Fig. 1: Schematic sketches of surfactant monolayers at the surface of aqueous solutions (left), in emulsions (middle), and stabilizing liquid films (e.g. in foams)
Fig. 1: Schematic sketches of surfactant monolayers at the surface of aqueous solutions
(left), in emulsions (middle), and stabilizing liquid films (e.g. in foams)
The lungs are also covered by such sheets in order to lower the surface tension of the tissue and thereby reduce the mechanical work of breathing. (More on lung surfactant)
These quasi-two-dimensional systems are usually subjected to the water-air interfacial tension. The tension can be relieved by applying lateral pressure (e.g. in a Langmuir trough or by the lungs).
Since the system is not strictly two-dimensional but can exchange molecules with the adjacent solution, a monolayer under progressive compression with fixed number of molecules is not at equilibrium. Yet, because of the extremely low solubility of the typical molecules (e.g. phospholipids), stressed monolayers remain stable over hours and, furthermore, exhibit various two-dimensional phases and domain structures (Fig. 2 A) upon changing pressure or temperature.
Fig. 2: Flueorescence microscopy images of a mixed phopholipid monolayer
(7:3 DPPC:POPG) at the air-water interface. At a critical surface pressure localized
folds appear. The four images are consecutive video frames capturing a folding event.
(Experiment done by Ajaykumar Gopal, Ka Yee Lee's lab.)
We have been interested in the elastic properties of biphasic monolayers such as the one shown in Fig. 2. Certain such monolayers are found in experiments to form localized folds upon compression (Fig. 2 C-D). The folding is peculiar because, when it happens, the monolayer is under net tension. This phenomenon is believed to be important for the function of lungs because it allows the lung surfactant monolayer to gently yield during exhalation without breakage or loss of material.
Our model relies on two observations: i) monolayers have an up-down asymmetry and thus must possess a non-zero spontaneous curvature; ii) biphasic monolayers are made of different domains with different elastic properties (different spontaneous curvature and/or bending rigidity). These two facts immediately imply that biphasic monolayers are not flat. The dark and bright regions in Fig. 2A have different heights and the monolayer has an inflected shape at each domain boundary. Thus, the domains are accompanied by a topography of "mesas" (Fig. 3).
Fig. 3: Sketches of the inflected shape of the monolayer near a domain
boundary (left), and the corresponding "mesa" topography (right)
The mesa height is of order K(dc)/s, where K is the bending rigidity, dc the difference in spontaneous curvature, and s the surface tension. This is typically only a few Å up to 1-2 nm. Yet, as the lateral pressure is increased (i.e. surface tension is decreased) the mesa walls get steeper, develop overhangs, and finally become unstable, making the monolayer yield to further compression. This instability occurs at tension of the order of K(dc)2. We believe it might initiate the observed folding.
As the mesa forms, elastic energy is gained per unit length of the domain boundary. This effectively reduces the line tension of the boundary. Thus, if the bare line tension between the two phases of the monolayer is low enough, then, upon lateral compression, the mesa will cause the total line tension to become negative, and the domain boundary will ripple (Fig. 4). This rippling instability occurs for bare line tension smaller than about K(dc), which is of the same order as measured values of line tension in such systems (typically a few kBT per nm). A possibly related phenomenon is observed in experiments (Fig. 5).
Fig. 4: Schematic sketch of the mesa wall rippling
Fig. 5: Fluorescence micrographs of a biphasic phopholipid (DPPC)
monolayer exhibiting roughened domain boundaries upon compression.
(Experiment done by Canay Ege, Ka Yee Lee's lab.)
H. Diamant, T. A. Witten, C. Ege, A. Gopal and K. Y. C. Lee
Topography and instability of monolayers near domain boundaries
Physical Review E 63, 061602 (2001)
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H. Diamant, T. A. Witten, A. Gopal and K. Y. C. Lee
Unstable topography of biphasic surfactant monolayers
Europhysics Letters 52, 171 (2000)
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