1
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Jambon-Puillet E, Testa A, Lorenz C, Style RW, Rebane AA, Dufresne ER. Phase-separated droplets swim to their dissolution. Nat Commun 2024; 15:3919. [PMID: 38724503 PMCID: PMC11082165 DOI: 10.1038/s41467-024-47889-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 04/15/2024] [Indexed: 05/12/2024] Open
Abstract
Biological macromolecules can condense into liquid domains. In cells, these condensates form membraneless organelles that can organize chemical reactions. However, little is known about the physical consequences of chemical activity in and around condensates. Working with model bovine serum albumin (BSA) condensates, we show that droplets swim along chemical gradients. Active BSA droplets loaded with urease swim toward each other. Passive BSA droplets show diverse responses to externally applied gradients of the enzyme's substrate and products. In all these cases, droplets swim toward solvent conditions that favor their dissolution. We call this behavior "dialytaxis", and expect it to be generic, as conditions which favor dissolution typically reduce interfacial tension, whose gradients are well-known to drive droplet motion through the Marangoni effect. These results could potentially suggest alternative physical mechanisms for active transport in living cells, and may enable the design of fluid micro-robots.
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Affiliation(s)
- Etienne Jambon-Puillet
- Department of Materials, ETH Zürich, Zürich, Switzerland
- LadHyX, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
| | - Andrea Testa
- Department of Materials, ETH Zürich, Zürich, Switzerland
| | - Charlotta Lorenz
- Department of Materials, ETH Zürich, Zürich, Switzerland
- Department of Materials Science and Engineering, Department of Physics, Cornell University, Ithaca, NY, USA
| | - Robert W Style
- Department of Materials, ETH Zürich, Zürich, Switzerland
| | - Aleksander A Rebane
- Department of Materials, ETH Zürich, Zürich, Switzerland
- Life Molecules and Materials Lab, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, Zürich, Switzerland.
- Department of Materials Science and Engineering, Department of Physics, Cornell University, Ithaca, NY, USA.
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2
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Fernández-Rico C, Schreiber S, Oudich H, Lorenz C, Sicher A, Sai T, Bauernfeind V, Heyden S, Carrara P, Lorenzis LD, Style RW, Dufresne ER. Elastic microphase separation produces robust bicontinuous materials. Nat Mater 2024; 23:124-130. [PMID: 37884672 DOI: 10.1038/s41563-023-01703-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 09/22/2023] [Indexed: 10/28/2023]
Abstract
Bicontinuous microstructures are essential to the function of diverse natural and synthetic systems. Their synthesis has been based on two approaches: arrested phase separation or self-assembly of block copolymers. The former is attractive for its chemical simplicity and the latter, for its thermodynamic robustness. Here we introduce elastic microphase separation (EMPS) as an alternative approach to make bicontinuous microstructures. Conceptually, EMPS balances the molecular-scale forces that drive demixing with large-scale elasticity to encode a thermodynamic length scale. This process features a continuous phase transition, reversible without hysteresis. Practically, EMPS is triggered by simply supersaturating an elastomeric matrix with a liquid, resulting in uniform bicontinuous materials with a well-defined microscopic length scale tuned by the matrix stiffness. The versatility of EMPS is further demonstrated by fabricating bicontinuous materials with superior mechanical properties and controlled anisotropy and microstructural gradients. Overall, EMPS presents a robust alternative for the bulk fabrication of homogeneous bicontinuous materials.
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Affiliation(s)
| | | | - Hamza Oudich
- Department of Mechanical and Process Engineering, ETH Zürich, Zürich, Switzerland
| | | | - Alba Sicher
- Department of Materials, ETH Zürich, Zürich, Switzerland
| | - Tianqi Sai
- Department of Materials, ETH Zürich, Zürich, Switzerland
| | - Viola Bauernfeind
- Adolphe Merkle Institute, University of Fribourg, Fribourg, Switzerland
| | | | - Pietro Carrara
- Department of Mechanical and Process Engineering, ETH Zürich, Zürich, Switzerland
| | - Laura De Lorenzis
- Department of Mechanical and Process Engineering, ETH Zürich, Zürich, Switzerland
| | - Robert W Style
- Department of Materials, ETH Zürich, Zürich, Switzerland
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, Zürich, Switzerland.
- Department of Materials Science and Engineering, Department of Physics, Cornell University, Ithaca, NY, USA.
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3
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Gerber D, Wilen LA, Dufresne ER, Style RW. Polycrystallinity Enhances Stress Buildup around Ice. Phys Rev Lett 2023; 131:208201. [PMID: 38039453 DOI: 10.1103/physrevlett.131.208201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Revised: 08/11/2023] [Accepted: 09/08/2023] [Indexed: 12/03/2023]
Abstract
Damage caused by freezing wet, porous materials is a widespread problem but is hard to predict or control. Here, we show that polycrystallinity significantly speeds up the stress buildup process that underpins this damage. Unfrozen water in grain-boundary grooves feeds ice growth at temperatures below the freezing temperature, leading to fast stress buildup. These stresses can build up to levels that can easily break many brittle materials. The dynamics of the process are very variable, which we ascribe to local differences in ice-grain orientation and to the surprising mobility of many grooves-which further accelerates stress buildup. Our Letter will help understand how freezing damage occurs and in developing accurate models and effective damage-mitigation strategies.
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Affiliation(s)
- Dominic Gerber
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Lawrence A Wilen
- Center for Engineering Innovation and Design, School of Engineering and Applied Sciences, Yale University, New Haven, Connecticut 06520, USA
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
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4
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Testa A, Spanke HT, Jambon-Puillet E, Yasir M, Feng Y, Küffner AM, Arosio P, Dufresne ER, Style RW, Rebane AA. Surface Passivation Method for the Super-repellence of Aqueous Macromolecular Condensates. Langmuir 2023; 39:14626-14637. [PMID: 37797324 PMCID: PMC10586374 DOI: 10.1021/acs.langmuir.3c01886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Revised: 09/21/2023] [Indexed: 10/07/2023]
Abstract
Solutions of macromolecules can undergo liquid-liquid phase separation to form droplets with ultralow surface tension. Droplets with such low surface tension wet and spread over common surfaces such as test tubes and microscope slides, complicating in vitro experiments. The development of a universal super-repellent surface for macromolecular droplets has remained elusive because their ultralow surface tension requires low surface energies. Furthermore, the nonwetting of droplets containing proteins poses additional challenges because the surface must remain inert to a wide range of chemistries presented by the various amino acid side chains at the droplet surface. Here, we present a method to coat microscope slides with a thin transparent hydrogel that exhibits complete dewetting (contact angles θ ≈ 180°) and minimal pinning of phase-separated droplets in aqueous solution. The hydrogel is based on a swollen matrix of chemically cross-linked polyethylene glycol diacrylate of molecular weight 12 kDa (PEGDA), and can be prepared with basic chemistry laboratory equipment. The PEGDA hydrogel is a powerful tool for in vitro studies of weak interactions, dynamics, and the internal organization of phase-separated droplets in aqueous solutions.
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Affiliation(s)
- Andrea Testa
- Department
of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Etienne Jambon-Puillet
- Department
of Materials, ETH Zürich, 8093 Zürich, Switzerland
- LadHyX,
CNRS, Ecole Polytechnique, Institut Polytechnique
de Paris, Palaiseau 91120, France
| | - Mohammad Yasir
- Department
of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Yanxia Feng
- Department
of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Andreas M. Küffner
- Department
of Chemistry and Applied Biosciences, Institute
for Chemical and Bioengineering, ETH Zürich, 8093 Zürich, Switzerland
| | - Paolo Arosio
- Department
of Chemistry and Applied Biosciences, Institute
for Chemical and Bioengineering, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Robert W. Style
- Department
of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Aleksander A. Rebane
- Department
of Materials, ETH Zürich, 8093 Zürich, Switzerland
- Life
Molecules and Materials Laboratory, Programs in Chemistry and in Physics, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates
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5
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Lorenz C, Forsting J, Style RW, Klumpp S, Köster S. Keratin filament mechanics and energy dissipation are determined by metal-like plasticity. Matter 2023; 6:2019-2033. [PMID: 37332398 PMCID: PMC10273143 DOI: 10.1016/j.matt.2023.04.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Revised: 03/22/2023] [Accepted: 04/24/2023] [Indexed: 06/20/2023]
Abstract
Cell mechanics are determined by an intracellular biopolymer network, including intermediate filaments that are expressed in a cell-type-specific manner. A prominent pair of intermediate filaments are keratin and vimentin, as they are expressed by non-motile and motile cells, respectively. Therefore, the differential expression of these proteins coincides with a change in cellular mechanics and dynamic properties of the cells. This observation raises the question of how the mechanical properties already differ on the single filament level. Here, we use optical tweezers and a computational model to compare the stretching and dissipation behavior of the two filament types. We find that keratin and vimentin filaments behave in opposite ways: keratin filaments elongate but retain their stiffness, whereas vimentin filaments soften but retain their length. This finding is explained by fundamentally different ways to dissipate energy: viscous sliding of subunits within keratin filaments and non-equilibrium α helix unfolding in vimentin filaments.
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Affiliation(s)
- Charlotta Lorenz
- Institute for X-Ray Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 1-5/10, 8093 Zürich, Switzerland
| | - Johanna Forsting
- Institute for X-Ray Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Robert W. Style
- Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 1-5/10, 8093 Zürich, Switzerland
| | - Stefan Klumpp
- Institute for the Dynamics of Complex Systems, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- Max Planck School “Matter to Life”, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Sarah Köster
- Institute for X-Ray Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- Max Planck School “Matter to Life”, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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6
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Heyden S, Style RW, Dufresne ER. Strain stiffening elastomers with swelling inclusions. Soft Matter 2023. [PMID: 37272410 DOI: 10.1039/d3sm00496a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Inhomogeneously swollen elastomers are an emergent class of materials, comprising elastic matrices with inclusion phases in the form of microgel particles or osmolytes. Inclusion phases can undergo osmotically driven swelling and deswelling over orders of magnitude. In the swollen state, the inclusions typically have negligible Young's modulus, and the matrix is strongly deformed. In that regime, the effective mechanical properties of the composite are governed by the matrix. Laying the groundwork for a generic analysis of inhomogeneously swollen elastomers, we develop a model based on incremental mean-field homogenization of a hyperelastic matrix. The framework allows for the computation of the macroscopic effective stiffness for arbitrary hyperelastic matrix materials. For an in-depth quantification of the local effective stiffness, we extend the concept of elastic stiffness maps to incompressible materials. For strain-stiffening materials, stiffness maps in the swollen state highlight pronounced radial stiffening with a non-monotonic change in stiffness in the hoop direction. Stiffening characteristics are sensitive to the form of constitutive models, which may be exploited in the design of hydrated actuators, soft composites and metamaterials. For validation, we apply this framework to a Yeoh material, and compare to recently published data. Model predictions agree well with experimental data on elastomers with highly swollen embedded microgel particles. We identify three distinct regimes related to an increasing degree of particle swelling: first, an initial decrease in composite stiffness is attributed to particle softening upon liquid intake. Second, dilute particle swelling leads to matrix stiffening dominating over particle softening, resulting in an increase in composite stiffness. Third, for swelling degrees beyond the dilute limit, particle interactions dominate further matrix stiffening.
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Affiliation(s)
- Stefanie Heyden
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
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7
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Moser S, Feng Y, Yasa O, Heyden S, Kessler M, Amstad E, Dufresne ER, Katzschmann RK, Style RW. Hydroelastomers: soft, tough, highly swelling composites. Soft Matter 2022; 18:7229-7235. [PMID: 36102833 PMCID: PMC9516556 DOI: 10.1039/d2sm00946c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Accepted: 09/05/2022] [Indexed: 06/15/2023]
Abstract
Inspired by the cellular design of plant tissue, we present an approach to make versatile, tough, highly water-swelling composites. We embed highly swelling hydrogel particles inside tough, water-permeable, elastomeric matrices. The resulting composites, which we call hydroelastomers, combine the properties of their parent phases. From their hydrogel component, the composites inherit the ability to highly swell in water. From the elastomeric component, the composites inherit excellent stretchability and fracture toughness, while showing little softening as they swell. Indeed, the fracture properties of the composite match those of the best-performing, tough hydrogels, exhibiting fracture energies of up to 10 kJ m-2. Our composites are straightforward to fabricate, based on widely-available materials, and can easily be molded or extruded to form shapes with complex swelling geometries. Furthermore, there is a large design space available for making hydroelastomers, since one can use any hydrogel as the dispersed phase in the composite, including hydrogels with stimuli-responsiveness. These features make hydroelastomers excellent candidates for use in soft robotics and swelling-based actuation, or as shape-morphing materials, while also being useful as hydrogel replacements in other fields.
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Affiliation(s)
- Simon Moser
- Department of Materials, ETH Zürich, Switzerland.
| | - Yanxia Feng
- Department of Materials, ETH Zürich, Switzerland.
| | - Oncay Yasa
- Department of Mechanical and Process Engineering, ETH Zürich, Switzerland.
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8
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Bain N, Heyden S, Xu Q, Style RW, Dufresne ER. Reply to the 'Comment on "Surface elastic constants of a soft solid"' by E. Gutman, Soft Matter, 2022, 18, DOI: 10.1039/D1SM01412A. Soft Matter 2022; 18:4641-4642. [PMID: 35678167 DOI: 10.1039/d2sm00249c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In response to Gutman's comment, we clarify the derivation of the Shuttleworth equation. In addition, we discuss the findings of our original paper in light of recent theoretical and experimental work on surface elasticity in soft solids.
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Affiliation(s)
- Nicolas Bain
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Stefanie Heyden
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Qin Xu
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China.
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
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9
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Böddeker TJ, Rosowski KA, Berchtold D, Emmanouilidis L, Han Y, Allain FHT, Style RW, Pelkmans L, Dufresne ER. Erratum: Publisher Correction: Non-specific adhesive forces between filaments and membraneless organelles. Nat Phys 2022; 18:601. [PMID: 35583413 PMCID: PMC9106589 DOI: 10.1038/s41567-022-01600-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
[This corrects the article DOI: 10.1038/s41567-022-01537-8.].
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Affiliation(s)
| | | | - Doris Berchtold
- Department of Molecular Life Sciences, University of Zurich, Zurich, Switzerland
| | | | - Yaning Han
- Institute of Biochemistry, ETH Zurich, Zurich, Switzerland
| | | | | | - Lucas Pelkmans
- Department of Molecular Life Sciences, University of Zurich, Zurich, Switzerland
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10
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Abstract
Phase separation is a ubiquitous process and finds applications in a variety of biological, organic, and inorganic systems. Nature has evolved the ability to control phase separation to both regulate cellular processes and make composite materials with outstanding mechanical and optical properties. Striking examples of the latter are the vibrant blue and green feathers of many bird species, which are thought to result from an exquisite control of the size and spatial correlations of their phase-separated microstructures. By contrast, it is much harder for material scientists to arrest and control phase separation in synthetic materials with such a high level of precision at these length scales. In this Perspective, we briefly review some established methods to control liquid-liquid phase separation processes and then highlight the emergence of a promising arrest method based on phase separation in an elastic polymer network. Finally, we discuss upcoming challenges and opportunities for fabricating microstructured materials via mechanically controlled phase separation.
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11
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Leniart A, Pula P, Style RW, Majewski PW. Pathway-Dependent Grain Coarsening of Block Copolymer Patterns under Controlled Solvent Evaporation. ACS Macro Lett 2022; 11:121-126. [PMID: 35574792 PMCID: PMC8772373 DOI: 10.1021/acsmacrolett.1c00677] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 12/27/2021] [Indexed: 11/28/2022]
Abstract
Solvent evaporation annealing (SEA) is a straightforward, single-step casting and annealing method of block copolymers (BCP) processing yielding large-grained morphologies in a very short time. Here, we present a quantitative analysis of BCP grain-coarsening in thin films under controlled evaporation of the solvent. Our study is aimed at understanding time and BCP concentration influence on the rate of the lateral growth of BCP grains. By systematically investigating the coarsening kinetics at various BCP concentrations, we observed a steeply decreasing exponential dependence of the kinetics power-law time exponent on polymer concentration. We used this dependence to formulate a mathematical model of BCP ordering under nonstationary conditions and a 2D, time- and concentration-dependent coarsening rate diagram, which can be used as an aid in engineering the BCP processing pathway in SEA and also in other directed self-assembly methods that utilize BCP-solvent interactions such as solvent vapor annealing.
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Affiliation(s)
| | - Przemyslaw Pula
- Department
of Chemistry, University of Warsaw, Warsaw 02089, Poland
| | - Robert W. Style
- Department
of Materials, Soft and Living Materials, ETH Zürich, Vladimir-Prelog-Weg 10, 8093 Zürich, Switzerland
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12
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Böddeker TJ, Rosowski KA, Berchtold D, Emmanouilidis L, Han Y, Allain FHT, Style RW, Pelkmans L, Dufresne ER. Non-specific adhesive forces between filaments and membraneless organelles. Nat Phys 2022; 18:571-578. [PMID: 35582428 PMCID: PMC9106579 DOI: 10.1038/s41567-022-01537-8] [Citation(s) in RCA: 33] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 02/04/2022] [Indexed: 05/07/2023]
Abstract
Many membraneless organelles are liquid-like domains that form inside the active, viscoelastic environment of living cells through phase separation. To investigate the potential coupling of phase separation with the cytoskeleton, we quantify the structural correlations of membraneless organelles (stress granules) and cytoskeletal filaments (microtubules) in a human-derived epithelial cell line. We find that microtubule networks are substantially denser in the vicinity of stress granules. When microtubules are depolymerized, the sub-units localize near the surface of the stress granules. We interpret these data using a thermodynamic model of partitioning of particles to the surface and bulk of the droplets. In this framework, our data are consistent with a weak (≲k B T) affinity of the microtubule sub-units for stress granule interfaces. As microtubules polymerize, their interfacial affinity increases, providing sufficient adhesion to deform droplets and/or the network. Our work suggests that proteins and other objects in the cell have a non-specific affinity for droplet interfaces that increases with the contact area and becomes most apparent when they have no preference for the interior of a droplet over the rest of the cytoplasm. We validate this basic physical phenomenon in vitro through the interaction of a simple protein-RNA condensate with microtubules.
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Affiliation(s)
| | | | - Doris Berchtold
- Department of Molecular Life Sciences, University of Zurich, Zurich, Switzerland
| | | | - Yaning Han
- Institute of Biochemistry, ETH Zurich, Zurich, Switzerland
| | | | | | - Lucas Pelkmans
- Department of Molecular Life Sciences, University of Zurich, Zurich, Switzerland
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13
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Rolland M, Truong NP, Parkatzidis K, Pilkington EH, Torzynski AL, Style RW, Dufresne ER, Anastasaki A. Shape-Controlled Nanoparticles from a Low-Energy Nanoemulsion. JACS Au 2021; 1:1975-1986. [PMID: 34841413 PMCID: PMC8611665 DOI: 10.1021/jacsau.1c00321] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Indexed: 06/13/2023]
Abstract
Nanoemulsion technology enables the production of uniform nanoparticles for a wide range of applications. However, existing nanoemulsion strategies are limited to the production of spherical nanoparticles. Here, we describe a low-energy nanoemulsion method to produce nanoparticles with various morphologies. By selecting a macro-RAFT agent (poly(di(ethylene glycol) ethyl ether methacrylate-co-N-(2-hydroxypropyl) methacrylamide) (P(DEGMA-co-HPMA))) that dramatically lowers the interfacial tension between monomer droplets and water, we can easily produce nanoemulsions at room temperature by manual shaking for a few seconds. With the addition of a common ionic surfactant (SDS), these nanoscale droplets are robustly stabilized at both the formation and elevated temperatures. Upon polymerization, we produce well-defined block copolymers forming nanoparticles with a wide range of controlled morphologies, including spheres, worm balls, worms, and vesicles. Our nanoemulsion polymerization is robust and well-controlled even without stirring or external deoxygenation. This method significantly expands the toolbox and availability of nanoemulsions and their tailor-made polymeric nanomaterials.
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Affiliation(s)
- Manon Rolland
- Laboratory
for Polymeric Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, 8093 Zürich, Switzerland
| | - Nghia P. Truong
- Laboratory
for Polymeric Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, 8093 Zürich, Switzerland
- Monash
Institute of Pharmaceutical Sciences, Monash
University, Parkville, Victoria 3052, Australia
| | - Kostas Parkatzidis
- Laboratory
for Polymeric Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, 8093 Zürich, Switzerland
| | - Emily H. Pilkington
- Monash
Institute of Pharmaceutical Sciences, Monash
University, Parkville, Victoria 3052, Australia
| | - Alexandre L. Torzynski
- Laboratory
of Soft and Living Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, 8093 Zürich, Switzerland
| | - Robert W. Style
- Laboratory
of Soft and Living Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, 8093 Zürich, Switzerland
| | - Eric R. Dufresne
- Laboratory
of Soft and Living Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, 8093 Zürich, Switzerland
| | - Athina Anastasaki
- Laboratory
for Polymeric Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, 8093 Zürich, Switzerland
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14
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Bain N, Jagota A, Smith-Mannschott K, Heyden S, Style RW, Dufresne ER. Surface Tension and the Strain-Dependent Topography of Soft Solids. Phys Rev Lett 2021; 127:208001. [PMID: 34860052 DOI: 10.1103/physrevlett.127.208001] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Revised: 08/23/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
When stretched in one direction, most solids shrink in the transverse directions. In soft silicone gels, however, we observe that small-scale topographical features grow upon stretching. A quantitative analysis of the topography shows that this counterintuitive response is nearly linear, allowing us to tackle it through a small-strain analysis. We find that the surprising increase of small-scale topography with stretch is due to a delicate interplay of the bulk and surface responses to strain. Specifically, we find that surface tension changes as the material is deformed. This response is expected on general grounds for solid materials, but challenges the standard description of gel and elastomer surfaces.
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Affiliation(s)
- Nicolas Bain
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Anand Jagota
- Departments of Bioengineering, and of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18017, USA
| | | | - Stefanie Heyden
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
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15
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Meng X, Sonn-Segev A, Schumacher A, Cole D, Young G, Thorpe S, Style RW, Dufresne ER, Kukura P. Micromirror Total Internal Reflection Microscopy for High-Performance Single Particle Tracking at Interfaces. ACS Photonics 2021; 8:3111-3118. [PMID: 34692901 PMCID: PMC8532162 DOI: 10.1021/acsphotonics.1c01268] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Indexed: 06/01/2023]
Abstract
Single particle tracking has found broad applications in the life and physical sciences, enabling the observation and characterization of nano- and microscopic motion. Fluorescence-based approaches are ideally suited for high-background environments, such as tracking lipids or proteins in or on cells, due to superior background rejection. Scattering-based detection is preferable when localization precision and imaging speed are paramount due to the in principle infinite photon budget. Here, we show that micromirror-based total internal reflection dark field microscopy enables background suppression previously only reported for interferometric scattering microscopy, resulting in nanometer localization precision at 6 μs exposure time for 20 nm gold nanoparticles with a 25 × 25 μm2 field of view. We demonstrate the capabilities of our implementation by characterizing sub-nanometer deterministic flows of 20 nm gold nanoparticles at liquid-liquid interfaces. Our results approach the optimal combination of background suppression, localization precision, and temporal resolution achievable with pure scattering-based imaging and tracking of nanoparticles at interfaces.
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Affiliation(s)
- Xuanhui Meng
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K.
| | - Adar Sonn-Segev
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K.
| | - Anne Schumacher
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K.
| | - Daniel Cole
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K.
| | - Gavin Young
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K.
| | - Stephen Thorpe
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K.
| | | | | | - Philipp Kukura
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K.
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16
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Sicher A, Ganz R, Menzel A, Messmer D, Panzarasa G, Feofilova M, Prum RO, Style RW, Saranathan V, Rossi RM, Dufresne ER. Structural color from solid-state polymerization-induced phase separation. Soft Matter 2021; 17:5772-5779. [PMID: 34027537 DOI: 10.1039/d1sm00210d] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Structural colors are produced by wavelength-dependent scattering of light from nanostructures. While living organisms often exploit phase separation to directly assemble structurally colored materials from macromolecules, synthetic structural colors are typically produced in a two-step process involving the sequential synthesis and assembly of building blocks. Phase separation is attractive for its simplicity, but applications are limited due to a lack of robust methods for its control. A central challenge is to arrest phase separation at the desired length scale. Here, we show that solid-state polymerization-induced phase separation can produce stable structures at optical length scales. In this process, a polymeric solid is swollen and softened with a second monomer. During its polymerization, the two polymers become immiscible and phase separate. As free monomer is depleted, the host matrix resolidifies and arrests coarsening. The resulting polymeric composites have a blue or white appearance. We compare these biomimetic nanostructures to those in structurally-colored feather barbs, and demonstrate the flexibility of this approach by producing structural color in filaments and large sheets.
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Affiliation(s)
- Alba Sicher
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
- Laboratory for Biomimetic Membranes and Textiles, Empa, Swiss Federal Laboratories for Materials Science and Technology, 9014 St. Gallen, Switzerland.
| | - Rabea Ganz
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Andreas Menzel
- Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen PSI, Switzerland
| | - Daniel Messmer
- Laboratory of Polymeric Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Guido Panzarasa
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Maria Feofilova
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Richard O Prum
- Department of Ecology and Evolutionary Biology and the Peabody Museum, Yale University, New Haven, CT 06520, USA
| | - Robert W Style
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | | | - René M Rossi
- Laboratory for Biomimetic Membranes and Textiles, Empa, Swiss Federal Laboratories for Materials Science and Technology, 9014 St. Gallen, Switzerland.
| | - Eric R Dufresne
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
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17
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Smith-Mannschott K, Xu Q, Heyden S, Bain N, Snoeijer JH, Dufresne ER, Style RW. Droplets Sit and Slide Anisotropically on Soft, Stretched Substrates. Phys Rev Lett 2021; 126:158004. [PMID: 33929254 DOI: 10.1103/physrevlett.126.158004] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Revised: 01/21/2021] [Accepted: 03/03/2021] [Indexed: 06/12/2023]
Abstract
Anisotropically wetting substrates enable useful control of droplet behavior across a range of applications. Usually, these involve chemically or physically patterning the substrate surface, or applying gradients in properties like temperature or electrical field. Here, we show that a flat, stretched, uniform soft substrate also exhibits asymmetric wetting, both in terms of how droplets slide and in their static shape. Droplet dynamics are strongly affected by stretch: glycerol droplets on silicone substrates with a 23% stretch slide 67% faster in the direction parallel to the applied stretch than in the perpendicular direction. Contrary to classical wetting theory, static droplets in equilibrium appear elongated, oriented parallel to the stretch direction. Both effects arise from droplet-induced deformations of the substrate near the contact line.
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Affiliation(s)
| | - Qin Xu
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China
| | - Stefanie Heyden
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Nicolas Bain
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Jacco H Snoeijer
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+Institute, University of Twente, 7500 AE Enschede, Netherlands
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
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18
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Neumann LN, Oveisi E, Petzold A, Style RW, Thurn-Albrecht T, Weder C, Schrettl S. Dynamics and healing behavior of metallosupramolecular polymers. Sci Adv 2021; 7:7/18/eabe4154. [PMID: 33910908 PMCID: PMC8081362 DOI: 10.1126/sciadv.abe4154] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Accepted: 03/10/2021] [Indexed: 05/28/2023]
Abstract
Self-healing or healable polymers can recuperate their function after physical damage. This process involves diffusion of macromolecules across severed interfaces until the structure of the interphase matches that of the pristine material. However, monitoring this nanoscale process and relating it to the mechanical recovery remain elusive. We report that studying diffusion across healed interfaces and a correlation of contact time, diffusion depth, and mechanical properties is possible when two metallosupramolecular polymers assembled with different lanthanoid salts are mended. The materials used display similar properties, while the metal ions can be tracked with high spatial resolution by energy-dispersive x-ray spectrum imaging. We find that healing actual defects requires an interphase thickness in excess of 100 nm, 10 times more than previously established for self-adhesion of smooth films of glassy polymers.
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Affiliation(s)
- Laura N Neumann
- Adolphe Merkle Institute, University of Fribourg, Chemin des Verdiers 4, 1700 Fribourg, Switzerland
| | - Emad Oveisi
- Interdisciplinary Centre for Electron Microscopy, EPFL, 1015 Lausanne, Switzerland
| | - Albrecht Petzold
- Naturwissenschaftliche Fakultät II-Chemie, Physik und Mathematik, Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, von-Danckelmann-Platz 3, 06120 Halle (Saale), Germany
| | - Robert W Style
- Department of Materials, Soft and Living Materials, ETH Zürich, Vladimir-Prelog-Weg 10, 8093 Zürich, Switzerland
| | - Thomas Thurn-Albrecht
- Naturwissenschaftliche Fakultät II-Chemie, Physik und Mathematik, Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, von-Danckelmann-Platz 3, 06120 Halle (Saale), Germany
| | - Christoph Weder
- Adolphe Merkle Institute, University of Fribourg, Chemin des Verdiers 4, 1700 Fribourg, Switzerland.
| | - Stephen Schrettl
- Adolphe Merkle Institute, University of Fribourg, Chemin des Verdiers 4, 1700 Fribourg, Switzerland.
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19
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Palin D, Style RW, Zlopaša J, Petrozzini JJ, Pfeifer MA, Jonkers HM, Dufresne ER, Estroff LA. Forming Anisotropic Crystal Composites: Assessing the Mechanical Translation of Gel Network Anisotropy to Calcite Crystal Form. J Am Chem Soc 2021; 143:3439-3447. [PMID: 33647198 DOI: 10.1021/jacs.0c12326] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
The promise of crystal composites with direction-specific properties is an attractive prospect for diverse applications; however, synthetic strategies for realizing such composites remain elusive. Here, we demonstrate that anisotropic agarose gel networks can mechanically "mold" calcite crystal growth, yielding anisotropically structured, single-crystal composites. Drying and rehydration of agarose gel films result in the affine deformation of their fibrous networks to yield fiber alignment parallel to the drying plane. Precipitation of calcium carbonate within these anisotropic networks results in the formation of calcite crystal composite disks oriented parallel to the fibers. The morphology of the disks, revealed by nanocomputed tomography imaging, evolves with time and can be described by linear-elastic fracture mechanics theory, which depends on the ratio between the length of the crystal and the elastoadhesive length of the gel. Precipitation of calcite in uniaxially deformed agarose gel cylinders results in the formation of rice-grain-shaped crystals, suggesting the broad applicability of the approach. These results demonstrate how the anisotropy of compliant networks can translate into the desired crystal composite morphologies. This work highlights the important role organic matrices can play in mechanically "molding" biominerals and provides an exciting platform for fabricating crystal composites with direction-specific and emergent functional properties.
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Affiliation(s)
- Damian Palin
- Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, United States.,Materials & Environment section, Department 3MD Faculty of Civil and Engineering and Geosciences Delft University of Technology 2628 CN, Delft, The Netherlands
| | - Robert W Style
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland
| | - Jure Zlopaša
- Department of Biotechnology, Faculty of Applied Sciences, Delft University of Technology, 2629 HZ, Delft, The Netherlands
| | - Jonathan J Petrozzini
- Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, United States
| | - Mark A Pfeifer
- Cornell Center for Materials Research, Cornell University, Ithaca, New York 14853, United States
| | - Henk M Jonkers
- Materials & Environment section, Department 3MD Faculty of Civil and Engineering and Geosciences Delft University of Technology 2628 CN, Delft, The Netherlands
| | - Eric R Dufresne
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland
| | - Lara A Estroff
- Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, United States.,Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, United States
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20
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Ijavi M, Style RW, Emmanouilidis L, Kumar A, Meier SM, Torzynski AL, Allain FHT, Barral Y, Steinmetz MO, Dufresne ER. Surface tensiometry of phase separated protein and polymer droplets by the sessile drop method. Soft Matter 2021; 17:1655-1662. [PMID: 33367441 DOI: 10.1039/d0sm01319f] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Phase separated macromolecules play essential roles in many biological and synthetic systems. Physical characterization of these systems can be challenging because of limited sample volumes, particularly for phase-separated proteins. Here, we demonstrate that a classic method for measuring the surface tension of liquid droplets, based on the analysis of the shape of a sessile droplet, can be effectively scaled down to measure the interfacial tension between a macromolecule-rich droplet phase and its co-existing macromolecule-poor continuous phase. The connection between droplet shape and surface tension relies on the density difference between the droplet and its surroundings. This can be determined with small sample volumes in the same setup by measuring the droplet sedimentation velocity. An interactive MATLAB script for extracting the capillary length from a droplet image is included in the ESI.
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Affiliation(s)
| | | | | | - Anil Kumar
- Laboratory of Biomolecular Research, Paul Scherrer Institute, Switzerland
| | - Sandro M Meier
- Institute of Biochemistry, ETH Zürich, Switzerland and Laboratory of Biomolecular Research, Paul Scherrer Institute, Switzerland
| | | | | | - Yves Barral
- Institute of Biochemistry, ETH Zürich, Switzerland
| | - Michel O Steinmetz
- Laboratory of Biomolecular Research, Paul Scherrer Institute, Switzerland
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21
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Abstract
We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu
et al.
2018
Soft Matter
14, 916–920 (doi:10.1039/C7SM02431B)). Following a Green’s function approach, we extend the surface-stress regularized Flamant–Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two free parameters, the surface Lamé coefficients. In comparison with experiments, we find that observed opening angles are more accurately captured using finite kinematics, especially with increasing levels of applied pre-strain. These fits qualitatively agree with the results of Xu
et al
., but revise values of the surface elastic constants.
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Affiliation(s)
- Stefanie Heyden
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Nicolas Bain
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Qin Xu
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Robert W. Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
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22
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Hui CY, Liu Z, Bain N, Jagota A, Dufresne ER, Style RW, Kiyama R, Gong JP. How surface stress transforms surface profiles and adhesion of rough elastic bodies. Proc Math Phys Eng Sci 2020; 476:20200477. [PMID: 33362416 DOI: 10.1098/rspa.2020.0477] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 10/06/2020] [Indexed: 01/07/2023] Open
Abstract
The surface of soft solids carries a surface stress that tends to flatten surface profiles. For example, surface features on a soft solid, fabricated by moulding against a stiff-patterned substrate, tend to flatten upon removal from the mould. In this work, we derive a transfer function in an explicit form that, given any initial surface profile, shows how to compute the shape of the corresponding flattened profile. We provide analytical results for several applications including flattening of one-dimensional and two-dimensional periodic structures, qualitative changes to the surface roughness spectrum, and how that strongly influences adhesion.
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Affiliation(s)
- Chung-Yuen Hui
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.,Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan
| | - Zezhou Liu
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
| | - Nicolas Bain
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Anand Jagota
- Departments of Bioengineering and of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA 18015, USA
| | - Eric R Dufresne
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Robert W Style
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Ryuji Kiyama
- Graduate School of Life Science, Hokkaido University, Sapporo 001-0021, Japan
| | - Jian Ping Gong
- Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan.,Faculty of Advanced Life Science, Hokkaido University, Sapporo 001-0021, Japan.,WPI-ICReDD, Hokkaido University, Sapporo 001-0021, Japan
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23
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Xu Q, Wilen LA, Jensen KE, Style RW, Dufresne ER. Viscoelastic and Poroelastic Relaxations of Soft Solid Surfaces. Phys Rev Lett 2020; 125:238002. [PMID: 33337191 DOI: 10.1103/physrevlett.125.238002] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Revised: 09/21/2020] [Accepted: 10/28/2020] [Indexed: 06/12/2023]
Abstract
Understanding surface mechanics of soft solids, such as soft polymeric gels, is crucial in many engineering processes, such as dynamic wetting and adhesive failure. In these situations, a combination of capillary and elastic forces drives the motion, which is balanced by dissipative mechanisms to determine the rate. While shear rheology (i.e., viscoelasticity) has long been assumed to dominate the dissipation, recent works have suggested that compressibility effects (i.e., poroelasticity) could play roles in swollen networks. We use fast interferometric imaging to quantify the relaxation of surface deformations due to a displaced contact line. By systematically measuring the profiles at different time and length scales, we experimentally observe a crossover from viscoelastic to poroelastic surface relaxations.
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Affiliation(s)
- Qin Xu
- Laboratory of Soft and Living Materials, ETH Zurich, 8093 Zurich, Switzerland
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China
- HKUST Shenzhen Research Institute, Shenzhen, China 518057
| | - Lawrence A Wilen
- School of Engineering and Applied Science, Yale University, New Haven, Connecticut 06511, USA
| | - Katharine E Jensen
- Department of Physics, Williams College, Williamstown, Massachusetts 01267, USA
| | - Robert W Style
- Laboratory of Soft and Living Materials, ETH Zurich, 8093 Zurich, Switzerland
| | - Eric R Dufresne
- Laboratory of Soft and Living Materials, ETH Zurich, 8093 Zurich, Switzerland
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24
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Spanke HT, Style RW, François-Martin C, Feofilova M, Eisentraut M, Kress H, Agudo-Canalejo J, Dufresne ER. Wrapping of Microparticles by Floppy Lipid Vesicles. Phys Rev Lett 2020; 125:198102. [PMID: 33216584 DOI: 10.1103/physrevlett.125.198102] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Accepted: 10/13/2020] [Indexed: 06/11/2023]
Abstract
Lipid membranes, the barrier defining living cells and many of their subcompartments, bind to a wide variety of nano- and micrometer sized objects. In the presence of strong adhesive forces, membranes can strongly deform and wrap the particles, an essential step in crossing the membrane for a variety of healthy and disease-related processes. A large body of theoretical and numerical work has focused on identifying the physical properties that underly wrapping. Using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure a wrapping phase diagram and make quantitative comparisons to theoretical models. Our data are consistent with a model of membrane-particle interactions accounting for the adhesive energy per unit area, membrane bending rigidity, particle size, and vesicle radius.
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Affiliation(s)
| | | | | | | | - Manuel Eisentraut
- Department of Physics, University of Bayreuth, 95447 Bayreuth, Germany
| | - Holger Kress
- Department of Physics, University of Bayreuth, 95447 Bayreuth, Germany
| | - Jaime Agudo-Canalejo
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
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25
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Testa P, Chappuis B, Kistler S, Style RW, Heyderman LJ, Dufresne ER. Switchable adhesion of soft composites induced by a magnetic field. Soft Matter 2020; 16:5806-5811. [PMID: 32469030 DOI: 10.1039/d0sm00626b] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Switchable adhesives have the potential to improve the manufacturing and recycling of parts, and to enable new modes of motility for soft robots. Here, we demonstrate magnetically-switchable adhesion of a two-phase composite to non-magnetic objects. The composite's continuous phase is a silicone elastomer, and the dispersed phase is a magneto-rheological fluid. The composite is simple to prepare, and to mold into different shapes. When a magnetic field is applied, the magneto-rheological fluid develops a yield stress, which dramatically enhances the composite's adhesive properties. We demonstrate up to a nine-fold increase of the pull-off force of non-magnetic objects in the presence of a 250 mT field.
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Affiliation(s)
- Paolo Testa
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
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26
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Abstract
Michael Bartlett and Robert Style introduce the Soft Matter themed collection on liquid composites.
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Affiliation(s)
- Michael D Bartlett
- Materials Science and Engineering, Iowa State University of Science and Technology, Ames, IA 50011, USA.
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27
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Abstract
When liquid droplets nucleate and grow in a polymer network, compressive stresses can significantly increase their internal pressure, reaching values that far exceed the Laplace pressure. When droplets have grown in a polymer network with a stiffness gradient, droplets in relatively stiff regions of the network tend to dissolve, favoring growth of droplets in softer regions. Here, we show that this elastic ripening can be strong enough to reverse the direction of Ostwald ripening: large droplets can shrink to feed the growth of smaller ones. To numerically model these experiments, we generalize the theory of elastic ripening to account for gradients in solubility alongside gradients in mechanical stiffness.
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Affiliation(s)
| | | | - David Zwicker
- Max Planck Institute for Dynamics and Self-Organization, 37077, Göttingen, Germany
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
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28
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Rosowski KA, Sai T, Vidal-Henriquez E, Zwicker D, Style RW, Dufresne ER. Elastic ripening and inhibition of liquid-liquid phase separation. Nat Phys 2020; 16:422-425. [PMID: 32273899 PMCID: PMC7145441 DOI: 10.1038/s41567-019-0767-2] [Citation(s) in RCA: 59] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Accepted: 12/02/2019] [Indexed: 05/07/2023]
Abstract
Phase separation is a central concept of materials physics [1-3] and has recently emerged as an important route to compartmentalization within living cells [4-6]. Biological phase separation features activity [7], complex compositions [8], and elasticity [9], which reveal important gaps in our understanding of this universal physical phenomenon. Here, we explore the impact of elasticity on phase separation in synthetic polymer networks. We show that compressive stresses in a polymer network can suppress phase separation of the solvent that swells it, stabilizing mixtures well beyond the liquid-liquid phase separation boundary. Network stresses also drive a new form of ripening, driven by transport of solute down stiffness gradients. This elastic ripening can be much faster than conventional surface tension driven Ostwald ripening.
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Affiliation(s)
| | - Tianqi Sai
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | | | - David Zwicker
- Max Planck Institute for Dynamics and Self-Organization, 37077, Göttingen, Germany
| | - Robert W. Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
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29
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Kim JY, Liu Z, Weon BM, Cohen T, Hui CY, Dufresne ER, Style RW. Extreme cavity expansion in soft solids: Damage without fracture. Sci Adv 2020; 6:eaaz0418. [PMID: 32258404 PMCID: PMC7101206 DOI: 10.1126/sciadv.aaz0418] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2019] [Accepted: 01/03/2020] [Indexed: 05/07/2023]
Abstract
Cavitation is a common damage mechanism in soft solids. Here, we study this using a phase separation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make stable cavities of different sizes, as well as the huge range of accessible strains, allows us to systematically study the early stages of cavity expansion. Cavities grow in a scale-free manner, accompanied by irreversible bond breakage that is distributed around the growing cavity rather than being localized to a crack tip. Furthermore, cavities appear to grow at constant driving pressure. This has strong analogies with the plasticity that occurs surrounding a growing void in ductile metals. In particular, we find that, although elastomers are normally considered as brittle materials, small-scale cavity expansion is more like a ductile process. Our results have broad implications for understanding and controlling failure in soft solids.
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Affiliation(s)
- Jin Young Kim
- School of Advanced Materials Science and Engineering, SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, Suwon 16419, South Korea
| | - Zezhou Liu
- Department of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
| | - Byung Mook Weon
- School of Advanced Materials Science and Engineering, SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, Suwon 16419, South Korea
| | - Tal Cohen
- Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chung-Yuen Hui
- Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | | - Robert W. Style
- Department of Materials, ETH Zürich, Zürich 8093, Switzerland
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30
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Testa P, Style RW, Cui J, Donnelly C, Borisova E, Derlet PM, Dufresne ER, Heyderman LJ. Magnetically Addressable Shape-Memory and Stiffening in a Composite Elastomer. Adv Mater 2019; 31:e1900561. [PMID: 31161627 DOI: 10.1002/adma.201900561] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Revised: 04/11/2019] [Indexed: 06/09/2023]
Abstract
With a specific stimulus, shape-memory materials can assume a temporary shape and subsequently recover their original shape, a functionality that renders them relevant for applications in fields such as biomedicine, aerospace, and wearable electronics. Shape-memory in polymers and composites is usually achieved by exploiting a thermal transition to program a temporary shape and subsequently recover the original shape. This may be problematic for heat-sensitive environments, and when rapid and uniform heating is required. In this work, a soft magnetic shape-memory composite is produced by encasing liquid droplets of magneto-rheological fluid into a poly(dimethylsiloxane) matrix. Under the influence of a magnetic field, this material undergoes an exceptional stiffening transition, with an almost 30-fold increase in shear modulus. Exploiting this transition, fast and fully reversible magnetic shape-memory is demonstrated in three ways, by embossing, by simple shear, and by unconstrained 3D deformation. Using advanced synchrotron X-ray tomography techniques, the internal structure of the material is revealed, which can be correlated with the composite stiffening and shape-memory mechanism. This material concept, based on a simple emulsion process, can be extended to different fluids and elastomers, and can be manufactured with a wide range of methods.
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Affiliation(s)
- Paolo Testa
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Paul Scherrer Institute, 5232, Villigen, Switzerland
| | - Robert W Style
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
| | - Jizhai Cui
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Paul Scherrer Institute, 5232, Villigen, Switzerland
| | - Claire Donnelly
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Paul Scherrer Institute, 5232, Villigen, Switzerland
| | | | | | - Eric R Dufresne
- Laboratory for Soft and Living Materials, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
| | - Laura J Heyderman
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Paul Scherrer Institute, 5232, Villigen, Switzerland
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31
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Liu Z, Jensen KE, Xu Q, Style RW, Dufresne ER, Jagota A, Hui CY. Effects of strain-dependent surface stress on the adhesive contact of a rigid sphere to a compliant substrate. Soft Matter 2019; 15:2223-2231. [PMID: 30758375 DOI: 10.1039/c8sm02579g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Recent experiments have reported that the surface stress of soft elastic solids can increase rapidly with surface strain. For example, when a small hard sphere in adhesive contact with a soft silicone gel is slowly retracted from its rest position, it was found that the retraction force versus displacement relation cannot be explained either by the Johnson-Kendall-Roberts (JKR) theory or a recent indentation theory based on an isotropic surface stress that is independent of surface strain. In this paper, we address this problem using a finite element method to simulate the retraction process. Our numerical model does not have the restrictions of the aforementioned theories; that is, it can handle large nonlinear elastic deformation as well as a surface-strain-dependent surface stress. Our simulation is in good agreement with experimental force versus displacement data with no fitting parameters. Therefore, our results lend further support to the claim that significant strain-dependent surface stresses can occur in simple soft elastic gels. However, significant challenges remain in the reconciliation of theory and experiments, particularly regarding the geometry of the contact and substrate deformation.
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Affiliation(s)
- Zezhou Liu
- Department of Mechanical & Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA.
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32
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Berman JD, Randeria M, Style RW, Xu Q, Nichols JR, Duncan AJ, Loewenberg M, Dufresne ER, Jensen KE. Singular dynamics in the failure of soft adhesive contacts. Soft Matter 2019; 15:1327-1334. [PMID: 30540331 DOI: 10.1039/c8sm02075b] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We characterize the mechanical recovery of compliant silicone gels following adhesive contact failure. We establish broad, stable adhesive contacts between rigid microspheres and soft gels, then stretch the gels to large deformations by pulling quasi-statically on the contact. Eventually, the adhesive contact begins to fail, and ultimately slides to a final contact point on the bottom of the sphere. Immediately after detachment, the gel recoils quickly with a self-similar surface profile that evolves as a power law in time, suggesting that the adhesive detachment point is singular. The singular dynamics we observe are consistent with a relaxation process driven by surface stress and slowed by viscous flow through the porous, elastic network of the gel. Our results emphasize the importance of accounting for both the liquid and solid phases of gels in understanding their mechanics, especially under extreme deformation.
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Affiliation(s)
- Justin D Berman
- Department of Physics, Williams College, Williamstown, MA, USA.
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33
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Abstract
In the fall of 2015, Martin Müser suggested a Contact Mechanics Challenge for the Tribology community. The challenge was an ambitious effort to compare a wide variety of theoretical and computational contact-mechanics approaches, and involved researchers voluntarily tackling the same hypothetical contact problem. The result is an impressive collection of innovative approaches - including a surprise experimental effort - that highlight the continuing importance of surface contact mechanics and the challenges of solving these large-scale problems. Here, we describe how the Contact Mechanics Challenge also reveals exciting opportunities for the Soft Matter community to engage intensely with classical and emerging problems in tribology, surface science, and contact mechanics.
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Affiliation(s)
- Robert W Style
- Department of Materials, ETH Zürich, Zürich, Switzerland
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34
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Abstract
Recent experiments have shown that surface stresses in soft materials can have a significant strain-dependence. Here we explore the implications of this surface elasticity to show how, and when, we expect it to arise. We develop the appropriate boundary condition, showing that it simplifies significantly in certain cases. We show that surface elasticity's main role is to stiffen a solid surface's response to in-plane tractions, in particular at length-scales smaller than a characteristic elastocapillary length. We also investigate how surface elasticity affects the Green's-function problem of a line force on a flat, incompressible, linear-elastic substrate. There are significant changes to this solution, especially in that the well-known displacement singularity is regularised. This raises interesting implications for soft phenomena like wetting contact lines, adhesion and friction. Finally, we discuss open questions, future directions, and close ties with existing fields of research.
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35
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Abstract
Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched substrate, we measure two surface-elastic constants that quantify the linear dependence of the surface stress of a soft polymer gel on its strain. With these two parameters, one can predict surface stresses for general deformations of the material in the linear-elastic limit.
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Affiliation(s)
- Qin Xu
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland.
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36
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Box F, Vella D, Style RW, Neufeld JA. Indentation of a floating elastic sheet: geometry versus applied tension. Proc Math Phys Eng Sci 2017; 473:20170335. [PMID: 29118662 PMCID: PMC5666232 DOI: 10.1098/rspa.2017.0335] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2017] [Accepted: 09/08/2017] [Indexed: 11/12/2022] Open
Abstract
The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force-indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations, the force-indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes.
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Affiliation(s)
- Finn Box
- BP Institute, University of Cambridge, CB3 0EZ Cambridge, UK.,Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, UK
| | - Dominic Vella
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, UK
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Jerome A Neufeld
- BP Institute, University of Cambridge, CB3 0EZ Cambridge, UK.,Bullard Laboratories, Department of Earth Sciences, University of Cambridge, CB3 0EZ Cambridge, UK.,Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
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37
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Xu Q, Jensen KE, Boltyanskiy R, Sarfati R, Style RW, Dufresne ER. Direct measurement of strain-dependent solid surface stress. Nat Commun 2017; 8:555. [PMID: 28916752 PMCID: PMC5601460 DOI: 10.1038/s41467-017-00636-y] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2016] [Accepted: 07/14/2017] [Indexed: 11/09/2022] Open
Abstract
Surface stress, also known as surface tension, is a fundamental material property of any interface. However, measurements of solid surface stress in traditional engineering materials, such as metals and oxides, have proven to be very challenging. Consequently, our understanding relies heavily on untested theories, especially regarding the strain dependence of this property. Here, we take advantage of the high compliance and large elastic deformability of a soft polymer gel to directly measure solid surface stress as a function of strain. As anticipated by theoretical work for metals, we find that the surface stress depends on the strain via a surface modulus. Remarkably, the surface modulus of our soft gels is many times larger than the zero-strain surface tension. This suggests that surface stresses can play a dominant role in solid mechanics at larger length scales than previously anticipated.Solid surface stress is a fundamental property of solid interfaces. Here authors measure the solid surface stress of a gel, and show its dependence on surface strain through a surface modulus.
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Affiliation(s)
- Qin Xu
- Department of Materials, ETH Zürich, 8093, Zürich, Switzerland.,Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, 06511, USA
| | - Katharine E Jensen
- Department of Materials, ETH Zürich, 8093, Zürich, Switzerland.,Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, 06511, USA
| | - Rostislav Boltyanskiy
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, 06511, USA
| | - Raphaël Sarfati
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, 06511, USA
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093, Zürich, Switzerland. .,Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK.
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093, Zürich, Switzerland. .,Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, 06511, USA.
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38
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Samudrala N, Nam J, Sarfati R, Style RW, Dufresne ER. Mechanical stability of particle-stabilized droplets under micropipette aspiration. Phys Rev E 2017; 95:012805. [PMID: 28208345 DOI: 10.1103/physreve.95.012805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Indexed: 06/06/2023]
Abstract
We investigate the mechanical behavior of particle-stabilized droplets using micropipette aspiration. We observe that droplets stabilized with amphiphilic dumbbell-shaped particles exhibit a two-stage response to increasing suction pressure. Droplets first drip, then wrinkle and buckle like an elastic shell. While particles have a dramatic impact on the mechanism of failure, the mechanical strength of the droplets is only modestly increased. On the other hand, droplets coated with the molecular surfactant sodium dodecyl sulfate are even weaker than bare droplets. In all cases, the magnitude of the critical pressure for the onset of instabilities is set by the fluid surface tension.
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Affiliation(s)
| | - Jin Nam
- AMOREPACIFIC Co., Gyeonggi-do, Seoul 446-729, South Korea
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39
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Howland CJ, Antkowiak A, Castrejón-Pita JR, Howison SD, Oliver JM, Style RW, Castrejón-Pita AA. It's Harder to Splash on Soft Solids. Phys Rev Lett 2016; 117:184502. [PMID: 27835002 DOI: 10.1103/physrevlett.117.184502] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2015] [Indexed: 06/06/2023]
Abstract
Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity, and air pressure. By imaging ethanol drops impacting silicone gels of different stiffnesses, we show that substrate stiffness also affects the splashing threshold. Splashing is reduced or even eliminated: droplets on the softest substrates need over 70% more kinetic energy to splash than they do on rigid substrates. We show that this is due to energy losses caused by deformations of soft substrates during the first few microseconds of impact. We find that solids with Young's moduli ≲100 kPa reduce splashing, in agreement with simple scaling arguments. Thus, materials like soft gels and elastomers can be used as simple coatings for effective splash prevention. Soft substrates also serve as a useful system for testing splash-formation theories and sheet-ejection mechanisms, as they allow the characteristics of ejection sheets to be controlled independently of the bulk impact dynamics of droplets.
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Affiliation(s)
| | - Arnaud Antkowiak
- Institut Jean Le Rond d'Alembert, UMR 7190 CNRS/UPMC, Sorbonne Universités, F-75005 Paris, France
- Surface du Verre et Interfaces, UMR 125 CNRS/Saint-Gobain, F-93303 Aubervilliers, France
| | - J Rafael Castrejón-Pita
- School of Engineering and Materials Science, Queen Mary, University of London, London E1 4NS, United Kingdom
| | - Sam D Howison
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - James M Oliver
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Robert W Style
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
- Department of Materials, ETH Zürich, Zürich 8093, Switzerland
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40
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Abstract
Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R, to an elastocapillary lengthscale, L. Interfacial tension substantially impacts the effective elastic moduli of the composite when [Formula: see text]. When R<3L/2 (R=3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.
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Affiliation(s)
| | - Robert W Style
- Mathematical Institute, University of Oxford , Oxford OX2 6GG, UK
| | - John S Wettlaufer
- Nordic Institute for Theoretical Physics (NORDITA), 10691 Stockholm, Sweden; Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK; Yale University, New Haven, CT 06520, USA
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41
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Schollick JMH, Style RW, Curran A, Wettlaufer JS, Dufresne ER, Warren PB, Velikov KP, Dullens RPA, Aarts DGAL. Segregated Ice Growth in a Suspension of Colloidal Particles. J Phys Chem B 2016; 120:3941-9. [DOI: 10.1021/acs.jpcb.6b00742] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Julia M. H. Schollick
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - Robert W. Style
- Mathematical
Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Arran Curran
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - John S. Wettlaufer
- Mathematical
Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
- Yale University, New Haven, Connecticut 06520, United States
- Nordita, Royal Institute of Technology and Stockholm University, SE-10691 Stockholm, Sweden
| | - Eric R. Dufresne
- Yale University, New Haven, Connecticut 06520, United States
- ETH Zürich, CH-8093 Zürich, Switzerland
| | | | - Krassimir P. Velikov
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Roel P. A. Dullens
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - Dirk G. A. L. Aarts
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
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42
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Andreotti B, Bäumchen O, Boulogne F, Daniels KE, Dufresne ER, Perrin H, Salez T, Snoeijer JH, Style RW. Solid capillarity: when and how does surface tension deform soft solids? Soft Matter 2016; 12:2993-2996. [PMID: 26936296 DOI: 10.1039/c5sm03140k] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Soft solids differ from stiff solids in an important way: their surface stresses can drive large deformations. Based on a topical workshop held in the Lorentz Center in Leiden, this Opinion highlights some recent advances in the growing field of solid capillarity and poses key questions for its advancement.
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Affiliation(s)
- Bruno Andreotti
- Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI-CNRS, Université Paris-Diderot, 10 rue Vauquelin, 75005, Paris, France
| | - Oliver Bäumchen
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - François Boulogne
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Karen E Daniels
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - Eric R Dufresne
- School of Engineering and Applied Sciences, Yale University, New Haven, CT 06520, USA and Department of Materials, ETH Zürich, CH-8093 Zurich, Switzerland.
| | - Hugo Perrin
- Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI-CNRS, Université Paris-Diderot, 10 rue Vauquelin, 75005, Paris, France
| | - Thomas Salez
- PCT Lab, UMR CNRS 7083 Gulliver, ESPCI ParisTech, PSL Research University, 75005 Paris, France
| | - Jacco H Snoeijer
- Physics of Fluids Group, Faculty of Science and Technology, and Burgers Center for Fluid Dynamics, University of Twente, 7500AE Enschede, The Netherlands and Mesoscopic Transport Phenomena, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands
| | - Robert W Style
- Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK
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43
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Mancarella F, Style RW, Wettlaufer JS. Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids. Soft Matter 2016; 12:2744-2750. [PMID: 26854096 DOI: 10.1039/c5sm03029c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size approaches the elastocapillarity length L≡γ/E. Here, we use a three-phase generalized self-consistent method to calculate the elastic moduli of composites comprised of an isotropic, linear-elastic compliant solid hosting a spatially random monodisperse distribution of spherical liquid droplets. As opposed to similar approaches, we explicitly capture the liquid-solid interfacial stress when it is treated as an isotropic, strain-independent surface tension. Within this framework, the composite stiffness depends solely on the ratio of the elastocapillarity length L to the inclusion radius R. Independent of inclusion volume fraction, we find that the composite is stiffened by the inclusions whenever R < 3L/2. Over the same range of parameters, we compare our results with alternative approaches (dilute and Mori-Tanaka theories that include surface tension). Our framework can be easily extended to calculate the composite properties of more general soft materials where surface tension plays a role.
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Affiliation(s)
- Francesco Mancarella
- Nordic Institute for Theoretical Physics, Royal Institute of Technology and Stockholm University, SE-106 91 Stockholm, Sweden
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44
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Abstract
Soft particles can be better emulsifiers than hard particles because they stretch at fluid interfaces. This deformation can increase adsorption energies by orders of magnitude relative to rigid particles. The deformation of a particle at an interface is governed by a competition of bulk elasticity and surface tension. When particles are partially wet by the two liquids, deformation is localized within a material-dependent distance L from the contact line. At the contact line, the particle morphology is given by a balance of surface tensions. When the particle radius R≪L, the particle adopts a lenticular shape identical to that of an adsorbed fluid droplet. Particle deformations can be elastic or plastic, depending on the relative values of the Young modulus, E, and yield stress, σp. When surface tensions favour complete spreading of the particles at the interface, plastic deformation can lead to unusual fried-egg morphologies. When deformable particles have surface properties that are very similar to one liquid phase, adsorption can be extremely sensitive to small changes of their affinity for the other liquid phase. These findings have implications for the adsorption of microgel particles at fluid interfaces and the performance of stimuli-responsive Pickering emulsions.
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Affiliation(s)
- Robert W Style
- Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK.
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45
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Abstract
Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which has recently been shown to control many processes in soft materials such as gels, elastomers and biological tissue. To extend Eshelby's theory of inclusions to soft materials, we consider liquid inclusions within an isotropic, compressible, linear-elastic solid. We solve for the displacement and stress fields around individual stretched inclusions, accounting for the bulk elasticity of the solid and the surface tension (i.e. isotropic strain-independent surface stress) of the solid-liquid interface. Surface tension significantly alters the inclusion's shape and stiffness as well as its near- and far-field stress fields. These phenomena depend strongly on the ratio of the inclusion radius, R, to an elastocapillary length, L. Surface tension is significant whenever inclusions are smaller than 100L. While Eshelby theory predicts that liquid inclusions generically reduce the stiffness of an elastic solid, our results show that liquid inclusions can actually stiffen a solid when R<3L/2. Intriguingly, surface tension cloaks the far-field signature of liquid inclusions when R=3L/2. These results are have far-reaching applications from measuring local stresses in biological tissue, to determining the failure strength of soft composites.
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46
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Style RW, Boltyanskiy R, German GK, Hyland C, MacMinn CW, Mertz AF, Wilen LA, Xu Y, Dufresne ER. Traction force microscopy in physics and biology. Soft Matter 2014; 10:4047-55. [PMID: 24740485 DOI: 10.1039/c4sm00264d] [Citation(s) in RCA: 178] [Impact Index Per Article: 17.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Adherent cells, crawling slugs, peeling paint, sessile liquid drops, bearings and many other living and non-living systems apply forces to solid substrates. Traction force microscopy (TFM) provides spatially-resolved measurements of interfacial forces through the quantification and analysis of the deformation of an elastic substrate. Although originally developed for adherent cells, TFM has no inherent size or force scale, and can be applied to a much broader range of mechanical systems across physics and biology. In this paper, we showcase the wide range of applicability of TFM, describe the theory, and provide experimental details and code so that experimentalists can rapidly adopt this powerful technique.
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47
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Style RW, Hyland C, Boltyanskiy R, Wettlaufer JS, Dufresne ER. Surface tension and contact with soft elastic solids. Nat Commun 2013; 4:2728. [DOI: 10.1038/ncomms3728] [Citation(s) in RCA: 221] [Impact Index Per Article: 20.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2013] [Accepted: 10/08/2013] [Indexed: 11/09/2022] Open
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48
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Style RW. Drops and Bubbles in Contact with Solid Surfaces. THE YALE JOURNAL OF BIOLOGY AND MEDICINE 2013. [PMCID: PMC3767230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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49
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Style RW, Boltyanskiy R, Che Y, Wettlaufer JS, Wilen LA, Dufresne ER. Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses. Phys Rev Lett 2013; 110:066103. [PMID: 23432280 DOI: 10.1103/physrevlett.110.066103] [Citation(s) in RCA: 157] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2012] [Indexed: 06/01/2023]
Abstract
Droplets deform soft substrates near their contact lines. Using confocal microscopy, we measure the deformation of silicone gel substrates due to glycerol and fluorinated-oil droplets for a range of droplet radii and substrate thicknesses. For all droplets, the substrate deformation takes a universal shape close to the contact line that depends on liquid composition, but is independent of droplet size and substrate thickness. This shape is determined by a balance of interfacial tensions at the contact line and provides a novel method for direct determination of the surface stresses of soft substrates. Moreover, we measure the change in contact angle with droplet radius and show that Young's law fails for small droplets when their radii approach an elastocapillary length scale. For larger droplets the macroscopic contact angle is constant, consistent with Young's law.
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Style RW, Peppin SSL, Cocks ACF, Wettlaufer JS. Ice-lens formation and geometrical supercooling in soils and other colloidal materials. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 84:041402. [PMID: 22181141 DOI: 10.1103/physreve.84.041402] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2011] [Indexed: 05/31/2023]
Abstract
We present a physically intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil and the geometrical supercooling of the water in the soil, a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with the limited experimental data that are currently available. Finally we suggest experiments that might be performed in order to verify this theory in more detail. The theory is generalizable to complex natural-soil scenarios and should therefore be useful in the prediction of macroscopic frost-heave rates.
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Affiliation(s)
- Robert W Style
- Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, UK.
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