Shape-programmable liquid crystal elastomer structures with arbitrary three-dimensional director fields and geometries

AbstractLiquid crystal elastomers exhibit large reversible strain and programmable shape transformations, enabling various applications in soft robotics, dynamic optics, and programmable origami and kirigami. The morphing modes of these materials depend on both their geometries and director fields. In two dimensions, a pixel-by-pixel design has been accomplished to attain more flexibility over the spatial resolution of the liquid crystal response. Here we generalize this idea in two steps. First, we create independent, cubic light-responsive voxels, each with a predefined director field orientation. Second, these voxels are in turn assembled to form lines, grids, or skeletal structures that would be rather difficult to obtain from an initially connected material sample. In this way, the orientation of the director fields can be made to vary at voxel resolution to allow for programmable optically- or thermally-triggered anisotropic or heterogeneous material responses and morphology changes in three dimensions that would be impossible or hard to implement otherwise.

Download Full-text

Light-Actuated Liquid Crystal Elastomer Prepared by Projection Display

Materials ◽

10.3390/ma14237245 ◽

2021 ◽

Vol 14 (23) ◽

pp. 7245

Author(s):

Juan Chen ◽

Oluwafemi Isaac Akomolafe ◽

Jinghua Jiang ◽

Chenhui Peng

Keyword(s):

Liquid Crystal ◽

Three Dimensional ◽

Topological Defects ◽

Soft Materials ◽

Liquid Crystal Elastomer ◽

Projection Display ◽

Liquid Crystal Elastomers ◽

Spatially Varying ◽

External Stimuli ◽

3D Shapes

Soft materials with programmability have been widely used in drug delivery, tissue engineering, artificial muscles, biosensors, and related biomedical engineering applications. Liquid crystal elastomers (LCEs) can easily morph into three-dimensional (3D) shapes by external stimuli such as light, heat, and humidity. In order to program two-dimensional (2D) LCE sheets into desired 3D morphologies, it is critical to precisely control the molecular orientations in LCE. In this work, we propose a simple photopatterning method based on a maskless projection display system to create spatially varying molecular orientations in LCE films. By designing different synchronized rotations of the polarizer and projected images, diverse configurations ranging from individual to 2D lattice of topological defects are fabricated. The proposed technique significantly simplified the photopatterning procedure without using fabricated masks or waveplates. Shape transformations such as a cone and a truncated square pyramid, and functionality mimicking the responsive Mimosa Pudica are demonstrated in the fabricated LCE films. The programmable LCE morphing behaviors demonstrated in this work will open opportunities in soft robotics and smart functional devices.

Download Full-text

Free partition functions and an averaged holographic duality

Journal of High Energy Physics ◽

10.1007/jhep01(2021)130 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Nima Afkhami-Jeddi ◽

Henry Cohn ◽

Thomas Hartman ◽

Amirhossein Tajdini

Keyword(s):

Partition Function ◽

Spectral Gap ◽

Central Charge ◽

Three Dimensional ◽

Two Dimensions ◽

Three Dimensions ◽

Partition Functions ◽

General Constraints ◽

Dimensional Gravity ◽

Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Download Full-text

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.30 ◽

2012 ◽

Vol 696 ◽

pp. 228-262 ◽

Cited By ~ 24

Author(s):

A. Kourmatzis ◽

J. S. Shrimpton

Keyword(s):

Spatial Data ◽

Three Dimensional ◽

Reynolds Numbers ◽

Two Dimensions ◽

Three Dimensions ◽

Energy Budgets ◽

Turbulent Regime ◽

Scalar Flux ◽

Wide Range ◽

Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

Download Full-text

Effect of stretching angle on the stress plateau behavior of main-chain liquid crystal elastomers

Soft Matter ◽

10.1039/d0sm02244f ◽

2021 ◽

Vol 17 (11) ◽

pp. 3128-3136

Author(s):

Suzuka Okamoto ◽

Shinichi Sakurai ◽

Kenji Urayama

Keyword(s):

Liquid Crystal ◽

Main Chain ◽

Stress Plateau ◽

Liquid Crystal Elastomer ◽

Ultimate Elongation ◽

Liquid Crystal Elastomers

Stretching angle for a main-chain liquid crystal elastomer has pronounced effects on the width of the stress plateau as well as the ultimate elongation, while it has no effect on the plateau height.

Download Full-text

On the forces that cable webs under tension can support and how to design cable webs to channel stresses

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2018.0781 ◽

2019 ◽

Vol 475 (2223) ◽

pp. 20180781 ◽

Cited By ~ 5

Author(s):

Guy Bouchitté ◽

Ornella Mattei ◽

Graeme W. Milton ◽

Pierre Seppecher

Keyword(s):

Linear Programming ◽

Convex Hull ◽

Structural Engineering ◽

Three Dimensional ◽

Two Dimensions ◽

Three Dimensions ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Finite Dimensional ◽

Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 , f 2 , …, f N applied at prescribed points x 1 , x 2 , …, x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 , x 2 , …, x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 , f 2 , …, f N applied at points strictly within the convex hull of x 1 , x 2 , …, x N . In three dimensions, we show that, by slightly perturbing f 1 , f 2 , …, f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

Download Full-text

Bio-inspired thermal-responsive inverse opal films with dual structural colors based on liquid crystal elastomer

Journal of Materials Chemistry C ◽

10.1039/c5tc00548e ◽

2015 ◽

Vol 3 (17) ◽

pp. 4424-4430 ◽

Cited By ~ 37

Author(s):

Huihui Xing ◽

Jun Li ◽

Jinbao Guo ◽

Jie Wei

Keyword(s):

Liquid Crystal ◽

Inverse Opal ◽

Liquid Crystal Elastomer ◽

Structural Colors ◽

Thermal Switching ◽

Liquid Crystal Elastomers

The fabrication of inverse opal micropatterns based on liquid crystal elastomers with dual structural colors and their thermal switching behaviors are described.

Download Full-text

The House of Marie Shannon

10.26686/wgtn.16998166 ◽

2021 ◽

Author(s):

◽

Sally Margaret Apthorp

Keyword(s):

Three Dimensional ◽

Two Dimensions ◽

Domestic Architecture ◽

Three Dimensions ◽

Camera Obscura ◽

Architectural Space ◽

Domestic Lives ◽

Architectural Tradition ◽

Light And Shadow ◽

Insight Into

<p>This thesis creatively explores the architectural implications present in the photographs by New Zealand photographer Marie Shannon. The result of this exploration is a house for Shannon. The focus is seven of Shannon's interior panoramas from 1985-1987 in which architectural space is presented as a domestic stage. In these photograph's furniture and objects are the props and Shannon is an actress. This performance, with Shannon both behind and in front of her camera, creates a double insight into her world; architecture as a stage to domestic life, and a photographers view of domestic architecture. Shannon's view on the world enables a greater understanding to our ordinary, domestic lives. Photography is a revealing process that teaches us to see more richly in terms of detail, shading, texture, light and shadow. Through an engagement with photographs and understanding architectural space through a photographer's eye, the hidden, secret or unnoticed aspects to Shannon's reality will be revealed. This insight into another's reality may in turn enable a deeper understanding of our own. The methodology was a revealing process that involved experimenting with Shannon's panoramic photographs. Models and drawing, through photographic techniques, lead to insights both formally in three dimensions and at surface level in two dimensions. These techniques and insights were applied to the site through the framework of a camera obscura. Shannon's new home is created by looking at her photographs with an architect's 'eye'. Externally the home acts as a closed vessel, a camera obscura. But internally rich and intriguing forms, surfaces, textures and shadings are created. Just as the camera obscura projects an exterior scene onto the interior, so does the home. Shannon will inhabit this projection of the shadows which oppose 30 O'Neill Street, Ponsonby, Auckland; her past home and site of her photographs. Photographers, and in particular Shannon, look at the architectural world with fresh eyes, free from an architectural tradition. Photography and the camera enable an improved power of sight. More is revealed to the camera. Beauty is seen in the ordinary, with detail, tone, texture, light and dark fully revealed. As a suspended moment, a deeper understanding and opportunity is created to observe and appreciate this beauty. Through designing with a photographer's eye greater insight is gained into Shannon's 'reality'. This 'revealing' process acts as a means of teaching us how to see pictorial beauty that is inherent in our ordinary lives. This is the beauty that is often hidden in secret, due to our unseeing eyes. This project converts the photographs beauty back into three dimensional architecture.</p>

Download Full-text

Diffraction by crystals

Outline of Crystallography for Biologists ◽

10.1093/oso/9780198510512.003.0009 ◽

2002 ◽

Author(s):

David Blow

Keyword(s):

Fourier Transform ◽

Three Dimensional ◽

Incident Beam ◽

Two Dimensions ◽

Three Dimensions ◽

Dimensional Structure ◽

Angle Of Incidence ◽

X Ray ◽

Max Von Laue ◽

The Fourier Transform

In Chapter 4 many two-dimensional examples were shown, in which a diffraction pattern represents the Fourier transform of the scattering object. When a diffracting object is three-dimensional, a new effect arises. In diffraction by a repetitive object, rays are scattered in many directions. Each unit of the lattice scatters, but a diffracted beam arises only if the scattered rays from each unit are all in phase. Otherwise the scattering from one unit is cancelled out by another. In two dimensions, there is always a direction where the scattered rays are in phase for any order of diffraction (just as shown for a one-dimensional scatterer in Fig. 4.1). In three dimensions, it is only possible for all the points of a lattice to scatter in phase if the crystal is correctly oriented in the incident beam. The amplitudes and phases of all the scattered beams from a three-dimensional crystal still provide the Fourier transform of the three-dimensional structure. But when a crystal is at a particular angular orientation to the X-ray beam, the scattering of a monochromatic beam provides only a tiny sample of the total Fourier transform of its structure. In the next section, we are going to find what is needed to allow a diffracted beam to be generated. We shall follow a treatment invented by Lawrence Bragg in 1913. Max von Laue, who discovered X-ray diffraction in 1912, used a different scheme of analysis; and Paul Ewald introduced a new way of looking at it in 1921. These three methods are referred to as the Laue equations, Bragg’s law and the Ewald construction, and they give identical results. All three are described in many crystallographic text books. Bragg’s method is straightforward, understandable, and suffices for present needs. I had heard J.J. Thomson lecture about…X-rays as very short pulses of radiation. I worked out that such pulses…should be reflected at any angle of incidence by the sheets of atoms in the crystal as if these sheets were mirrors.…It remained to explain why certain of the atomic mirrors in the zinc blende [ZnS] crystal reflected more powerfully than others.

Download Full-text

Radiolaria: validating the Turing theory

The Turing Guide ◽

10.1093/oso/9780198747826.003.0046 ◽

2017 ◽

Author(s):

Bernard Richards

Keyword(s):

Diffusion Mechanism ◽

Three Dimensional ◽

Reaction Diffusion ◽

Two Dimensions ◽

Three Dimensions ◽

Black And White ◽

Alan Turing ◽

School Sports ◽

The University ◽

University Of Manchester

In his 1952 paper ‘The chemical basis of morphogenesis’ Turing postulated his now famous Morphogenesis Equation. He claimed that his theory would explain why plants and animals took the shapes they did. When I joined him, Turing suggested that I might solve his equation in three dimensions, a new problem. After many manipulations using rather sophisticated mathematics and one of the first factory-produced computers in the UK, I derived a series of solutions to Turing’s equation. I showed that these solutions explained the shapes of specimens of the marine creatures known as Radiolaria, and that they corresponded very closely to the actual spiny shapes of real radiolarians. My work provided further evidence for Turing’s theory of morphogenesis, and in particular for his belief that the external shapes exhibited by Radiolaria can be explained by his reaction–diffusion mechanism. While working in the Computing Machine Laboratory at the University of Manchester in the early 1950s, Alan Turing reignited the interests he had had in both botany and biology from his early youth. During his school-days he was more interested in the structure of the flowers on the school sports field than in the games played there (see Fig. 1.3). It is known that during the Second World War he discussed the problem of phyllotaxis (the arrangement of leaves and florets in plants), and then at Manchester he had some conversations with Claude Wardlaw, the Professor of Botany in the University. Turing was keen to take forward the work that D’Arcy Thompson had published in On Growth and Form in 1917. In his now-famous paper of 1952 Turing solved his own ‘Equation of Morphogenesis’ in two dimensions, and demonstrated a solution that could explain the ‘dappling’—the black-and-white patterns—on cows. The next step was for me to solve Turing’s equation in three dimensions. The two-dimensional case concerns only surface features of organisms, such as dappling, spots, and stripes, whereas the three-dimensional version concerns the overall shape of an organism. In 1953 I joined Turing as a research student in the University of Manchester, and he set me the task of solving his equation in three dimensions. A remarkable journey of collaboration began. Turing chatted to me in a very friendly fashion.

Download Full-text

Deuteron NMR investigation on orientational order parameter in polymer dispersed liquid crystal elastomers

Physical Chemistry Chemical Physics ◽

10.1039/d0cp04143b ◽

2020 ◽

Vol 22 (40) ◽

pp. 23064-23072

Author(s):

Andraž Rešetič ◽

Jerneja Milavec ◽

Valentina Domenici ◽

Blaž Zupančič ◽

Alexej Bubnov ◽

...

Keyword(s):

Liquid Crystal ◽

Order Parameter ◽

Orientational Order ◽

Orientational Order Parameter ◽

Liquid Crystal Elastomer ◽

H Nmr ◽

Polymer Dispersed Liquid Crystal ◽

Polymer Dispersed ◽

Liquid Crystal Elastomers ◽

Magnetically Aligned

Orientational order parameter of magnetically aligned liquid crystal elastomer particles suspended in a cured silicone matrix is assessed using 2H-NMR spectroscopy. Obtained results correspond well with the composite's thermomechanical response.

Download Full-text