Nonequilibrium pattern formation in chiral Langmuir monolayers with transmembrane flows

Studies of pattern formation in nonequilibrium soft matter are essential for understanding the operation of biological cells and for potential applications [1]. Biological membranes including active molecular pumps or channels can develop shape oscillations and show persistent wave propagation [2, 3]. If a membrane contains rotating molecular motors, interactions between them may lead to the development of regular arrays with the crystalline order [4]. Phase separation in two-component lipid layers is responsible for budding and replication of vesicles [5, 6]. Closely related to biomembranes, Langmuir monolayers are formed by organic lipid or amphiphilic molecules disposed on a liquid-gas interface [7]. Nonequilibrium patterns of traveling orientation waves in illuminated two-component Langmuir monolayers, where illumination leads to transitions between different conformational states of molecules, have been experimentally and theoretically investigated [8, 9, 10, 11]. Recently, Tabe and Yokoyama have demonstrated that Langmuir liquid-crystal monolayers including chiral molecules (”molecular rotors”) are easily brought to and maintained at nonequilibrium conditions by transmembrane flows [12]. If there is a gradient of small molecules across a Langmuir monolayer, i.e. their concentrations in the liquid and the gas are different, this produces a flow of such molecules through the monomolecular layer. Such transmembrane flow gives rise to coherent collective precession of molecular rotors. Experiments using reflectedlight polarizing microscopy have revealed that the precession is not uniform and complex orientational wave patterns are observed. This behavior is apparently universal; it has been verified for a number of chiral chemicals and different experimental conditions [12].