Dynamic Transitions of Material Sheets
Faculty Coordinators: T. Witten, W. Zhang
Understanding the interplay between applied stresses and deformable boundaries is an outstanding challenge in engineering and materials processing. Forces on the boundary often produce a self-amplifying response that creates shape transitions and drives the system far from equilibrium. When a material has the form of a thin sheet, its susceptibility to bending creates singular responses, such as the sudden appearance of sharp points and ridges when a sheet of paper crumples. Crumpled structures confer useful resiliency in e.g., cushioning shock and may stabilize lung tissue against collapse. Moving fluid sheets can undergo dynamical transitions as when a fluid mass undergoes a collision. At such transitions the interplay between internal and applied force is most nonlinear and least understood. At Chicago we have developed the tools for probing these transitions both experimentally and theoretically.
Recent experiments in our Center have revealed striking dynamical transitions in material sheets. For example we discovered that the splashing of a liquid drop, in which a thin sheet of fluid is ejected from the point of impact, is strongly influenced by the surrounding atmosphere]. This discovery, and similar ones on buckling of molecular thin films and on two-dimensional cavitation, reveal unexpected aspects of these dynamical transitions. These transitions provide levers to understand the self-amplifying interplay between applied force and boundary deformation at a new level. Stimulated by these results and building on our discovery that the dynamics can possess a precise memory of the sheet¡¯s transient evolution, our Center has developed the theoretical tools that allow an investigation of the singular deformations that goes beyond the usual description in terms of universal scaling dynamics.
Our IRG is organized to probe two underlying questions common to these transitions. First, we explore the limits of deformability attainable by the transitions. Second, we seek the means by which the ultimate form of the transition may be controlled by the initial forcing - i.e., the transition's “memory” of its precursor state. Our deepened understanding of the interplay between stress and deformation will fuel advances in materials processing that exploit dynamic shape transitions.
The transitions we will study arise from nonlocal stress in two-dimensional materials in three different ways: (i) the sheet itself is produced dynamically in a fluid or in granular matter; (ii) the transitions arise from the special properties of molecular-scale sheets; (iii) the transition creates fractal structures that develop within a sheet. We discuss these in turn below. The combined breadth of chemical (Ismagilov, Lee, Sibener), materials (Jaeger, Nagel), and theoretical (Gruzberg, Kadanoff, Wiegmann, Witten, Zhang) expertise and our past record of fruitful interaction uniquely qualifies the Chicago MRSEC for this fundamental study.
The current state of the art for shaping fluid and solid films relies largely on using explicit constraints to dictate the shape, as in the extrusion of polyethylene film through a slit orifice. Here the spontaneous structures created by interacting stress and shape are viewed as instabilities to be avoided. However, such instabilities, especially if they have a precise memory, represent opportunities to shape materials in desired ways that can be more powerful and effective than explicit constraints. An example of this opportunity is the use of the Rayleigh instability to create engineered droplets for the widespread benefits of ink-jet printing. As seen above, analogous opportunities of dynamical shaping in films and sheets are rich and varied. These can create structure on the micron and nanometer scale, where explicit shaping is impractical. Such structure is desirable for producing mechanical resiliency (monolayer folding), intimate bicontinuous contact between materials (Laplacian growth) or controlled coating, abrasion and chemical reaction when fluids collide with a surface. This IRG will establish the limits of structure creation implicit in the newly-identified phenomena described above. We are able to study a broad range of materials thanks in part to the other IRGs: e.g. nanoparticle arrays (IRG 3) and granular materials (IRG 1). Using these systems, we will find the material and forcing conditions required to create structures of a desired size and precision. These fundamental studies will offer greatly expanded capabilities for engineers to form future two-dimensional materials.