Geometric Instabilities of Filamentous Matter

University Of Massachusetts Amherst, Amherst MA

Investigators

Abstract

NONTECHNICAL ABSTRACT This award supports theoretical research and education to advance understanding of the structure and response in "filamentous matter," a notion which encompasses biological and synthetic nanostructured materials, ranging from carbon nanotubes and some assemblies of interconnected long chainlike molecules to filamentous proteins within and around biological cells. Project research will develop and investigate theoretical models of multi-filament material structures and related phenomena that derive from the generic, yet poorly understood, interplay between patterns of orientation and spatial organization. Developed theories will advance understanding of structure formation and organized mechanical motion of important classes of biological materials, including networks, bundles and fibers of filamentous proteins, as well as technologically valuable materials, like nanotube-based yarns and textiles. Beyond currently existing materials, studies will lay the groundwork for designing and engineering new classes of synthetic, responsive filamentous materials by uncovering new principles for manipulating their structure spanning from single filaments across assemblies. The project will advance the training of a postdoctoral and graduate researcher in a diverse set of quantitative methods, from mechanics and geometry to statistical and computational physics. Ongoing research goals will be integrated with undergraduate research projects and development of graduate curriculum in soft materials theory. The project also involves new collaboration with pre-K educators in Northampton, MA to develop an in-class curriculum centered on the connections between shape and materials that will stimulate interest and foster curiosity in STEM at the pre-K level and engage with the emerging mathematical thinking of students at 4-5 age range. TECHNICAL ABSTRACT This award supports theoretical research and education to advance understanding of the structure and response in "filamentous matter." Focusing on generic models of two prototypical assembly architectures, ordered bundles and isotropic networks, the research will study novel collective behaviors of multi-filament assemblies stemming from generic, geometric nonlinearities of filamentous matter, and their associated multi-scale, geometric instabilities. The project builds from emerging frameworks that connect geometric and mechanical principles of multi-filament structures to those of thin, 2D structures, including elastic sheets and crystalline membranes. While the geometrically-nonlinear principles of 2D membranes are now well-established in soft matter physics, an understanding of the basic methods and consequences of analogous principles for multi-filament bundles or networks, which this project seeks to develop, is in its infancy. Project research will consider physical models of multi-filament assemblies in which intrinsic or extrinsic stresses vary in magnitude, sign and direction throughout the structure, leading to variations in local stability, and ultimately, new classes of inhomogeneous and non-linear behaviors: 1) Building on an emerging understanding of the metric geometry of filament arrays, the project will study structural instabilities of incompatible bundles, in which uniform inter-filament spacing is frustrated. Two generic models will be studied: i) defect driven shape-instabilities of cohesive bundles and ii) ground-state order and geometry of long-range repulsive filaments under lateral confinement. 2) The project will advance geometric descriptions of inter-filament packing in contorted configurations of bundles, where the metric properties necessarily vary along the bundle. The present understanding of metric constraints is limited to only simplified geometries (straight, constant-twist bundles), and this study will advance the knowledge of optimal inter-filament organization to models of bent, toroidal and folded bundles relevant to observed phenomena from condensation of biopolymers to "in viro" packing of dsDNA chains. 3) Drawing on parallels between the stress-collapse behavior of 2D elastic sheets subject to spatially non-uniform compression, the project will investigate generic consequences of the compressive (buckling) instability of constituent filaments in isotropic network models, driven far beyond the buckling threshold. This "far-from threshold" regime reveals new universal behaviors, including the renormalization of far-field stresses due to compressive collapse of networks near to locally-applied loads. The project will advance the training of a postdoctoral and graduate researcher in a diverse set of quantitative methods, from mechanics and geometry to statistical and computational physics. Ongoing research goals will be integrated with undergraduate research projects and development of graduate curriculum in soft materials theory. The project also involves new collaboration with pre-K educators in Northampton, MA to develop an in-class curriculum centered on the connections between shape and materials that will stimulate interest and foster curiosity in STEM at the pre-K level and engage with the emerging mathematical thinking of students at 4-5 age range.