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Thijssen K, Liverpool TB, Royall CP, Jack RL. Necking and failure of a particulate gel strand: signatures of yielding on different length scales. SOFT MATTER 2023; 19:7412-7428. [PMID: 37743690 DOI: 10.1039/d3sm00681f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/26/2023]
Abstract
"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.
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Affiliation(s)
- Kristian Thijssen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100, Denmark
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | | | - C Patrick Royall
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK
- School of Chemistry, University of Bristol, Cantock's Close, Bristol, BS8 1TS, UK
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
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Dong J, Turci F, Jack RL, Faers M, Royall CP. Direct Imaging of Contacts and Forces in Colloidal Gels. J Chem Phys 2022; 156:214907. [DOI: 10.1063/5.0089276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Colloidal dispersions are prized as model systems to understand basic properties of materials, and are central to a wide range of industries from cosmetics to foods to agrichemicals. Among the key developments in using colloids to address challenges in condensed matter is to resolve the particle coordinates in 3D, allowing a level of analysis usually only possible in computer simulation. However in amorphous materials, relating mechanical properties, and failure in particular to microscopic structure remains problematic. Here we address this challenge by studying the contacts and the forces between particles, as well as their positions. To do so, we use a colloidal model system (an emulsion) in which the interparticle forces and local stress can be linked to the microscopic structure. We demonstrate the potential of our method to reveal insights into the failure mechanisms of soft amorphous solids by determining local stress in a colloidal gel. In particular, we identify "force chains" of load--bearing droplets, and local stress anisotropy, and investigate their connection with locally rigid packings of the droplets.
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Affiliation(s)
- Jun Dong
- University of Bristol, United Kingdom
| | | | - Robert L. Jack
- DAMTP, University of Cambridge Department of Applied Mathematics and Theoretical Physics, United Kingdom
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Royall CP, Faers MA, Fussell SL, Hallett JE. Real space analysis of colloidal gels: triumphs, challenges and future directions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:453002. [PMID: 34034239 DOI: 10.1088/1361-648x/ac04cb] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 05/25/2021] [Indexed: 06/12/2023]
Abstract
Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.
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Affiliation(s)
- C Patrick Royall
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, United Kingdom
| | - Malcolm A Faers
- Bayer AG, Crop Science Division, Formulation Technology, Alfred Nobel Str. 50, 40789 Monheim, Germany
| | - Sian L Fussell
- School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, United Kingdom
- Bristol Centre for Functional Nanomaterials, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - James E Hallett
- Physical and Theoretical Chemistry Laboratory, South Parks Road, University of Oxford, OX1 3QZ, United Kingdom
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Ferreiro-Córdova C, Royall CP, van Duijneveldt JS. Anisotropic viscoelastic phase separation in polydisperse hard rods leads to nonsticky gelation. Proc Natl Acad Sci U S A 2020; 117:3415-3420. [PMID: 32005711 PMCID: PMC7035602 DOI: 10.1073/pnas.1909357117] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Spinodal demixing into two phases having very different viscosities leads to viscoelastic networks-i.e., gels-usually as a result of attractive particle interactions. Here, however, we demonstrate demixing in a colloidal system of polydisperse, rod-like clay particles that is driven by particle repulsions instead. One of the phases is a nematic liquid crystal with a highly anisotropic viscosity, allowing flow along the director, but suppressing it in other directions. This phase coexists with a dilute isotropic phase. Real-space analysis and molecular-dynamics simulations both reveal a long-lived network structure that is locally anisotropic, yet macroscopically isotropic. We show that our system exhibits the characteristics of colloidal gelation, leading to nonsticky gels.
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Affiliation(s)
- Claudia Ferreiro-Córdova
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, University of Bristol, Bristol BS8 1FD, United Kingdom
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - C Patrick Royall
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom;
- Centre for Nanoscience and Quantum Information, University of Bristol, Bristol BS8 1FD, United Kingdom
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
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Feng SD, Chan KKC, Zhao L, Wang LM, Liu RP. Molecular Dynamics Simulation of Structural Signals of Shear-Band Formation in Zr 46Cu 46Al₈ Metallic Glasses. MATERIALS (BASEL, SWITZERLAND) 2018; 11:E2564. [PMID: 30562968 PMCID: PMC6316119 DOI: 10.3390/ma11122564] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Revised: 12/13/2018] [Accepted: 12/14/2018] [Indexed: 11/22/2022]
Abstract
The evolution from initiation to formation of a shear band in Zr46Cu46Al₈ metallic glasses is presented via molecular dynamics simulation. The increase in number and the decrease in average size of clusters with the quasi-nearest atoms being 0 correspond to the shear-band evolution from initiation to formation. When the shear band is completely formed, the distribution of the bond orientational order q₆ reaches a minimum. The maximum of the number of the polyhedral loss of Cu-centered <0, 0, 12, 0> and the minimum of the number of the polyhedral loss of Zr-centered <0, 2, 8, 5> correspond to the shear-band formation. These findings provide a strong foundation for characterizing the evolution from initiation to formation of shear bands.
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Affiliation(s)
- Shi-Dong Feng
- State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China.
- Advanced Manufacturing Technology Research Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom 999077, Hong Kong.
| | - Keith K C Chan
- Advanced Manufacturing Technology Research Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom 999077, Hong Kong.
| | - Lei Zhao
- Advanced Manufacturing Technology Research Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom 999077, Hong Kong.
| | - Li-Min Wang
- State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China.
| | - Ri-Ping Liu
- State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China.
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Griffiths S, Turci F, Royall CP. Local structure of percolating gels at very low volume fractions. J Chem Phys 2017; 146:014905. [DOI: 10.1063/1.4973351] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Royall CP, Eggers J, Furukawa A, Tanaka H. Probing Colloidal Gels at Multiple Length Scales: The Role of Hydrodynamics. PHYSICAL REVIEW LETTERS 2015. [PMID: 26197149 DOI: 10.1103/physrevlett.114.258302] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Colloidal gels are out-of-equilibrium structures, made up of a rarefied network of colloidal particles. Comparing experiments to numerical simulations, with hydrodynamic interactions switched off, we demonstrate the crucial role of the solvent for gelation. Hydrodynamic interactions suppress the formation of larger local equilibrium structures of closed geometry, and instead lead to the formation of highly anisotropic threads, which promote an open gel network. We confirm these results with simulations which include hydrodynamics. Based on three-point correlations, we propose a scale-resolved quantitative measure for the anisotropy of the gel structure. We find a strong discrepancy for interparticle distances just under twice the particle diameter between systems with and without hydrodynamics, quantifying the role of hydrodynamics from a structural point of view.
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Affiliation(s)
- C Patrick Royall
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
| | - Jens Eggers
- School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
| | - Akira Furukawa
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
| | - Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
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Kim J, Sung BJ. Dynamic decoupling and local atomic order of a model multicomponent metallic glass-former. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:235102. [PMID: 25993620 DOI: 10.1088/0953-8984/27/23/235102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The dynamics of multicomponent metallic alloys is spatially heterogeneous near glass transition. The diffusion coefficient of one component of the metallic alloys may also decouple from those of other components, i.e., the diffusion coefficient of each component depends differently on the viscosity of metallic alloys. In this work we investigate the dynamic heterogeneity and decoupling of a model system for multicomponent Pd43Cu27Ni10P20 melts by using a hard sphere model that considers the size disparity of alloys but does not take chemical effects into account. We also study how such dynamic behaviors would relate to the local atomic structure of metallic alloys. We find, from molecular dynamics simulations, that the smallest component P of multicomponent Pd43Cu27Ni10P20 melts becomes dynamically heterogeneous at a translational relaxation time scale and that the largest major component Pd forms a slow subsystem, which has been considered mainly responsible for the stabilization of amorphous state of alloys. The heterogeneous dynamics of P atoms accounts for the breakdown of Stokes-Einstein relation and also leads to the dynamic decoupling of P and Pd atoms. The dynamically heterogeneous P atoms decrease the lifetime of the local short-range atomic orders of both icosahedral and close-packed structures by orders of magnitude.
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Affiliation(s)
- Jeongmin Kim
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 121-742, Republic of Korea
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Klich I, Lee SH, Iida K. Glassiness and exotic entropy scaling induced by quantum fluctuations in a disorder-free frustrated magnet. Nat Commun 2014; 5:3497. [PMID: 24686398 PMCID: PMC3988808 DOI: 10.1038/ncomms4497] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2013] [Accepted: 02/21/2014] [Indexed: 11/25/2022] Open
Abstract
When spins are arranged in a lattice of triangular motif, the phenomenon of frustration leads to numerous energetically equivalent ground states, and results in exotic states such as spin liquid and spin ice. Here we report an alternative situation: a system, classically a liquid, freezes in the clean limit into a glassy state induced by quantum fluctuations. We call such glassy state a spin jam. The case in point is a frustrated magnet, where spins are arranged in a triangular network of bipyramids. Quantum corrections break the classical degeneracy into a set of aperiodic spin configurations forming local minima in a rugged energy landscape. This is established by mapping the problem into tiling with hexagonal tiles. The number of tessellations scales with the boundary length rather than its volume, showing the absence of local zero-energy modes. Low-temperature thermodynamics is discussed to compare it with other glassy materials. Spin liquids and spin ices arise when spins arranged on a lattice have several states that are close in energy, a phenomenon referred to as frustration. Here, Klich et al. show that quantum fluctuations can induce a spin liquid to freeze into a glassy state.
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Affiliation(s)
- I Klich
- 1] Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA [2]
| | - S-H Lee
- 1] Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA [2]
| | - K Iida
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
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