Coarse-grained approaches for multiscale computations of fibrous assemblies

Abstract

Fibrous assemblies are inherently hierarchical and their properties are a natural consequence of multi-scale interactions across length- and time-scales. In several cases, the relation between their hierarchical structure and properties is mediated by morphology of the filamentous building blocks. As such, scale bridging efforts become necessary to develop a fundamental understanding of their properties at experimental scales. In this thesis, we present coarse-grained, discrete particle strategies to fully characterize the response of two distinct classes of assemblies. In each case, atomic-scale interactions set the interactions of the building blocks, and they are serve as a basis for coarse-grained approaches that make contact with experiments. We first study the mechanics of sickle hemoglobin (HbS) macrofibers that lead to deformation of healthy erythrocytes. Deoxygenation of sickle hemoglobin tetramers during their venous return results in their intra-cellular polymerization HbS macrofibers. While the kinetics of polymerization is well-studied, the interaction of the polymerizing fibers with the cell membrane that leads to the onset of sickling remains poorly understood. Sporadic observations of fibers buckling within the cell or protruding through the membrane have been reported as precursors to cell deformation. Motivated by these studies, we focus on the buckling transition of the polymerizing fibers during their local interactions with the membranes. We develop coarse-grained approaches to model the polymerizing HbS macrofibers as well as the actin-spectrin cytoskeletal network that dominates the mechanical response of the fluctuating membrane. Computations with varying morphologic features of the fibers such as radius, length, and polymerization rate reveal that the strain accommodation is dominated by a combination of in-plane and axial forces that eventually result in spicule formation, or intracellular buckling. The presence of in-plane forces modify the end conditions for classical Euler buckling of the fiber and their collapse occurs along the membrane, thereby vii modifying the subsequent intracellular network of polymerizing. The results suggest that the network topology is central to sickling of the membranes. We develop a phase diagram that relates the buckling transition to the fiber morphology as a first step toward target therapies aimed at disrupting HbS polymerization. In the second part of the thesis, we focus on inorganic assemblies of stiff and/or semiflexible filaments, viz. carbon nanotubes (CNTs). Using a coarse-grained methodology based on cylindrical elements to model micron-long CNTs, we first study the effect of twist between fiber ends and the transition to plectoneme (snarl) formation as a way to study mechanics of these instabilities. We relate geometry of the plectoneme - loop size and pitch length of the coiled neck - to global constrains such as the Linking number and size of the fiber. Our computations show that local fluctuations in twist density along the fiber cascade into (critical) twist nuclei that serves as precursors to the supercoiling. Computations of disordered CNT assemblies reveal that these instabilities are amplified by local changes in alignment, significantly reducing the critical twist and Link number associated with the supercoiling process. We use this approach to understand the effect of fusion between CNTs and the mechanics of the fibers. Electrical treatment via Joule heating has emerged as a viable technique to fuse the fibers and engineer multi-functional properties. Experimental characterization reveal changes in nanotube-scale structure of these fibers following fusion. We focus on five key structural parameters - density, degree of mis-alignment, bundling extent, length distribution of the CNTs and extent of graphitization - on the mechanical strength of these fibers, including their viscoelastic response. We first develop a novel coarse-grained approach that self-consistently models graphitized domains in these assemblies. Our results show that the mechanical response is most sensitive to graphitization, resulting in increasingly brittle fibers. Among the nanotube-scale structure features, the degree of misalignment emerges as a key structural variable. Our results offer guiding principles for design of electrical fusion of CNT fibers, as well as more general inorganic assemblies of nanotubes, nanorods and nanowires.