Session S7: Theory and Simulation of Fiber-Based Materials

How much can we learn from athermal models of the mechanical response of biopolymer networks?

Biopolymer networks of crosslinked, semiflexible filaments exhibit a wide variety of remarkable mechanical properties with distinct biological functionality. In recent years we have shown that network models of discrete, athermal filaments with deformable, yet static, crosslinkers to study the time-independent elastic properties of actin. Here I will summarise the key findings, including the effect of crosslink stiffness on nonlinear strain stiffening, to show that this athermal model captures all experimental trends. Inspired by this success, we now proceed with studying network viscoelasticity, and postulate that it arises solely from the independent unbinding and rebinding of crosslinkers. With a view on extracting the necessary insight to derive a constitutive law for polymer networks, we focus on a minimal system comprising two cross-linked filaments in a crosslinker heat bath. The simulations combine Grand Canonical Monte Carlo for the thermodynamically consistent dynamics of cross-linkers with athermal filament elasticity, including nonlinear elastic effects such as buckling.   

Mechanical critical phenomena and the elastic response of fiber networks

The mechanics of cells and tissues are largely governed by scaffolds of filamentous proteins that make up the cytoskeleton, as well as extracellular matrices. Evidence is emerging that such networks can exhibit rich mechanical phase behavior. A classic example of a mechanical phase transition was identified by Maxwell for macroscopic engineering structures: networks of struts or springs exhibit a continuous, second-order phase transition at the isostatic point, where the number of constraints imposed by connectivity just equals the number of mechanical degrees of freedom. We present recent theoretical predictions and experimental evidence for mechanical phase transitions in in both synthetic and biopolymer networks. We show, in particular, excellent quantitative agreement between the mechanics of collagen matrices and the predictions of a strain-controlled phase transition in sub-isostatic networks.   

Anisotropic contraction of hydrogel reinforced by aligned fibers

Hydrogel reinforced by aligned fibers can have strong anisotropic contraction or swelling behavior triggered by external stimuli, which has been largely employed in realizing soft actuators for artificial muscles as well as many biological systems. In this work, we investigate how this anisotropic behavior is controlled by the dimension of the embedded fibers and their reinforcement to the surrounding hydrogel. We describe the anisotropic contraction of hydrogels with rigid fibers using the Flory-Rehner thermodynamic model under periodic boundary conditions. It is found that a hydrogel reinforced by aligned fibers exhibits larger anisotropy when it is pre-stretched before contraction. Using finite element method, we further observe that the anisotropic contraction is dampened by reducing the fiber-fiber distance due to the finite size of the fibers.   

Competing Morphological Responses to Chirality-Induced Frustration in Twisted Filament Bundles

In various biological fibers, including collagen and fibrin, cohesive filaments assemble together in a twisting, helical geometry. It is generally understood that the helical geometry of these fibers is driven by chirality at the molecular scale. The inter-filament twist favored by chiral interactions is incompatible with regular columnar ordering of one-dimensional filaments, frustrating their lateral assembly in bundles. In response to this frustration, chiral filament bundles adopt a spectrum of competing, inhomogeneous morphologies. To understand the principles of morphology selection, we use both discrete-filament simulations and continuum elasticity theory to model the equilibrium structure’s cross section, with particular focus where inter-filament stresses are relaxed at the expense of introducing “excess” surface in anisotropic, tape-like helical bundles. We show further that the perimeter anisotropy competes with the adoption of topological defects (excess 5-fold disclination) in the bulk. We show that competition between isotropic/anisotropic and defective vs. hexagonally-ordered states is controlled by filament number, the chiral twist of bundles, and the ratio cohesive strength to stiffness of inter-filament bonds.   

Atomistics of carbon nanotube-polyacrylonitrile interfaces for next-generation carbon fibers: A multiscale computational study

Atomic-scale understanding of the carbon nanotube (CNT) -- polyacrylonitrile (PAN) interfaces is a critical missing element for the development of next-generation carbon fibers. In this presentation, we provide the systematic atomistic analyses of the CNT-PAN interfaces based on a multiscale computational approach combining density-functional theory (DFT) and force-fields molecular dynamics (FFMD) simulations. Based on DFT calculations, we identify the preferable CNT-PAN configurations and furthermore elucidate the electronic origin of the CNT-PAN binding. Next, via FFMD simulations, we extract more realistic large-scale interfacial CNT-PAN atomic configurations and confirm that they faithfully reflect the geometric motives identified in DFT calculations. Implications of our findings in the context of development of advanced carbon fibers will be discussed.   

Mesoscopic Distinct Element Method Simulations of the Mechanical Properties of Hybrid Nanoparticle-Carbon Nanotube Films

The recently proposed mesoscopic distinct element method (mDEM) for carbon nanotubes (CNT) is extended to account for a second nanoparticle (NP) phase and used to investigate the impact NP fillers on the mechanical properties of the CNT networks. High throughput mDEM simulations explore the large parameter space (size, type, and concentration of the filling NPS, CNT network topology, degree of bundling, CNT length) with the goal of developing a fundamental understanding and informing experiments with parameters that optimize the system-scale properties of interest: stability, flexibility, fatigue, yield and failure resistance. Our simulations suggest that NP filling of the CNT network could represent a new solution to the currently open problem of carbon nanotube film stability based on an "excluded volume" approach.   

Supercapacitors based on Carbon Nanotube Forests

\\ Supercapacitors made of fibrous nano-materials have stirred the curiosity of the scientific community for the past three decades. Vertically aligned Carbon Nanotube forests (CNT) are excellent candidates for the supercapacitor electrode due to high surface area, tensile strength and electrical conductivity. Despite large efforts and rapid progress in developing CNT forests-based devices, our fundamental understanding of the underlying molecular mechanisms remain incomplete. We use molecular simulations to understand charging of CNT forests and the pore filling phenomena. The most serious uncertainty with previous simulations of CNT based supercapacitors was definition of the actual composition of the pores. We perform direct simulations of filling of these pores with a widely used electrolyte solution, tetra-ethylammonium tetra-fluoroborate in propylene carbonate, (TEABF4/PC). We choose several pore sizes and nanotube charges and compare our MD results with experimentally measured values for the same system(CNT/TEABF4/PC). The potentials and capacitances calculated using the Poisson equation are consistent with experimentally measured values. We discuss the role of pore sizes on the capacitance of these systems.   

Objective Molecular Dynamics with Self-consistent Charge Density Functional Tight-Binding (SCC-DFTB) Method

We discus the coupling of the objective boundary conditions [1] into the SCC density functional-based tight binding code DFTB+[2]. The implementation is enabled by a generalization to the helical case of the classical Ewald method, specifically by Ewald-like formulas that do not rely on a unit cell with translational symmetry [3]. The robustness of the method in addressing complex hetero-nuclear nano- and bio-fibrous systems is demonstrated with illustrative simulations on a helical boron nitride nanotube, a screw dislocated zinc oxide nanowire, and an ideal double-strand DNA. [1] T. Dumitrica and R. D. James, J. Mech. Phys. Solids 55, 2206 (2007). [2] B. Aradi, B. Hourahine, and T. Frauenheim, J. Phys. Chem. A 111, 5678 (2007). [3] I. Nikiforov, B. Hourahine, B. Aradi, Th. Frauenheim and T. Dumitrica, J. Chem. Phys. 139, 094110 (2013).   

Algebraic Test of Material Conservation in Self-Consistent Field Theory

The self-consistent field theory (SCFT) of polymers using Gaussian chain model has been established as a standard for the statistical mechanical treatment of polymer materials. Even though it is a perfectly accurate mean field theory, its numerical treatment often exhibits problems in keeping the amount of polymer materials in the system. Recently, our research group has developed an algebraic test for the mass conservation. This method is extremely versatile in that practically all numerical algorithms can be tested by using matrix and bra-ket notation. The test reveals that when Crank-Nicolson method is adopted, finite volume method (FVM) is the only way to conserve material perfectly in the cylindrical and spherical coordinate systems. Alternating direction implicit method combined with FVM cannot conserve material, though it is still a good candidate after considering speed and accuracy simultaneously. We also confirm that the widely used pseudospectral method in the Cartesian coordinate system has the ability to conserve material.   

Molecular Dynamics Modeling of Carbon Nanotube Composite Fracture using ReaxFF

Carbon nanotube (CNT) fiber reinforced composites with specific tensile strengths and moduli approaching those of aerospace grade carbon fiber composites have recently been reported. This achievement was enabled by the emerging availability of high N/tex yarns in kilometer-scale quantities. While the production of this yarn is an impressive advance, its strength is still much lower than that of the individual CNTs comprising the yarn. Closing this gap requires understanding load transfer between CNTs at the nanometer dimensional scale. This work uses reactive molecular dynamics simulations to gain an understanding at the nanometer scale of the key factors that determine CNT nanocomposite mechanical performance, and to place more realistic upper bounds on the target properties.   

Fiber networks stabilized by cohesion: limits of stability and mechanical behavior

Networks composed from nanofibers are controlled by strong cohesive forces acting between filaments. These include structures assembled from electrospun polymeric fibers, dense assemblies of carbon nanotubes and some biological networks. In all these cases, the cohesive energy of the system is comparable or larger than the strain energy stored in bending, torsion or axial deformation modes of the filaments. This leads to fiber bundling and complex structural reorganizations which, in turn, influence the mechanical behavior of such networks. In this study we determine the limits of stability of such structures and the resulting range of stochastic configurations, in terms of the parameters controlling fiber-fiber interactions and the fiber properties. Further, we explore the mechanical behavior of the resulting stable structures. These results provide guidelines for the design of materials made from nanoscale fibers such as high strength structural panels made from strongly aligned carbon nanotubes.