Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session F16: Focus Session: Extreme Mechanics: Filaments and their Assemblies, Elasticity and Defects |
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Sponsoring Units: GSNP DPOLY Chair: Christian Santangelo, University of Massachusetts-Amherst Room: 401 |
Tuesday, March 4, 2014 8:00AM - 8:12AM |
F16.00001: Twisted Ribbons: Theory, Experiment and Applications Julien Chopin, Benjamin Davidovitch, Flavio A. Silva, Romildo D. Toledo Filho, Arshad Kudrolli We investigate, experimentally and theoretically, the buckling and wrinkling instabilities of a pre-stretched ribbon upon twisting and propose strategies for the fabrication of structured yarns. Our experiment consists in a thin elastic sheet in the form of a ribbon which is initially stretched by a fixed load and then subjected to a twist by rotating the ends through a prescribed angle. We show that a wide variety of shapes and instabilities can be obtained by simply varying the applied twist and tension. The observed structures which include helicoids with and without longitudinal and transverse wrinkles, and spontaneous creases, can be organized in a phase diagram with the tension and twist angle as control parameters [J. Chopin and A. Kudrolli, PRL (2013)]. Using a far-from-threshold analysis and a slender body approximation, we provide a comprehensive understanding of the longitudinal and transverse instabilities and show that several regimes emerge depending on subtle combinations of loading and geometrical parameters. Further, we show that the wrinkling instabilities can be manipulated to fabricate structured yarns which may be used to encapsulate amorphous materials or serve as efficient reinforcements for cement-based composites. [Preview Abstract] |
Tuesday, March 4, 2014 8:12AM - 8:24AM |
F16.00002: Elastocapillarity and the curling of fibers Anupam Pandey, Suzie Protiere, Douglas Holmes Coalescence of paintbrush bristles removed from a bath of fluid is the result of competing elastic and surface energies. The lengthscale that emerges out of this energy balance is called the ``elastocapillary'' lengthscale. This phenomenon has been well studied both experimentally and theoretically at the desktop scale as well as microscale. But in many natural and synthetic systems, the fluid between the flexible fibers can swell the material and causes the fibers to curl. A natural example is human hair, which swells in humid conditions, dilating and becoming frizzy. In this presentation, we demonstrate experimental results on this coupled ``elastocapillary-elastoswelling'' system. Specifically, we identify two distinct regimes dominated by capillarity and swellability, and the transition between these two regimes is governed by the ``elastoswelling'' lengthscale. We also show that in the swelling dominated regime a small fluid droplet is being carried upward by the curling fibers that mimic a pipetting mechanism. [Preview Abstract] |
Tuesday, March 4, 2014 8:24AM - 8:36AM |
F16.00003: Handedness and self assembly of chiral rods Efi Efrati When handed building blocks, such as twisted fusilli, self-assemble the resulting assembled object is typically also handed (as are its physical response properties). This phenomenon plays a central role in fields raging from biological self-assembly to optimizing the design of optical meta-materials. Despite the importance of this problem, predicting the relation between the handedness of the constituents of an assembled object and its overall handedness has remained an elusive goal even for the simplest of cases. At the heart of this problem lies the difficulty of quantifying the handedness of even a single building block. In this talk I will show how a recent orientation-dependent interpretation of handedness as a relation between directions and rotations sidesteps most of the difficulties associated with the quantification of handedness and resolves an existing puzzle regarding the self-assembly of handed colloidal rods. [Preview Abstract] |
Tuesday, March 4, 2014 8:36AM - 8:48AM |
F16.00004: Spontaneous formation and evolution of kinks in elastic helical structures Shuangping Liu, Zhenwei Yao, Monica Olvera de la Cruz A variety of linear entities in many biological and chemical systems can spontaneously form helical structures to realize specific functions, notably the helical ribbons found in peptide amphiphiles whose closure can further lead to the formation of tubes. Of particular interest is the coexistence of helices with opposite chiralities connected by kinks in one structure that has been found inbacterial flagella, plant tendrils and peptide amphiphiles etc, in analogy to domain walls separating regions of spin up and spin down. The spatial distribution of chirality is completely controlled by these kinks. There is no topological constraint on the number of kinks in a helical system. The introduction and evolution of kinks are largely determined energetically. In this work, using the three-dimensional pre-strained elastomeric bi-strip model, we investigate the general principles underlying the emergence of regular helical shapes and the proliferation of kinks. Specifically, it is found that if the ends of the belt can freely rotate can have significant influence on the behavior of kinks, opening the possibility of using boundary conditions to control the chirality of these systems. [Preview Abstract] |
Tuesday, March 4, 2014 8:48AM - 9:00AM |
F16.00005: Stretchable nanoparticle helical ribbons through asymmetric cross-sectional geometry Alfred Crosby, Jonathan Pham, Jimmy Lawrence, Gregory Grason, Todd Emrick Helical objects are ubiquitous. From macroscopic plant tendrils to nanoscopic DNA, the geometry of a coiled helix is fundamentally interesting for its mechanical energy storage and tunable mechanical properties, like the spring stiffness. To create helices on micro- and nano- length scales, it is often necessary to have bilayer materials systems or chiral structures. However, we show in thin ribbons, where the thickness is on a similar order to the elastocapillary length, that having an asymmetric cross-sectional geometry can drive helical formation. We create long, nanoparticle-based ribbons using an evaporative assembly technique called flow coating, which produces non-rectangular cross-sections on the nanoscale. When released into water, interfacial tension balances with elasticity to form spring-like structures. These helical ribbons can be extended to high strains, show good shape recovery, and can display mechanical stiffness values ranging from 10-6 N/m at low strains to 10-2 N/m when highly stretched. In addition, the mechanical properties of these structures can be predictably tuned by controlling the ribbon dimensions or the material composition. [Preview Abstract] |
Tuesday, March 4, 2014 9:00AM - 9:12AM |
F16.00006: Theory of equilibria of elastic braids with applications to DNA supercoiling Gert van der Heijden, Eugene Starostin Motivated by supercoiling of DNA and other filamentous structures, we formulate a new theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. Unlike in previous work no assumption is made on the shape of the contact curve. Rather, this shape is solved for. The theory is developed in terms of a moving frame of directors attached to one of the strands with one of the directors pointing to the position of the other strand. The constant-distance constraint is automatically satisfied by the introduction of what we call braid strains. The price we pay is that the potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Both open braid and closed braid solutions (links and knots) are computed and current applications to DNA supercoiling are discussed. [Preview Abstract] |
Tuesday, March 4, 2014 9:12AM - 9:48AM |
F16.00007: Geometrically frustrated filament assemblies: Unravelling the connection between bundle shape and inter-filament order Invited Speaker: Gregory Grason From steel cables and textile fibers to filamentous protein bundles in cells and tissues, densely-packed assemblies of filaments are vital structural elements of the worlds around us and inside of us. Despite the ubiquity and utility of dense-filament assemblies in such diverse materials (across 7 orders of magnitude in size!) surprisingly little is known about the fundamental rules that govern their structure. This talk will discuss recent progress in our understanding of the non-linear relationship between the geometry of a rope-like assembly and the structure and energetics of inter-filament packing. In particular, we focus on mathematical models of the geometric frustration between twist -- as in macroscopic cables or chiral biofilament bundles -- and the preference for isometric, or ``constant spacing,'' packing of filaments in the cross section. Any measure of twist makes it geometrically impossible to evenly space filaments in bundles, begging the question what is the optimal packing of a twisted bundle? We show that geometry of interfilament contact can be mapped formally onto a problem of packing on a 2D non-Euclidean surfaces, whose intrinsically-curved geometry points to the necessity of a complex spectrum defects in the ground-state packing. We confirm the existence of defects and their sensitivity to bundle twist and radius through simulations of energy-minimizing assemblies of cohesive filaments. [Preview Abstract] |
Tuesday, March 4, 2014 9:48AM - 10:00AM |
F16.00008: Defect-induced shape transitions in filament bundles Isaac Bruss, Gregory Grason From extracellular proteins to artificially fabricated materials, cohesive filament bundles are found across many systems. Employing continuum elasticity theory and numerical simulations, we study the interdependence between the organization of cohesive filaments arranged into a bundle, and their global structure, focusing on the effects of topological defects on equilibrium bundle shape. We analyze the structural stability of parallel filament bundles possessing 5- and 7-fold disclinations in their cross section, whose presence gives rise to inhomogeneous patterns of compressive and tensile stress. We argue that a generic coupling between filament tilt and inter-filament strains leads to a class of defect-induced shape instabilities, which are the filamentary analogue of defect-induced buckling transitions of 2D membranes, and can be understand as a consequence of the generic Helfrich-Hurault instability of layered materials under tension. We show that bundles containing 5-fold disclinations prefer twisted motifs, and 7-fold disclinations give rise to radial undulations. Furthermore, the pitch and wavelength of these deformations are conditional on the relative cost of filament bending and cohesive interactions. [Preview Abstract] |
Tuesday, March 4, 2014 10:00AM - 10:12AM |
F16.00009: Optimal packing of curved filaments Luis Cajamarca, Gregory Grason The interactions between straight filaments generically favor a uniform hexagonal arrangement, a packing motif that is frustrated when filaments are {\it curved} which forces a compromise between uniform spacing and uniform shape. Examples of curved biological filaments include bacterial flagella and filamentous components of the bacterial cytoskeleton. We address a simple question: what is the optimal ground state packing of $N$ curved filaments? We present a geometric and mechanical model that incorporates the helical shape of the filaments and adhesive interactions, described by hard tube short-range repulsion and larger range of inter-filament attraction. We discuss two generic geometric classes of helical filament packings: vertically-stacked ($N$-plies) and side-to-side (N-packs). While $N$-plies maintain constant spacing with neighbors at constant shape, the cylindrical structure of the enclosing packing space limits the number and coordination of helices of a given geometry, resulting in fewer adhesive contacts than the ``looser" $N$-pack class, where the lateral packing is unconstrained. We show that this geometric interplay gives rise to rich phase diagram of optimal packing, sensitively dependent to helical geometry, range of adhesion and filament number. [Preview Abstract] |
Tuesday, March 4, 2014 10:12AM - 10:24AM |
F16.00010: 3D Filament Network Segmentation with Multiple Active Contours Ting Xu, Dimitrios Vavylonis, Xiaolei Huang Fluorescence microscopy is frequently used to study two and three dimensional network structures formed by cytoskeletal polymer fibers such as actin filaments and microtubules. While these cytoskeletal structures are often dilute enough to allow imaging of individual filaments or bundles of them, quantitative analysis of these images is challenging. To facilitate quantitative, reproducible and objective analysis of the image data, we developed a semi-automated method to extract actin networks and retrieve their topology in 3D. Our method uses multiple Stretching Open Active Contours (SOACs) that are automatically initialized at image intensity ridges and then evolve along the centerlines of filaments in the network. SOACs can merge, stop at junctions, and reconfigure with others to allow smooth crossing at junctions of filaments. The proposed approach is generally applicable to images of curvilinear networks with low SNR. We demonstrate its potential by extracting the centerlines of synthetic meshwork images, actin networks in 2D TIRF Microscopy images, and 3D actin cable meshworks of live fission yeast cells imaged by spinning disk confocal microscopy. [Preview Abstract] |
Tuesday, March 4, 2014 10:24AM - 10:36AM |
F16.00011: Elasticity using Nambu-Goldstone modes of isometries Salem Al Mosleh, Christian Santangelo, Arthur Evans Thin shells have a natural separation in energetic scales between bending and stretching. Owing to the prohibitively high cost for stretching, the elastic energy is approximately invariant under isometric deformations, associated with symmetry there will be Nambu-Goldstone modes which can be described by an effective theory in the diffuse deformation limit. We apply this method to study small deformations of elastic shells, and to the evolution of growing shells under an imposed swelling pattern as well as the effect of imperfection in the swelling pattern on bending and stretching rigidities. [Preview Abstract] |
Tuesday, March 4, 2014 10:36AM - 10:48AM |
F16.00012: Optomechanical elastomeric engine Milos Knezevic, Mark Warner Efficiently converting solar energy to mechanical or electrical energy is one of the greatest contemporary challenges in science and technology. We present a conceptual design for an engine based on liquid crystal elastomers (LCEs) that extracts mechanical work from heat or light. Unusual properties of LCEs arise from a coupling between the liquid crystalline ordering of mesogenic molecules and the elasticity of the underlying polymer network. The external heat or light cause reversible contractions of monodomain LCEs along their nematic director, with recovery elongations on stimuli removal. The contraction-elongation cycle can be repeated many times, and can be exploited to construct a continuosly operating engine. The material parameters and the geometry of such an engine are explored, and it is shown that its efficiency can go up to 20\%. \\[4pt] [1] M. Kne\v{z}evi\'c and M. Warner, Phys. Rev. E 88, 040501(R) (2013)\\[0pt] [2] I. Z. Steinberg, A. Oplatka, and A. Katchalsky, Nature 210, 568 (1966) [Preview Abstract] |
Tuesday, March 4, 2014 10:48AM - 11:00AM |
F16.00013: Defect interactions in blueprinted Liquid Crystal Polymer Networks Vianney Gimenez-Pinto, Andrew Konya, Robin Selinger, Fangfu Ye Using finite element simulation we investigate the shape transformation in liquid crystal elastomers imprinted with several defects of different topological charge arranged in a pattern. We investigate how the distance between defects affects the overall shape distortion of the material. These numerical studies represent an efficient method to predict shape distortions in elastomers imprinted with defects depending on the defect's topological charge, the number or disclinations in the director field, the spatial distribution of the defects cores, among other design aspects. Supported by NSF-DMR 1106014. [Preview Abstract] |
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