This award supports theoretical and computational research in contact with experiment on the interplay among order, defects and geometry in soft matter systems on curved surfaces and interfaces with a focus on crystalline, hexatic, vector and nematic order.
Topological defects frequently appear even in the ground state of ordered systems on curved surfaces. Some defects are required by certain topologies such as the sphere and others form to lower the total energy of the system. Defect regions are natural places for biological activity, chemical linking, unusual elastic response and aggregation of disorder. This project will develop a thorough understanding of the preferred types of defect configurations for crystalline, hexatic, vector and nematic order on a variety of curved surfaces. This will pave the way for the first-principles design of entire libraries of mesoscale components (mesoatoms) that could serve as the building blocks of novel mesomolecules or bulk materials via self-assembly or controlled fabrication. A suite of tools from the fields of geometry, topology, statistical mechanics and computational science will be employed in this investigation which will be closely coupled with experimental groups.
The techniques and tools developed in the course of the proposed research, including methods of analysis, simulation applets, and databases, would be made freely available to researchers across disciplines.
The PI plans to involve undergraduates, graduate students and postdoctoral associates in his research program. A particular effort will be made to recruit and retain Physics majors, particularly women, by involving them in soft condensed matter research projects. The PI also plans to bring his research into the classroom through a new Soft Matter undergraduate and to the wider community through public lectures in the Saturday Morning Physics program and the Syracuse chapter of Cafe Scientifique as well as visits to local K-12 schools. Demonstrations of soap bubble arrays on curved surfaces developed as research projects can be used in both the classroom and public lectures.
NON-TECHNICAL SUMMARY
This award supports theoretical and computational research and education in contact with experiments that lies at the intersection of condensed matter physics, mathematics, and biology. The PI will study how particles organize themselves on curved surfaces and at the interfaces between two materials or media. For example, experiment has been able to place small particles with an electrostatic charge on the spherical surface of a water droplet suspended in oil. The particles attempt to organize themselves in a regular geometric pattern. But because they are on a sphere rather than a flat surface, ?scars? form where the ordered array on one side does not match up with that on the other. As shown by the PI, theory is at least able to make useful predictions about features of the self-organized system. The PI will study a wider variety of systems with an aim to understand the ?scars? or defects in ordering that emerge and how geometry might be used to control how particles self-assemble into desired structures. The structure of the protein coat on a virus is another example of interest to the PI. In this case, molecules might preferentially bind to areas where there are defects on curved surface of the virus protein coat suggesting strategies for drug development. The general challenging problem of how interacting particles arrange themselves on curved surfaces has been of general interest in the field of mathematics.
The techniques and tools developed in the course of the proposed research, including methods of analysis, simulation applets, and databases, would be made freely available to researchers across disciplines.
The PI plans to involve undergraduates, graduate students and postdoctoral associates in his research program. A particular effort will be made to recruit and retain Physics majors, particularly women, by involving them in soft condensed matter research projects. The PI also plans to bring his research into the classroom through a new Soft Matter undergraduate and to the wider community through public lectures in the Saturday Morning Physics program and the Syracuse chapter of Cafe Scientifique as well as visits to local K-12 schools. Demonstrations of soap bubble arrays on curved surfaces developed as research projects can be used in both the classroom and public lectures.
Soft Matter is the science of easily deformable matter. The low cost of deforming soft matter means that entropic contributions play a very important role in the statistical mechanics of soft materials. When entropic fluctuations dominate the appropriate free energy of a soft matter system the resultant behavior is frequently very different from typical hard systems. More surprisingly soft matter also exhibits unsusial behavior at zero-temperature. This occurs most notably in the nature of ordered phases on spatially curved surfaces. Research funded by this award has proven influential in establishing several paradigms in the nature of condensed matter order on curved surfaces. These are reviewed in Two-dimensional matter: order, curvature and defects: Mark J. Bowick and Luca Giomi, Adv. Phys. 58 (5) 449-563 (2009) DOI: 10.1080/00018730903043166 Key results are that ground states may exhibit highly unsual features such as topological defects that are NOT required by topological constraints or by boundary conditions. Instead the defects arise because they are energy minimizers. A state with defects can have lower energy than a defect free state. Examples include the crystalline ground state on the 2-sphere (the surface of a ball in three dimensions), the crystalline ground state on the 2-torus surface of revolution embedded in 3d flat space (a bicycle tire), the crystalline ground state on a paraboloidal surface of revolution (a 2D mirror surface), the crystalline ground state on constant mean curvature surfaces of revolution (capillary bridges) and the hexatic ground state (characterized by long range bond-orientational order) on the 2-torus. The extra defects in the case of a crystal on the surface of a ball or spherical droplet occur above a critical sytems size and occur in the form of 12 scars - i.e. 12 linear grain boundaries each with a net disclinicity of one. This structure is now standard knowledge in the field ans was established by the PI and collaborators. It has proven a fruiful structure in a wide variety of fields ranging from crystallography to thin shell elasticity to mathematical physics. Another unusual ground state or minumum occurs when the texture of a (curved) ordered phase competes with shape deformations of a flexible (ordered) surface. A paradigm was analyzed in Morphology of nematic and smectic vesicles: Xiangjun Xing, Homin Shinb, Mark J. Bowick, Zhenwei Yao, Lin Jiad, and Min-Hui Li, PNAS 109 (14) 5203-5206 (2012). When the liquid-crystalline (LC) order (nematic or smectic) is more costly than bending deformations a spherical LC vesicle will adopt a shape that is as flat as possible everywhere whilst retaining the toplogy of the 2-sphere. This is acheived by adopting a face-wise flat (polyhedral) shape. For LC order the actual polyhedral shape is the tetrahedron. LC vesicles exist in the form of rod-coil block copolymers with LC sidechains or for lipid vesicles in the appropriate part of their phase diagram. A perfect crystal is hard to find. Even the best prepared materials are marred by microscopic flaws that limit the material's conductivity or strength. Wouldn't it be nice if a material could heal itself? In XXX we show how self-healing can be achieved in thin-shell colloidal crystals. The system is a small-scale version of ranch dressing. Water droplets (vinegar) are dispersed in oil (olive oil) with solid colloids (mustard seeds) spontaneously assembling and crystallizing at the oil-water interface. The coated water droplets are visualized by confocal microscopy. A very common defect known as an interstitial (just one extra colloidal particle) is created from the pure crystal by grabbing a charged colloid from the surrounding oil with laser tweezers and forcing it onto the coated water droplet. The perfect crystal structure itself already has different kinds of unavoidable defects known as scars. When the interstitial is inserted near a scar it gets completely swallowed up by the scar, which acts like a nano-scale version of a black hole sucking debris from the surrounding universe. But when the interstitial is placed midway between two scars both scars compete to capture the interstitial. The result – the interstitial splits into two halves with one half going to each scar, leaving behind a perfect crystal. This is a classical version of the fractional charge found in strongly correlated electron systems. Here it is demonstrated for the first time in a classical but spatially curved soft matter system. So how can one cure defects in that most wonderful electronic crystal graphene? Simply flex it. Voila! The induced curvature will drive self-healing! This work was highlighted by NSF press release http://nsf.gov/discoveries/disc_summ.jsp?cntn_id=125494&org=NSF
