How geometric frustration shapes twisted fibres, inside and out: competing morphologies of chiral filament assembly

Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure—finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. ‘frustration escape’). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.

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A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

10.26434/chemrxiv.12098142.v1 ◽

2020 ◽

Author(s):

Frederik Haase ◽

Gavin Craig ◽

Mickaele Bonneau ◽

kunihisa sugimoto ◽

Shuhei Furukawa

Keyword(s):

Topological Defects ◽

Porous Metal ◽

Building Blocks ◽

Structural Features ◽

Equilibrium Structure ◽

Sorption Behavior ◽

Building Unit ◽

Geometric Frustration ◽

Secondary Building Units ◽

Hydrogen Bonded

Reticular framework materials thrive on designability, but unexpected reaction outcomes are crucial in exploring new structures and functionalities. By combining “incompatible” building blocks, we employed geometric frustration in reticular materials leading to emergent structural features. The combination of a pseudo C5 symmetrical organic building unit based on a pyrrole core, with a C4 symmetrical copper paddlewheel synthon led to three distinct frameworks by tuning the synthetic conditions. The frameworks show structural features typical for geometric frustration: self-limiting assembly, internally stressed equilibrium structures and topological defects in the equilibrium structure, which manifested in the formation of a hydrogen bonded framework, distorted and broken secondary building units and dangling functional groups, respectively. The influence of geometric frustration on the CO2 sorption behavior and the discovery of a new secondary building unit shows geometric frustration can serve as a strategy to obtain highly complex porous frameworks.

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A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

10.26434/chemrxiv.12098142 ◽

2020 ◽

Author(s):

Frederik Haase ◽

Gavin Craig ◽

Mickaele Bonneau ◽

kunihisa sugimoto ◽

Shuhei Furukawa

Keyword(s):

Topological Defects ◽

Porous Metal ◽

Building Blocks ◽

Structural Features ◽

Equilibrium Structure ◽

Sorption Behavior ◽

Building Unit ◽

Geometric Frustration ◽

Secondary Building Units ◽

Hydrogen Bonded

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Dynamical arrest of topological defects in 2D hyperuniform disk packings

EPJ Web of Conferences ◽

10.1051/epjconf/202124915002 ◽

2021 ◽

Vol 249 ◽

pp. 15002

Author(s):

Sungyeon Hong ◽

Michael A. Klatt ◽

Gerd Schröder-Turk ◽

Nicolas François ◽

Mohammad Saadatfar

Keyword(s):

Topological Defects ◽

2D Systems ◽

Voronoi Cells ◽

Geometric Frustration ◽

Energy Minimisation ◽

Hexatic Phase ◽

Collective Motions ◽

Disk Packings

We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.

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Effect of angular stability and other locking parameters on the mechanical performance of intramedullary nails

Biomedical Engineering / Biomedizinische Technik ◽

10.1515/bmt-2014-0100 ◽

2015 ◽

Vol 60 (2) ◽

Cited By ~ 8

Author(s):

Stefanie Hoffmann ◽

Claus Gerber ◽

Geert von Oldenburg ◽

Manuel Kessler ◽

Daniel Stephan ◽

...

Keyword(s):

Mechanical Performance ◽

Angular Stability ◽

Generic Model ◽

Mechanical Stiffness ◽

Intramedullary Nails ◽

Optimal Arrangement ◽

Locking Screws ◽

Loading Modes ◽

Im Nailing ◽

Locking Screw

AbstractTo extend the indications of intramedullary nails for distal or proximal fractures, nails with angle stable locking options have been developed. Studies on the mechanical efficacy of these systems have been inconsistent likely due to confounding variables such as number, geometry, or orientation of the screws, as well as differences in the loading mode. Therefore, the aim of this study was to quantify the effect of angular stability on the mechanical performance of intramedullary nails. The results could then be compared with the effects of various locking screw parameters and loading modes. A generic model was developed consisting of artificial bone material and titanium intramedullary nail that provided the option to systematically modify the locking screw configuration. Using a base configuration, the following parameters were varied: number of screws, distance and orientation between screws, blocking of screws, and simulation of freehand locking. Tension/compression, torsional, and bending loads were applied. Stiffness and clearance around the zero loading point were determined. Angular stability had no effect on stiffness but completely blocked axial clearance (p=0.003). Simulation of freehand locking reduced clearance for all loading modes by at least 70% (p<0.003). The greatest increases in torsional and bending stiffness were obtained by increasing the number of locking screws (up to 80%, p<0.001) and by increasing the distance between them (up to 70%, p<0.001). In conclusion, our results demonstrate that the mechanical performance of IM nailing can be affected by various locking parameters of which angular stability is only one. While angular stability clearly reduces clearance of the screw within the nail, mechanical stiffness depends more on the number of screws and their relative distance. Thus, optimal mechanical performance in IM nailing could potentially be obtained by combining angular stability with optimal arrangement of locking screws.

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Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100076834 ◽

1983 ◽

Vol 41 ◽

pp. 646-647

Author(s):

Joseph A. Zasadzinski

Keyword(s):

Liquid Crystalline ◽

Freeze Fracture ◽

Continuum Theory ◽

Closed Surfaces ◽

Straight Line ◽

Low Weight ◽

Concentric Spheres ◽

Membrane Geometry ◽

Dupin Cyclides ◽

Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

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The need of electron microscopy in the study of domains and domain walls in ferroelectrics

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100170487 ◽

1994 ◽

Vol 52 ◽

pp. 550-551

Author(s):

Wenwu Cao

Keyword(s):

Domain Wall ◽

Domain Walls ◽

High Mobility ◽

Continuum Theory ◽

Polarization Vector ◽

Ferroelectric Materials ◽

Dielectric Constants ◽

Nonlocal Coupling ◽

Cubic Symmetry ◽

Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

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Vesicles as an equilibrium structure of a simple surfactant-water system

Journal de Physique II ◽

10.1051/jp2:1994219 ◽

1994 ◽

Vol 4 (9) ◽

pp. 1585-1604 ◽

Cited By ~ 20

Author(s):

L. Cantù ◽

M. Corti ◽

E. Del Favero ◽

A. Raudino

Keyword(s):

Water System ◽

Equilibrium Structure

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A Generic Model of Clinical Practice

Methods of Information in Medicine ◽

10.1055/s-0038-1634245 ◽

2003 ◽

Vol 42 (03) ◽

pp. 203-211 ◽

Cited By ~ 5

Author(s):

J. L. G. Dietz ◽

A. Hasman ◽

P. F. de Vries Robbé ◽

H. J. Tange

Keyword(s):

Clinical Practice ◽

Theoretical Model ◽

Action Theory ◽

Human Subjects ◽

Shared Care ◽

Patient Record ◽

Generic Model ◽

Problem Solver ◽

Record Keeping ◽

Process View

Summary Objectives: Many shared-care projects feel the need for electronic patient-record (EPR) systems. In absence of practical experiences from paper record keeping, a theoretical model is the only reference for the design of these systems. In this article, we review existing models of individual clinical practice and integrate their useful elements. We then present a generic model of clinical practice that is applicable to both individual and collaborative clinical practice. Methods: We followed the principles of the conversation-for-action theory and the DEMO method. According to these principles, information can only be generated by a conversation between two actors. An actor is a role that can be played by one or more human subjects, so the model does not distinguish between inter-individual and intra-individual conversations. Results: Clinical practice has been divided into four actors: service provider, problem solver, coordinator, and worker. Each actor represents a level of clinical responsibility. Any information in the patient record is the result of a conversation between two of these actors. Connecting different conversations to one another can create a process view with meta-information about the rationale of clinical practice. Such process view can be implemented as an extension to the EPR. Conclusions: The model has the potential to cover all professional activities, but needs to be further validated. The model can serve as a theoretical basis for the design of EPR-systems for shared care, but a successful EPR-system needs more than just a theoretical model.

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