Structure and fluctuations of smectic membranes

Abstract

Smectic membranes are perfect model systems for studying low-dimensional phase transitions and the associated fluctuations. During the last two decades we have seen important progress in the understanding of the structure and fluctuation behavior of these systems, driven by both new experimental techniques and theoretical developments. Phase transitions are reviewed involving liquid, hexatic, and crystalline layers, which provide several types of model system for low-dimensional melting. The authors discuss the influence of the surfaces on the physical properties of the membranes as well as the crossover from three-to two-dimensional behavior. The layer-displacement fluctuations in smectic membranes have been investigated by specular and diffuse x-ray reflectivity. Theoretical and experimental aspects of the displacement-displacement correlation function are discussed. Of special interest is the quenching or enhancement of fluctuations at surfaces, which is directly related to the phenomenon of surface ordering. The authors consider the conditions under which fluctuations are conformal throughout a membrane, and then the dynamic aspects of the layer-displacement correlation function, which include the effects of finite size, surface tension, and viscous dissipation. This leads in smectic membranes to a discrete spectrum of elastic and viscous relaxation modes, which have been studied experimentally with coherent x rays at third-generation synchrotron sources. The fluctuating character of crystalline-B membranes is also considered. Finally, the article looks briefly at thinning transitions, smectic membranes of chiral molecules, smectic films on substrates, and applications to biologically relevant systems. Open questions and future trends in the field are discussed. CONTENTS I. Motivation and Scope 182 II. Smectic Membranes 183 A. Smectic liquid-crystal phases 183 B. Main features of x-ray patterns 185

Surface and Bulk Elasticity Determined Fluctuation Regimes in Smectic Membranes

“…XPCS gives a difference in correlation times at specular and off-specular positions that can be related to different detection schemes. Low-dimensional ordering and the associated fluctuation behavior are of considerable general interest and have been studied for a wide variety of systems comprising smectic membranes (freestanding smectic films), Langmuir films, Newtonian black films, and surfactant and lipid membranes [1,2]. In this context, smectic membranes provide unique, substrate-free, and almost perfectly oriented model systems [1].…”

“…Low-dimensional ordering and the associated fluctuation behavior are of considerable general interest and have been studied for a wide variety of systems comprising smectic membranes (freestanding smectic films), Langmuir films, Newtonian black films, and surfactant and lipid membranes [1,2]. In this context, smectic membranes provide unique, substrate-free, and almost perfectly oriented model systems [1]. In these systems, the thermal fluctuations increase along with the size of the sample and eventually destroy the ordering of the liquid layers (Landau-Peierls instability) [3].…”

Phase ordering of zig-zag and bow-shaped hard needles in two dimensions

“…7 The formation of liquid-crystal phases on twodimensional surfaces is also key for various nanotechnological applications. [8][9][10] Control over self-assembly has already enabled the formation of two-dimensional aggregates with quasicrystal, [11][12][13][14] hexagonal, 15 crystal, 16 and liquid crystal [17][18][19] orders. Improving control on the spontaneous formation of ordered structures, however, requires a deep understanding of how molecular geometry influences supramolecular ordering.…”

Dynamic properties of smectic films

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