Theory of Defects in Condensed Phases of Langmuir Monolayers
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THEORY OF DEFECTS IN CONDENSED PHASES OF LANGMUIIR MONOLAYERS JONATHAN V. SELINGER Department of Physics, University of California, Los Angeles, CA 90024, and Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125 ABSTRACT Recent fluorescence-microscopy experiments have observed two types of defects-star defects and striped textures-in the liquid-condensed phases of Langmuir monolayers. These defects can be understood through a continuum elastic theory. This theory predicts both splay stripes, which are driven by the asymmetry between molecular heads and tails, and bend stripes, which are driven by a spontaneous breaking of chiral symmetry in the monolayer. These predictions are compared with experimental observations. INTRODUCTION In a recent series of experiments, Qiu et at. [1-3] have observed defect textures in the liquid-condensed phases of Langmuir monolayers of fatty acids and methyl and ethyl esters. These observations use fluorescence microscopy, which is sensitive to the orientation of the molecular tilt across the monolayer. They reveal two remarkable classes of defects: star defects and striped textures. In an earlier paper (1], we discussed the theory of the star defects. In this paper, we briefly review the star defects and then concentrate on the striped textures. The star defects observed in monolayers are very similar to star defects that have been seen in tilted hexatic phases of free-standing liquid-crystal films [4,5]. In both systems, the defects consist of several sharp arms extending outward from a central point. Across each arm, the direction of the molecular tilt jumps rapidly. Two features of the star defects in monolayers are particularly interesting. First, there are normally six arms if the defect is in a finite domain of liquid-condensed phase surrounded by liquid-expanded phase, and five arms if the defect is in a macroscopic region of liquid-condensed phase. This number of arms can be understood through a continuum elastic theory [1,4,6]. Second, the defect arms exhibit a spiral form in monolayers of certain nonchiral compounds, including pentadecanoic acid and methyl esters shorter than methyl octadecanoate. The direction of the spirals is randomly clockwise or counter-clockwise. The observation of star defects give two important pieces of information about the symmetry of the phases where they occur. First, the existence of five-arm star defects is evidence that these phases are hexatic rather than liquid or crystalline. In a liquid with no bond-orientational order, a star defect would shrink down to a point vortex. In a crystalline phase, the crystalline axes would not be able to rotate smoothly between the arms to give a structure with five-fold symmetry. By contrast, in a hexatic phase, the bond-orientational order does lead to defect arms, with the tilt direction jumping with respect to the bond directions, and the bond directions can rotate smoothly between the arms to give a five-fold symmetric defect. Second, the observation of spiral defe
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