This is a collaborative project with CBET-0730626 / Case Western Reserve Univ., and 0730630 / Harvey Mudd College.
This project aims to quantitatively characterize, by linking experiment to mathematical and numerical analysis, domain dynamics within molecularly thin layers confined at the fluid/fluid interface (Langmuir layers). Motion within these layers is confined to the plane of the surface, and thus in two dimensions. However, molecular configurations can change freely with respect to the surface, and the layer can buckle out of the surface. Such layers present an enormous richness of surface phases: gases and liquids, liquid crystals, and elastic "solids." Experimental developments over the last 15 years have allowed a much clearer understanding of these phases. Dynamic processes, while essential to characterize macro-and mesoscopic properties of the film, prove much more difficult to measure experimentally and understand quantitatively through mathematical analysis. The dynamics in these layers are important due to the analogue dynamics controlling cell membrane processes, but also because they are probes into the physical-chemical nature of the Langmuir layer.
The PIs begin by describing their new results for dynamics within fluid monolayers, as the domains move towards equilibrium shape and size. Hydrodynamic flow involves motion within the Langmuir layer, but also within the subfluid, where it may not be parallel to the surface. Preliminary results from the group explore cases that show how combining high-quality experiments, detailed knowledge of surface chemistry, careful dimensional analysis, mathematical modeling, analytical techniques, intelligently-designed numerical methods and data analysis allows a deeper understanding of the physics of these problems. With comparisons between simulations and experiment going far beyond small perturbations in shape and size by application of our 4-roll mill technology, they will improve both accuracy and precision on measurements of the line tension, a critical parameter for both dynamics and layer morphology. They will also explore beyond the line tension, to include the effect of electrostatics and the compressibility of the layer. For this comparison, they will refine the experiment, include electrostatic and other contributions to the analysis, and develop the numerical analysis. As the project develops, they will reach beyond fluid-monolayer systems, in particular to those involving elastic solids that buckle out of the plane.
Intellectual Merit. Langmuir monolayers provide an experimentally accessible two-dimensional system, which require a combination of careful experiment, analysis, and simulation to probe effectively. Dynamic processes within these layers have been difficult to analyze, both experimentally and theoretically. The principle investigators in this project have demonstrated that in collaboration, they can identify useful cases in which theories amenable to numerical analysis can be developed and compared to the corresponding experiment. This project will deepen and extend that approach. We have improved both the precision and the accuracy of measurements of the line tension by more than an order of magnitude. This will allow them to directly probe the effect of long-range forces on this parameter, and to explore the effect of temperature and composition, including line-active molecules, on the line tension, which plays a critical role on the morphology within the Langmuir layer and its analogues.
Broader Impact. Dynamics within molecularly thin layers is critical for understanding such systems as biological membranes. The recognition of the functional importance of domains in biological cell membranes grows exponentially: domains may sequester proteins needed for signaling or provide structural conditions for shape changes. Langmuir monolayers provide a model system for all such layers. Furthermore, the domain size is potentially controllable over a wide range of sizes from the nano to the micro scales, so that arrays of domains with different physical and chemical properties can be formed by transferring the Langmuir layer to a solid substrate, providing more control than possible with self-assembled monolayers. The students in this project will be involved in a project that cuts across three disciplines (physics, chemical engineering and mathematics), and experience the value of combining different approaches to a common problem with both fundamental and practical implications. Both undergraduate and graduate students are included in this project, and the group also has a history of deep commitment to involving underrepresented groups in their research. (The E.K. Mann group, for example, is headed by a woman.)
