0) in the direction shown by the arrow. Row of tilted lines show director orientation at master substrate, which becomes homogenized at slave substrate (z = d). 12

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14 ϕ s PMMA (slave) PI-2555 (master) z=d ϕ LC 10 µm z=0