1
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Hou J, Xu HN. Guest-guided anchoring patterns of cyclodextrin supramolecular microcrystals on droplet surfaces. Carbohydr Polym 2024; 337:122142. [PMID: 38710551 DOI: 10.1016/j.carbpol.2024.122142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2024] [Revised: 04/07/2024] [Accepted: 04/08/2024] [Indexed: 05/08/2024]
Abstract
The growth of cyclodextrin inclusion complexes (ICs) on oil/water interfaces represents a beautiful example of spontaneous pattern formation in nature. How the supramolecules evolve remains a challenge because surface confinement can frustrate microcrystal growth and give rise to unusual phase transitions. Here we investigate the self-assembly of ICs on droplet surfaces using microfluidics, which allows directly visualizing packing, wetting and ordering of the microcrystals anchored on the surface. The oil guests of distinct molecular structures can direct the assembly of the ICs and largely affect anchoring dynamics of the ICs microcrystals, leading to a range of behaviors including orientating, slipping, buckling, jamming, or merging. We discuss the behaviors observed in terms of the flexibility of the building blocks, which offers a new degree of freedom through which to tailor their properties and gives rise to a striking feature of anchoring patterns that have no counterpart in normal colloidal crystals.
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Affiliation(s)
- Jie Hou
- State Key Laboratory of Food Science and Resources, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, People's Republic of China; School of Food Science and Technology, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, People's Republic of China; International Joint Laboratory on Food Safety, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, People's Republic of China
| | - Hua-Neng Xu
- State Key Laboratory of Food Science and Resources, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, People's Republic of China; School of Food Science and Technology, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, People's Republic of China; International Joint Laboratory on Food Safety, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, People's Republic of China.
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2
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Hutton RS, Vitral E, Hamm E, Hanna J. Buckling mediated by mobile localized elastic excitations. PNAS NEXUS 2024; 3:pgae083. [PMID: 38562580 PMCID: PMC10983783 DOI: 10.1093/pnasnexus/pgae083] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 02/09/2024] [Indexed: 04/04/2024]
Abstract
Experiments reveal that structural transitions in thin sheets are mediated by the passage of transient and stable mobile localized elastic excitations. These "crumples" or "d-cones" nucleate, propagate, interact, annihilate, and escape. Much of the dynamics occurs on millisecond time scales. Nucleation sites correspond to regions where generators of the ideal unstretched surface converge. Additional stable intermediate states illustrate two forms of quasistatic inter-crumple interaction through ridges or valleys. These interactions create pairs from which extended patterns may be constructed in larger specimens. The onset of localized transient deformation with increasing sheet size is correlated with a characteristic stable crumple size, whose measured scaling with thickness is consistent with prior theory and experiment for localized elastic features in thin sheets. We offer a new theoretical justification of this scaling.
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Affiliation(s)
- Robert S Hutton
- Department of Mechanical Engineering, University of Nevada, 1664 N. Virginia St. (0312), Reno, NV 89557-0312, USA
| | - Eduardo Vitral
- Department of Mechanical Engineering, Rose-Hulman Institute of Technology, 5500 Wabash Ave., Terre Haute, IN 47803, USA
| | - Eugenio Hamm
- Departamento de Física, Facultad de Ciencia, Universidad de Santiago de Chile, Av. Víctor Jara 3493, Estación Central, Santiago 9160000, Chile
| | - James Hanna
- Department of Mechanical Engineering, University of Nevada, 1664 N. Virginia St. (0312), Reno, NV 89557-0312, USA
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3
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Sun H, Yao Z. Plastic instability of annular crystalline membrane in circular confinement. Phys Rev E 2024; 109:044802. [PMID: 38755936 DOI: 10.1103/physreve.109.044802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2024] [Accepted: 03/27/2024] [Indexed: 05/18/2024]
Abstract
Understanding the mechanical instabilities of two-dimensional membranes has strong connection to the subjects of structure instabilities, morphology control, and materials failures. In this work, we investigate the plastic mechanism developed in the annular crystalline membrane system for adapting to the shrinking space, which is caused by the controllable gradual expansion of the inner boundary. In the process of plastic deformation, we find the continuous generation of dislocations at the inner boundary and their collective migration to the outer boundary; this neat dynamic scenario of dislocation current captures the complicated reorganization process of the particles. We also reveal the characteristic vortex structure arising from the interplay of topological defects and the displacement field. These results may find applications in the precise control of structural instabilities in packings of particulate matter and covalently bonded systems.
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Affiliation(s)
- Honghui Sun
- School of Physics and Astronomy, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhenwei Yao
- School of Physics and Astronomy, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
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4
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Stein-Montalvo L, Guerra A, Almeida K, Kodio O, Holmes DP. Wrinkling and developable cones in centrally confined sheets. Phys Rev E 2023; 108:035002. [PMID: 37849112 DOI: 10.1103/physreve.108.035002] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 08/17/2023] [Indexed: 10/19/2023]
Abstract
Thin sheets respond to confinement by smoothly wrinkling or by focusing stress into small, sharp regions. From engineering to biology, geology, textiles, and art, thin sheets are packed and confined in a wide variety of ways, and yet fundamental questions remain about how stresses focus and patterns form in these structures. Using experiments and molecular dynamics simulations, we probe the confinement response of circular sheets, flattened in their central region and quasistatically drawn through a ring. Wrinkles develop in the outer, free region, then are replaced by a truncated cone, which forms in an abrupt transition to stress focusing. We explore how the force associated with this event, and the number of wrinkles, depend on geometry. Additional cones sequentially pattern the sheet until axisymmetry is recovered in most geometries. The cone size is sensitive to in-plane geometry. We uncover a coarse-grained description of this geometric dependence, which diverges depending on the proximity to the asymptotic d-cone limit, where the clamp size approaches zero. This paper contributes to the characterization of general confinement of thin sheets, while broadening the understanding of the d cone, a fundamental element of stress focusing, as it appears in realistic settings.
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Affiliation(s)
- Lucia Stein-Montalvo
- Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Arman Guerra
- Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Kanani Almeida
- Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Ousmane Kodio
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Douglas P Holmes
- Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
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5
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Foster B, Knobloch E. Elastic fingering in a rotating Hele-Shaw cell. Phys Rev E 2023; 107:065104. [PMID: 37464645 DOI: 10.1103/physreve.107.065104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 06/05/2023] [Indexed: 07/20/2023]
Abstract
We consider the steady-state fingering instability of an elastic membrane separating two fluids of different density under external pressure in a rotating Hele-Shaw cell. Both inextensible and highly extensible membranes are considered, and the role of membrane tension is detailed in each case. Both systems exhibit a centrifugally driven Rayleigh-Taylor-like instability when the density of the inner fluid exceeds that of the outer one, and this instability competes with the restoring forces arising from curvature and tension, thereby setting the finger scale. Numerical continuation is used to compute not only strongly nonlinear primary finger states up to the point of self-contact, but also secondary branches of mixed modes and circumferentially localized folds as a function of the rotation rate and the externally imposed pressure. Both reflection-symmetric and symmetry-broken chiral states are computed. The results are presented in the form of bifurcation diagrams. The ratio of system scale to the natural length scale is found to determine the ordering of the primary bifurcations from the unperturbed circle state as well as the solution profiles and onset of secondary bifurcations.
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Affiliation(s)
- Benjamin Foster
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - Edgar Knobloch
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
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6
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Riccobelli D, Al-Terke HH, Laaksonen P, Metrangolo P, Paananen A, Ras RHA, Ciarletta P, Vella D. Flattened and Wrinkled Encapsulated Droplets: Shape Morphing Induced by Gravity and Evaporation. PHYSICAL REVIEW LETTERS 2023; 130:218202. [PMID: 37295111 DOI: 10.1103/physrevlett.130.218202] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 04/07/2023] [Indexed: 06/12/2023]
Abstract
We report surprising morphological changes of suspension droplets (containing class II hydrophobin protein HFBI from Trichoderma reesei in water) as they evaporate with a contact line pinned on a rigid solid substrate. Both pendant and sessile droplets display the formation of an encapsulating elastic film as the bulk concentration of solute reaches a critical value during evaporation, but the morphology of the droplet varies significantly: for sessile droplets, the elastic film ultimately crumples in a nearly flattened area close to the apex while in pendant droplets, circumferential wrinkling occurs close to the contact line. These different morphologies are understood through a gravito-elastocapillary model that predicts the droplet morphology and the onset of shape changes, as well as showing that the influence of the direction of gravity remains crucial even for very small droplets (where the effect of gravity can normally be neglected). The results pave the way to control droplet shape in several engineering and biomedical applications.
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Affiliation(s)
- Davide Riccobelli
- MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Hedar H Al-Terke
- Department of Applied Physics, Aalto University School of Science, Espoo, Finland
- Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, Espoo, Finland
| | - Päivi Laaksonen
- HAMK Tech, Häme University of Applied Sciences, 13100 Hämeenlinna, Finland
| | - Pierangelo Metrangolo
- Department of Applied Physics, Aalto University School of Science, Espoo, Finland
- Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, Espoo, Finland
- Department of Chemistry, Materials, and Chemical Engineering "Giulio Natta", Politecnico di Milano, 20131 Milano, Italy
| | - Arja Paananen
- VTT Technical Research Centre of Finland Ltd, Tekniikantie 21, 02150 Espoo, Finland
| | - Robin H A Ras
- Department of Applied Physics, Aalto University School of Science, Espoo, Finland
- Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, Espoo, Finland
| | - Pasquale Ciarletta
- MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Dominic Vella
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
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7
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He M, Démery V, Paulsen JD. Cross-sections of doubly curved sheets as confined elastica. Proc Natl Acad Sci U S A 2023; 120:e2216786120. [PMID: 36897985 PMCID: PMC10089198 DOI: 10.1073/pnas.2216786120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2022] [Accepted: 01/28/2023] [Indexed: 03/12/2023] Open
Abstract
Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional (3D) shapes, producing a plethora of structures across multiple length scales. To understand this complex response, previous studies have either focused on the overall gross shape or the small-scale buckling that decorates it. A geometric model, which considers the sheet as inextensible yet free to compress, has been shown to capture the gross shape of the sheet. However, the precise meaning of such predictions, and how the gross shape constrains the fine features, remains unclear. Here, we study a thin-membraned balloon as a prototypical system that involves a doubly curved gross shape with large amplitude undulations. By probing its side profiles and horizontal cross-sections, we discover that the mean behavior of the film is the physical observable that is predicted by the geometric model, even when the buckled structures atop it are large. We then propose a minimal model for the horizontal cross-sections of the balloon, as independent elastic filaments subjected to an effective pinning potential around the mean shape. Despite the simplicity of our model, it reproduces a broad range of phenomena seen in the experiments, from how the morphology changes with pressure to the detailed shape of the wrinkles and folds. Our results establish a route to combine global and local features consistently over an enclosed surface, which could aid the design of inflatable structures, or provide insight into biological patterns.
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Affiliation(s)
- Mengfei He
- Department of Physics, Syracuse University, Syracuse, NY13244
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY13244
| | - Vincent Démery
- Gulliver, CNRS, École Supérieure de Physique et Chimie Industrielles de Paris, Paris Sciences et Lettres Research University, Paris75005, France
- Univ Lyon, École Normale Supérieure de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, LyonF-69342, France
| | - Joseph D. Paulsen
- Department of Physics, Syracuse University, Syracuse, NY13244
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY13244
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8
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Smith K, Retallick A, Melendrez D, Vijayaraghavan A, Heil M. Modeling Graphene-Polymer Heterostructure MEMS Membranes with the Föppl-von Kármán Equations. ACS APPLIED MATERIALS & INTERFACES 2023; 15:9853-9861. [PMID: 36748982 PMCID: PMC9951177 DOI: 10.1021/acsami.2c21096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 01/26/2023] [Indexed: 06/18/2023]
Abstract
Ultra-thin graphene-based membranes have shown significant promise for high-performance nano-electro-mechanical (NEMS) devices. The key challenge in the modeling of such membranes is that they often operate in deflection regimes where the assumptions or approximations of "pure bending" or "pure stretching" are not satisfied. We present a model of graphene-polymer heterostructure (GPH) NEMS membranes based on Föppl-von Kármán (FvK) equations which take into account both bending and stretching forces. The experimental GPH membrane shape obtained through atomic force microscopy topography mapping is compared to the inflation shapes predicted by FvK-based finite element method simulation, and they show excellent agreement with each other. When the GPH membranes are deflected under pressure in a capacitive pressure sensor configuration, the effectiveness of this model is further exemplified through accurately predicting the capacitance change of deflecting GPH membrane devices at varying pressures. This model serves as a powerful new tool in the design and development of graphene-based NEMS devices, being able to predict the performance of graphene NEMS devices or to aid in the design of device geometries to match required performances.
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Affiliation(s)
- Katherine Smith
- Department
of Materials and National Graphene Institute, The University of Manchester, ManchesterM13 9PL, U.K.
| | - Aidan Retallick
- Department
of Mathematics, The University of Manchester, ManchesterM13 9PL, U.K.
| | - Daniel Melendrez
- Department
of Materials and National Graphene Institute, The University of Manchester, ManchesterM13 9PL, U.K.
| | - Aravind Vijayaraghavan
- Department
of Materials and National Graphene Institute, The University of Manchester, ManchesterM13 9PL, U.K.
| | - Matthias Heil
- Department
of Mathematics, The University of Manchester, ManchesterM13 9PL, U.K.
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9
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Liu E, Zhang X, Ji H, Li Q, Li L, Wang J, Han X, Yu S, Xu F, Cao Y, Lu C. Polarization‐Dependent Ultrasensitive Dynamic Wrinkling on Floating Films Induced by Photo‐Orientation of Azopolymer. Angew Chem Int Ed Engl 2022; 61:e202203715. [DOI: 10.1002/anie.202203715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2022] [Indexed: 11/09/2022]
Affiliation(s)
- Enping Liu
- School of Materials Science and Engineering Tianjin University Tianjin 300072 P. R. China
| | - Xiaoliang Zhang
- Department of Aeronautics and Astronautics Fudan University Shanghai 200433 P. R. China
| | - Haipeng Ji
- China Aerospace Science and Industry Corporation Sixth Academy No. 46 Institute Hohhot 010010 P. R. China
| | - Qifeng Li
- School of Precision Instruments and Optoelectronics Engineering Tianjin University Tianjin 300072 P. R. China
| | - Lele Li
- School of Materials Science and Engineering Tianjin University Tianjin 300072 P. R. China
| | - Juanjuan Wang
- School of Materials Science and Engineering Tianjin Key Laboratory of Building Green Functional Materials Tianjin Chengjian University Tianjin 300384 P. R. China
| | - Xue Han
- School of Materials Science and Engineering Tianjin Key Laboratory of Building Green Functional Materials Tianjin Chengjian University Tianjin 300384 P. R. China
| | - Shixiong Yu
- School of Materials Science and Engineering Tianjin University Tianjin 300072 P. R. China
| | - Fan Xu
- Department of Aeronautics and Astronautics Fudan University Shanghai 200433 P. R. China
| | - Yanping Cao
- Department of Engineering Mechanics Tsinghua University Beijing 100084 P. R. China
| | - Conghua Lu
- School of Materials Science and Engineering Tianjin University Tianjin 300072 P. R. China
- School of Materials Science and Engineering Tianjin Key Laboratory of Building Green Functional Materials Tianjin Chengjian University Tianjin 300384 P. R. China
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10
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Chen J, Yao Z. Geometry and physics in the deformations of crystalline caps. SOFT MATTER 2022; 18:5323-5328. [PMID: 35796205 DOI: 10.1039/d2sm00246a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic regimes. Based on the revealed quasi-conformal ordering, we discover the partial but uniform screening of the substrate curvature by the induced curvature underlying the inhomogeneous lattice. This scenario is fundamentally different from the conventional screening mechanism based on topological defects. In the plastic regime, the yield of highly stressed caps leads to fractures with featured morphologies not found in planar systems. We also demonstrate the strategy of engineering stress and fractures by vacancies. These results advance our general understanding of the organization and adaptivity of the geometrically frustrated crystalline order.
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Affiliation(s)
- Jingyuan Chen
- School of Physics and Astronomy, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Zhenwei Yao
- School of Physics and Astronomy, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
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11
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Liu E, Zhang X, Ji H, Li Q, Li L, Wang J, Han X, Yu S, Xu F, Cao Y, Lu C. Polarization‐Dependent Ultrasensitive Dynamic Wrinkling on Floating Films Induced by Photo‐Orientation of Azopolymer. Angew Chem Int Ed Engl 2022. [DOI: 10.1002/ange.202203715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Enping Liu
- Tianjin University School of Materials Science and Engineering 300072 Tianjin CHINA
| | - Xiaoliang Zhang
- Fudan University Department of Aeronautics and Astronautics CHINA
| | - Haipeng Ji
- China Aerospace Science and Industry Corp Sixth Academy No. 46 Institute 010010 Hohhot CHINA
| | - Qifeng Li
- Tianjin University School of Precision Instruments and Optoelectronics Engineering 300072 Tianjin CHINA
| | - Lele Li
- Tianjin University School of Materials Science and Engineering CHINA
| | - Juanjuan Wang
- Tianjin Chengjian University School of Materials Science and Engineering, Tianjin Key Laboratory of Building Green Functional Materials 300384 Tianjin CHINA
| | - Xue Han
- Tianjin Chengjian University School of Materials Science and Engineering, Tianjin Key Laboratory of Building Green Functional Materials 300384 Tianjin CHINA
| | - Shixiong Yu
- Tianjin University School of Materials Science and Engineering 300072 Tianjin CHINA
| | - Fan Xu
- Fudan University Department of Aeronautics and Astronautics 200433 Shanghai CHINA
| | - Yanping Cao
- Tsinghua University Department of Engineering Mechanics 100084 Beijing CHINA
| | - Conghua Lu
- Tianjin University Nankai District, Weijin Road No.92 300384 Tianjin CHINA
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12
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Liu A, Yao Y, Yao J, Liu T. Droplet Spreading Induced Wrinkling and Its Use for Measuring the Elastic Modulus of Polymeric Thin Films. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00345] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Aishuang Liu
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Soochow 215123, P. R. China
| | - Yanbo Yao
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Soochow 215123, P. R. China
| | - Jingwen Yao
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Soochow 215123, P. R. China
| | - Tao Liu
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Soochow 215123, P. R. China
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13
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Mowitz AJ. Finite curved creases in infinite isometric sheets. Phys Rev E 2022; 105:035001. [PMID: 35428117 DOI: 10.1103/physreve.105.035001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 02/07/2022] [Indexed: 06/14/2023]
Abstract
Geometric stress focusing, e.g., in a crumpled sheet, creates pointlike vertices that terminate in a characteristic local crescent shape. The observed scaling of the size of this crescent is an open question in the stress focusing of elastic thin sheets. According to experiments and simulations, this size depends on the outer dimension of the sheet, but intuition and rudimentary energy balance indicate it should only depend on the sheet thickness. We address this discrepancy by modeling the observed crescent with a more geometric approach, where we treat the crescent as a curved crease in an isometric sheet. Although curved creases have already been studied extensively, the crescent in a crumpled sheet has its own unique features: the material crescent terminates within the material, and the material extent is indefinitely larger than the extent of the crescent. These features together with the general constraints of isometry lead to constraints linking the surface profile to the crease-line geometry. We construct several examples obeying these constraints, showing finite curved creases are fully realizable. This approach has some particular advantages over previous analyses, as we are able to describe the entire material without having to exclude the region around the sharp crescent. Finally, we deduce testable relations between the crease and the surrounding sheet and discuss some of the implications of our approach with regards to the scaling of the crescent size.
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Affiliation(s)
- Aaron J Mowitz
- Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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14
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Barakat J, Squires TM. Curvature-Mediated Forces on Elastic Inclusions in Fluid Interfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:1099-1105. [PMID: 35015555 PMCID: PMC8793860 DOI: 10.1021/acs.langmuir.1c02709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 12/28/2021] [Indexed: 06/14/2023]
Abstract
Heterogeneous fluid interfaces often include two-dimensional solid domains that mechanically respond to changes in interfacial curvature. While this response is well-characterized for rigid inclusions, the influence of solid-like elasticity remains essentially unexplored. Here, we show that an initially flat, elastic inclusion embedded in a curved, fluid interface will exhibit qualitatively distinct behavior depending on its size and stiffness. Small, stiff inclusions are limited by bending and experience forces directed up gradients of Gaussian curvature, in keeping with prior findings for rigid discoids. By contrast, larger and softer inclusions are driven down gradients of squared Gaussian curvature in order to minimize the elastic penalty for stretching. Our calculations of the force on a solid inclusion are shown to collapse onto a universal curve spanning the bending- and stretching-limited regimes. From these results, we make predictions for the curvature-directed motion of deformable solids embedded within a model interface of variable Gaussian curvature.
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15
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Oshri O. Asymptotic softness of a laterally confined sheet in a pressurized chamber. Phys Rev E 2021; 104:055005. [PMID: 34942726 DOI: 10.1103/physreve.104.055005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2021] [Accepted: 10/18/2021] [Indexed: 11/07/2022]
Abstract
Elastohydrodynamic models, that describe the interaction between a thin sheet and a fluid medium, have been proven successful in explaining the complex behavior of biological systems and artificial materials. Motivated by these applications we study the quasistatic deformation of a thin sheet that is confined between the two sides of a closed chamber. The two parts of the chamber, above and below the sheet, are filled with an ideal gas. We show that the system is governed by two dimensionless parameters, Δ and η, that account respectively for the lateral compression of the sheet and the ratio between the amount of fluid filling each part of the chamber and the bending stiffness of the sheet. When η≪1 the bending energy of the sheet dominates the system, the pressure drop between the two sides of the chamber increases, and the sheet exhibits a symmetric configuration. When η≫1 the energy of the fluid dominates the system, the pressure drop vanishes, and the sheet exhibits an asymmetric configuration. The transition between these two limiting scenarios is governed by a third branch of solutions that is characterized by a rapid decrease of the pressure drop. Notably, across the transition the energetic gap between the symmetric and asymmetric states scales as δE∼Δ^{2}. Therefore, in the limit Δ≪1 small variations in the energy are accompanied by relatively large changes in the elastic shape.
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Affiliation(s)
- Oz Oshri
- Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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16
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Cordella G, Tripodo A, Puosi F, Pisignano D, Leporini D. Nanoscale Elastoplastic Wrinkling of Ultrathin Molecular Films. Int J Mol Sci 2021; 22:11732. [PMID: 34769167 PMCID: PMC8583903 DOI: 10.3390/ijms222111732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Revised: 10/20/2021] [Accepted: 10/25/2021] [Indexed: 11/25/2022] Open
Abstract
Ultrathin molecular films deposited on a substrate are ubiquitously used in electronics, photonics, and additive manufacturing methods. The nanoscale surface instability of these systems under uniaxial compression is investigated here by molecular dynamics simulations. We focus on deviations from the homogeneous macroscopic behavior due to the discrete, disordered nature of the deformed system, which might have critical importance for applications. The instability, which develops in the elastoplastic regime above a finite critical strain, leads to the growth of unidimensional wrinkling up to strains as large as 0.5. We highlight both the dominant wavelength and the amplitude of the wavy structure. The wavelength is found to scale geometrically with the film length, λ∝L, up to a compressive strain of ε≃0.4 at least, depending on the film length. The onset and growth of the wrinkling under small compression are quite well described by an extended version of the familiar square-root law in the strain ε observed in macroscopic systems. Under large compression (ε≳0.25), we find that the wrinkling amplitude increases while leaving the cross section nearly constant, offering a novel interpretation of the instability with a large amplitude. The contour length of the film topography is not constant under compression, which is in disagreement with the simple accordion model. These findings might be highly relevant for the design of novel and effective wrinkling and buckling patterns and architectures in flexible platforms for electronics and photonics.
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Affiliation(s)
- Gianfranco Cordella
- Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa, Italy; (G.C.); (A.T.); (F.P.); (D.P.)
| | - Antonio Tripodo
- Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa, Italy; (G.C.); (A.T.); (F.P.); (D.P.)
| | - Francesco Puosi
- Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa, Italy; (G.C.); (A.T.); (F.P.); (D.P.)
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa, Italy
| | - Dario Pisignano
- Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa, Italy; (G.C.); (A.T.); (F.P.); (D.P.)
- NEST, Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, I-56127 Pisa, Italy
| | - Dino Leporini
- Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa, Italy; (G.C.); (A.T.); (F.P.); (D.P.)
- Istituto per i Processi Chimico-Fisici-Consiglio Nazionale delle Ricerche (IPCF-CNR), Via G. Moruzzi 1, I-56124 Pisa, Italy
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17
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Timounay Y, Hartwell AR, He M, King DE, Murphy LK, Démery V, Paulsen JD. Sculpting Liquids with Ultrathin Shells. PHYSICAL REVIEW LETTERS 2021; 127:108002. [PMID: 34533328 DOI: 10.1103/physrevlett.127.108002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
Thin elastic films can spontaneously attach to liquid interfaces, offering a platform for tailoring their physical, chemical, and optical properties. Current understanding of the elastocapillarity of thin films is based primarily on studies of planar sheets. We show that curved shells can be used to manipulate interfaces in qualitatively different ways. We elucidate a regime where an ultrathin shell with vanishing bending rigidity imposes its own rest shape on a liquid surface, using experiment and theory. Conceptually, the pressure across the interface "inflates" the shell into its original shape. The setup is amenable to optical applications as the shell is transparent, free of wrinkles, and may be manufactured over a range of curvatures.
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Affiliation(s)
- Yousra Timounay
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, New York 13244, USA
| | | | - Mengfei He
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, New York 13244, USA
| | - D Eric King
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
| | - Lindsay K Murphy
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
| | - Vincent Démery
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, (10 rue Vauquelin), 75005 Paris, France
- Université Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Joseph D Paulsen
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, New York 13244, USA
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18
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Prasath SG, Marthelot J, Govindarajan R, Menon N. Shapes of a filament on the surface of a bubble. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0353] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore, by experiments and theoretical analysis, the morphological phase space of a filament confined to the surface of a spherical bubble. The morphology is controlled by varying bending stiffness and weight of the filament, and its length relative to the bubble radius. When the dominant considerations are the geometry of confinement and elastic energy, the filament lies along a geodesic and when gravitational energy becomes significant, a bifurcation occurs, with a part of the filament occupying a longitude and the rest along a curve approximated by a latitude. Far beyond the transition, when the filament is much longer than the diameter, it coils around the selected latitudinal region. A simple model with filament shape as a composite of two arcs captures the transition well. For better quantitative agreement with the subcritical nature of bifurcation, we study the morphology by numerical energy minimization. Our analysis of the filament’s morphological space spanned by one geometric parameter, and one parameter that compares elastic energy with body forces, may provide guidance for packing slender structures on complex surfaces.
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Affiliation(s)
- S. Ganga Prasath
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- International Centre for Theoretical Sciences (ICTS-TIFR) Shivakote, Hesaraghatta Hobli, Bengaluru 560089, India
| | - Joel Marthelot
- Aix-Marseille University, CNRS, IUSTI (Institut Universitaire des Systémes Thermiques Industriels), 13013 Marseille, France
| | - Rama Govindarajan
- International Centre for Theoretical Sciences (ICTS-TIFR) Shivakote, Hesaraghatta Hobli, Bengaluru 560089, India
| | - Narayanan Menon
- Department of Physics, University of Massachusetts Amherst, Amherst, MA 01003, USA
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19
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Yamamoto KK, Shearman TL, Struckmeyer EJ, Gemmer JA, Venkataramani SC. Nature's forms are frilly, flexible, and functional. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:95. [PMID: 34255210 DOI: 10.1140/epje/s10189-021-00099-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 06/25/2021] [Indexed: 06/13/2023]
Abstract
A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces.
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Affiliation(s)
- Kenneth K Yamamoto
- Department of Mathematics, Southern Methodist University, Dallas, TX, 75275, USA
| | - Toby L Shearman
- School of Mathematical Sciences, University of Arizona, Tucson, AZ, 85721, USA
| | - Erik J Struckmeyer
- School of Mathematical Sciences, University of Arizona, Tucson, AZ, 85721, USA
| | - John A Gemmer
- Department of Mathematics and Statistics, Wake Forest University, Winston Salem, NC, 27109, USA
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20
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Xin M, Davidovitch B. Stretching Hookean ribbons part II: from buckling instability to far-from-threshold wrinkle pattern. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:94. [PMID: 34241720 DOI: 10.1140/epje/s10189-021-00088-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Accepted: 06/02/2021] [Indexed: 06/13/2023]
Abstract
We address the fully developed wrinkle pattern formed upon stretching a Hookean, rectangular-shaped sheet, when the longitudinal tensile load induces transverse compression that far exceeds the stability threshold of a purely planar deformation. At this "far-from-threshold" parameter regime, which has been the subject of the celebrated Cerda-Mahadevan model (Cerda and Mahadevan in Phys Rev Lett 90:074302, 2003), the wrinkle pattern expands throughout the length of the sheet and the characteristic wavelength of undulations is much smaller than its width. Employing Surface Evolver simulations over a range of sheet thicknesses and tensile loads, we elucidate the theoretical underpinnings of the far-from-threshold framework in this setup. We show that the evolution of wrinkles comes in tandem with collapse of transverse compressive stress, rather than vanishing transverse strain (which was hypothesized by Cerda and Mahadevan in Phys Rev Lett 90:074302, 2003), such that the stress field approaches asymptotically a compression-free limit, describable by tension field theory. We compute the compression-free stress field by simulating a Hookean sheet that has finite stretching modulus but no bending rigidity, and show that this singular limit encapsulates the geometrical nonlinearity underlying the amplitude-wavelength ratio of wrinkle patterns in physical, highly bendable sheets, even though the actual strains may be so small that the local mechanics is perfectly Hookean. Finally, we revisit the balance of bending and stretching energies that gives rise to a favorable wrinkle wavelength, and study the consequent dependence of the wavelength on the tensile load as well as the thickness and length of the sheet.
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Affiliation(s)
- Meng Xin
- Physics Department, University of Massachusetts, Amherst, MA, 01003, USA
| | - Benny Davidovitch
- Physics Department, University of Massachusetts, Amherst, MA, 01003, USA.
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21
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Oshri O. Volume-constrained deformation of a thin sheet as a route to harvest elastic energy. Phys Rev E 2021; 103:033001. [PMID: 33862743 DOI: 10.1103/physreve.103.033001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2020] [Accepted: 02/08/2021] [Indexed: 11/07/2022]
Abstract
Thin sheets exhibit rich morphological structures when subjected to external constraints. These structures store elastic energy that can be released on demand when one of the constraints is suddenly removed. Therefore, when adequately controlled, shape changes in thin bodies can be utilized to harvest elastic energy. In this paper, we propose a mechanical setup that converts the deformation of the thin body into a hydrodynamic pressure that potentially can induce a flow. We consider a closed chamber that is filled with an incompressible fluid and is partitioned symmetrically by a long and thin sheet. Then, we allow the fluid to exchange freely between the two parts of the chamber, such that its total volume is conserved. We characterize the slow, quasistatic, evolution of the sheet under this exchange of fluid, and derive an analytical model that predicts the subsequent pressure drop in the chamber. We show that this evolution is governed by two different branches of solutions. In the limit of a small lateral confinement we obtain approximated solutions for the two branches and characterize the transition between them. Notably, the transition occurs when the pressure drop in the chamber is maximized. Furthermore, we solve our model numerically and show that this maximum pressure behaves nonmonotonically as a function of the lateral compression.
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Affiliation(s)
- Oz Oshri
- Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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22
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Xu HN, Hou J, Liu H, Zhang L. Stress buffering in cyclodextrin-based membranes coated on emulsion droplet surfaces. SOFT MATTER 2021; 17:3895-3901. [PMID: 33885451 DOI: 10.1039/d0sm02198a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Surface instability of membranes not only plays a critical role in the morphological evolution observed in natural and biological systems, but also underpins a promising way for the bottom-up fabrication of novel functional materials. There is an urgent need for the design of novel building blocks into membranes, and the understanding of the abilities of the membranes to cope with mechanical stress is therefore of considerable importance. Here, we design membranes built with cyclodextrin-oil inclusion complexes, which are formed spontaneously at the oil/water interface by a self-assembly process. We select the oil phases of distinct molecular structures, namely, branched triglyceride oil and straight-chain n-dodecane, and examine the patterns in which the membranes adopt morphological transitions to buffer stress. We discuss two possible buffering scenarios for the behaviors observed in view of structural arrest and interfacial rheology, which are most closely linked to the rigidity of the membranes. The membranes represent fascinating models and shed some light on the origin of arrested stress relaxation.
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Affiliation(s)
- Hua-Neng Xu
- State Key Laboratory of Food Science and Technology, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, People's Republic of China.
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23
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Evaporation mediated translation and encapsulation of an aqueous droplet atop a viscoelastic liquid film. J Colloid Interface Sci 2021; 581:334-349. [DOI: 10.1016/j.jcis.2020.07.123] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 07/22/2020] [Accepted: 07/23/2020] [Indexed: 11/23/2022]
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24
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Oratis AT, Bush JWM, Stone HA, Bird JC. A new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside down. Science 2020; 369:685-688. [PMID: 32764069 DOI: 10.1126/science.aba0593] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2019] [Accepted: 06/25/2020] [Indexed: 11/02/2022]
Abstract
Viscous bubbles are prevalent in both natural and industrial settings. Their rupture and collapse may be accompanied by features typically associated with elastic sheets, including the development of radial wrinkles. Previous investigators concluded that the film weight is responsible for both the film collapse and wrinkling instability. Conversely, we show here experimentally that gravity plays a negligible role: The same collapse and wrinkling arise independently of the bubble's orientation. We found that surface tension drives the collapse and initiates a dynamic buckling instability. Because the film weight is irrelevant, our results suggest that wrinkling may likewise accompany the breakup of relatively small-scale, curved viscous and viscoelastic films, including those in the respiratory tract responsible for aerosol production from exhalation events.
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Affiliation(s)
- Alexandros T Oratis
- Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA
| | - John W M Bush
- Department of Applied Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - James C Bird
- Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA.
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25
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Oshri O, Biswas S, Balazs AC. Buckling-induced interaction between circular inclusions in an infinite thin plate. Phys Rev E 2020; 102:033004. [PMID: 33075943 DOI: 10.1103/physreve.102.033004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Accepted: 08/14/2020] [Indexed: 11/07/2022]
Abstract
Design of slender artificial materials and morphogenesis of thin biological tissues typically involve stimulation of isolated regions (inclusions) in the growing body. These inclusions apply internal stresses on their surrounding areas that are ultimately relaxed by out-of-plane deformation (buckling). We utilize the Föppl-von Kármán model to analyze the interaction between two circular inclusions in an infinite plate that their centers are separated a distance of 2ℓ. In particular, we investigate a region in phase space where buckling occurs at a narrow transition layer of length ℓ_{D} around the radius of the inclusion, R (ℓ_{D}≪R). We show that the latter length scale defines two regions within the system, the close separation region, ℓ-R∼ℓ_{D}, where the transition layers of the two inclusions approximately coalesce, and the far separation region, ℓ-R≫ℓ_{D}. While the interaction energy decays exponentially in the latter region, E_{int}∝e^{-(ℓ-R)/ℓ_{D}}, it presents nonmonotonic behavior in the former region. While this exponential decay is predicted by our analytical analysis and agrees with the numerical observations, the close separation region is treated only numerically. In particular, we utilize the numerical investigation to explore two different scenarios within the final configuration: The first where the two inclusions buckle in the same direction (up-up solution) and the second where the two inclusions buckle in opposite directions (up-down solution). We show that the up-down solution is always energetically favorable over the up-up solution. In addition, we point to a curious symmetry breaking within the up-down scenario; we show that this solution becomes asymmetric in the close separation region.
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Affiliation(s)
- Oz Oshri
- Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Santidan Biswas
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Anna C Balazs
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
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26
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Wang LM, Tsai ST, Lee CY, Hsiao PY, Deng JW, Fan Chiang HC, Fei Y, Hong TM. Crumpling-origami transition for twisting cylindrical shells. Phys Rev E 2020; 101:053001. [PMID: 32575209 DOI: 10.1103/physreve.101.053001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2019] [Accepted: 04/17/2020] [Indexed: 11/07/2022]
Abstract
Origami and crumpling are two processes to reduce the size of a membrane. In the shrink-expand process, the crease pattern of the former is ordered and protected by its topological mechanism, while that of the latter is disordered and generated randomly. We observe a morphological transition between origami and crumpling states in a twisted cylindrical shell. By studying the regularity of the crease pattern, acoustic emission, and energetics from experiments and simulations, we develop a model to explain this transition from frustration of geometry that causes breaking of rotational symmetry. In contrast to solving von Kármán-Donnell equations numerically, our model allows derivations of analytic formulas that successfully describe the origami state. When generalized to truncated cones and polygonal cylinders, we explain why multiple and/or reversed crumpling-origami transitions can occur.
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Affiliation(s)
- Li-Min Wang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Sun-Ting Tsai
- Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Chih-Yu Lee
- Hsinchu Senior High School, Hsinchu 30013, Taiwan, Republic of China
| | - Pai-Yi Hsiao
- Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Jia-Wei Deng
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Hung-Chieh Fan Chiang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Yicheng Fei
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Tzay-Ming Hong
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
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27
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Ripp MM, Démery V, Zhang T, Paulsen JD. Geometry underlies the mechanical stiffening and softening of an indented floating film. SOFT MATTER 2020; 16:4121-4130. [PMID: 32255145 DOI: 10.1039/d0sm00250j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute forces, leading to nonlinear responses rooted in purely geometric effects. Here we study the indentation of a polymer film on a liquid bath. Our experiments and simulations support a recently-predicted stiffening response [D. Vella and B. Davidovitch, Phys. Rev. E, 2018, 98, 013003], and we show that the system softens at large slopes, in agreement with our theory that addresses small and large deflections. We show how stiffening and softening emanate from nontrivial yet generic features of the stress and displacement fields.
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Affiliation(s)
- Monica M Ripp
- Department of Physics, Syracuse University, Syracuse, NY 13244, USA. and BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY 13244, USA
| | - Vincent Démery
- Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France. and Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Teng Zhang
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY 13244, USA and Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, NY 13244, USA.
| | - Joseph D Paulsen
- Department of Physics, Syracuse University, Syracuse, NY 13244, USA. and BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY 13244, USA
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28
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Bense H, Tani M, Saint-Jean M, Reyssat E, Roman B, Bico J. Elastocapillary adhesion of a soft cap on a rigid sphere. SOFT MATTER 2020; 16:1961-1966. [PMID: 31967168 DOI: 10.1039/c9sm02057h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the capillary adhesion of a spherical elastic cap on a rigid sphere of a different radius. Caps of small area accommodate the combination of flexural and in-plane strains induced by the mismatch in curvature, and fully adhere to the sphere. Conversely, wider caps delaminate and exhibit only partial contact. We determine the maximum size of the cap enabling full adhesion and describe its dependence on experimental parameters through a balance of stretching and adhesion energies. Beyond the maximum size, complex adhesion patterns such as blisters, bubbles or star shapes are observed. We rationalize these different states in configuration diagrams where stretching, bending and adhesion energies are compared through two dimensionless parameters.
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Affiliation(s)
- H Bense
- Laboratoire PMMH, ESPCI Paris-PSL, CNRS UMR 7636, Sorbonne Université, Université de Paris, Paris, France. and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - M Tani
- Laboratoire PMMH, ESPCI Paris-PSL, CNRS UMR 7636, Sorbonne Université, Université de Paris, Paris, France. and Department of Physics, Tokyo Metropolitan University, Japan
| | - M Saint-Jean
- Laboratoire PMMH, ESPCI Paris-PSL, CNRS UMR 7636, Sorbonne Université, Université de Paris, Paris, France.
| | - E Reyssat
- Laboratoire PMMH, ESPCI Paris-PSL, CNRS UMR 7636, Sorbonne Université, Université de Paris, Paris, France.
| | - B Roman
- Laboratoire PMMH, ESPCI Paris-PSL, CNRS UMR 7636, Sorbonne Université, Université de Paris, Paris, France.
| | - J Bico
- Laboratoire PMMH, ESPCI Paris-PSL, CNRS UMR 7636, Sorbonne Université, Université de Paris, Paris, France.
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29
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Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases. Proc Natl Acad Sci U S A 2020; 117:3938-3943. [PMID: 32047032 DOI: 10.1073/pnas.1916221117] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in plant leaves and animal epithelia and perhaps even the formation of human fingerprints. We elucidate a primary source of this morphological complexity-an incompatibility between an elastically favored "microstructure" of uniformly spaced wrinkles and a "macrostructure" imparted through the wrinkle director and dictated by confinement forces. Our theory is borne out of experiments and simulations of floating sheets subjected to radial stretching. By analyzing patterns of grossly radial wrinkles we find two sharply distinct morphologies: defect-free patterns with a fixed number of wrinkles and nonuniform spacing and patterns of uniformly spaced wrinkles separated by defect-rich buffer zones. We show how these morphological types reflect distinct minima of a Ginzburg-Landau functional-a coarse-grained version of the elastic energy, which penalizes nonuniform wrinkle spacing and amplitude, as well as deviations of the actual director from the axis imposed by confinement. Our results extend the effective description of wrinkle patterns as liquid crystals [H. Aharoni et al, Nat. Commun. 8, 15809 (2017)], and we highlight a fascinating analogy between the geometry-energy interplay that underlies the proliferation of defects in the mechanical equilibrium of confined sheets and in thermodynamic phases of superconductors and chiral liquid crystals.
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30
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Misra S, Trinavee K, Gunda NSK, Mitra SK. Encapsulation with an interfacial liquid layer: Robust and efficient liquid-liquid wrapping. J Colloid Interface Sci 2020; 558:334-344. [DOI: 10.1016/j.jcis.2019.09.099] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Revised: 09/25/2019] [Accepted: 09/26/2019] [Indexed: 12/13/2022]
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31
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Lee HR, Park S, Choi SQ. Irremovable Blood Stain in Lung: Air-to-Interface Transport of Albumin and Its Mechanical Response to Biaxial Compression/Expansion. ACS APPLIED BIO MATERIALS 2019; 2:5551-5558. [PMID: 35021550 DOI: 10.1021/acsabm.9b00623] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Serum proteins are believed to trigger a sudden failure of lung function, but to date the mechanism remains elusive. Most studies have focused on the transport of the proteins from the subphase to the lung surfactant interface, although the opposite direction of transport, i.e., from air-to-interface, could be equally important. Here, we report that physiological concentrations of serum droplets can rapidly form a film upon exposure to air, and the entire film can be transferred to the lung surfactant interface upon coalescence, displacing it. This film was mechanically stable and remains intact even for multiple biaxial compression/expansion cycles. Our findings provide a mechanism of lung surfactant replacement by serum proteins that is fundamentally different from the subphase-to-interface transport and demonstrate that it is nearly impossible to remove the film from the interface where the lung surfactant should be, thus impairing the lung in a permanent way.
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Affiliation(s)
- Hyun-Ro Lee
- Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Sujin Park
- Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Siyoung Q Choi
- Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
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32
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Krieger MS, Dias MA. Tunable wrinkling of thin nematic liquid crystal elastomer sheets. Phys Rev E 2019; 100:022701. [PMID: 31574719 DOI: 10.1103/physreve.100.022701] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Indexed: 11/07/2022]
Abstract
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rodlike molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to compression of a thin sheet of nematic liquid crystal elastomer atop an elastic or fluid substrate. We find the scaling of the wrinkle wavelength in terms of material parameters and the applied compression. The wavelength of the wrinkles is found to be nonmonotonic in the compressive strain due to the presence of the nematic. Finally, due to soft modes, the critical stress for the appearance of wrinkles can be much higher than in an isotropic elastomer and depends nontrivially on the manner in which the elastomer was prepared.
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Affiliation(s)
- Madison S Krieger
- Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Marcelo A Dias
- Department of Engineering, Aarhus University, Inge Lehmanns Gade 10, 8000 Aarhus C, Denmark.,Aarhus University Centre for Integrated Materials Research-iMAT, Ny Munkegade 120, 8000 Aarhus C, Denmark
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33
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Oshri O, Biswas S, Balazs AC. Modeling the behavior of inclusions in circular plates undergoing shape changes from two to three dimensions. Phys Rev E 2019; 100:043001. [PMID: 31771006 DOI: 10.1103/physreve.100.043001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Indexed: 06/10/2023]
Abstract
Growth of biological tissues and shape changes of thin synthetic sheets are commonly induced by stimulation of isolated regions (inclusions) in the system. These inclusions apply internal forces on their surroundings that, in turn, promote 2D layers to acquire complex 3D configurations. We focus on a fundamental building block of these systems, and consider a circular plate that contains an inclusion with dilative strains. Based on the Föppl-von Kármán (FvK) theory, we derive an analytical model that predicts the 2D-to-3D shape transitions in the system. Our findings are summarized in a phase diagram that reveals two distinct configurations in the post-buckling region. One is an extensive profile that holds close to the threshold of the instability, and the second is a localized profile, which preempts the extensive solution beyond the buckling threshold. While the former solution is derived as a perturbation around the flat configuration, assuming infinitesimal amplitudes, the latter solution is derived around a buckled state that is highly localized. We show that up to vanishingly small corrections that scale with the thickness, this localized configuration is equivalent to that expected for ultra-thin sheets, which completely relax compressive stresses. Our findings agree quantitatively with direct numerical minimization of the FvK energy. Furthermore, we extend the theory to describe shape transitions in polymeric gels, and compare the results with numerical simulations that account for the complete elastodynamic behavior of the gels. The agreement between the theory and these simulations indicates that our results are observable experimentally. Notably, our findings can provide guidelines to the analysis of more complicated systems that encompass interaction between several buckled inclusions.
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Affiliation(s)
- Oz Oshri
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Santidan Biswas
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Anna C Balazs
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
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Godaba H, Zhang ZQ, Gupta U, Foo CC, Zhu J. Instabilities in dielectric elastomers: buckling, wrinkling, and crumpling. SOFT MATTER 2019; 15:7137-7144. [PMID: 31435627 DOI: 10.1039/c9sm01145e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Instabilities in a thin sheet are ubiquitous and can be induced by various stimuli, such as a uniaxial force, liquid-vapor surface tension, etc. This paper investigates voltage-induced instabilities in a membrane of a dielectric elastomer. Instabilities including buckling, wrinkling, and crumpling are observed in the experiments. The prestretches of the dielectric elastomer are found to play a significant role in determining its instability mode. When the prestretch is small, intermediate, or large, the membrane may undergo buckling, wrinkling, or crumpling, respectively. Finite element analysis is conducted to study these instability modes, and the simulations are well consistent with the experimental observations. We hope that this investigation of mechanical and physical properties of dielectric elastomers can enhance their extensive and significant applications in soft devices and soft robots.
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Affiliation(s)
- Hareesh Godaba
- Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117576, Singapore.
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35
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Reynolds MF, McGill KL, Wang MA, Gao H, Mujid F, Kang K, Park J, Miskin MZ, Cohen I, McEuen PL. Capillary Origami with Atomically Thin Membranes. NANO LETTERS 2019; 19:6221-6226. [PMID: 31430164 DOI: 10.1021/acs.nanolett.9b02281] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Small-scale optical and mechanical components and machines require control over three-dimensional structure at the microscale. Inspired by the analogy between paper and two-dimensional materials, origami-style folding of atomically thin materials offers a promising approach for making microscale structures from the thinnest possible sheets. In this Letter, we show that a monolayer of molybdenum disulfide (MoS2) can be folded into three-dimensional shapes by a technique called capillary origami, in which the surface tension of a droplet drives the folding of a thin sheet. We define shape nets by patterning rigid metal panels connected by MoS2 hinges, allowing us to fold micron-scale polyhedrons. Finally, we demonstrate that these shapes can be folded in parallel without the use of micropipettes or microfluidics by means of a microemulsion of droplets that dissolves into the bulk solution to drive folding. These results demonstrate controllable folding of the thinnest possible materials using capillary origami and indicate a route forward for design and parallel fabrication of more complex three-dimensional micron-scale structures and machines.
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Affiliation(s)
- Michael F Reynolds
- Laboratory of Atomic and Solid State Physics , Cornell University , Ithaca , New York 14850 , United States
| | - Kathryn L McGill
- Laboratory of Atomic and Solid State Physics , Cornell University , Ithaca , New York 14850 , United States
- Department of Physics , University of Florida , Gainesville , Florida 32611 , United States
| | - Maritha A Wang
- Laboratory of Atomic and Solid State Physics , Cornell University , Ithaca , New York 14850 , United States
- Department of Chemistry, Institute for Molecular Engineering, and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Hui Gao
- Department of Chemistry and Chemical Biology , Cornell University , Ithaca , New York 14850 , United States
- Department of Chemistry, Institute for Molecular Engineering, and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Fauzia Mujid
- Department of Chemistry, Institute for Molecular Engineering, and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Kibum Kang
- Department of Chemistry and Chemical Biology , Cornell University , Ithaca , New York 14850 , United States
- Department of Chemistry, Institute for Molecular Engineering, and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
- Department of Materials Science and Engineering , Korea Advanced Institute of Science and Technology (KAIST) , Daejeon 34141 , Korea
| | - Jiwoong Park
- Department of Chemistry, Institute for Molecular Engineering, and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Marc Z Miskin
- Laboratory of Atomic and Solid State Physics , Cornell University , Ithaca , New York 14850 , United States
- Kavli Institute at Cornell for Nanoscale Science , Cornell University , Ithaca , New York 14850 , United States
- Department of Electrical and Systems Engineering , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Itai Cohen
- Laboratory of Atomic and Solid State Physics , Cornell University , Ithaca , New York 14850 , United States
| | - Paul L McEuen
- Laboratory of Atomic and Solid State Physics , Cornell University , Ithaca , New York 14850 , United States
- Kavli Institute at Cornell for Nanoscale Science , Cornell University , Ithaca , New York 14850 , United States
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Abstract
Inflatable structures offer a path for light deployable structures in medicine, architecture, and aerospace. In this study, we address the challenge of programming the shape of thin sheets of high-stretching modulus cut and sealed along their edges. Internal pressure induces the inflation of the structure into a deployed shape that maximizes its volume. We focus on the shape and nonlinear mechanics of inflated rings and more generally, of any sealed curvilinear path. We rationalize the stress state of the sheet and infer the counterintuitive increase of curvature observed on inflation. In addition to the change of curvature, wrinkles patterns are observed in the region under compression in agreement with our minimal model. We finally develop a simple numerical tool to solve the inverse problem of programming any 2-dimensional (2D) curve on inflation and illustrate the application potential by moving an object along an intricate target path with a simple pressure input.
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37
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Qu C, Shi S, Ma M, Zheng Q. Rotational Instability in Superlubric Joints. PHYSICAL REVIEW LETTERS 2019; 122:246101. [PMID: 31322388 DOI: 10.1103/physrevlett.122.246101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2019] [Revised: 03/15/2019] [Indexed: 06/10/2023]
Abstract
Surface and interfacial energies play important roles in a number of instability phenomena in liquids and soft matter, but rarely have similar effects in solids. Here, a mechanical instability is reported which is controlled by surface and interfacial energies and is valid for a large class of materials, in particular two-dimensional layered materials. When sliding a top flake cleaved from a square microscale graphite mesa by using a probe acting on the flake through a point contact, it was observed that the flake moved unrotationally for a certain distance before it suddenly transferred to a rotating-moving state. The theoretical analysis was consistent with the experimental observation and revealed that this mechanical instability was an interesting effect of the structural superlubricity (a state of nearly zero friction). Further analysis showed that this type of instability was applicable generally for various sliding joints on different scales, as long as the friction was ultralow. Thus, the uncovered mechanism provides useful knowledge for manipulating and controlling these sliding joints, and can guide the design of future superlubricity-based devices.
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Affiliation(s)
- Cangyu Qu
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
| | - Songlin Shi
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
| | - Ming Ma
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
- Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
| | - Quanshui Zheng
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
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38
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Guzowski J, Gim B. Particle clusters at fluid-fluid interfaces: equilibrium profiles, structural mechanics and stability against detachment. SOFT MATTER 2019; 15:4921-4938. [PMID: 31169851 DOI: 10.1039/c9sm00425d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We investigate clustering of particles at an initially flat fluid-fluid interface of surface tension γ under an external force f directed perpendicular to the interface. We employ analytical theory, numerical energy minimization (Surface Evolver) and computational fluid dynamics (the Lattice-Boltzmann method) to study the equilibrium deformation of the interface and structural mechanics of the clusters, in particular at the onset of instability. In the case of incompressible clusters, we find that the equilibrium 3D interface profiles are uniquely determined by the length scale γ/(fn0), where n0 is the particle surface number density, and a non-dimensional shape parameter f2Nn0/γ2. The scaling remains valid in the whole regime of forces f, i.e., even close to the stability limit fcrit. In the cases with an initial hexagonal arrangement of the particles, upon f approaching fcrit, our simulations additionally reveal the emergence of curvature-induced defects and 2D stress anisotropy. We develop stability diagrams in terms of f, N (we study 7 ≤ N ≤ 61), and the contact angle θp at the particles and identify three unstable regimes corresponding to (i) collective detachment of the whole cluster from the interface, (ii) ejection of individual particles, and (iii) both detachment and ejection. We also discuss possible metastable states. Altogether, our results may help in better understanding and controlling the particle interfacial instabilities with potential uses in synthesis of new materials, environmental sciences and microfluidics.
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Affiliation(s)
- Jan Guzowski
- Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224, Warsaw, Poland.
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39
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Yu S, Sun Y, Zhang X, Lu C, Zhou H, Ni Y. Hierarchical wrinkles and oscillatory cracks in metal films deposited on liquid stripes. Phys Rev E 2019; 99:062802. [PMID: 31330630 DOI: 10.1103/physreve.99.062802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2019] [Indexed: 06/10/2023]
Abstract
Fascinating crack and wrinkle patterns driven by stresses are ubiquitous in natural and artificial systems. It is of great interest to control the morphologies of stress-driven patterns by using facile techniques. Here we report on the spontaneous formation of hierarchical wrinkles and oscillatory cracks in metal films deposited on liquid (or soft polymer) stripes. It is found that the metal film is under a tensile stress during deposition owing to the thermal expansion of the liquid substrate. As the film thickness is beyond a critical value, oscillatory cracks with sawtoothlike shapes form on the liquid stripes. The ratio of crack oscillation period to amplitude is independent of the stripe width and film material, which can be well explained by the "brittle adhesive joints" model. After deposition, the metal film is under a compressive stress, which is relieved by formation of various wrinkle patterns. Hierarchical wrinkles with changing wavelengths form near the stripe edge while labyrinth or wavy wrinkles form at the center. Energy analysis was adopted to explain the formation and evolution of the wrinkle patterns. This study could promote better understanding of the formations of crack and wrinkle patterns in constrained film structures and controllable fabrication of stress-driven patterns by prefabricating liquid (or soft polymer) interlayer arrays.
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Affiliation(s)
- Senjiang Yu
- Innovative Center for Advanced Materials (ICAM), Hangzhou Dianzi University, Hangzhou 310012, People's Republic of China
| | - Yadong Sun
- Department of Physics, China Jiliang University, Hangzhou 310018, People's Republic of China
| | - Xiaofei Zhang
- Department of Physics, China Jiliang University, Hangzhou 310018, People's Republic of China
| | - Chenxi Lu
- Innovative Center for Advanced Materials (ICAM), Hangzhou Dianzi University, Hangzhou 310012, People's Republic of China
| | - Hong Zhou
- Department of Physics, China Jiliang University, Hangzhou 310018, People's Republic of China
| | - Yong Ni
- CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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40
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Coppola S, Nasti G, Vespini V, Mecozzi L, Castaldo R, Gentile G, Ventre M, Netti PA, Ferraro P. Quick liquid packaging: Encasing water silhouettes by three-dimensional polymer membranes. SCIENCE ADVANCES 2019; 5:eaat5189. [PMID: 31139742 PMCID: PMC6534387 DOI: 10.1126/sciadv.aat5189] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2018] [Accepted: 04/17/2019] [Indexed: 05/05/2023]
Abstract
One of the most important substances on Earth is water. It is an essential medium for living microorganisms and for many technological and industrial processes. Confining water in an enclosed compartment without manipulating it or by using rigid containers can be very attractive, even more if the container is biocompatible and biodegradable. Here, we propose a water-based bottom-up approach for facile encasing of short-lived water silhouettes by a custom-made adaptive suit. A biocompatible polymer self-assembling with unprecedented degree of freedom over the water surface directly produces a thin membrane. The polymer film could be the external container of a liquid core or a free-standing layer with personalized design. The membranes produced have been characterized in terms of physical properties, morphology and proposed for various applications from nano- to macroscale. The process appears not to harm cells and microorganisms, opening the way to a breakthrough approach for organ-on-chip and lab-in-a-drop experiments.
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Affiliation(s)
- Sara Coppola
- Institute of Applied Sciences and Intelligent Systems “E. Caianiello,” Via Campi Flegrei 34, 80078 Pozzuoli, Italy
| | - Giuseppe Nasti
- Institute of Applied Sciences and Intelligent Systems “E. Caianiello,” Via Campi Flegrei 34, 80078 Pozzuoli, Italy
| | - Veronica Vespini
- Institute of Applied Sciences and Intelligent Systems “E. Caianiello,” Via Campi Flegrei 34, 80078 Pozzuoli, Italy
| | - Laura Mecozzi
- Institute of Applied Sciences and Intelligent Systems “E. Caianiello,” Via Campi Flegrei 34, 80078 Pozzuoli, Italy
| | - Rachele Castaldo
- Institute for Polymers, Composites and Biomaterials, CNR, Via Campi Flegrei 34, 80078 Pozzuoli, Italy
| | - Gennaro Gentile
- Institute for Polymers, Composites and Biomaterials, CNR, Via Campi Flegrei 34, 80078 Pozzuoli, Italy
| | - Maurizio Ventre
- Department of Chemical, Materials and Industrial Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, 80125 Naples, Italy
| | - Paolo A. Netti
- Department of Chemical, Materials and Industrial Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, 80125 Naples, Italy
- Center for Advanced Biomaterials For Healthcare @CRIB, Istituto Italiano di Tecnologia, Largo Barsanti e Matteucci 53, 80125 Naples, Italy
| | - Pietro Ferraro
- Institute of Applied Sciences and Intelligent Systems “E. Caianiello,” Via Campi Flegrei 34, 80078 Pozzuoli, Italy
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41
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Oshri O, Biswas S, Balazs AC. Modeling the formation of double rolls from heterogeneously patterned gels. Phys Rev E 2019; 99:033003. [PMID: 30999426 DOI: 10.1103/physreve.99.033003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2018] [Indexed: 11/07/2022]
Abstract
Both stimuli-responsive gels and growing biological tissue can undergo pronounced morphological transitions from two-dimensional (2D) layers into 3D geometries. We derive an analytical model that allows us to quantitatively predict the features of 2D-to-3D shape changes in polymer gels that encompasses different degrees of swelling within the sample. We analyze a particular configuration that emerges from a flat rectangular gel that is divided into two strips (bistrips), where each strip is swollen to a different extent in solution. The final configuration yields double rolls that display a narrow transition layer between two cylinders of constant radii. To characterize the rolls' shapes, we modify the theory of thin incompatible elastic sheets to account for the Flory-Huggins interaction between the gel and the solvent. This modification allows us to derive analytical expressions for the radii, the amplitudes, and the length of the transition layer within a given roll. Our predictions agree quantitatively with available experimental data. In addition, we carry out numerical simulations that account for the complete nonlinear behavior of the gel and show good agreement between the analytical predictions and the numerical results. Our solution sheds light on a stress focusing pattern that forms at the border between two dissimilar soft materials. Moreover, models that provide quantitative predictions on the final morphology in such heterogeneously swelling hydrogels are useful for understanding growth patterns in biology as well as accurately tailoring the structure of gels for various technological applications.
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Affiliation(s)
- Oz Oshri
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Santidan Biswas
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Anna C Balazs
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
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42
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Moshe M, Esposito E, Shankar S, Bircan B, Cohen I, Nelson DR, Bowick MJ. Kirigami Mechanics as Stress Relief by Elastic Charges. PHYSICAL REVIEW LETTERS 2019; 122:048001. [PMID: 30768297 DOI: 10.1103/physrevlett.122.048001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2018] [Indexed: 06/09/2023]
Abstract
We develop a geometric approach to understand the mechanics of perforated thin elastic sheets, using the method of strain-dependent image elastic charges. This technique recognizes the buckling response of a hole under an external load as a geometrically tuned mechanism of stress relief. We use a diagonally pulled square paper frame as a model system to quantitatively test and validate our approach. Specifically, we compare nonlinear force-extension curves and global displacement fields in theory and experiment. We find a strong softening of the force response accompanied by curvature localization at the inner corners of the buckled frame. Counterintuitively, though in complete agreement with our theory, for a range of intermediate hole sizes, wider frames are found to buckle more easily than narrower ones. Upon extending these ideas to many holes, we demonstrate that interacting elastic image charges can provide a useful kirigami design principle to selectively relax stresses in elastic materials.
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Affiliation(s)
- Michael Moshe
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
| | - Edward Esposito
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | - Suraj Shankar
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Baris Bircan
- School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA
| | - Itai Cohen
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | - David R Nelson
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Mark J Bowick
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
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43
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Abstract
The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current-day efforts to engineer flexible sensors that conform to the human body. We introduce a theoretical principle, broadly generalizing Euler's elastica-a core concept of continuum mechanics that invokes the energetic preference of bending over straining a thin solid object and that has been widely applied to classical and modern studies of beams and rods. We define a class of geometrically incompatible confinement problems, whereby the topography imposed on a thin solid body is incompatible with its intrinsic ("target") metric and, as a consequence of Gauss' Theorema Egregium, induces strain. By focusing on a prototypical example of a sheet attached to a spherical substrate, numerical simulations and analytical study demonstrate that the mechanics is governed by a principle, which we call the "Gauss-Euler elastica" This emergent rule states that-despite the unavoidable strain in such an incompatible confinement-the ratio between the energies stored in straining and bending the solid may be arbitrarily small. The Gauss-Euler elastica underlies a theoretical framework that greatly simplifies the daunting task of solving the highly nonlinear equations that describe thin solids at mechanical equilibrium. This development thus opens possibilities for attacking a broad class of phenomena governed by the coupling of geometry and mechanics.
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44
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Schulman RD, Dalnoki-Veress K. Droplets Capped with an Elastic Film Can Be Round, Elliptical, or Nearly Square. PHYSICAL REVIEW LETTERS 2018; 121:248004. [PMID: 30608717 DOI: 10.1103/physrevlett.121.248004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Indexed: 06/09/2023]
Abstract
We present experiments that show that the partial wetting of droplets capped by taut elastic films is highly tunable. Adjusting the tension allows the contact angle and droplet morphology to be controlled. By exploiting these elastic boundaries, droplets can be made elliptical, with an adjustable aspect ratio, and can even be transformed into a nearly square shape. This system can be used to create tunable liquid lenses and, moreover, presents a unique approach to liquid patterning.
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Affiliation(s)
- Rafael D Schulman
- Department of Physics and Astronomy, McMaster University, 1280 Main Street W, Hamilton, Ontario L8S 4M1, Canada
| | - Kari Dalnoki-Veress
- Department of Physics and Astronomy, McMaster University, 1280 Main Street W, Hamilton, Ontario L8S 4M1, Canada
- Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 75005 Paris, France
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45
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Mitchell NP, Carey RL, Hannah J, Wang Y, Cortes Ruiz M, McBride SP, Lin XM, Jaeger HM. Conforming nanoparticle sheets to surfaces with Gaussian curvature. SOFT MATTER 2018; 14:9107-9117. [PMID: 30339166 DOI: 10.1039/c8sm01640b] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Nanoparticle monolayer sheets are ultrathin inorganic-organic hybrid materials that combine highly controllable optical and electrical properties with mechanical flexibility and remarkable strength. Like other thin sheets, their low bending rigidity allows them to easily roll into or conform to cylindrical geometries. Nanoparticle monolayers not only can bend, but also cope with strain through local particle rearrangement and plastic deformation. This means that, unlike thin sheets such as paper or graphene, nanoparticle sheets can much more easily conform to surfaces with complex topography characterized by non-zero Gaussian curvature, like spherical caps or saddles. Here, we investigate the limits of nanoparticle monolayers' ability to conform to substrates with Gaussian curvature by stamping nanoparticle sheets onto lattices of larger polystyrene spheres. Tuning the local Gaussian curvature by increasing the size of the substrate spheres, we find that the stamped sheet morphology evolves through three characteristic stages: from full substrate coverage, where the sheet extends over the interstices in the lattice, to coverage in the form of caps that conform tightly to the top portion of each sphere and fracture at larger polar angles, to caps that exhibit radial folds. Through analysis of the nanoparticle positions, obtained from scanning electron micrographs, we extract the local strain tensor and track the onset of strain-induced dislocations in the particle arrangement. By considering the interplay of energies for elastic and plastic deformations and adhesion, we construct arguments that capture the observed changes in sheet morphology as Gaussian curvature is tuned over two orders of magnitude.
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Affiliation(s)
- Noah P Mitchell
- James Franck Institute and Department of Physics, University of Chicago, Chicago, IL, USA.
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46
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Ganguly S, Das D, Horbach J, Sollich P, Karmakar S, Sengupta S. Plastic deformation of a permanently bonded network: Stress relaxation by pleats. J Chem Phys 2018; 149:184503. [DOI: 10.1063/1.5051312] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Saswati Ganguly
- Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Debankur Das
- TIFR Centre for Interdisciplinary Sciences, 36/P Gopanapally, Hyderabad 500107, India
| | - Jürgen Horbach
- Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Peter Sollich
- Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom
| | - Smarajit Karmakar
- TIFR Centre for Interdisciplinary Sciences, 36/P Gopanapally, Hyderabad 500107, India
| | - Surajit Sengupta
- TIFR Centre for Interdisciplinary Sciences, 36/P Gopanapally, Hyderabad 500107, India
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47
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Chang J, Toga KB, Paulsen JD, Menon N, Russell TP. Thickness Dependence of the Young’s Modulus of Polymer Thin Films. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00602] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | | | - Joseph D. Paulsen
- Department of Physics and Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, United States
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48
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Démery V, Dinh HP, Damman P. Cylinder morphology of a stretched and twisted ribbon. Phys Rev E 2018; 98:012801. [PMID: 30110788 DOI: 10.1103/physreve.98.012801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Indexed: 11/07/2022]
Abstract
A rich zoology of morphologies emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all the observed shapes are not quantitatively described. This is the case of the cylindrical shape that prevails at large tension and twist, which emerges from a transverse buckling instability of the helicoid. Here, we propose a simple description of this cylindrical shape. By comparing its energy to the energy of other configurations, helicoidal and facetted, we are able to determine its location on the tension-twist phase diagram. The theoretical predictions are in good quantitative agreement with the experimental results and complement previous results from linear stability analysis.
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Affiliation(s)
- Vincent Démery
- Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, Paris, France.,Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Huy Pham Dinh
- Laboratoire Interfaces & Fluides Complexes, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium
| | - Pascal Damman
- Laboratoire Interfaces & Fluides Complexes, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium
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49
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Oshri O, Liu Y, Aizenberg J, Balazs AC. Delamination of a thin sheet from a soft adhesive Winkler substrate. Phys Rev E 2018; 97:062803. [PMID: 30011476 DOI: 10.1103/physreve.97.062803] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2018] [Indexed: 11/07/2022]
Abstract
A uniaxially compressed thin elastic sheet that is resting on a soft adhesive substrate can form a blister, which is a small delaminated region, if the adhesion energy is sufficiently weak. To analyze the equilibrium behavior of this system, we model the substrate as a Winkler or fluid foundation. We develop a complete set of equations for the profile of the sheet at different applied pressures. We show that at the edge of delamination, the height of the sheet is equal to sqrt[2]ℓ_{c}, where ℓ_{c} is the capillary length. We then derive an approximate solution to these equations and utilize them for two applications. First, we determine the phase diagram of the system by analyzing possible transitions from the flat and wrinkled to delaminated states of the sheet. Second, we show that our solution for a blister on a soft foundation converges to the known solution for a blister on a rigid substrate that assumed a discontinuous bending moment at the blister edges. This continuous convergence into a discontinuous state marks the formation of a boundary layer around the point of delamination. The width of this layer relative to the extent length of the blister, ℓ, scales as w/ℓ∼(ℓ_{c}/ℓ_{ec})^{1/2}, where ℓ_{ec} is the elastocapillary length scale. Notably, our findings can provide guidelines for utilizing compression to remove thin biofilms from surfaces and thereby prevent the fouling of the system.
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Affiliation(s)
- Oz Oshri
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Ya Liu
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Joanna Aizenberg
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.,Wyss Institute for Biologically Inspired Engineering and Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, Massachusetts 02138, USA.,Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Anna C Balazs
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
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50
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Vella D, Davidovitch B. Regimes of wrinkling in an indented floating elastic sheet. Phys Rev E 2018; 98:013003. [PMID: 30110841 DOI: 10.1103/physreve.98.013003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2018] [Indexed: 06/08/2023]
Abstract
A thin, elastic sheet floating on the surface of a liquid bath wrinkles when poked at its center. We study the onset of wrinkling as well as the evolution of the pattern as indentation progresses far beyond the wrinkling threshold. We use tension field theory to describe the macroscopic properties of the deformed film and show that the system passes through a host of different regimes, even while the deflections and strains remain small. We show that the effect of the finite size of the sheet ultimately plays a key role in determining the location of the wrinkle pattern, and obtain scaling relations that characterize the number of wrinkles at threshold and its variation as the indentation progresses.
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Affiliation(s)
- Dominic Vella
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Benny Davidovitch
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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