Anisotropy in Langmuir Layers of a Bent-Core Liquid Crystal

Upon decompression, the film broke into uniform islands or domains. .... P. García-Vázquez , O.G. Morales-Saavedra , G. Pelzl , J. Guadalupe Bañuel...
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Langmuir 2006, 22, 3198-3206

Anisotropy in Langmuir Layers of a Bent-Core Liquid Crystal Ji Wang,† Lu Zou,† Antal Ja´kli,‡ Wolfgang Weissflog,§ and Elizabeth K. Mann*,† Department of Physics, and Liquid Crystal Institute, Kent State UniVersity, Kent, Ohio 44242-0001, and Institut fuer Physikalische Chemie, UniVersitaet Halle-Wittenberg, D-06109 Halle Germany ReceiVed NoVember 23, 2005. In Final Form: January 24, 2006 Langmuir layers of a symmetric bent-core molecule with hydrocarbon end chains and two chlorine atoms substituted on the central phenyl ring of the bent core were characterized by a combination of surface pressure isotherms, Brewster angle microscopy, and surface potential measurements. These layers were found to be optically anisotropic, in contrast to Langmuir layers of similar molecules with different substitutions on the core. After compression, the orientation of the optical axis was essentially uniform over the film. Upon decompression, the film broke into uniform islands or domains. Measuring domain reflectivity while changing the domain orientation allowed the determination of the tilt angle with respect to both domain features and the film normal, as well as the refractive index anisotropy. The tilt angle, near 90°, suggests that the bent-core molecules lie quite flat on the surface.

Introduction Bent-core molecules have attracted more and more attention recently due to the rich variety of phases they exhibit.1 Ferroelectric phases appear because the special structure of the bent-core molecules constrains the molecule packing and the mobility. Chiral liquid crystalline phases are obtained by the spontaneous chiral organization of the achiral bent-core molecules.2 A dozen different liquid phases3 and five smectic phases4 have been suggested. The long-sought biaxial nematic phase was recently claimed in molecules with this architecture.5 The usefulness of bent-core molecules in scattering switching and in storage devices has been demonstrated.6 It has also been suggested that the unique properties of these molecules can make them useful for electromechanical devices.7 As molecular functional materials, bent-core molecules can be used in various kinds of organic devices.8 Usually, organic functional materials have been processed in the form of films serving as active layers in devices; thus, studies of growth mechanism, molecular ordering, and the overall film morphology are of prime importance for device design.7 Several groups have explored the molecular packing of such molecules in bulk both experimentally9,10 and theoretically.11 Dong et al.,10 using 13C NMR, found the bending angle for * Corresponding author. E-mail: [email protected]. Tel: 330-672-9750. Fax: 330-672-2959. † Department of Physics, Kent State University. ‡ Liquid Crystal Institute, Kent State University. § Universitaet Halle-Wittenberg. (1) Pelzl, G.; Diele, S.; Weissflog, W. AdV. Mater 1999, 11, 707. (2) Link, D. R.; Natale, G.; Shao, R.; Maclennan, J. E.; Clark, N. A.; Korblova, E.; Walba, D. M. Science 1997, 278, 1924. (3) Lubensky, T. C.; Radzihovsky, L. Phys. ReV. E 2002, 66, 031704. (4) Brand, H. R.; Cladis, P. E.; Pleiner, H. Eur. Phys. J. B 1998, 6, 347. Roy, A.; Madhusudana, N. V.; Toledano, P.; Figueiredo Neto, A. M. Phys. ReV. Lett. 1999, 82, 1466. (5) Acharya, B.; Primak, A.; Kumar, S. Phys. ReV. Lett. 2004, 92, 145506. Madsen, L. A.; Dingemans, T. J.; Nakata, M.; Samulski, E. T. Phys. ReV. Lett. 2004, 92, 145505. (6) Ja´kli, A.; Kru¨erke, D.; Sawade, H.; Chien, L. C.; Heppke, G. Liq. Cryst. 2002, 29, 377. (7) Ja´kli, A.; Kru¨erke, D.; Nair, G. G. Phys. ReV. E 2003, 67, 051702. (8) Tong, Y.; Wang, Y.; Wang, G.; Wang, H.; Wang, L.; Yan, D. J. Phys. Chem. B 2004, 108, 12921 (9) Szydlowska, J.; Mieczkowski, J.; Matraszek, J.; Bruce, D. W.; Gorecka, E.; Pociecha, D.; Guillon, D. Phys. ReV. E 2003, 67, 031702. (10) Dong, R. Y.; Xu, J.; Benyei, G.; Fodor-Csorba, K. Phys. ReV. E 2004, 70, 011704. (11) Dewar, A.; Camp, P. J. Phys. ReV. E 2004, 70, 011704.

different substitution compound of a series of bent-core molecules and a nonzero twist angle. Dewar et al.11 found that a molecular model consisting of seven Lennard-Jones spheres gave better agreement with experimental phases than a less detailed model consisting of two hard-spherocylinders. They found that the phases exhibited by the bent-core molecules depend greatly on the bentcore angle, especially at a surface. Langmuir layers can give additional insight into the molecular packing within layers. A stable Langmuir layer, transferred to a solid interface, may form a natural alignment layer for bentcore liquid crystals. To our knowledge, four sets of articles consider Langmuir layers of such molecules. The first considers a single bent-core molecule with long hydrophobic side chains.12 A very recent article, Blinov et al.,13 considers the dielectric, ferroelectric, and antiferroelectric properties of LangmuirBlodgett films of similar bent core molecules. A third set of articles considers two different cores with very short hydrophobic side chains.14 Previously,15 we studied Langmuir layers of five bent core molecules varying both the core and the end-chains but maintaining molecular symmetry, with identical end-chains on either end of the core. The characterization includes systematic surface pressure isotherms, Brewster angle microscopy (BAM),16 and surface potential measurements. We demonstrated that it is possible to make stable Langmuir layers of a variety of different bent-core molecules. Two were siloxane end-chain molecules. With these amphiphilic end-chains, the molecules lie quite flat on the surface, with both core and end-chains in direct contact with the air/water interface. The other three molecules were hydrocarbon end-chain molecules, with groups of different hydrophobicity substituted at the inner angle of the core. With these hydrophobic chains, the molecules form a complex multilayer structure; surface potential, surface pressure, and other (12) Kinoshita, Y.; Park, B.; Takezoe, H.; Niori, T.; Watanabe, J. Langmuir 1998, 14, 6256. (13) Blinov, L. M.; Geivandov, A. R.; Lazarev, V. V.; Palto, S. P.; Yuding, S. G.; Pelzl, G.; Weissflog, W. Appl. Phys. Lett. 2005, 87, 241913 (14) Ashwell, G. J.; Amiri, M. A.; Mater, J. J. Mater. Chem. 2002, 10, 2181. Baldwin, J. W.; Amaresh, R. R.; Peterson, I. R.; Shumate, W. J.; Cava, M. P.; Amiri, M. A.; Hamilton, R.; Ashwell, G. J.; Metzger, R. M. J. Phys. Chem. B 2002, 106, 12158. (15) Zou, L.; Wang, J.; Beleva, V. J.; Kooijman, E. E.; Primak, S. V.; Risse, J.; Weissflog, W.; Ja´kli, A.; Mann, E. K. Langmuir 2004, 20, 2772. (16) He´non, S.; Meunier, J. ReV. Sci. Instrum. 1991, 62, 936. Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590.

10.1021/la0531805 CCC: $33.50 © 2006 American Chemical Society Published on Web 02/23/2006

Anisotropy in a Bent-Core Liquid Crystal

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Figure 1. Molecule formula (a) and space filling model (b) for the Bc-2Cl. The phase sequence in bulk is Cr 106 °C (SmC 88 °C) N 143 °C I.18 The phase in parentheses appears only in cooling.

results suggest that these structures are quite similar with the different cores. However, the precise organization of the bentcore molecules within the film was difficult to assess due to the complexity of the molecules and the number of imaginable configurations. This work considers a very similar bent-core molecule, but with two chlorine atoms attached on the outside of the center phenyl ring (positions 4 and 6), compared to various compounds substituted in the inner angle of this phenyl ring (position 2) reported in the previous article.14 The material under study, Bc2Cl, belongs to the first class of compounds derived from the original bent-core liquid crystals,17 but unlike most of those, it exhibits conventional smectic phases. To understand this behavior, extensive NMR measurements have been performed in the liquid crystalline state of bent-core mesogens. It was shown that the bending angle grows from 120° to about 165° with the attachment of lateral substituents near to the connecting groups, in the positions 4 and 6 of the central ring.18,19 The nearly rodlike shape of these molecules could be independently confirmed by singlecrystal X-ray studies.18,20 Recently, this behavior was further supported by investigations of compounds having the same structure as the compound under study but bearing fluorine and chlorine atoms, respectively, at the outer rings. The bending angle is fundamentally determined by the substituents at the inner ring, and furthermore, the bending angle decreases with decreasing temperature.21,22 Because of the large angle, smectic phases appear in bulk. In thin layers on water, we find that much of its behavior is very similar to the hydrocarbon molecules previously studied, with multilayers forming at about the same area per molecule. The striking difference is that the films of the molecules with chlorine are obviously optically anisotropic. The goal of this work is to measure that anisotropy and to relate it to the domain structure. Brewster angle microscopy has been used previously to determine the tilt angle of the extraordinary axis in Langmuir layers.23,24 Hosoi et al.22 determined the molecular tilt angle in domains through a (17) Niori, T.; Sekine, F.; Watanabe, J.; Furukawa, T.; Takezoe, H. J. Mater. Chem. 1996, 6, 1231. (18) Pelzl, G.; Diele, S.; Grande, S.; Jakli, A.; Lischka, Ch.; Kresse, H.; Schmalfuss, H.; Wirth, I.; Weissflog, W. Liq. Cryst. 1999, 26, 401. (19) Weissflog, W.; Lischka, Ch.; Diele, S.; Pelzl, G.; Wirth, I.; Grande, S.; Kresse, H.; Schmalfuss, H.; Hartung, H.; Stettler, A. Mol. Cryst. Liq. Cryst. 1999, 333, 203. (20) Hartung, H.; Stettler, A.; Weissflog, W. J. Mol. Struct. 2000, 526, 31. (21) Eremin, A.; Nadasi, H.; Pelzl, G.; Diele, S.; Kresse, H.; Weissflog, W.; Grande, S. Phys. Chem. Chem. Phys. 2004, 6, 1290. (22) Weissflog, W.; Dunemann, U.; Schroeder, M. W.; Diele, S.; Pelzl, G.; Kresse, H.; Grande, S. J. Mater. Chem. 2005, 15, 939. (23) Hosoi, K.; Ishikawa, T.; Tomioka, A.; Miyano, T. Jpn. J. Appl. Phys. 1993, 32, 135.

quantitative analysis of their Brewster angle microscopic images, assuming that different reflective intensities correspond to a uniform tilt angle but the whole range of the orientation in the plane of the film (azimuth angle). Lautz et al.23 used Brewster angle autocorrelation spectroscopy to measure the tilt angle of the extraordinary axis of the layer, again assuming the whole range of the azimuthal angle from 0° to 360°. These methods are not appropriate to the present case, where the horizontal (azimuthal) orientation of the extraordinary axis is essentially constant over the whole layer, roughly perpendicular to the compressing barriers. By rotating the domain, we were able to determine both the orientation of an extraordinary axis and an optical anisotropy from direct optical measurements on single domains, which has never been done on a Langmuir layer, to the best of our knowledge. We also provide systematic surface pressure isotherms, Brewster angle microscopy, and surface potential measurements. Materials and Methods The chemical structure of the bent-core molecule studied, which we will call Bc-2Cl, is shown in Figure 1. The material is deposited with a chloroform (Aldrich, A.C.S, HPLC grade) spreading solution onto a pure water surface. Water was purified with a Purelab Plus UV system (US Filter, resistivity 18.2 MΩ/cm) and held in a homemade Teflon minitrough, which performed well in tests against leakage around the KSV hydrophilic barriers. The minitrough was cleaned with KOH solution (KOH, 25 g; water, 24 g; C2H6O, 136 g) and rinsed copiously with pure water. A platinum wire was used to change the orientation of the multilayer domains. It was cleaned first by KOH solution followed by chloroform. All of the experiments were carried out at 17 °C ( 1 °C and ∼50% humidity. The Langmuir films were characterized by surface pressure and surface potential measurements and imaged by Brewster angle microscopy. The surface pressure measurements were performed via the Wilhelmy method. Surface potential measurements were performed with the KSV SPOT1 surface potential meter, which works via the vibrating plate capacitor method. The probe head diameter was 17 mm. The BAM was assembled in our laboratory with the standard design. Incident light at 668 nm (SDL 7470-P6), polarized (GlanTayler, Lambrecht MGTYE15) in the plane of incidence, was reflected off the layer at the Brewster angle to a biconvex lens that focused the image on a CCD camera (Panasonic GP-MF602, image pixel 704 × 874). The field of view was either 12.1 mm × 15.5 mm or 3.1 mm × 3.9 mm. A diachroic sheet analyzer (Melles-Griot) was installed before the camera to check for any in-plane optical anisotropy in the layer. During the experiments, images were captured directly (24) Lautz, C.; Fischer, Th. M. Mater. Sci. Eng. 1996, C5, 271. Lautz, C.; Fischer, Th. M.; Kildea. J. J. Chem. Phys. 1997, 106 (17), 7448.

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from the camera output by a frame grabber to a PC. Surface pressure and surface potential measurements were recorded simultaneously using the KSV system. The gray level in the CCD image depends on the reflectivity R of the surface and with care can be used to quantitatively deterimineR for different domains. Grey levels G ranged from 0 for saturation to 255 for complete darkness. A standard test25 comparing the gray level for light transmitted through two polarizers onto the camera with Malus’ law for the light intensity, I ∝ cos2 R, to the relative gray level Gr ) Gb - G

(1)

as a function of analyzer angle R with respect to fixed incoming polarized light demonstrated that the gray level was linear in incoming light intensity within the (2% uncertainty. R ) (θp - θA) is the angle of the second polarizer (the analyzer, with angle θA) with respect to the first polarizer (angle θp), and Gb is the gray level associated with the background signal (stray light, dark current, etc.). In analyzing the reflectivity, we took the background Gb as the gray level observed with a pure water surface and the same incoming light intensity Iinc, to maintain consistent experimental conditions. In principle, pure water is rough and thus also reflects light at the Brewster angle, which here is improperly included in Gb. However, typical values for Gr were much greater than the variation of Gb with Iinc, which includes the entire roughness contribution in Gb, so this complication can be ignored. Reflectivities varied by a factor of ∼2000 for different layers, so that Iinc was adjusted during the different experiments to maintain reasonable contrast without saturating the camera. A power meter (LaserCheck, Coherent) was used to measure Iinc often, normally before and after each video was taken. Since Gr is linearly related to the light onto the detector, the CCD gray level is linearly related to the reflected intensity for a fixed incoming beam Gr Iref ∝ )R Iinc Iinc

(2)

The constant of the proportionality can be found through careful calibration. We used 5 filters (Edmund, Absorptive Neutral Density Filters in the range 3 × 10-5-3 × 10-4) to find Gr ) (5.5 ( 0.2) × 105R for the reference incident intensity. For anisotropic domains, the reflectivity depends on the orientation of the molecules. To study the anisotropy of the multilayer, a platinum wire was used to stir the surface so the domain turned by 360°. We varied R in the range from 0° to 180°. For each R, we measured domain orientation φm as the angle between some obvious domain feature and the x axis, which is parallel to the barrier. Note that the reflectivity for a uniaxial layer, given by eq A-7, depends on φ ) φ0 + φm, the angle between the projection of the extraordinary axis on the surface and the x axis (Figure 2), where φ0 gives the difference of the orientation of the obvious surface feature and the projection of the extraordinary axis on the surface. Fitting software was designed based on eq A-7. Using R as a known parameter of R(φ,R;t,φ0,h,⊥,∆), we can deduce the film dielectric constant perpendicular to the extraordinary axis ⊥ and the anisotropy ∆ ) | - ⊥, the angle t between the extraordinary axis and -z axis, the azimuth angle φ0 and the layer thickness h. The extent to which these can be determined independently will be discussed later.

Experimental Results Three bent-core molecules with hydrocarbon end-chains BcH, Bc-NO2, and Bc-CH3 were previously characterized.14 These molecules have similar structure to the Bc-2Cl molecule but with H in place of the Cl and different groups H, NO2, and CH3 at the inner angle of the central phenyl ring, in the obtuse angle of the bent molecule. Compared to these three molecules, (25) de Mul, M. N. G.; Adin Mann, J., Jr. Langmuir 1998, 14, 2455.

Figure 2. (a) Optical model for the uniaxial layer. (b) Reflection of a plane wave by a stratified anisotropic slab sandwiched between air and water. θB is the Brewster angle. The mutually orthogonal axes X and Y are in the ambient/slab interface, parallel and perpendicular to the plane of incidence, respectively; the Z axis is in the direction of stratification.

Figure 3. Thin layers observed on the water surface under BAM. (a) Very dilute layers of Bc-2Cl, σ ∼ 58.3 nm2/molecule. (b) Thin layers of Bc-2Cl before the compression, σ ∼ 0.41 nm2/molecule. The reflectivity of the domain in panel a is about 10 times smaller than for those in panel b. The bars are 1 mm.

Bc-2Cl shows both similarities and differences. The thinnest layers of Bc-2Cl (Figure 3a) are similar to the Bc-H, Bc-NO2, and Bc-CH3. Both types of layers are uniform with curved edges and jagged corners. Bright bands form along the domain edge in some cases of the very thin layer of Bc-H26 and not in Bc-2Cl. In this regime, the surface pressure measurements were indistinguishable from pure water, even when compressed as far as possible. It was necessary to deposit several times more material on the water before an isotherm measurement (Figure 3b). Figure 3b shows the surface right before the compression. The brightness of the layer is 10 times greater than the very dilute layer shown in Figure 3a. The boundaries between regions of different reflectivity are less distinct in Figure 3b than in Figure 3a. The reflectivity varies by about 50% over Figure 3b, which would correspond to a 25% difference in layer thickness. However, we will see that this layer is anisotropic, so the difference in reflectivity may be due to the different orientation of the molecules rather than the difference in layer thickness. A representative isotherm is shown in Figure 4a. Both surface pressure and surface potential measurements have been made. The compression and decompression speed are both 5 mm/min. Like isotherms for the previous bent-core molecules, the surface pressure measurement of the first compression is not reproducible, with the pressure beginning to rise for σ in the range 0.27-0.35 nm2/molecule. Unlike isotherms for the other three molecules, Bc-2Cl isotherms all have a shoulder within 0.2-0.3 nm2/ molecule after the surface pressure starts increasing, at 16-18 mN/m. The second compression is much more reproducible. The co-area of the second compression is 0.11 ( 0.01 nm2/ molecule, similar to 0.12 ( 0.01, 0.13 ( 0.01, and 0.14 ( 0.02 (26) Zou, L. unpublished.

Anisotropy in a Bent-Core Liquid Crystal

Figure 4. Representative isotherm for Bc-2Cl. (a) Surface pressure π versus σ and (b) surface potential ∆V versus σ, for the first compression (straight line) and decompression (dash line).

nm2/molecule for the three previous three hydrocarbon bentcore molecules Bc-H, Bc-NO2, and Bc-CH3 respectively. These co-areas certainly represent multilayers, since even a single hydrocarbon chain covers ∼0.2 nm2. Figure 4b, shows the surface potential isotherms for the first compression and first decompression. In the first compression, the surface potential reached 0.4 V as the pressure started to increase. As the surface pressure increases, the surface potential increases steadily, by up to 60% after a factor of 3 decreases in area. For the other molecules, in the first compression, Bc-NO2, Bc-H, and Bc-CH3 reached 0.45, 0.4, and 0.38 V, respectively as the pressure started to increase. For these molecules, as the surface pressure increases, the surface potential increased no more than 30% over the same range. The larger increase in surface potential of Bc-Cl2 in the multilayer regime may indicate less compensation between layers, less symmetry, or more rearrangement as the layer become thicker, for this molecule compared with the others. The morphology of the Bc-2Cl is also different from that of the other three molecules during compression/decompression cycles. Bc-NO2, Bc-H, and Bc-CH3 show at least three different reflectivities at the beginning of the compression, whereas the layer brightness for Bc-2Cl varies by at most 50% within the field of view. As σ decreases, uniform layers form defect lines parallel to the barriers (Figure 5a-c). As σ decreases further, the brightness of the whole layer continuously increases, by a factor of ∼9. When turning the analyzer, the thicker layers are obviously optically anisotropic. Small domains are clearly visible with the analyzer crossed with the polarizer (Figure 5d). With decompression, the layer (Figure 5e) breaks up immediately into several small pieces. The gray level of the layers then remains constant as σ increased. These isolated pieces were turned (Figure 6) using a platinum needle to stir the underlying fluid, to determine the optical characteristics of the anisotropic layer by measuring the reflectivity of individual pieces as a function of orientation and of analyzer angle. The orientation is given by the angle between an obvious surface feature, typically a straight domain boundary, and the barriers (the x axis in Figure 1b). Characterization of the Layer Optical Anisotropy. In a uniaxial model, at a particular analyzer angle R, the relative reflective intensity R as a function of domain orientation depends on five variables: the analyzer angle R, the tilt angle with respect to the surface normal t, the difference φ0 between the orientation of the obvious surface feature used to determine the domain orientation and the projection of the extraordinary axis on the surface, the film dielectric constant perpendicular to the extraordinary axis ⊥, and the anisotropy ∆. However, only two

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of these, φ0 and t, can be determined independently, whereas three of these variables (the dielectric constant ⊥, the anisotropy ∆ ) | - ⊥, and the thickness of the layer h) are correlated with each other in the fitting. Which parameters can be deduced independently from the data can be seen quite directly from the form of the curves (see Figure 7). Each curve exhibits two maxima for small R and, depending on t, exhibits two or four maxima for large R. The position of these maxima and minima are given directly by φ0, which can thus be determined by inspection within a constant of 180°. The general shape of the curve at a given R is dominated by t. When R > 74°, t will determine how many peaks appear, as well as the difference in peak height. Thus, the tilt t can be determined uniquely when t is large, as we find in these experiments by looking at experiments with large R. For example, Figure 7c shows the reflected intensity as a function of domain orientation in the layer after the first decompression with R ) 90°. These curves show 4 peaks that are nearly equal in height. This directly implies that t is close to 90°. The remaining obvious characteristics of the curve are the average reflected intensity, which depends on a combination of ⊥, h, and ∆, and the variation from minimum, which depends on h, ∆, and t. Three parameters cannot be determined uniquely from these remaining two curve characteristics at a given R. Any more subtle curve characteristics cannot be distinguished within the experimental uncertainty. The anisotropy is most easily seen in condensed multilayers. After the first decompression at σ ∼ 0.28 nm2/molecule, the multilayers cover about 45% of the surface. The remaining surface was optically indistinguishable from pure water. We could then rotate the domain without major disturbance of the Langmuir layer. Any material deposited on the platinum wire affects the remaining layer negligibly. The reflected intensity was measured in uniform regions (avoiding defect structures) as the domains turned for values of R from 0° to 180° in 30° steps. As the domain rotated on the surface, the light intensity changed, as shown in Figure 6. The measured R from the BAM images compared to the computed R for R ) 0°, 150°, and 90° are shown in Figure 7. Three different domains were used in the fitting over a total of 6 values for R. The dielectric constant ⊥ and the anisotropy ∆ cannot be determined uniquely, but t and φ0 can be: t ) 89° ( 1° and φ0 ) 90°( 2°. All domains and all R gave the same values for ∆ and t, within their uncertainties. The same domain with different R gave the same value for h, with 10% uncertainty, but two different values were found for h, implying two different domain thicknesses (discussed below). For the layers before compression, it is not clear directly from the still images whether the layer is anisotropic since the layers are quite uniform except for the defect structure (Figure 5a), and the signal for crossed polarizers is so small that it is difficult to distinguish it from zero without the contrast that different orientations provides. We thus repeated the experiment rotating the domains at σ ∼ 0.4 nm2/molecule with coverage ∼90%. The tilt angle t is best determined for R close to 90°. However the domains are sufficiently thin that the intensity was insufficient. We chose R ) 70° or 110° as the angle closest to 90° with sufficient domain contrast. The gray levels of the domains at different orientation were measured at the R value at 30°, 60°, 110°, and 150°. The fitting is much more challenging since the layer thickness is small. When stirring the surface to change the orientation of the domains, the water surface is unavoidably disturbed. The small surface tilt with the vibrations of the water substrate brings the surface a little off the Brewster angle, where the intensity depends very strongly on the angle of incidence. The intensity

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Figure 5. Representative BAM images of Bc-2Cl layers on water at different molecular areas σ during successive compression. (The bar represents 1 mm.) The barriers are parallel to the horizontal axis. (a) The image at the beginning of the compression with σ ∼ 0.4 nm2/molecule; (b) the image at the end of the compression with σ ∼ 0.068 nm2/molecule (c) the image at the end of the compression with σ ∼ 0.068 nm2/molecule; (d) the image with crossed polarizer with σ ∼ 0.068 nm2/molecule; and (e) the image at the first decompression with σ ∼ 0.28 nm2/molecule.

Figure 6. Typical domain showing different brightness at different orientation φ. Here the angle of the analyzer with respect to the polarizer is R ) 30°. Bars correspond to 1 mm.

change due to vibrations is about 20%. All of these effects account for the large uncertainty. Representative fitting graphs are presented in Figure 8. In most cases (6 out of 7 domains in thick layer fitting after the first decompression and 4 out of 6 domains in thin layer fitting just before the compression), the extraordinary axis is perpendicular to the long, straight edge of the domain as shown in Figure 9.

In eq A-7, ⊥ and ∆ are too correlated in the fits to be obtained independently with this method. Instead, one can find the relationship between ⊥ and ∆. Our fitting results reveal that the extraordinary axis is almost flat on the water surface. For t ) 90°, the maxima (Rmax) and minima (Rmin) provide the major characterizations for the graph. As shown in the contour plot in Figure 10, for R ) 0°, 30°, and 60°, the contour surface 2(Rmax - Rmin)/(Rmax + Rmin) versus ∆ and ⊥ is flat. For different

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Figure 9. Schematic image of the orientation of the extraordinary axis on a domain after a compression/decompression cycle. The bar represents 1 mm, and the arrow represents the extraordinary axis. Figure 7. Representative computed reflectivity as a function of domain orientation φ(line), compared to the experimental result (squares) three typical domains after the first compression/ decompression cycle. (a) R ) 0°, (b) R ) 150°, (c) R ) 90°.

Figure 10. Contour graph of ratio 2(Rmax - Rmin)/(Rmax + Rmin) versus dielectric constant ⊥ and the anisotropy ∆ ) | - ⊥ at (a) R ) 0°, (b) R ) 30°, and (c) R ) 60°. The dashed line in each graph represents the experimental ratios. Note that the lines are essentially parallel in the two graphs.

Figure 8. Representative computed reflectivity as a function of domain orientation φ (line) compared to the experiment result (square dot) four typical domains before the first compression. (a) R ) 30°, (b) R ) 60°, (c) R ) 110°, (d) R ) 150°.

R, these flat surfaces are parallel to each other. Above R ) 60°, the minimum is about zero, and a better measure for all R, as shown in Figure 11, compares the average (Rmax + Rmin)/2 of each R with the average value for R ) 0°. The contour surfaces are still parallel to each other for all R. The linear relationship between ∆ and ⊥ is ∆ ) a + b⊥ (2) where we find a ) -0.93 ( 0.01 and b ) 0.49 ( 0.01. More detailed information about the surface and the incoming beam is needed to determine ⊥ and ∆ separately. In fitting eq A-7, only the layer thickness h correlates to ⊥ and ∆ for a given R(φ,R;t,φ0,h,⊥,∆). The observed molecular areas of ∼0.09 nm2 (at the first decompression, where 95% of the film was very uniform except for defect lines and the coarea was a good estimate of the molecular area for that film) would, in this simplified model, correspond to a film thickness ∼15 ( 2 nm. This leads to ⊥ ) 2.26 ( 0.05 and ∆ ) 0.18 ( 0.025, which correspond to the refractive indexes n0 ) 1.505 ( 0.015 and ne ) 1.56 (

0.02. A small number of domains with layer thickness 10% less were also found. The presence of these regions and of the defect lines are included in the uncertainty given for the film thickness. The solutions discussed above are the only ones within the physically reasonable range of parameters. The quantity χ2 ) Σ[(Ri,theo - Ri,exp)/σ]2/(N - 1), where Rtheo and Rexp are the calculated and experimental reflectivities respectively and σ is the estimated uncertainty, measures the goodness of fit. One example (for the set of data shown in Figure 7b with alpha angle R ) 150°) of the contour graph of χ2 versus ⊥ and ∆, taking the best-fit layer thickness h, is shown in Figure 12a. The minimum calculated χ2 is ∼ 2.3. We consider the highlighted area, with χ2 less than 4.5, as acceptable fitting results. Figure 12b shows the contour graph of the best-fit layer thickness h of the layer after the first compression versus ⊥ and ∆. As discussed in the text, the isotherm suggests h ) 15 ( 1 nm. The intersection of the two highlighted areas will represent acceptable fitting results for the layer. The thin layer before the compression shows similar R(R) behavior to the thick layers. The layer thickness was estimated to be ∼3.0 ( 0.2 nm by fitting the curves using the same dielectric constants as found for the thicker layer. The grey level was related to the reflectivity by normalizing for the increased intensity of the incoming light.

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Figure 11. Contour graph of the ratio (Rmax + Rmin)R/(Rmax + Rmin)R ) 0° for (a) R ) 30°, (b) R ) 60°, and (c) R ) 90° versus the dielectric constant ⊥ and the anisotropy ∆ ) | - ⊥. The dashed line in each graph represents the experimental ratios. Note that the lines are essentially parallel in the three graphs.

Wang et al.

Figure 13. Layer thickness of the different layers observed at zero pressure for Bc-2Cl. Dilute: σ ∼ 58.3 nm2/molecule. 0 Cycle: σ ∼ 0.4 nm2/molecule before first compression. 1 Cycle: σ ∼ 0.28 nm2/molecule, after one compression/decompression cycles. The error bars indicate the variations between domains of the determined thickness, consistent with the uncertainties in the measurements. Note that for each case the background is consistent with a pure water surface, much less than even the thinnest dilute layer.

a pure water surface, much less than even the dilute layer (the uncertainty for the background thickness can barely be seen to the left of each set of layers).

Discussions and Conclusion

Figure 12. (a) Contour graph of χ2 versus ⊥ and ∆ (taking the best-fit for the film thickness h) with analyzer angle R ) 150°. The minimum calculated χ2 is ∼2.3. We consider χ2 less than 4.5 (highlighted area) as acceptable fitting results. (b) Contour graph of the best-fit layer thickness h of the layer after the first compression versus ⊥ and ∆. As discussed in the text, the isotherm suggests h ) 15 ( 1 nm. The intersection of the two highlighted areas will represent acceptable fitting results for the layer.

An example of the layer thickness, as estimated from the gray levels at different incident intensities, of these different layers is given in Figure 13. The layers at 0 cycles and after 1 cycle are anisotropic. The layer observed at very dilute surface concentrations also appears to be anisotropic, but the uncertainties were too large for the fitting above. If the optical density of the layers remains constant, the reflectivity is proportional to the square of the layer thickness for a given R angle. By comparing the dilute layer and the layer before compression at R ) 0°, the layer thickness of the dilute layer is estimated to be ∼0.6 nm. Although the two thick layers after one cycle appear to be within error limits of each other, these errors combine uncertainties from all different measurements. By comparing two domains in the same set of images, the difference in thickness of these layers is ∆L ) 1.5 ( 0.2 nm, more than twice the thickness of the dilute layer. Note that for each case the background is consistent with

The bent-core molecule Bc-2Cl has two chlorine atoms at the outer side of the center of the phenyl ring (as shown in Figure 1). The phenyl rings themselves are amphiphilic, whereas the existence of the chlorines increases its hydrophobicity. The two hydrocarbon end chains are hydrophobic. One can expect the center core of molecules to prefer good contact with the water surface, whereas the end chains are more willing to leave it. Brewster angle microscopy immediately tells us that the molecule can form thin layers of constant thickness, where this thickness can have more than one value. The surface pressure measurement shows similar results to the three bent-core molecules with hydrocarbon end chains we studied previously.14 The coarea of the second compression is about 0.12 ( 0.01 nm2/molecule, which is within 20% of the coarea of the other three bent core molecules with hydrocarbon chains. We thus expect the layers to have similar thicknesses and perhaps similar structures. Note that all of these films must be multilayers, since even a single vertical hydrocarbon chain has a coarea of ∼0.2 nm2. Many different multilayer configurations of these complex molecules may give similar co-areas. For example, if the molecules lie as bows flat to the surface, it would take about 27 layers to give this coarea. On the other hand, if the molecules stood up straight on one end, it would take about four layers to give this co-area. Other information is needed to determine layer structure. One such piece of information is the optical anisotropy and in particular the orientation of any optical axes. Although the bent-core films studied here show very similar coareas to films of the previous set of bent core molecules, Langmuir films of the bent-core molecule studied here are very different in showing measurable optical anisotropy. Such anisotropy is sometimes seen with more rod-shaped mesogens,24 as these may be compared to the usual bent-core ones. However, simpler mesogens forming smectic liquid crystals show simple, stable monolayers as well as the multilayers observed here and the spontaneous appearance of domains of different in-plane orientation.24 Here, after compression the optical axis appears well-aligned with respect to the direction of the compression. The optical anisotropy of the Bc-2Cl layers provides additional information on the layer structures. We successfully fit the dependence of the reflectivity on analyzer angle and on the domain orientation at the surface to a uniaxial model for the layer. The

Anisotropy in a Bent-Core Liquid Crystal

fitting results for the refractive indexes are reasonable for this kind of material. However, by the nature of these experiments, we cannot exclude the possibility of a biaxial structure, with one of the axes perpendicular to the water surface. This is indistinguishable from the uniaxial case because that direction is the symmetry axis of the microscopy. A tentative trial to fit the data to a biaxial structure demonstrates, as expected, that the fitting results are not unique. The observed tilt of t ) 89° ( 1° can in principle be compared with the molecular structure. Bent-core molecules are intrinsically biaxial. The natural axes of such a molecule are27 (1) along a line drawn between the end phenyl groups; (2) perpendicular to this long axis, in the plane of the bent core; (3) perpendicular to the long axis and to the bent core. In many condensed phases, averaging leads to a single optical axis, the uniaxial model assumed here. Because of the many different configurations possible for these multilayers, the orientation of a major optical axis is not alone enough information to determine the molecular structure but, in conjunction with future results, may be a valuable clue. The uniaxial fitting of domain reflectivity, as domains rotate between polarizers with different relative orientation, demonstrates that an extraordinary axis lies almost flat on the water surface and perpendicular to the long straight domain edge. Judging by the orientation of the optical axis with respect to the defect lines in these small domains, the optical axis in the original layer is probably perpendicular to the barriers which compress the film. The underlying molecular orientation is not clear, since many possibilities exist for molecule packing. However, the observation is consistent with the preliminary results of molecular dynamic simulations28 which also suggest a possible configuration with the molecules quite flat on the surface. As expected, the two chlorine atoms keep a good contact with the water surface, the core is on average at the surface and the end chains are on average at a slightly lager angle with respect to the surface. This is consistent with the optical fitting result of t ) 89° ( 1°. This general orientation appears to be maintained with groups of several molecules, although simulations have not yet extended to multilayers. A flat monolayer thickness is estimated to be ∼1 nm. The very dilute layer we observed (shown in Figure 13) may be such a monolayer, whereas the difference in thickness between our two thickest layers is a little more than that. Our results suggest that the flat orientation is maintained within the multilayer. The molecule lying nearly flat on the surface would explain the tilt angle of the extraordinary axis. Further simulations and experiments are required to determine the origin of the difference in anisotropy between Langmuir layers of different bent-core molecules. It could lie in the orientation of the molecules with respect to the surface or in how they pack on the surface. Another possibility would be that the isotropic layer is locally anisotropic but exhibits random oriented domains on a scale much smaller than the wavelength of the light (668 nm).29 We plan to carry out atomic force microscopy (AFM) studies on layers transferred to a solid substance to begin to address this question. Acknowledgment. This material is based upon work partially supported by the National Science Foundation under Grant No. 9984304. The authors would like to thank Daniel J. Lacks for sharing preliminary results on molecular simulations of bentcore molecules on the water surface, HaiJun Yuan for sharing his code for determining the optical properties of anisotropic (27) Peizl, G.; Diele, S.; Grande, S.; Jakli, A.; Lischika, C. H.; Kresse, H.; Schmalfuss, H.; Wirth, I.; Weissflog, W. Liq. Crys 1999, 26, 401. (28) Lacks, D. J. personal communication. (29) Liao, G.; Stojadinovic, S.; Pelzl, G.; Weissflog, W.; Sprunt, S.; Jakli, A. Phys. ReV. E 2005, 72, 021710.

Langmuir, Vol. 22, No. 7, 2006 3205

thin layers, for comparison purposes, and Guangxun Liao for help in programming.

Appendix The reflectivity of uniaxial Langmuir films was first considered by He´non.30 The following is a treatment of the reflectivity of a unaxial thin film using 4 × 4 matrix methods, as discussed in the classic text by Azzam and Bashara.31 Similar published results,30,32,33 are in different formats but give the same fitting results. A uniaxial medium was considered with ∆ ) | - ⊥ and with arbitrary director orientation t and φ as shown in Figure 2a. The medium was bounded by two planes: z ) z1 and z ) z2 (Figure 2b). Light is incident from air onto the plane z1with an angle of θB to the z axis. The dielectric tensor can be expressed by

[

) ⊥ + ∆ sin2 t cos2 φ ∆ sin2 t sin φ cos φ -∆ cos φ cos t sin t 2 2 ∆ sin2 t cos φ sin φ ⊥ + ∆ sin t sin φ -∆ sin φ cos t sin t -∆ cos φ cos t sin t -∆ sin φ cos t sin t ⊥ + ∆ cos2 t

]

From Maxwell’s equations, a set of four linear differential equations can be derived for the tangential components of the electric and magnetic field vectors

dψ ) - ik0(z)ψ dz

(A-1)

with Ψ ) (Ex,Hy,Ey, - Hx)T, k0 ) ω/c and where

[

∆11 ∆ ∆(z) ) 21 0 ∆23 ∆11 ) -

∆12 ∆11 0 ∆13

0 0 ∆34 0

]

∆ sin t cos t cos φ η 33

∆12 ) 1 ∆13 )

∆13 ∆23 0 ∆43

η2 33

∆ sin t cos t sin φ η 33

⊥ ∆ sin2 t cos2 φ ∆21 ) ⊥ + 33 ⊥ ∆ sin2 t sin φ cos φ ∆23 ) 33 ∆34 ) 1 ∆43 ) ⊥ +

⊥ ∆ sin2 t sin2 φ - η2 33

33 ) ⊥ + ∆ cos2 t η ) sin θB (30) He´non, S. Ph.D. Thesis; University of Paris: Paris, 1991. http:// tel.ccsd.cnrs.fr/docs/00/04/47/72/PDF/tel-0000B113.pdf. (31) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and polarized light; Elsevier Science Publishers: New York, 1989; Chapter 4. (32) Tabe, Y.; Yokoyama, H. Langmuir 1995, 11, 699. (33) Inge´s-Mullol, J.; Claret, J.; Sague´s, F. J. Phys. Chem. B 2004, 108, 612.

3206 Langmuir, Vol. 22, No. 7, 2006

Wang et al.

The solution of eq A-1 can be written by use of a 4 × 4 transfer matrix (z2,z1) as follows:

ψ(z2) ) P(z2,z1)ψ(z1)

and

(A-2)

When the medium is homogeneous, there exists an expression for (z2,z1)

k0h (k0h)22 (z2,z1) ) exp(-ik0h(z)) ) -i + ... 1! 2!

(A-3)

Rsp )

[ ] [ l12 l22 l32 l42

l13 l23 l33 l43

l14 l24 l34 ) l44

1 - ik0h∆11 -ik0h∆21 0 -ik0h∆23

IR ) |E|2 ) |Erp cos R + Ers sin R|2 By eqs A-4-A-6

- ik0h∆12 1 - ik0h∆11 0 -ik0h∆13

-ik0h∆13 - ik0h∆23 1 -ik0h∆43

0 0 -ik0h∆34 1

]

By using the 4 × 4 matrix method, the reflection for the Langmuir layer can be calculated as follows:

[ ] [

(A-6)

An analyzer with orientation R with respect to p-polarization is used to modify the polarization state of the reflected light beam before it falls on the camera. The light intensity at the camera is then equal to

where h ) z2 - z1 is the thickness of the layer. Only the first two terms were kept because the thickness of the Langmuir layer in our case is within 20 nm

l11 l (z2,z1) ) l21 31 l41

l41 cos θB + l42 1/cos θB

][ ]

Erp Rpp Rps Eip Ers ) Rsp Rss Eis

[(

- ⊥ + 2

1-

sin θB ⊥ + ∆ cos t

[ ] [ ] Erp RppEip Ers ) RspEip

2

]

)

⊥∆ sin2 t cos2 φ ⊥ + ∆ cos t 2

+ sin R

cos2 θB +

2∆ sin t sin φ (cos t sin θB + ⊥ + ∆ cos2 t

}

2

⊥ sin t cos φ cos θB)

(A-4)

Eis is zero in this case since the incident light is p polarized

{

1 1 R ) cos2 θB(k0h)2 cos R 2 × 4 cos θB

(A-7)

This equation A-7 was used directly to fit the data. The results of the fitting software agreed with those from software developed independently using a slightly different method of calculating the reflectivity.34

where LA0531805

- l21cos2 θB + l12 Rpp ) 2 cos θB

(A-5)

(34) Yuan, H.; Kosa, W.; Palffy-Muhoray, P. Mol. Cry. Liq. Cryst. Sci. Technol. Sect. A 1999, 331, 2351.