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Divoux T, Agoritsas E, Aime S, Barentin C, Barrat JL, Benzi R, Berthier L, Bi D, Biroli G, Bonn D, Bourrianne P, Bouzid M, Del Gado E, Delanoë-Ayari H, Farain K, Fielding S, Fuchs M, van der Gucht J, Henkes S, Jalaal M, Joshi YM, Lemaître A, Leheny RL, Manneville S, Martens K, Poon WCK, Popović M, Procaccia I, Ramos L, Richards JA, Rogers S, Rossi S, Sbragaglia M, Tarjus G, Toschi F, Trappe V, Vermant J, Wyart M, Zamponi F, Zare D. Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions. SOFT MATTER 2024. [PMID: 39028363 DOI: 10.1039/d3sm01740k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.
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Affiliation(s)
- Thibaut Divoux
- ENSL, CNRS, Laboratoire de physique, F-69342 Lyon, France.
| | - Elisabeth Agoritsas
- Department of Quantum Matter Physics (DQMP), University of Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland
| | - Stefano Aime
- Molecular, Macromolecular Chemistry, and Materials, ESPCI Paris, Paris, France
| | - Catherine Barentin
- Univ. de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Jean-Louis Barrat
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Roberto Benzi
- Department of Physics & INFN, Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France
| | - Dapeng Bi
- Department of Physics, Northeastern University, Boston, MA 02115, USA
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Daniel Bonn
- Soft Matter Group, van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands
| | - Philippe Bourrianne
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité, Paris, France
| | - Mehdi Bouzid
- Univ. Grenoble Alpes, CNRS, Grenoble INP, 3SR, F-38000 Grenoble, France
| | - Emanuela Del Gado
- Georgetown University, Department of Physics, Institute for Soft Matter Synthesis and Metrology, Washington, DC, USA
| | - Hélène Delanoë-Ayari
- Univ. de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Kasra Farain
- Soft Matter Group, van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands
| | - Suzanne Fielding
- Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University & Research, Stippeneng 4, 6708WE Wageningen, The Netherlands
| | - Silke Henkes
- Lorentz Institute, Leiden University, 2300 RA Leiden, The Netherlands
| | - Maziyar Jalaal
- Institute of Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - Yogesh M Joshi
- Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India
| | - Anaël Lemaître
- Navier, École des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France
| | - Robert L Leheny
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | | | | | - Wilson C K Poon
- SUPA and the School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Marko Popović
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str.38, 01187 Dresden, Germany
| | - Itamar Procaccia
- Dept. of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
- Sino-Europe Complex Science Center, School of Mathematics, North University of China, Shanxi, Taiyuan 030051, China
| | - Laurence Ramos
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France
| | - James A Richards
- SUPA and the School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Simon Rogers
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Saverio Rossi
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Pl. Jussieu, F-75005 Paris, France
| | - Mauro Sbragaglia
- Department of Physics & INFN, Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - Gilles Tarjus
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Pl. Jussieu, F-75005 Paris, France
| | - Federico Toschi
- Department of Applied Physics and Science Education, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- CNR-IAC, Via dei Taurini 19, 00185 Rome, Italy
| | - Véronique Trappe
- Department of Physics, University of Fribourg, Chemin du Musée 3, Fribourg 1700, Switzerland
| | - Jan Vermant
- Department of Materials, ETH Zürich, Vladimir Prelog Weg 5, 8032 Zürich, Switzerland
| | - Matthieu Wyart
- Department of Quantum Matter Physics (DQMP), University of Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland
| | - Francesco Zamponi
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Davoud Zare
- Fonterra Research and Development Centre, Dairy Farm Road, Fitzherbert, Palmerston North 4442, New Zealand
- Nestlé Institute of Food Sciences, Nestlé Research, Vers Chez les Blancs, Lausanne, Switzerland
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2
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Jocteur T, Figueiredo S, Martens K, Bertin E, Mari R. Yielding Is an Absorbing Phase Transition with Vanishing Critical Fluctuations. PHYSICAL REVIEW LETTERS 2024; 132:268203. [PMID: 38996301 DOI: 10.1103/physrevlett.132.268203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 05/21/2024] [Indexed: 07/14/2024]
Abstract
The yielding transition in athermal complex fluids can be interpreted as an absorbing phase transition between an elastic, absorbing state with high mesoscopic degeneracy and a flowing, active state. We characterize quantitatively this phase transition in an elastoplastic model under fixed applied shear stress, using a finite-size scaling analysis. We find vanishing critical fluctuations of the order parameter (i.e., the shear rate), and relate this property to the convex character of the phase transition (β>1). We locate yielding within a family of models akin to fixed-energy sandpile (FES) models, only with long-range redistribution kernels with zero modes that result from mechanical equilibrium. For redistribution kernels with sufficiently fast decay, this family of models belongs to a short-range universality class distinct from the conserved directed percolation class of usual FES, which is induced by zero modes.
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Vasisht VV, Chaudhuri P, Martens K. Residual stress in athermal soft disordered solids: insights from microscopic and mesoscale models. SOFT MATTER 2022; 18:6426-6436. [PMID: 35980086 DOI: 10.1039/d2sm00615d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In soft amorphous materials, shear cessation after large shear deformation leads to configurations having residual shear stress. The origin of these states and the distribution of the local shear stresses within the material is not well understood, despite its importance for the change in material properties and consequent applications. In this work, we use molecular dynamics simulations of a model dense non-Brownian soft amorphous material to probe the non-trivial relaxation process towards a residual stress state. We find that, similar to thermal glasses, an increase in shear rate prior to the shear cessation leads to lower residual stress states. We rationalise our findings using a mesoscopic elasto-plastic description that explicitly includes a long range elastic response to local shear transformations. We find that after flow cessation the initial stress relaxation indeed depends on the pre-sheared stress state, but the final residual stress is majorly determined by newly activated plastic events occurring during the relaxation process, a scenario consistent with the phenomenology of avalanche dynamics in the low shear rate limit of steadily sheared amorphous solids. Our simplified coarse grained description not only allows capturing the phenomenology of residual stress states but also rationalising the altered material properties that are probed using small and large deformation protocols applied to the relaxed material.
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Affiliation(s)
- Vishwas V Vasisht
- Department of Physics, Indian Institute of Technology, Palakkad 678557, India.
| | | | - Kirsten Martens
- The Institute of Mathematical Sciences, Taramani, Chennai 600113, India
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Cuny N, Bertin E, Mari R. Dynamics of microstructure anisotropy and rheology of soft jammed suspensions. SOFT MATTER 2022; 18:328-339. [PMID: 34881757 DOI: 10.1039/d1sm01345a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We explore the rheology predicted by a recently proposed constitutive model for jammed suspensions of soft elastic particles derived from particle-level dynamics [Cuny et al., Phys. Rev. Lett., 2021, 127, 218003]. Our model predicts that the orientation of the anisotropy of the microstructure, governed by an interplay between advection and contact elasticity, plays a key role at yielding and in flow. It generates normal stress differences contributing significantly to the yield criterion and Trouton ratio. It gives rise to non-trivial transients such as stress overshoots in step increases of shear rate, residual stresses after flow cessation and power-law decay of the shear rate in creep. Finally, it explains the collapse of storage modulus as measured in parallel superposition for a yielded suspension.
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Affiliation(s)
- Nicolas Cuny
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France.
| | - Eric Bertin
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France.
| | - Romain Mari
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France.
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5
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Cuny N, Mari R, Bertin E. Microscopic Theory for the Rheology of Jammed Soft Suspensions. PHYSICAL REVIEW LETTERS 2021; 127:218003. [PMID: 34860106 DOI: 10.1103/physrevlett.127.218003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Accepted: 10/21/2021] [Indexed: 06/13/2023]
Abstract
We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a nonlinear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain-rate and vorticity tensors. The coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle-level parameters. This constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. More complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.
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Affiliation(s)
- Nicolas Cuny
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Romain Mari
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Eric Bertin
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
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Morita J, Otsuki M. Memory effect of external oscillation on residual stress in a paste. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:106. [PMID: 34409512 DOI: 10.1140/epje/s10189-021-00111-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 08/09/2021] [Indexed: 06/13/2023]
Abstract
We numerically investigate the stress distribution of a paste when an external oscillation is applied. The paste memorizes the oscillation through plastic deformation. Due to the plastic deformation, the residual stress remains after the oscillation, where the residual stress distribution depends on the number of cycles in the oscillation. As this number increases, the symmetry of the stress distribution is enhanced, which is consistent with the crack patterns observed in the experiments using a drying paste.
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Affiliation(s)
- Jumpei Morita
- Department of Physics and Material Science, Shimane University, Matsue, Shimane, 690-8504, Japan
- Neturen Co., Ltd., Hyogo, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan.
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8
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Colloidal and polymeric contributions to the yielding of dense microgel suspensions. J Colloid Interface Sci 2021; 587:437-445. [DOI: 10.1016/j.jcis.2020.11.101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Revised: 11/06/2020] [Accepted: 11/25/2020] [Indexed: 11/21/2022]
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9
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Cao C, Liao J, Breedveld V, Weeks ER. Rheology finds distinct glass and jamming transitions in emulsions. SOFT MATTER 2021; 17:2587-2595. [PMID: 33514990 DOI: 10.1039/d0sm02097d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We study the rheology of monodisperse and bidisperse emulsions with various droplet sizes (1-2 μm diameter). Above a critical volume fraction φc, these systems exhibit solid-like behavior and a yield stress can be detected. Previous experiments suggest that for small thermal particles, rheology will see a glass transition at φc = φg ≈ 0.58; for large athermal systems, rheology will see a jamming transition at φc = φJ ≈ 0.64. However, simulations point out that at the crossover of thermal and athermal regimes, the glass and jamming transitions may both be observed in the same sample. Here we conduct an experiment by shearing four oil-in-water emulsions with a rheometer. We observe both a glass and a jamming transition for our smaller diameter droplets, and only a jamming transition for our larger diameter droplets. The bidisperse sample behaves similarly to the small droplet sample, with two transitions observed. Our rheology data are well-fit by both the Herschel-Bulkley model and the three component model. Based on the fitting parameters, our raw rheological data would not collapse onto a master curve. Our results show that liquid-solid transitions in dispersions are not universal, but depend on particle size.
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Affiliation(s)
- Cong Cao
- Department of Physics, Emory University, Atlanta, GA 30322, USA.
| | - Jianshan Liao
- School of Chemical & Biomolecular Engineering, Georgia Tech, Atlanta, GA 30332, USA
| | - Victor Breedveld
- School of Chemical & Biomolecular Engineering, Georgia Tech, Atlanta, GA 30332, USA
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, GA 30322, USA.
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10
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Abstract
Suspensions of soft and highly deformable microgels can be concentrated far more than suspensions of hard colloids, leading to their unusual mechanical properties. Microgels can accommodate compression in suspensions in a variety of ways such as interpenetration, deformation, and shrinking. Previous experiments have offered insightful, but somewhat conflicting, accounts of the behavior of individual microgels in compressed suspensions. We develop a mesoscale computational model to probe the behavior of compressed suspensions consisting of microgels with different architectures at a variety of packing fractions and solvent conditions. We find that microgels predominantly change shape and mildly shrink above random close packing. Interpenetration is only appreciable above space filling, remaining small relative to the mean distance between cross-links. At even higher packing fractions, microgels solely shrink. Remarkably, irrespective of the single-microgel properties, and whether the suspension concentration is changed via changing the particle number density or the swelling state of the particles, which can even result in colloidal gelation, the mechanics of the suspension can be quantified in terms of the single-microgel bulk modulus, which thus emerges as the correct mechanical measure for these type of soft-colloidal suspensions. Our results rationalize the many and varied experimental results, providing insights into the relative importance of effects defining the mechanics of suspensions comprising soft particles.
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Tsai JC, Chou MR, Huang PC, Fei HT, Huang JR. Soft granular particles sheared at a controlled volume: rate-dependent dynamics and the solid-fluid transition. SOFT MATTER 2020; 16:7535-7543. [PMID: 32700708 DOI: 10.1039/d0sm00405g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We study the responses of fluid-immersed soft hydrogel spheres that are sheared under controlled volume fractions. Slippery, deformable particles along with the density-matched interstitial fluid are sandwiched between two opposing rough cones, allowing studies for a wide range of volume fraction φ both above and below the jamming of granular suspension. We utilize sudden cessations of shearing, accompanied by refraction-matched internal imaging, to supplement the conventional flow-curve measurements. At sufficiently high volume fractions, the settling of particles after the cessations exhibits a continuous yet distinct transition over the change of the shear rate. Such changes back out the qualitative difference in the state of flowing prior to the cessations: the quasi-static yielding of a tightly packed network, as opposed to the rapid sliding of particles mediated by the interstitial fluid whose dynamics depends on the driving rate. In addition, we determine the solid-fluid transition using two independent methods: the extrapolation of stress residues and the estimated yield stress from high values of φ, and the settling of particles upon shear cessations as φ goes across the transition. We also verify the power law on values of characteristic stress with respect to the distance from jamming φ - φc, with an exponent close to 2. These results demonstrate a multitude of relaxation timescales behind the dynamics of soft particles, and raise questions on how we extend the existing paradigms of the flow of a densely packed system when the softness is actively involved.
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Affiliation(s)
- J-C Tsai
- Institute of Physics, Academia Sinica, Taipei, Taiwan.
| | - M-R Chou
- Institute of Physics, Academia Sinica, Taipei, Taiwan. and Department of Physics, National Taiwan University, Taiwan
| | - P-C Huang
- Institute of Physics, Academia Sinica, Taipei, Taiwan. and Department of Physics, National Taiwan University, Taiwan
| | - H-T Fei
- Institute of Physics, Academia Sinica, Taipei, Taiwan.
| | - J-R Huang
- Institute of Physics, Academia Sinica, Taipei, Taiwan.
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Wang JG, Li Q, Peng X, McKenna GB, Zia RN. "Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics. SOFT MATTER 2020; 16:7370-7389. [PMID: 32696798 DOI: 10.1039/d0sm00999g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.
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Affiliation(s)
- J Galen Wang
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
| | - Qi Li
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Xiaoguang Peng
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Gregory B McKenna
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Roseanna N Zia
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
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Pradeep S, Hsiao LC. Contact criterion for suspensions of smooth and rough colloids. SOFT MATTER 2020; 16:4980-4989. [PMID: 32432605 DOI: 10.1039/d0sm00072h] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We report a procedure to obtain the search distance used to determine particle contact in dense suspensions of smooth and rough colloids. This method works by summing physically relevant length scales in an uncertainty analysis and does not require detailed quantification of the surface roughness. We suspend sterically stabilized, fluorescent poly(methyl methacrylate) colloids in a refractive index-matched solvent, squalene, in order to ensure hard sphere-like behavior. High speed centrifugation is used to pack smooth and rough colloids to their respective jamming points, φJ. The jammed suspensions are subsequently diluted with known volumes of solvent to φ < φJ. Structural parameters obtained from confocal laser scanning micrographs of the diluted colloidal suspensions are extrapolated to φJ to determine the mean contact number at jamming, 〈z〉J. Contact below jamming refers to nearest neighbors at a length scale below which the effects of hydrodynamic or geometric friction come into play. Sensitivity analyses show that a deviation of the search distance by 1% of the particle diameter results in 〈z〉 changing by up to 10%, with the error in contact number distribution being magnified in dense suspensions (φ > 0.50) due to an increased number of nearest neighbors in the first coordination shell.
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Affiliation(s)
- Shravan Pradeep
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695, USA.
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Hendricks J, Louhichi A, Metri V, Fournier R, Reddy N, Bouteiller L, Cloitre M, Clasen C, Vlassopoulos D, Briels WJ. Nonmonotonic Stress Relaxation after Cessation of Steady Shear Flow in Supramolecular Assemblies. PHYSICAL REVIEW LETTERS 2019; 123:218003. [PMID: 31809142 DOI: 10.1103/physrevlett.123.218003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Revised: 05/27/2019] [Indexed: 06/10/2023]
Abstract
Stress relaxation upon cessation of shear flow is known to be described by single-mode or multimode monotonic exponential decays. This is considered to be ubiquitous in nature. However, we found that, in some cases, the relaxation becomes anomalous in that an increase in the relaxing stress is observed. Those observations were made for physicochemically very different systems, having in common, however, the presence of self-associating units generating structures at large length scales. The nonmonotonic stress relaxation can be described phenomenologically by a generic model based on a redistribution of energy after the flow has stopped. When broken bonds are reestablished after flow cessation, the released energy is partly used to locally increase the elastic energy by the formation of deformed domains. If shear has induced order such that these elastic domains are partly aligned, the reestablishing of bonds gives rise to an increase of the overall stress.
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Affiliation(s)
- Jan Hendricks
- Department of Chemical Engineering, KU Leuven, 3001 Leuven, Belgium
| | - Ameur Louhichi
- Institute of Electronic Structure and Laser, FORTH, P.O. Box 1527, 70013 Heraklion, Crete Greece
- Department of Materials Science and Technology, University of Crete, Voutes Campus, 70013 Heraklion, Crete Greece
| | - Vishal Metri
- Computational Chemical Physics, Faculty of Science and Technology, and MESA+Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE, Enschede, Netherlands
| | - Rémi Fournier
- Molecular, Macromolecular Chemistry, and Materials, ESPCI Paris, CNRS, PSL University, 75005 Paris, France
| | - Naveen Reddy
- Faculty of Industrial Engineering, Hasselt University, Martelarenlaan 42, 3500 Hasselt, Belgium, and IMO-IMOMEC, Hasselt University, Wetenschapspark 1, 3590 Diepenbeek, Belgium
| | - Laurent Bouteiller
- Sorbonne Université, CNRS, IPCM, Equipe Chimie des Polymères, 75005 Paris, France
| | - Michel Cloitre
- Molecular, Macromolecular Chemistry, and Materials, ESPCI Paris, CNRS, PSL University, 75005 Paris, France
| | - Christian Clasen
- Department of Chemical Engineering, KU Leuven, 3001 Leuven, Belgium
| | - Dimitris Vlassopoulos
- Institute of Electronic Structure and Laser, FORTH, P.O. Box 1527, 70013 Heraklion, Crete Greece
- Department of Materials Science and Technology, University of Crete, Voutes Campus, 70013 Heraklion, Crete Greece
| | - W J Briels
- Computational Chemical Physics, Faculty of Science and Technology, and MESA+Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE, Enschede, Netherlands
- ICS 3, Forschungszentrum Jülich, Wilhelm-Johnen-Straße, 52428 Jülich, Germany
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15
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Experimental synthesis and characterization of rough particles for colloidal and granular rheology. Curr Opin Colloid Interface Sci 2019. [DOI: 10.1016/j.cocis.2019.04.003] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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16
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Lidon P, Villa L, Manneville S. A mesoscale study of creep in a microgel using the acoustic radiation force. SOFT MATTER 2019; 15:2688-2702. [PMID: 30821300 DOI: 10.1039/c8sm02294a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We study the motion of a sphere of diameter 330 μm embedded in a Carbopol microgel under the effect of the acoustic radiation pressure exerted by a focused ultrasonic field. The sphere motion within the microgel is tracked using videomicroscopy and compared to conventional creep and recovery measurements performed with a rheometer. We find that under moderate ultrasonic intensities, the sphere creeps as a power law of time with an exponent α ≃ 0.2 that is significantly smaller than the one inferred from global creep measurements below the yield stress of the microgel (α ≃ 0.4). Moreover, the sphere relaxation motion after creep and the global recovery are respectively consistent with these two different exponents. By allowing a rheological characterization at the scale of the sphere with forces of the order of micronewtons, the present experiments pave the way for acoustic "mesorheology" which probes volumes and forces an intermediate between standard macroscopic rheology and classical microrheology. They also open new questions about the effects of the geometry of the deformation field and of the sphere size and surface properties on the creep behaviour of soft materials.
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Affiliation(s)
- Pierre Lidon
- Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France.
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Liu T, Khabaz F, Bonnecaze RT, Cloitre M. On the universality of the flow properties of soft-particle glasses. SOFT MATTER 2018; 14:7064-7074. [PMID: 30116807 DOI: 10.1039/c8sm01153b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We identify the minimal interparticle interactions necessary for a particle dynamics simulation to predict the structure and flow behaviour of soft particle glasses (SPGs). Generally, two kinds of forces between the particles must be accounted for in simulations of SPGs: viscous or frictional drag forces and elastic contact forces. Far field drag forces are required to dissipate energy in the simulations and capture the effect of the rheology of the suspending fluid. Elastic forces are found to be dominant compared to near-field drag or other forms of friction forces and are the most important component to compute the rheology. The shear stress, the first and second normal stress differences for different interparticle force laws collapse onto universal master curves of the Herschel-Bulkley form by non-dimensionalizing the stress with the yield stress and the shear rate with the viscosity of the suspending fluid divided by the low-frequency shear modulus. The Herschel-Bulkley exponents are close to 0.5 with a slight dependence on the repulsive pairwise elastic forces.
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Affiliation(s)
- Tianfei Liu
- McKetta Department of Chemical Engineering and Texas Materials Institute, University of Texas at Austin, Austin, TX 78712, USA.
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Johnson LC, Landrum BJ, Zia RN. Yield of reversible colloidal gels during flow start-up: release from kinetic arrest. SOFT MATTER 2018; 14:5048-5068. [PMID: 29869670 DOI: 10.1039/c8sm00109j] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Yield of colloidal gels during start-up of shear flow is characterized by an overshoot in shear stress that accompanies changes in network structure. Prior studies of yield of reversible colloidal gels undergoing strong flow model the overshoot as the point at which network rupture permits fluidization. However, yield under weak flow, which is of interest in many biological and industrial fluids shows no such disintegration. The mechanics of reversible gels are influenced by bond strength and durability, where ongoing rupture and re-formation impart aging that deepens kinetic arrest [Zia et al., J. Rheol., 2014, 58, 1121], suggesting that yield be viewed as release from kinetic arrest. To explore this idea, we study reversible colloidal gels during start-up of shear flow via dynamic simulation, connecting rheological yield to detailed measurements of structure, bond dynamics, and potential energy. We find that pre-yield stress grows temporally with the changing roles of microscopic transport processes: early time behavior is set by Brownian diffusion; later, advective displacements permit relative particle motion that stretches bonds and stores energy. Stress accumulates in stretched, oriented bonds until yield, which is a tipping point to energy release, and is passed with a fully intact network, where the loss of very few bonds enables relaxation of many, easing glassy arrest. This is immediately followed by a reversal to growth in potential energy during bulk plastic deformation and condensation into larger particle domains, supporting the view that yield is an activated release from kinetic arrest. The continued condensation of dense domains and shrinkage of network surfaces, along with a decrease in the potential energy, permit the gel to evolve toward more complete phase separation, supporting our view that yield of weakly sheared gels is a 'non-equilibrium phase transition'. Our findings may be particularly useful for industrial or other coatings, where weak, slow application via shear may lead to phase separation, inhibiting smooth distribution.
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Affiliation(s)
- Lilian C Johnson
- Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY, USA
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Moghimi E, Jacob AR, Petekidis G. Residual stresses in colloidal gels. SOFT MATTER 2017; 13:7824-7833. [PMID: 29028062 DOI: 10.1039/c7sm01655g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A combination of experiments and Brownian Dynamics (BD) simulations is utilized to examine internal stresses in colloidal gels brought to rest from steady shear at different shear rates. A model colloidal gel with intermediate volume fraction is chosen where attractions between particles are introduced by adding non-adsorbing linear polymer chains. After flow cessation, the gel releases the stress in two distinct patterns: at high shear rates, where shear forces dominate over attractive forces, the shear-melted gel behaves as a liquid and releases stresses to zero after flow cessation. After low shear rates, though, stresses relax only partially, similar to the response of hard sphere glasses and jammed soft particles. The balance between shear and attractive forces which determines the intensity of structural distortion controls the amplitude of the residual stresses through a universal scaling. Stress decomposition to repulsive and attractive contributions in BD simulations reveals that internal stresses mainly originate from attractive forces. Moreover, analysis of particle dynamics indicates that internal stresses are associated with sub-diffusive particle displacements on average smaller than the attraction range as such short-range displacements are not sufficient to completely erase structural anisotropy caused during the course of shear.
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Affiliation(s)
- Esmaeel Moghimi
- FORTH/IESL and Department of Materials Science and Technology, University of Crete, 71110 Heraklion, Greece.
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Saitoh K, Mizuno H. Anomalous energy cascades in dense granular materials yielding under simple shear deformations. SOFT MATTER 2016; 12:1360-1367. [PMID: 26701740 DOI: 10.1039/c5sm02760h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
By using molecular dynamics (MD) simulations of dense granular particles in two dimensions, we study turbulent-like structures of their non-affine velocities under simple shear deformations. We find that the spectrum of non-affine velocities, introduced as an analog of the energy spectrum for turbulent flows, exhibits the power-law decay if the system is yielding in a quasi-static regime, where large-scale collective motions and inelastic interactions of granular particles are crucial for the anomalous cascade of kinetic energy. Based on hydrodynamic equations of dense granular materials, which include both kinetic and contact contributions in constitutive relations, we derive a theoretical expression for the spectrum, where a good agreement between the result of MD simulations and theoretical prediction is established over a wide range of length scales.
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Affiliation(s)
- Kuniyasu Saitoh
- Faculty of Engineering Technology, MESA+, University of Twente, Drienerlolaan 5, 7522 NB, Enschede, The Netherlands.
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Westermeier F, Pennicard D, Hirsemann H, Wagner UH, Rau C, Graafsma H, Schall P, Lettinga MP, Struth B. Connecting structure, dynamics and viscosity in sheared soft colloidal liquids: a medley of anisotropic fluctuations. SOFT MATTER 2016; 12:171-80. [PMID: 26451659 DOI: 10.1039/c5sm01707f] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Structural distortion and relaxation are central to any liquid flow. Their full understanding requires simultaneous probing of the mechanical as well as structural and dynamical response. We provide the first full dynamical measurement of the transient structure using combined coherent X-ray scattering and rheology on electrostatically interacting colloidal fluids. We find a stress overshoot during the start-up of shear which is due to the strong anisotropic overstretching and compression of nearest-neighbor distances. The rheological response is reflected in uncorrelated entropy-driven intensity fluctuations. While the structural distortion under steady shear is well described by Smoluchowski theory, we find an increase of the particle dynamics beyond the trivial contribution of flow. After the cessation of shear, the full fluid microstructure and dynamics are restored, both on the structural relaxation timescale. We thus find unique structure-dynamics relations in liquid flow, responsible for the macroscopic rheological behavior of the system.
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Affiliation(s)
- Fabian Westermeier
- Max Planck Institute for the Structure and Dynamics of Matter, CFEL, Luruper Chaussee 149, 22761 Hamburg, Germany.
| | - David Pennicard
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - Helmut Hirsemann
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - Ulrich H Wagner
- Diamond Light Source Ltd, Diamond House, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, UK
| | - Christoph Rau
- Diamond Light Source Ltd, Diamond House, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, UK
| | - Heinz Graafsma
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - Peter Schall
- Van der Waals-Zeeman Institute, University of Amsterdam, POSTBUS 94485, 1090 GL Amsterdam, The Netherlands
| | - M Paul Lettinga
- Forschungszentrum Jülich, Institute of Complex Systems (ICS-3), 52425 Jülich, Germany.
| | - Bernd Struth
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
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Gupta S, Camargo M, Stellbrink J, Allgaier J, Radulescu A, Lindner P, Zaccarelli E, Likos CN, Richter D. Dynamic phase diagram of soft nanocolloids. NANOSCALE 2015; 7:13924-13934. [PMID: 26219628 DOI: 10.1039/c5nr03702f] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
We present a comprehensive experimental and theoretical study covering micro-, meso- and macroscopic length and time scales, which enables us to establish a generalized view in terms of structure-property relationship and equilibrium dynamics of soft colloids. We introduce a new, tunable block copolymer model system, which allows us to vary the aggregation number, and consequently its softness, by changing the solvophobic-to-solvophilic block ratio (m : n) over two orders of magnitude. Based on a simple and general coarse-grained model of the colloidal interaction potential, we verify the significance of interaction length σint governing both structural and dynamic properties. We put forward a quantitative comparison between theory and experiment without adjustable parameters, covering a broad range of experimental polymer volume fractions (0.001 ≤ϕ≤ 0.5) and regimes from ultra-soft star-like to hard sphere-like particles, that finally results in the dynamic phase diagram of soft colloids. In particular, we find throughout the concentration domain a strong correlation between mesoscopic diffusion and macroscopic viscosity, irrespective of softness, manifested in data collapse on master curves using the interaction length σint as the only relevant parameter. A clear reentrance in the glass transition at high aggregation numbers is found, recovering the predicted hard-sphere (HS) value in the hard-sphere like limit. Finally, the excellent agreement between our new experimental systems with different but already established model systems shows the relevance of block copolymer micelles as a versatile realization of soft colloids and the general validity of a coarse-grained approach for the description of the structure and dynamics of soft colloids.
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Affiliation(s)
- Sudipta Gupta
- JCNS-1 and ICS-1, Forschungszentrum Jülich, Leo-Brandt-Straße, 52425 Jülich, Germany.
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Hsiao LC, Kang H, Ahn KH, Solomon MJ. Role of shear-induced dynamical heterogeneity in the nonlinear rheology of colloidal gels. SOFT MATTER 2014; 10:9254-9259. [PMID: 25323049 DOI: 10.1039/c4sm01375a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report the effect of flow-induced dynamical heterogeneity on the nonlinear elastic modulus of weakly aggregated colloidal gels that have undergone yielding by an imposed step strain deformation. The gels are comprised of sterically stabilized poly(methyl methacrylate) colloids interacting through short-ranged depletion attractions. When a step strain of magnitude varying from γ = 0.1 to 80.0 is applied to the quiescent gels, we observe the development of a bimodal distribution in the single-particle van Hove self-correlation function. This distribution is consistent with the existence of a fast and slow subpopulation of colloids within sheared gels. We evaluate the effect of incorporating the properties of the slow, rigid subpopulation of the colloids into a recent mode coupling theory for the nonlinear elasticity of colloidal gels.
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Affiliation(s)
- Lilian C Hsiao
- Department of Chemical Engineering, University of Michigan, MI, USA.
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Rogers MC, Chen K, Andrzejewski L, Narayanan S, Ramakrishnan S, Leheny RL, Harden JL. Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062310. [PMID: 25615096 DOI: 10.1103/physreve.90.062310] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2014] [Indexed: 06/04/2023]
Abstract
We report x-ray photon correlation spectroscopy experiments on a concentrated nanocolloidal gel subject to in situ oscillatory shear strain. The strain causes periodic echoes in the speckle pattern that lead to peaks in the intensity autocorrelation function. Above a threshold strain that is near the first yield point of the gel, the peak amplitude decays exponentially with the number of shear cycles, signaling irreversible particle rearrangements. The wave-vector dependence of the decay rate reveals a power-law distribution in the size of regions undergoing shear-induced rearrangement. The gel also displays strain softening well below the threshold, indicating a range of strains at which the rheology is nonlinear but the microscopic deformations are reversible.
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Affiliation(s)
- Michael C Rogers
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
| | - Kui Chen
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lukasz Andrzejewski
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
| | - Suresh Narayanan
- X-Ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Subramanian Ramakrishnan
- Department of Chemical and Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, Florida 32312, USA
| | - Robert L Leheny
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - James L Harden
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
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Fritschi S, Fuchs M, Voigtmann T. Mode-coupling analysis of residual stresses in colloidal glasses. SOFT MATTER 2014; 10:4822-4832. [PMID: 24841537 DOI: 10.1039/c4sm00247d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present results from computer simulation and mode-coupling theory of the glass transition for the nonequilibrium relaxation of stresses in a colloidal glass former after the cessation of shear flow. In the ideal glass, persistent residual stresses are found that depend on the flow history. The partial decay of stresses from the steady state to this residual stress is governed by the previous shear rate. We rationalize this observation in a schematic model of mode-coupling theory. The results from Brownian-dynamics simulations of a glassy two-dimensional hard-disk system are in qualitative agreement with the predictions of the theory.
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Affiliation(s)
- S Fritschi
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany.
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