Langmuir Monolayers under two-dimensional shear
We prepare a Langmuir Monolayer by dispersing Eicosanoic Acid (C22), a fatty acid which acts as a water insoluble surfactant, on the air/water interface. A teflon Langmuir trough contains the water. A moving barrier is used to adjust the surface area of the interface. The polar heads are in contact with the water surface, and the hydrophobic tails stick out into the air. Depending on the area per molecule at which the surfactant is confined, different thermodynamic phases are possible. We are interested in studying condensed phases in which liquid crystalline ordering is observed (see phase diagram below). For a given set of values of p and T, the polar tilt of the tails is set to a particular value, uniformly in the monolayer. The azimuthal tilt of the tails, however, is not constrained to any particular value, which results in a mosaic of domains of different reflectivity, which contain molecules with parallel tails. It is possible to relate the observed reflectivity under BAM condition with the azimuthal orientation of the domains, using the Transfer Matrix formalism. We apply two-dimensional shear cycles (a shear strain in one direction, followed by the same strain in the opposite direction) on the monolayer (see sketch of the setup), and study the coupling between the imposed flow and the structure of the monolayer. Different behaviors are observed, depending on the phase, p, and on the applied shear rate, g. Domain annealing: increase in domain size and contrast (L2, L2’, and Ov). example: L2', g = 0.6 s-1, T=17 ºC, p = 20 mN/m. A total of 20 shear cycles are applied in the sequence. Domain fragmentation (L2, L2’, and Ov), which can lead to the formation of labyrinthine structure (Ov and L2). example: L2, g = 0.4 s-1, T=39 ºC, p = 27 mN/m. Tumbling of domain orientation (L2 and L2’). The azimuthal orientation of the molecules in a region of the monolayer involving different domains performs a continuous rotation. example: L2', g = 0.3 s-1, T=17 ºC, p = 20 mN/m. Formation and propagation of shear bands either along the flow or perpendicular to the flow, spanning a single domain (L2, L2’, and Ov). In Ov phase, this leads to the alignment of the fatty acid tails. Avalanche-like shear bands across multiple domains (L2 and L2’). example: L2', g = 0.3 s-1, T=17 ºC, p = 24 mN/m.
Example of BAM image of a C22 monolayer, where a mosaic of domains with different azimuthal orientation can be observed.				p-T phase diagram of Docosanoic acid (C22). The shaded regions correspond to the tilted condensed phases that have been the object of this study.