Geometry and topology of entangled soft matter

• Applicant: Professorin Dr. Myfanwy E. Evans
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 265940164

Soft materials display complex physical behaviour. The macroscopic behaviour of these materials is often dictated by mesoscopic self organisation, which frequently reveals complicated geometric structure and entanglement. The study of entangled geometric structures in three-dimensional space is integral to the understanding of complex hierarchical soft matter, and is a key step towards designing self-organising soft materials with prescribed mesoscopic structure to fulfil specific rheological and optical functionality.Highly ordered mesoscale geometry often forms through complicated and delicate physical processes, mimicking visually spectacular mathematical structures. For example, the Gyroid triply-periodic minimal surface (a bicontinuous phase) is a visually arresting mathematical construction that pervades lipid membrane self-assembly, liquid crystals and cellular forms. Such minimal surfaces in nature are interesting from various perspectives, ranging from self assembly to functionality. A complementary phenomenon in soft materials is entanglement, from tangled defect lines in liquid crystals to filamentous materials and inter-threaded chemical frameworks. These entangled systems motivate interesting questions sitting at the boundary of soft matter and geometry: How can entanglement be quantified mathematically, and how does entanglement influence macroscopic physical properties?As an example that ties together many of these themes, we take human skin cells. Recent investigations of the internal geometry of dead skin cells found that the complicated yet highly symmetric ordering of keratin intermediate filaments is instrumental in the macroscopic swelling we observe on prolonged exposure to water, most readily observed as wrinkly fingers in the bath. Here, the entanglement of the filaments in this specific pattern creates an auxetic-like property that allows the swelling to occur without loss of mechanical integrity. This structure is also closely related to the Gyroid bicontinuous phases, where it is likely that the symmetric geometric arrangement of the filaments forms via membrane templating of a Gyroid bicontinuous lipid membrane phase: the filaments use the membrane as a scaffold for growth. This intriguing system exemplifies and motivates the general ideas of this project proposal, which plans to investigate mesoscale geometry and entanglement in soft and biological materials.

• DFG Programme: Independent Junior Research Groups